Collins CONCISE REVISION COURSE ® • SICS Peter DeFreitas I / Collins HarperCol!ins Publishers Ltd The News Building I London Bridge Street London SE I 9GF First edition 2016 109876S4321 © HarperCollins Publishers limited 2016 ISBN 978-0-00-815789-0 Coilinse is a registered trademark of HarperColiins Publishers limited Concise Revision Course: CSEC!! Physics is an independent publication and has not been authorised. sponsored or otherwise approved by CXC®. CSEC®is a registered trade mark of the Caribbean Examinations Council (CXC). www.collins.co.uklcaribbeanschools A catalogue record for this book is available from the British Library. Typeset by QBS Printed and bound by Grafica Veneta S.p.A., Italy All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission in writing of the Publisher. This book is sold subject to the conditions that it shall not, by way of trade or otherwise, be lent. re-sold, hired out or otherwise circulated without the Publisher's prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser. If any copyright holders have been omitted, please contact the Publisher who will make the necessary arrangements at the first opportunity. Author: Peter DeFreitas Publisher: Elaine Higgleton Commissioning Editor: Peter Dennis and Tom Hardy Managing Edito r: Sarah Thomas Copy Editor: Jane Roth Editor:Aidan Gill Proofreader:Tim Jackson Artwork: QBS Cover: Kevin Robbins and Gordon MacGilp Acknowledgements I am grateful to my employers and to all the parents who have shown appreciation for my work and dedication to education. I am also thankful to my students who have encouraged me in writing this text. and above all, to my wife Christere and children, Zoe. Zachary and Jenna for supporting me in my efforts. Peter DeFreitas Contents Failure is not an option 1 Scientific method Galileo's contribution to scientific methodology Experimental data and its analysis Drawing graphs Finding the grad ient (slope) of a straight-line graph Significant figures in measurements and calculations Random errors Systematic errors Reading measuring instruments Suitability of instruments Quantities and units Density Revision questions 2 3 4 6 7 1 1 1 1 3 3 4 4 4 5 6 8 8 Scalars and vectors 10 Finding the resultant of two vectors Resolving vectors into two perpendicular components Revision questions 10 11 12 Forces, mass and weight 13 Forces Mass and weight Revision questions 13 13 13 Moments 14 Calculatio ns on the equilibrium of bodies Determining the centre of gravity of an object Stable, unstable and neutral equi librium Common devices utilising the principle of moments Revision questions 5 vi 8 9 10 14 15 11 16 17 17 Deformation 18 Verifying Hooke's law Analysing force-ex tension graphs Revision questions 18 18 20 Kinematics 21 Displacement- time and velocity- time graphs 21 Distance- time and speed-time graphs 22 Revision questions 24 12 Newton's laws and momentum 25 Aristotle's theory Newton's laws of motion Applications of Newton's laws Momentum Revision questions 25 25 25 27 30 Energy 31 Some types of energy The principle of conservation of energy Ene rgy sources Efficiency Revision questions 31 32 34 35 36 Pressure and buoyancy 37 Pressure in fluid s Archimedes' principle Floating Submarines Balloons Revision questions 37 38 38 39 39 40 Exam-style questionsChapters 1 to 9 41 Nature of heat 43 Caloric theory Kinetic theory Joule's role in establishing the principle of conservation of energy Revision questions 43 43 Temperature and thermometers 44 44 45 Units of temperature Designing a thermometer Laboratory mercury thermometer Clin ical mercury thermometer Thermocouple Revision questions 45 45 States of matter 49 Solids Liquids Gases Revision questions 49 49 49 50 Contents 46 47 47 48 iii 13 Expansion Expansion in terms of the kinetic theory of matter Utilising expansion Avoiding problems due to expansion The bimetallic strip Revision question s 51 51 51 51 52 53 The ideal gas laws 54 Temperature scales The ideal gas laws Verifying the gas laws Gases and the kinetic theory Revision questions 54 54 55 57 58 Demonstrating expa nsion 14 15 16 17 51 Heat and temperature change 59 Calculations Determining specific heat capacity Revision questions 59 61 64 Heat and state change 65 Demonstrating a change of state Latent heat Determining specific latent heat Revision question s 65 66 68 70 Evaporation and boiling 71 Cooling due to evaporation Factors affecting th e rate of 71 evaporation 71 9 20 21 Refrigerator Air conditioner Other phenomena involving latent heat Revision questions 22 18 Thermal energy transfer Processes of thermal energy transfer Conduction Convection Radiation Applications of thermal energy transfer processes Revision questions Exam-style questionsChapter.' 10 to 18 IV Contents 78 80 81 83 84 86 88 90 Sou d waves 91 Production and propagation Pitch and loudness (volume) Classification of frequencies of sound Uses of ultrasound Estimating the speed of sound in air using echoes Other uses of echoes Behaviour of sound waves Revision questions 91 91 92 92 Electromagnetic waves 97 93 93 94 96 97 97 98 99 Light waves 100 Rival theories of light Diffraction and interference Revision questions 100 101 104 L.ght 'ays and 'ecflinear _ _ propagation 24 74 74 74 75 76 Types of waves Wave parameters General wave equations Graphs of waves Revision questions 23 71 72 72 73 73 83 General properties of electromagnetic waves Wavel engths and frequ encies of th e electromagnetic spectrum Uses of electromagnetic waves Revision questions Demonstrating cooling due to evaporation 0 25 105 Shadows Eci ipse of the Moon Eclipse of the Sun Th e pinhole camera Revision questions 105 105 106 106 107 Reflection and retraction 108 Reflection Refraction Dispersion Critical angle and total internal reflection Revision questions 108 109 112 Lenses 118 Magnification Determining the focal length of a converging lens Real and virtual images Constructing scale diagrams 119 113 117 119 120 120 26 27 28 The lens formula Revision questions 122 124 Exam-style questions Chapters 19 to 25 125 Static electricity 127 Introduction to electric charges Hazards of static charge Useful applications of static charge Electric fields Revision questions 127 129 129 131 132 Current electricity 133 Conductors and insulators Conventiona l current and electron flow Alternating and direct current Revision questions 133 Electrical quantities 136 Electromotive force and potential difference in a circuit Electrical power Importan ce of con serving electrical energy Revision questions 29 30 Circuits and components 31 32 133 134 135 136 137 138 139 33 140 Some important electrical components Series and parallel circuits Cells Resistance Ideal ammeters and voltmeters Ohm's law and I-V characteristic curves Current and voltage in complete circuits Energy and power in complete circui t s Electricity in the home Revision questions 150 151 154 Electronics 155 Rectification Logic gates Impact of electronic and technological advances in society Revision questions 155 155 140 141 141 144 145 146 147 34 M agnetism 159 Forces between magnetic poles Magnetic induction Testing for polarity Permanent and temporary magnets Magnetic fields Revision questions 159 159 159 160 160 162 Electromagnet ism 163 Magnetic fields and electric currents Electromagnets Force on a current-carrying conductor in a magnetic field Deflection of cha rged particles entering a magnetic fie ld Simple dc motor Electromagnetic induction Transferring electrical energy between coils Simple ac generator Transformer Long-distance ac distribution Revision questions 163 164 168 168 169 170 171 Exam-style questionsChapte rs 26 to 32 173 The atom 176 Models of the atom Structure of th e atom Revision questions 176 177 178 Radioactivity 179 Radioactive emissions 179 181 165 166 166 167 Equations of radioactive decay The nature of the radioactive decay process Calculations involving half-life Uses of radioisotopes Nuclear fission and fusion Hazards of ionising radiations Revision questions 182 183 186 188 190 191 Exam-style questions Chapters 33 to 34 193 Index 195 157 158 Contents v Failure is not an option Why this book is so very important to you The author has taught Physics for over 35 years. He is well aware of the issues which pose problems to students and of how to present the material in a manner so as to avoid such problems. This book is specifically designed to meet the needs of students preparing for the CSEC®Physics examination. • The (SEC" Physics syllabus has been closely followed in the layout of the book with respect to its 5 Sections (A to E) as well as to the order of the topics within each section. • Section A Chapters 1 - 9 Mechanics • Section B Chapters 10 -18 Thermal Physi cs and Kinetic Theory • Section C Chapters 19 - 25 Waves and Optics • Section D Chapters 26 - 32 Electricity and Magnetism • Section E Chapters 33 - 34 The Physics of the Atom • Every specific objective has been carefully addressed in a complete and concise manner. • (lear, annotated diagrams make it easier to fully understand the content of the text. • Laws and definitions are printed in colored, italic font so that they are emphasized for improved learning and are easily located. • A complete summary of necessary formulae is provided at the end of this introduction. • Worked examples are included to reinforce the theory of each topic. These demonstrate the application of the laws and equations to various situations as well as show the format to be used in calculations. • Revision questions, included at the end of each chapter, are designed to t est your knowledge and comprehension of the content of the chapter. • Exam-style questions, included at the end of each section, are specifically prepared to assess your knowledge and comprehension in the relevant areas as well as to test your use of knowledge in application to various situations. These questions are accompanied by the marks allotted to them, allowing you to obtain an accurate measure of your performance in relation to the CSEC· method of assessment. • Answers to the revision questions of each chapter and to the exam-style questions of each section are available online at www.collins.co.uk/ca ribbeanschools. The CSEC® Physics examination A starting point for all students in preparing for the CSEC® examination is to obtain a copy of the relevant syllabus. This is available online at http://cxc-store.com and provides an in-depth overview of the specific objectives together with important information regarding the School-Based Assessment (SBA) and the examination itself. A brief outline of the assessment profiles, the examination format and the SBA is provided below. Assessment profiles Your final grade will be determined by assessing your performance using the following pro{iles: • Knowledge and comprehension vi Failure is not an option • Use of knowledge • Experimental skills Examination format Paper 01 (1 '14 hours): Worth 60 marks (30% of the total exam mark) and comprised of 60 multiple choice questions. Paper 02 (2'12 hours): Worth 100 marks (50% of the total exam mark) and is comprised of Section A (questions 1 to 3) and Section B (questions 4 to 6). All questions are compulsory. • Section A consists of three structured questions. • Question 1 tests data analysis and is worth 25 marks. It usually involves compl eting a table of readings, plotting a graph and determining its slope, finding an intercept and making predictions from the plot. This is generally followed by questions testing your knowledge of the particular topic. Dedicate 35 minutes to this question. • Questions 2 and 3 are each worth 15 marks. Usually you will be required to complete a table or diagram and then to answer questions on the same topic. Dedicate 20 minutes to each question. • Section B consists of three extended response questions, each worth 15 marks. Usually you will be asked to describe an experiment or discuss certain issues related to Physics. Your essay writing skills and your ability to 'think outside the box' is more dominant in this section. Calculations are also generally included. Dedicate 20 minutes to each question. Paper 03/1 (School-Based Assessment) Developed throughout the course (20% of total exam mark) Paper 03/2 (For private candidates not doing SBA) 2 hours 10 minutes (20% of total exam mark) School-Based Assessment (SBA) School-Based Assessment provides a significant and unique influence on the development of necessary skills applicable to the subject together with a means of assessing and rewarding students for their accomplishments. For the diligent student, these laboratory exercises provide a golden opportunity to achieve a good grade since they are not performed under the usual stresses of examination conditions. • Your achievements under the profiles of Experimental Skills and Use of Knowledge (Analysis and Interpretation) will be assessed during Terms 1 to 5 of the two-year period leading up to your CSEC· examinations. • Competence in the following skills will be assessed: • Manipulation/Measurement • Planning and Designing • 0 bse rvation/Reco rd i ng/Reporti ng • Analysis and Interpretation • Assessments will be made during the usual practical sessions. You are required to keep a separate practical workbook for all your practical work. This must be maintained in good condition and must be available on demand for moderation by CXc. Your workbook should be collected at the end of each practical session. Failure is not an option VII • An Investigative Project, to be carried out in Year 2, is assessed in two parts; Planning and Designing, and Analysis and Interpretation. Students pursuing two or more of the subjects, Biology, Chemistry and Physics, may opt to carry out ONE investigation only from any of these subjects. Keywords used in Paper 02 In order to accurately interpret what is being asked, you must be familiar with the followi ng keywords. Annotate Apply Assess Calculate Cite Classify Comment Compare Construct Deduce Define Demonstrate Derive Describe Determine Design Develop Distinguish Discuss Draw Estimate Evaluate Explain Find Formulate Identify Illustrate Investigate Label VIII provide a short note to a label solve problems using knowledge and principles give reasons for the importance of particular structures, relationships or processes provide a numerical solution to a problem quote or make reference to partition into groups according to observed characteristics state an opinion or point of view validated by reasons state similarities and differences Represent data using a specific format to draw a graph, scale drawing or other device. logically connect two or more pieces of information; arrive at a conclusion by using data concisely state the meaning of a word or term show determine a relationship, formula or result from data by the use of a logical procedure give detailed factual information on the form of a structure or the sequence of a process find the value of a physical quality plan and present, with relevant practical detail expand on an idea or argument with the use of supportive reasoning briefly identify differences between items which can place them in separate categories present the relative merits of a situation with reasons for and against produce a line illustration depicting an accurate relationship between components arrive at an approximate quantitative result make judgements based on given criteria by consideration of supporting evidence make an account giving reasons based on recall locate or extract information of a feature develop a hypothesis point out specific constituents or characteristics clearly present by the use of examples, diagrams or sketches observe, log data and arrive at logical conclusions by using basic systematic procedures Identify parts of a diagram by means of names and pointers Failu re is not an option List Measure Name Note Observe Plan Predict Record Relate Sketch State Suggest Test produce a series of related items without detail make accurate quantitative observations with the use of suitable measuring instruments state the name only record observations examine and record changes which occur during a particular situation make preparation for the operation of a particular exercise suggest a possible conclusion based on given information give an accurate account of all observations made during a procedure show connections between sets of facts or data a freehand diagram illustrating relevant approximate proportions and characteristics give facts in concise form without explanations explain based on given information or on recall discover by the use of a set of procedures Revising efficiently and effectively Throughout the course From the onset of the two year CSE ~ programme you should be in a mode of regular revision. This will keep you on top of things and boost your confidence in the subject. • New material should be reviewed as early as the day of receiving it and then periodically browsed as the school year progresses. This reinforces the concepts and reveals weaker areas; it alerts the brain of the importance of the topic, allowing it to be readily available in our memory. • Notes should be kept up-to-date. • All assignments and tests should be filed in an organized manner. • Weak areas should be overcome immediately and not left to later in the term. The term before the examination About twelve weeks before the CSEC· examination, a concentrated revision technique should be employed. Due to the increased work-load, this period should be accompanied by maintaining a healthy balanced diet and leaving adequate time for rest and exercise. • Obtain the dates of your CSEC· examinations from www.cxc.org and prepare 'a revision timetable. This may be a bit difficult to stick to during the week due to homework assignments, but the times allotted for weekend study should be fairly stable. The Easter holidays provide a great opportunity to increase the number of hours dedicated to revision. • Select a suitable location for your revision, free from noise and other distractions. • A large desk which can hold all your texts, notebooks, a copy ofthe syllabus, past tests and examination papers, calculator and other items you may need for revision, is preferred. This avoids you having to break your concentration to locate materials during the sessions. The desk should be kept free of clutter to maintain an organized mood. • Six to eight hours of revision is recommended on days when you are not at school. This may be divided into TWO sessions positioned at times when your concentration is best. Relax and do unrelated things during the remainder of the day. Failure is not an option ix • Your posture should be comfortable since you will be seated for long periods, but not such that you feel drowsy; no lying or sitting in bed! • Take short breaks after each hour of study to walk around and have a brief stretch. This allows you to better focus and consolidate the information. • The following outlines some techniques which may be used to enhance your learning skills. The more you apply these techniques the greater will be your recall. • Carefully read through the topic, identifying key points with reference to definitions, laws, concepts, etc. Having a good understanding of the subject matter makes it much easier to reserve a high priority space in your memory. • Group discussions are very important since they help to - increase your confidence - alert you of things you were not aware of - improve understanding of your weaker areas • Create flow charts or other forms of linking diagrams to act as mind maps. By placing large amounts of information on one page you make it easier to review; the individual parts are then more meaningful and therefore readily remembered . • Prepare flash cards with important queues to information on a topic • Practice drawing, labeling and annotating diagrams • Use a key word, a short phrase, a mnemonic or an acronym, as a queue to trigger the recall of important information. - 'Richard Of York Gave Battle In Vain' is a mnemonic to remember the colours of the visible spectrum; 'Red, Orange, Yellow, Green, Blue, Indigo and Violet' - 'LED' is an acronym for 'Light Emitting Diode' • Topics are of varying length and complexity and therefore some sessions will cover more items than others. Set time periods for each session and goal/goals for what you want to accomplish within them. Finish each session with a brief overview of the items covered. • Read through the relevant section in the syllabus before you revise each topic and mark it off as you complete the revision. • Answer the end of Chapter revision questions at the end of each chapter and the Exam-style questions at the end of each section to obtain a measure of your competence. The answers can be checked online at www.collins.co.uk/ caribbeanschools. • Past CSEC· examination papers are available online through the CXC Store. Work through as many of these as possible. • Read through all your past tests and assignments and ensure that you understand the areas where you lost marks. Optimum examination technique • Preliminaries - just before the examination x • Ensure that you are ce rtain of the start time for the examination • Have a healthy breakfast • Arrive early to the venue • Have 8 hours sleep • Stay away from those who panic; think positive Failure is not an option • Carefully read and follow the instructions on the opening page, doing exactly as you are asked. • Plan the period of time to be applied to answer each question. This should be known before hand since you would have practiced on past CSEC· papers with the same format. • Although all questions must be answered, you should still read through the paper before attempting them. You would then be able to select the ones you can do well and start on the simplest first. This will enhance your confidence. • Before attempting a question, read it at least twice, circling important keywords and phrases. • Dedicate time to each part of a question in proportion to the marks allotted to it • As you do a question, recheck to ensure that you have attempted all the parts and have accurately answered what was asked. The typical CSEC® keywords listed earlier would be very important here in order for you to acquire the marks assigned to the question. • Appropriate scientific jargon makes your answers more meaningful and impressive. • Check the time periodically (could be at the beginning of each question) to ensure that you are in good standing to finish the paper. • For calculations: • Start by listing the equation in general form • Substitute the known values • Show each step in the solution, preferably on a new line • Represent your final answer with the correct SI unit • Show all working as well as any assisting statements • If several points are required in an answer, use bullets to clearly indicate their individuality. • If you are asked to I ist the pros and cons or benefits and costs, etc. of an issue, make sure to place sub headings over each list to distinguish between them. • Any time left over at the end of the exam should be spent on reading through your answers to ensure that they are free of errors. Pay special attention to calculations and to the use of units. Important Formulae One of the most important things to learn for a Physics examination is the formulae necessary for your calculations. The symbols used below have already been defined in the text. SECTION A density MECHANICS m p=- V v- u acceleration a=-t force F=ma weight W=mg F=m(v-u) t Failure is not an option XI pressure p=£ momentum p=mv moment T= Fd .L p= hpg A work or energy p= W p= Fv t ,.... . useful work or energy output x 100 = useful power output x 100 ellic/ency = power input work or energy input power kinetic energy EK = ~ mv' change in gravitational potential energy M p = mg6.h displacement - time graphs velocity v = 6.d (i.e. gradient) velocity - time graphs acceleration a = 6.v (i.e. gradient) M M distance = area between graph line and t - axis (all areas positive) displacement = area between graph line and t - axis areas above axis are positiVe) (areas below axis are negative SECTION B THERMAL PHYSICS AND KINETIC THEORY heat energy EH= mc6.T EH = ml heat power p = mcM p = ml t H p V P V equation of Ideal Gas _ , _, = - ' - ' SECTION C (note: T must be in kelvin) T, T, WAVES AND OPTICS within a medium v = Af t H v A sin 0 .,.. v . 1 1 1 magmllcatlOn m = Iens equatIOn - + - = u v f u SECTION D ELECTRICITY AND MAGNETISM charge Q = It Q = Nq energy and work E= VQ E = Vlt E = f2Rt power P = VI P = I'R E= - h, m =- ho V' t R E=- R tf, If, ideal transformers (100% efficient) N Pp V efficiency = ""if: = If: = I:I SECTION E ,THE PHYSICS OF THE ATOM Einstein's equation of mass - energy equivalence , . - -.... Failure is not an option frequency f = ~ V' emf = sum of pd's in circuit P = IR P N V efficiency = - ' x 100 = transformers xii 1/ changing mediums""!' = ....!. = _ _ , = -2 v, A, sin 0, 1/, 6.E = 6.mc' VI V ;/:x 100 1 Scientific method Galileo's contribution to scientific methodology Galileo Galilei was an Italian mathematics professor of the 16th century. He was the first to implement a scientific approach in order to investigate a problem, and is often referred to as the 'father of modern scientific methodology'. Today's scientists have the advantage of added tools for investigation, such as calculus mathematics invented by Newton, the processing speed of the computer and the web of pooled information available on the internet. However, the basis of Galileo's method is still adopted by scientists for their current investigations: 1. Observation: Observe an event in nature which needs to be investigated. 2. Hypothesis: Suggest a possible explanation based on the observation. 3. Experiment: Use quantitative data to obtain objective generalisations and perform several experiments to test the generalisations. The experiments should investigate only one variable at a time. 4. Conclusion: Make a solid conclusion on the truth of the hypothesis based on calculations from the experiments. The conclusion itself should be expressed in terms of an equation. For example, Galileo showed that an object fell through a distance (s) in a time (t) according to the equation s = 1- kt' where k is a constant. Experimental data and its analysis • A procedure to be undertaken is designed using the following types of variable. Ind('pend{'nl varitJb/c" Ih(' van.lbh' lhill is /)(,lnlj a/terccl or Invt'SlJgatC'd Dep<,tld"tl l variable: 1he variahl" Ih,/t mal' he ,,{{('cted b\' ,/ <hallge in the IIlci< I)endelll vdrJ.lble COlllrol "" jable.' .\ \' "ria/)It that i, kC'l)t mnstallt • The procedure is implemented. In an investigation of how the factors mass (m) and length (I) affect the period (Tl of a simple pendulum, the variables could be as shown in Table 1.1. Table 1.1 Types of variables Expt 1 length of string period mass of bob Expt 2 mass of bob period length of string If a third variable is to be investigated, such as the angular displacement of the string, the length of the string as well as the mass of the bob will have to be controlled as the angle is varied. • The experimental data in tables, charts and graphs is analysed. Drawing graphs Figure 1.1 illustrates the format used in presenting the plot of a graph. • The graph should have a title stating the variables being plotted and the purpose of the plot. • The first variable mentioned is placed on the y-axis; the other, on the x-axis. • Each axis is labelled with quantity and unit (if any). • Scales are selected which are easy to use; simple ratios such as 1:1, 1:2, 1:5. • Suitable scales should utilise at least two-thirds of the graph sheet. 1 Scientific method • Points are plotted either as x or 0 using a sharp pencil. • Sometimes, if both axes start at ze ro, the experim ental points are all cluttered together in one small section of the graph paper. In su ch cases the scale should be broken. • A long transparent ruler should be used to draw a line of best fit for straight-line graphs. • If the graph is not a straight line, th e best smooth curve through the points is sket ched. • Whether the graph is a straight line or a curve, th e following should be noted: a) The lin e will not necessarily pass through all the points. b) The mean deviation of the points from either side of the line should balance in order to reduce random error (discussed later) which may have occurred during the experiment. r2 vs 'to investigate how the length of the string A plot of affects the period of a simple pendulum 2.8 scale: y-axis 1 em = 0.20 S2 x-axis 1 em = 10 em 2.6 2.4 2.2 2.0 1.8 1.6 N . ;c.. 1. 4 ~ 1.2 1.0 0.8 0.6 0.4 0.2 0 0 10 20 30 40 50 60 I/ern Figure 1.1 Drawing graphs 2 1 Concise Revision Cou rse: CSEC' Physics 70 80 90 100 Finding the gradient (slope) of a straight-line graph • Select two points on the line, (x" y,) and (x,.y, ), which are far apart. Each point should be exactly on a corn er of one of the small squares of the graph sheet. Mark these points and use them to construct a large right-angled triangle as shown in Figure 1.2. 13.0.8.0) 8.0 m _ 8.0 - 2.0 V -3:Q:01i m= 6.0 ~ scale: y-axis 1.0 em = 1.0 V x-axis 1.Ocm=O.5A 3.0 A m = 2.0 VA-I 6.0 • Determine the gradient, m (slope) from the equation y, - y, m =-Xl -X l • The point (x" y, ) is always to the right of (x" Y,), which sometimes makes the slope negative. 2.0 ---- ---------- -- - ----------. 10.2.0) • The unit of the slope is the ratio: unit of y-axis o+-.~ unit of x-ax is o 2.0 1.0 3.0 currentjA Figure 1.2 Gradient of a straight-line graph Significant figures in measurements and calculations Measurements Generally, a reading can be read to the nearest half of an interval of the scale. For example, a reading on a metre rule, calibrated in mm, could be 23.5 mm. Calculations involving products and/or quotients Express to the least number of significant figures of the items in the calculation. p= 4.2 x 375 x 41.3 27 = 2409.166667 from calculator P = 2400 to 2 sig. fig. Calculations involving addition and/or subtraction We examine precision here, rather than significant figures. X = 21.3 + 325 + 2132.1 = 2478.4 from calculator X = 2478 to the correct level of precision The least precise of the three numbers is 325. Its least significant figure is in the units place value position and therefore the result must also have its least significant figure in the units place val ue position. 1 Scientific method 3 Random errors dl{' lho~' ",hfCh hav(, ('<tval chance Random ~ r or.s of causing the rc..,\<.;ufllo be greater u/" I('~ . . ('r than the 14 mm (parallax true va/u(', They may be caused by poor judgement or by slightly fluctuating conditions during the experiment which cannot be controlled. A typical example is parallax error. This occurs when the marking viewed on a scale is not coincident in position with the point to which the measurement should be made (Figure 1.3). Reducing parallax error er o r ~ -- _ __ ~ eye Figure 1.3 Parallax error o Ammeters and voltmeters with moving pointers usually have a mirror placed behind their scales. Readings should be taken from a position where the pointer is directly in front of the image it produces. o Observations should be made with the line of sight perpendicular to the scale. o The pointer should be as close as possible to the scale when taking readings. o If th e scale is vertical, such as with a measuring cylinder, eye level readings should be taken. Reducing the effects of random errors o The mean of several readings should be taken. o The line of the graph should have minimum deviation from its points. Systematic errors Sys lcnMlic errors arC' those' which rnak(' the result always too small or always too large by the silme an1()Unl. They are due to some inaccuracy in the system. They usually arise because of some problem with the measuring instrument, but can also be due to the experimenter. Examples are: o zero error of ammeters or voltmeters with moving pointers (when no current flows, the pointer may not be at the zero mark) o poorly calibrated scale. Reading systematic errors Systematic errors are not reduced by the methods that reduce random errors. They may be reduced by one of the following methods: o The value of the error must be discovered and then added or subtracted from each reading. o The instrument must be adjusted. Reading measuring instruments Measuring instruments can usually be read to the nearest half of an interval on a scale. However, the vernier calliper and the micrometer screw gauge require the examination of two scales before the actual reading is determined. , . 1 Concise Revision Course: CSEC· Physics Vernier calliper The vernier calliper (Figure 1.4) has an extra scale known as a vernier scale which is capable of measuring to one extra decimal rlace over that measured by the main scale. This calliper is suitable for measuring lengths between 1 cm and 10 cm. The following should be noted when using the instrument: o The jaws are adjusted by sliding the vernier scale over the main scale. o The main scale is read to the mark just before the zero marking on the vernier scale. o The marking on the vernier scale that best aligns with a mark on th e main sca le gives the added significant figure. 0.53 em these jaws can measure the internal diameter main scale ~ em of a cylinder sliding vernier scale these Jaws can measure the external diameter of a cylinder 0.53 em main scale 0.5 em vernier scale 0.03 em reading 0.53 em Figure 1.4 Vernier calliper Micrometer screw gauge Figure 1.5 shows a micrometer screw gauge. It is used mainly for measurements which are less than 1 cm. Like the vernier calliper, it produces a reading with greater precision than that of just the main scale. One revolution of the thimble moves the jaws by 0.5 mm. It is useful for measuring small lengths such as the diameter of a wire. The fo llowing should be noted when reading the instrument: o The main scale of the sleeve is read to the marking just before the thimble. o The thimble scale is read at the marking that coincides with the horizontal line on the sleeve. o The two readings are summed. jaws .r 5 0 ~ - 6. 12 mm \ 20 15 10 l 0:::- S t hi ~ bJ e sleeve sleeve 6.0 mm thimble O.1 2mm reading 6.12 mm rt Figure 1.5 Micrometer screw gauge Suitability of instruments The sensit ivity, accuracy and range of an instrument determine its suitabi lity for making particular meas urements. o A metre rule is used to measure the height of a table because it has the necessary range required. In most cases, accuracy to the nearest mm is sufficient for such a measurement. o A vernier calliper is used for measuring the internal diameter of a water pipe. Its sensitivity, accuracy and range are suitable, as well as its physical design of expanding jaws. 1 Scientific method 5 • A micrometer is suitable for measuring the diameter of an electrical wire because it has the required range, sensitivity and accuracy required by an engineer, as well as jaws fo r holding the wire firmly. • A mercury-in-glass laboratory thermometer is suitable for measuring temperatures in the school laboratory because the experiments generally performed are within its range. It does not have to be as accurate as a clinical thermometer. • A clinical thermometer needs to be very sensitive and accurate for the doctor or nurse to make adequate decisions regarding the patient. It requires only a small range because the temperatures for which it is used are only between 35°C and 42 dc. Quantities and units Table 1.2 shows the fundamental quantities with their 51 base units. '51' denotes the International System of units. Table 1.2 Fundamental quantities and their 51 base units 51 fundamental quantity mass kilogram kg length metre m time second s current ampere A temperature kelvin K amount of substance mole mol luminous intensity candela cd Other quantities are derived from these fundamental ones, and 51 derived units are combinations of the base units. For example, acceleration has the unit m s-'. Force (F) can be calculated from the product of mass (m) and acceleration (a), so its unit can be determined: Quantities F = ma 51 units N = kg m s-' The newton (N) is assigned as the 51 unit of force. Instead of speaking of a force of 25 kg m s-' , we say 25 N . Table 1.3 lists several derived quantities and their 51 units. Table 1.3 Derived quantities and their 51 units force work or energy 6 F F=ma WorE E= Fd power p pressure p 1 W p= - t F p=A 1 Concise Revision Course: C5EC· Physics N ~ kg m s-' kg m s-' Nm kg m' s-' w J S-I kg m' s-J Pa N m-1 kg m- I s-, Table 1.3 Derived quantities and their 51 units continued Constituent SI base units Q charge Q=1t C As As V =.£. Q V J C-' kg m' A-' s-' fl VA-' kg m' A-' s-' Hz s-' s-' t- voltage (pd or emf) V resistance R frequency f R=~ I 1 f=T Index notation A number expressed in standard form or index notation is represented as a power of 10: M x 10". M (th e ' mantissa') is a number in decimal form with only one non-zero digit before the decimal point and p is an integer. The value of p is obtained from the number of decimal places moved in representing the mantissa. A negative value of p indicates that the number being expressed is less than 1. 37 000 = 3.7 x 10' 0.00000055 = 5.5 x 10-7 Prefixes As an alternative to index notation, prefixes may also be used to express a quantity in a shorter way, as Table 1.4 shows. Table 1.4 Prefixes .. Abbreviation pico nano micro p n x 10-9 x lQ-6 x 10- 12 milli no prefix kilo mega giga tera m no prefix k M G T ~ X 10" x 10· X 10' x 10' X 10' • For each jump to an adjacent column in the table of prefixes. there is a shift of 3 decimal places . • Using a larger unit produces a smaller number; using a smaller unit produces a larger number. 0.00456 km = 4.56 m This is a jump of 1 column (3 decimal places) from kilo to no prefix; a larger to a smaller unit and therefore a smaller to a larger number. 5 200 000 000 W = 5.2 GW This is a jump of 3 columns (9 decimal places) from no prefix to giga; a smaller to a larger unit and therefore a larger to a smaller number. 1 Scientific method 7 Density The density of a substance is its Inass per unit volume. . den s1ty ~ mass --""':=-volume p ~ ­ m V The mass of the body can be obtained by the use of an electronic balance. Th e volume of the body can be obtained by one of the following methods: o If it is a liquid, it can simply be poured into a measuring cylinder and the reading taken. o If it is a regularly shaped solid, its dim ensions are measured and the necessary calculation performed. o If it is an irregularly shaped solid, it is immersed into a measuring cylinder of liquid in which it is inso luble; the increase in the reading gives its volume. Unit of density Density is usually expressed in kg m-' or g cm-' . This can be deduced from the relation p ~ ~ where kg and g are units of mass, and m J and em' are units of volume. V Revision questions 1 Express the following to the co rrect number of significant figures. a 2 27.2 x 14 x 12.22 State what is meant by each of the following terms, giving an example of each. a random e rror 3 b 17.62 + 11.2 -7.5 b systematic error Calculate the gradient of the graph in Figure 1.6. 10.0 8.0 ~ _: 6.0 4.0 2.0 o +-.---.--,---'\ o 1.0 2.0 3.0 4.0 VjV Figure 1.6 4 State the instrument which is most suitable for meas uring each of the following lengths. a The thickness of a piece of window glass b The width of a microwave oven c The width of a box of playing cards 8 1 Concise Revision Course: CSEC' Physics 5 What are the readings on the micrometer screw gauge and the verni er calliper shown in Figure 1.7? - f" 4 3 o 5 I1111I11 mm 11111111 0 45 o 5 10 vernier scale a b Figure 1.7 6 List FIVE fundamental quantities with their 51 base units. 7 What are the derived 51 units for each of the following? a pressure 8 c force d power b 0.000 123 Express: a 55 000 OOOJ in MJ 10 work Express the following in standard form. a 555.22 9 b b 0.0333 mA in ~A c 400mW in kW Calculate the mass of a stone of volume 4.0 em' if its density is 2.0 g cm-'. 1 Scientific method 2 Scalars and vectors Table 2.1 Scalars and vectors Scalar Vector Definition a quantity Ihal has only magnilude a quantily Ihal has magnilude and direction Common examples mass, length, time, temperature, area, volume, speed, pressure, di stance, force, momentum, displacement, velocity, acceleration Howadded algebraic summation work, energy, power, resistance, current vector summation Finding the resultant of two vectors Oblique vectors by scale diagram Figure 2.1 shows four cases of forces A and 8 either pushing or pulling on a particle. In each case, 8 is horizontal and A is at an angle, 8, above the horizontal. The resultant force can be found by using either of the following methods, which are illustrated in Figure 2.2. L B 7 - /lJL B ~ / / / -- -- -. B Figure 2.1 Oblique vectors • Parallelogram method: The vectors are represented to scale in magnitude and direction by arrows, starting at the same point and forming the adjacent sides of a parallelogram. The resultant vector is then represented in magnitude and direction by the arrow forming the diagonal of the parallelogram originating at the same point as the vectors ~ - A - R / /",/ / """'---=B--+ / parallelogram method being added. • Polygon method: The vectors are represented in magnitude and direction by arrows joined head to tail forming a chain. The resultant vector is then represented to scale by the arrow closing the polygon and originating from the beginning of the chain. polygon method Figure 2.2 Parallelogram and polygon methods of adding vectors A and B pull on an object with forces of A ~ 40 Nand 8 ~ 30 N. By means of a scale diagram, determine their resultant force if the angle between the forces is 30°. A scale of 1 cm ~ 10 N is appropriate. The resultant force has magnitude 68 Nand direction 17° anticlockwise from the direction of force 8. See Figure 2.3. B:30N Figure 2.3 2 Concise Revision Course: CSEC· Physics Parallel and anti-parallel vectors In cases like those in Figure 2.4, forces to the right are assigned positive values and those to the left are assigned negative values. 7N +2 N = 9N resultant: magnitude = 9 N direction = to the right 2N + 3N +(-7Nl= -2N resultant: magnitude = 2 N (drop the - sign) direction = to the left Figure 2.4 Parallel and anti-parallel vectors Perpendicular vectors In cases like that in Figure 2.5(a), upward forces and forces to the right are assigned positive values; downward forces and forces to the left are assigned negative values . • The resultant horizontal and vertical vectors are first found as in Figure 2.5(a) . • These resultants can then be combined using Pythagoras' theorem as shown in Figure 2.5(b). 1N horizontal: 6 N + (- 2 N) = 4 N magnitude = 4 N direction: right 2N vertical: 1 N + (-4 N) = - 3 N magnitude = 3 N direction: downward 4N • 4N magnitude: R = ~ R= 5 N R 3N direction: = ill e = tan- 1 i = 3r b Figure 2.5 Perpendicular vectors Resolving vectors into two perpendicular components .- ---- L2J A single vector, F, can be analysed as two perpendicular vectors as shown in Figure 2.6. 1 F 1 =f y=Fsin e COS8=f x= Fcos8 sinO 1 Y 1 e 1 , if e = 3~' and F=40 N, then Y= 40 N sin 30° = 20 N x = 40 N cos 30°= 35 N 1 Figure 2.6 Resolving vectors into perpendicular components 2 Scalars and vectors f 11 Examples of vector components • The velocity vector of a football kicked through the air has a vertical component causing it to rise and fall, and a horizontal component causing it to move across the field . • The force vector due to a groundsman pushing a heavy ro ller across a cricket pitch has a vertical component pushing it onto the ground and a horizontal component pushing it across the surface. Revision questions 1 List FIVE vectors and FIVE scalars. 2 A force of 50 N acts in an easterly direction on an object at the same time as a force of 80 N pushes on it in a direction N 45° E. Determine the magnitude and direction of the resultant force. 3 A man runs at 7.5 m S- 1 due east across the deck of a ship which moves at 10.0 m S- 1 due north. Determine the resultant ve locity of the man (hi s velocity relative to the water). 4 At a parti cular in stant, a football has a velocity of 25 m S- 1 and its direction makes an angle of 30° above th e horizontal. Determine the ve rti cal and horizo ntal components of its velocity. 5 Find the resultant of the following four forces. A = 25 N due north B = 50 N due east C=30Ndue west 0= 40 N due south 12 2 Concise Revision Course: CSEC· Physics 3 Forces, mass and weight Forces -\ force IS n ( >11 th. t chang~ thc<';lL( ... h.IPC' or t1lvtlOl1 o{ a bod\ There are several types of force. • Gravitational forces are attractive forces that exist between bodies due to their masses . The gravitational force of a planet on an object is the object's weight. The Moon is kept in orbit around the Earth by gravitational force. • Magnetic forces are attractive or repulsive forces that exist between bodies due to their magnetic polarities (see Chapter 31). • Electrostatic forces are attractive or repulsive forces that exist between bodies due to their electric charge (see Chapter 26). Electrons are kept in orbit around the atomic nucleus by such forces. • Nuclear forces are extremely strong attractive forces which bind together the subatomic particles of an atomic nucleus. • Elastic forces are restoring forces produced when a body is stretched or compressed. • Mechanical forces are those that exist between bodies in contact. These can be pushes, pulls, normal reactions, friction, etc. Friction is a mechanical force that opposes the relative motion of the surfaces of bodies in contact with each other. Mass and weight Th" m"" of d bod)' is Ihe quantll)' of mdllcr m"k,~ up Ih" bod), The weiMhl ofa bod) IS Ihe force ofgr,l\'IIV onlhe hOc/I. The weight of a body depends on the gravitational field strength that acts on it. On Earth, the generally accepted value of the gravitational field strength is 10 N kg- 1 • This is equal in value to the acceleration due to gravity = 10 m s-'. Both are given the symbol g. The units are equivalent. weight = mass x gravitational field strength W=mg An object of mass 1 kg therefore has a weight W = 1 kg x 10 N kg-' = 10 N. A breadfruit of mass 2.0 kg has a weight of 20 N on Earth but only just over 3.2 N on the Moon where the gravitationa l field st rength is much lower; it is comp lete ly weightless in outer space where there is no gravity. The mass of the breadfruit is the same at each location since it is comprised of the same quantity of matter. Revision questions 1 List FOUR types of forces other than friction. 2 What is a frictional force? 3 Define: a mass 4 b weight a Determine the mass of a football which has a weight of 0.80 N on a planet where the acceleration due to gravity is 2.0 m s-'. b What wou ld be the football's weight on Earth? 3 Forces, mass and weight 13. , . 4 Moments When we open a door, sit on a seesaw, use a spanner, raise the handles of a wheelbarrow or use a bottle opener, we are using forces that have a turning effect or moment about some pivot point. The moment of a force about a poml linc of dction froll) the point. IS the produ( I of the "H( (' and the perpendicular distance of ils moment = force x perpendicular distance T= Fd The 51 unit of moment is N m. Other units may be used, such as N em or kN m, depending on the size of the moment. Note that work (see Chapter 8) is the product of a force and the distance moved in the dire ction of the force. Its unit is therefore also the product N m. To indicate the difference between the two, the unit joule (J) is assigned to work. The direction of a moment must be stated as clockwise or anticlockwise. Calculate the anti clockwise moment T exerted by the force on the trapdoor shown in Figure 4.1. T = 8.0 N x 60 em T = 480 N em 8.0N hingedb=~ 6 60 em Figure 4.1 Calculations on the equilibrium of bodies The following conditions hold for a system of coplanar forces in equilibrium: 1. The sum of the forces in any direction (trallslational equili'mum). 15 equal 10 the sum of the forces m the oppoSile dlfec/ioll 2. The !:.um of the clock \Vise moments about any point is equal to the sum of the antic/ockwi5C mornenls about that same point (rolationdl C'qw!Jhriurn). This is the principle of moments. Tackling problems involving moments • Sketch a diagram showing all the forces acting on the body in equilibrium. These are: i) the weight, which acts through the centre of gravity ii) all other forces of the environment, which act on the body at points of contact. • Select a su itable point about which to take moments. If more than one force is unknown, choose a point through which one of them acts. That force then has no moment about the point and is excluded from the calculation. • Use the rules of translational and rotational equilibrium to formulate equations and solve for unknown forces and distances. • Whenever there is only one unknown force , it can easily be found from the rule of translational equilibrium. 4 Concise Revision Course: CSEC· PhYSics Figu re 4.2 shows a uniform metre rule of weight 2.0 N resting on a fulcrum and supported by a spring balance registering 5.0 N. Calculate: a b the reaction R the weight X 5.0 N O~ ~ =~ R 20 = 5fO = ~F x 2.0 N 80 = ~10 em Figure 4.2 Note the following: • Since the metre rule is uniform, its centre of gravity is at th e 50 em mark. • The downward force of the rule on the fulcrum and the downward force of the rule on the spring balance are not considered, because these forces are not on the rule. • A suitable point must be selected from which to take moments in order to eliminate one of the two unknown forces from the equation. Taking moments about the fulcrum eliminates R. a I anticlockwise moments = I clockwise moments (2.0 x 30) + (60X) = (5.0 x 80) 60 + 60X = 400 60X = 340 X= 340 60 X = 5.67 N = 5.7 N to 2 sig. fig. b I upward forces = I downward forces 5.0 + R = 5.67 + 2.0 R = 5.67 + 2.0 - 5.0 R = 2.67 N = 2.7 N to 2 sig. fig. Determining the centre of gravity of an object The cenlre of gra vily of a bod}' is Ihe pOinlth rough II'hieh the resultant gravilational force on the body acts. A stra ight rod The rod is balanced on the edge of a fulcrum or is suspended horizontally from a string until it balances. The point of support is then the centre of gravity. 4 Moments 15 An irregularly shaped lamina pin in small hole The lamina is hung so that it swings freely from a pin placed through a small hol e near its edge as shown in Figure 4.3. A plumb line is suspended from the pin and the position where it passes in front of th e lamina is marked by small crosses. A line is drawn through th e crosses. The procedure is repeated twice by suspending the lamina from other points near its edge. Where the lines intersect is the centre of gravity of the lamina. line through crosses irregularly shaped lamina 1- - - -- plumb line Figure 4.3 Finding the centre of gravity of a lamina Stable, unstable and neutral equilibrium • Stable equilibrium: A body is in stable equilibrium if, when slightly displaced, its centre of gravity rises and a restoring moment is created that returns th e body to its base. • Unstable equilibrium: A body is in unstable equilibrium if, when slightly displaced, its centre of gravity falls and a toppling moment is created which removes the body from its base. • Neutral equilibrium: A body is in neutral equilibrium if, when slightly displaced, the height of its centre of gravity is unchanged and the body remains at rest in its new position. See Figure 4.4. w w w STABLE restoring moment = Wx w w UNSTABLE toppling moment = Wx w NEUTRAL no moment Figure 4.4 Stable, unstable and neutral equilibrium Factors affecting the stability of an object 1. Height of its centre of gravity (see Figure 4.5(a)) 2. Width of its base (see Figure 4.5(b)) 3. Its weight. A larger weight increases the restoring moment of a stable body thereby increasing its stability. It also increases the toppling moment of an unstable body, thereby decreasing its stability. • Go·karts have wide wheel bases and low centres of gravity in order to be more stable. • Large cargo buses have their baggage compartments under the floor in order to lower the centre of gravity of the vehicle and to enhance stability. W W w W low centre of gravity STABLE high centre of gravity UNSTABLE narrow base UNSTABLE wide a base STABLE b ,...--, Figure 4.5 Factors affecting the stability of an object 16 4 Concise Revision Course: CSEC· Physics Common devices utilising the principle of moments For a give n momen t, the greate r th e perpendicula r distance from the pivot to the force, th e small er is the force. In each device of Figure 4.6, si nce dEis greater than d" the force of the effort (E) is less than the force of th e load (L). For this reaso n, these devices are known as force multipliers. £ block being raised £ wheelbarrow spanner crowbar Figure 4.6 Devices utilising the principle of moments Revision questions 1 a Define th e term moment about a point. b State the TWO conditions necessa ry for a system of coplanar forces to be in eq uilibrium . c Which of the two cond itions is known as the prin cipl e of moments? 2 What is meant by each of the fo llowing? a The centre of gravity of a body b Stable equilibrium c U nstable equilibrium 3 Describe with the aid of a diagram how you can determine th e pos ition of the centre of gravity of an irregularly shaped lamina. 4 State THREE factors which affect the stability of an object. 5 Figure 4.7 shows a non-uniform rod of length 3.0 m balancing on a fulcrum. The centre of gravity of th e rod is 1.2 m to the right of th e fulcrum. Calculate th e weight of the rod and the reaction from its support. o 60N. L 0.2 m 3.0m fulcrum Figure 4.7 4 Moments 11 5 Deformation Hooke's la<1 states that the force applied to a sprmg is proportional to its extension. Verifying Hooke's law • The apparatus is set up as shown in Figure 5.1. • The position of the pointer is recorded using the metre rule. • A mass of 20 g is placed on the mass holde r and the new position of the pointer is recorded. I-- retort stand and clamp metre rule - f--spring • The process is repeated by adding masses, one at a time, until six readings are taken. • The masses are removed, individually, and the position of the pointer on the scale is measured and recorded each time. -mass pointer • The average scale reading and the extension for each load is calculated and tabulated. Scale reading/em Load/N • A graph of load against extension is plotted. holder Load Unload A,. Ext./cm Provided the spring is not stretched to the extent that it is damaged, a straight-line graph through the origin should be obtained, thus verifying Hooke's law. The slope of the graph is the force constant (k) of the spring. Figure 5.1 Verifying Hooke's law Precautions to minimise errors • It is ensured that the pointer is fixed firmly to the mass holder during the experiment. • Eye level readings are taken to avoid parallax error. • Readings are taken when the spring is at rest. • To reduce random error, the spring is loaded and unloaded and the average scale reading is calculated. • It is ensured that the spring's support is firm so that it does not shift during the experiment. Analysing force-extension graphs Springs Figure 5.2 shows the relation between force and extension for a spring which has been stretched to the extent that it is damaged. • The proportiollallimit (P) is the point beyond which any further Increase III the load applied to a spring !"vill produce an extension that is no longer proportional to the forcc . • The elastic limit (E) is th e poml beyond which any furlhe r increasc In thc load applied 10 a spring will produce a permanent stretch. For loads (forces) within the elastic limit, there is elastic deformation; if the load is removed the spring returns to its original size and shape. Beyond the elastic limit, there is plastic deformation; the material is permanently stretched. The area between the graph line and the extension axis represents the work done on stretching the spring. If this i's within the proportional limit, it is represented by the area of the enclosed triangle. 18 5 Concise Revision Course: CSEC· Physics Elastic bands Unlike springs, elasti c rubber bands never obey Hooke's law; Figure 5.3 shows that th e graph is nowhere a straight line. As the elastic band is unloaded, the extension fo r a particular lo ad is greater tha n wh en it wa s b eing loaded. H eat energy is di ssipated in th e process. E p area enclosed unloading represents the potential energy area enclosed represents stored or work done on stretching o~- -L the energy converted to heat during the cycle -+ extension Figure 5.3 Force- extension graph for an elastic band Figure 5.2 Force-extension graph for a sp ring A load of 5.0 N stretches a spring by 10 cm. The relaxed length of the spring is 40 cm. Assuming that the proportional limit is not exceeded, determine the following: a the force constant of the spring b the load which will stretch it to 60 cm. Sketch: a graph of force against extension of the spring c d a graph of force against length of the spring. Calculate: e the work done in stretching the spring to 60 cm f the potential energy stored in the spring when it is stretched to 60 cm. a Hooke's law can be stated as F = ke where k is the force constant of the spring and e is the extension . 5.0 = k(0.10) k= ~ 0.10 k = 50 N m" b F= ke F = 50(0.60 - 0040) F = 10 N c, d See Figu re SA. :1zL o c 0.20 ~ ::1------ .. o elm ~ 0.40 0.60 Lim d Figure 5.4 Force- extension and force- length graphs 5 Deformation 19 e Work done = area under force-extension graph w= 10 x 0.20 2 W= 1.0 J Potential energy stored = work done = 1.0 J f Revision questions 1 State what you understand by each of the following terms associated with stretched springs. a Hooke's law 2 b the elastic limit c elastic deformation Sketch graphs of force against extension for each of the following: a a spring being stretched without exceeding the proportional limit b an elastic band being loaded and then unloaded. 3 A load of 80 N applied to a spring of length 40 cm extends it by 20 mm. Assuming that the proportional limit is not exceeded, calculate the following: a the force constant of the spring b the length of the spring when a load of 40 N is applied c the potential energy stored in the spring when the extension is 20 mm. (A simple sketch graph of force against extension can help you here.) 20 5 Concise Revision Course: CSEC· Physics 6 Kinematics Table 6.1 Variables in kinematics d15tance d t displacement ., speed I' evelocit)' I' acce/eratlOn a length hetween two points scalar m distance in a specified direction vector m rale of change of distance scalar m 5- 1 rate of change of distance in a specified direcl10n (rate of change of displacement) vector m 5- 1 rate of change of velocity vector Displacement-time and velocity-time graphs Displacement-time (s-t) graph Examp les of obtaining velocity from displacement-time graphs are shown in Figure 6.1. • = -tJ.s w h'IC h'IS t h e gra d'lent • ve IoClty M s~ o Starts at a positive displacement and remains at this displacement. The body IS therefore stationary. Zero gradient implies zero velocity, t s~ o Starts at zero displacement and moves to a positive displacement. Constant, positive gradient implies constant positive velocity. t s~ o Starts at a positive displacement moves to a zero displacement Constant negative gradient implies constant negative velocity. t lc . o Starts at zero displacement and moves to a positive displacement. Decreasing positive gradient implies decreasing positive velocity. t Figure 6.1 Displacement-time graphs Velocity-time (v-t) graph Examples of obtaining acceleration from velocity- time graphs are shown in Figure 6.2. • acceleration = tJ.v which is the gradient M • distance = area between graph line and time axis (all areas are positive) • displacement = area between graph line and time axis (areas above time axis are positive; areas below time axis are negative) 6 Kinematics 21 '~ Starts at a positive velocity and remains at this velocity. Zero gradient implies zero acceleration. o t 'L Starts at lero velocity and moves with increasing positive velocity. Constant, positive gradient implies constant positive acceleration. o t '~ Starts at a positive veloc ity which decreases uniformly to zero . Constant negative gradient implies constant negative acceleration. o t lc Starts at zero velocity and moves to a positive velocity. Decreasing positive gradient implies decreasing positive acceleration. o t Figure 6.2 VeloCity- tim e graphs ave rage spee d = total distance . tim e total di splace ment . ave rage ve IoCity = ----,.:-.- - - tim e Distance-time and speed-time graphs • The gradi ent of a di stan ce-tim e graph is the speed . • The gradient of a speed- tim e graph is th e magnitud e of th e acce le rati o n if th e m otion is in a straight lin e. Determin e the veloCity during each stage, A, Band C, shown in the displacement- time graph of Figure 6.3. s/m 17.0 ---------- --- c 10.0 ------B 4.0 -t--,AL-{ o 5.0 9.0 16.0 tis Figure 6.3 I1s = gra d.lent V= - I1t v = 4.0 - 4.0 = ~ =0m A 5.0 - 0 5.0 S· l v = 10.0 - 4.0 =~ = 1.5 m S· l B 9.0 - 5.0 4.0 , 17.0 - 10.0 v = --:-::--;:----:::_::__ 2::Q. = 1.0 m S·l c 16.0 - 9.0 7.0 22 6 Conci se Revision Course: CSEC· Physics Figu re 6.4 shows a velocity-time graph of an object moving to the left and then to the right. Determine: a b c d e f g the acceleration during the first 6.0 s the acceleration during the last 2.0 s the distance travelled in the first 6.0 s the displacement during the first 6.0 s the average speed during the first 6.0 s the average velocity during the first 6.0 s the time at which the object changed direction. vi m 5- 1 10.0 ----- ----- - 5.0 Figure 6.4 By inspection of the graph it can be seen that the initial velocity to the left has been assigned a negative value. Motion to the right is therefore positive. a a = 8V = 10.0 - -5.0 = 15.0 = 2.5 6.0 - 0 M 6.0 a = 2.5 m s-' The positive value indicates that the acceleration is directed to the right. During the first 2.0 s this is in the opposite direction to the velocity, so the object is slowing down. This is known as a deceleration. For the next 4.0 s it is speeding up as it moves to the right. b a= 8V = 0-10 = -10 =-5.0 M a=5m 8-6 2 in magnitude S- 2 The negative value indicates that the acce leration is directed to the left and the object is slowing down while still moving to the right. It is therefore decelerating at 5.0 m s-'. c distance = area of triangles d = 5.0 x 2.0 + 4.0 x 10.0 = 25 2 2 d=25 m d displacement s = _ 5.0 x 2.0 + 4.0 x 10.0 2 15 2 s = 15 m The positive value indicates that the displacement is to the right. distance e average speed = --,--'-'time average speed = 25 = 4.2 m 6.0 f S- 1 average velocity = displacement time average velocity = ~ = 2.5 m S-1 6.0 The positive value indicates that the average velocity is directed to the right. g The object changed direction at t = 2.0 s. This occurs when the velocity changes from negative to positive. 6 Kinematics 23 Revision questions 1 Define each of the following terms: a distance 2 b displacement c speed d velocity e acceleration a Without using values, sketch displacement- time graphs for the following motions: a stationary object " an object moving at constant velocity iii an object accelerating. b Without using values, sketch velocity-time graphs for the following motions: an object moving at constant velocity ii an object accelerating uniformly. 3 A car accelerates uniformly from rest to 20 m S- I during a period of 5.0 seconds and then remains at this constant velocity for the next 4.0 s. The brakes are then applied, bringing it uniformly to rest in a final 3.0 s. The motion is in a straight line. a Sketch a velocity-time graph of the motion. b Calculate: the acceleration during each stage of the motion ii the distance travelled during the first 9.0 seconds iii the average velocity for the first 9.0 seconds. __.....1 ..... 24 6 Concise Revision Course: CSEC· Physics 7 Newton's laws and momentum Ari stot le's theory Arist o tl e, a renowned Ancient Greek philosopher, believed that the force applied to a body dete rmin ed its velocity, that is, F ex v. Hi s arguments were based on o bservations, rather than on experim ent. They were: 1. To pull a chariot at a greater speed required more horses which provided a greater force. 2. A moving body comes to rest when the force on it is removed. But Aristotle 's observations were of real-life situations, with friction . If friction is negligible, an object will accelerate when pushed along a level surface by a constant force. There is no force that results in a unique velocity for the object and therefore Aristotle's ' law of motion', F ex v, cannot be correct. His theory was eventually discredited and replaced by that of Newton. Newton's laws of motion hIla ",,': A bod}' continues in its slate of rest or undonn motion ' sultan! forcc. In a straight line unless acted on b)' a I l nd I" ,,: The rate of change of momentum of a bod) IS proportIonal to the applied force and takes place in the direction of the force. F = mv- mu R t FR = resultant force, m a = acceleration = mass, u = initial velocity, v = final velocity, t = time of action of force, F = mv - mu R t Momentum is discussed later in the chapter. ',:,:,:,: ( v'--- -=u"-) = ma -.m t .lrd law: If body A exerts a force on body B, then bod)' Il exerts an equal but opposllely directed force Jf1 bodV A. In other \'\'ords, 'ever}' action has an equal, but OpPosltelv directed reaction'. O nly one of the two forces in the pair acts on a particula r body. Ap plications of Newton's laws • A rocket, with its engines off, moves through outer space at constant velocity in a straight line. The res ultant force on the rocket is zero; there is no forward force since the engines are off and there is no opposing force since there is no atmosphere to create friction with its surface. It will continue in a straight line at the particular velocity it has acquired due to forces which previously acted on it. (1s t law: uniform velocity if FR= 0) If an astronaut steps out of the rocket as it moves at 200 m S· I and then gently releas es the door ha ndle, he or she will continue to move at 200 m S·I alongside the vehicle. The velocity of the astronaut was 200 m S· I and remains at 200 m S· l until some resultant force acts to change this. (1st law: uniform velocity if FR= 0) 7 Newton 's laws and momentum I 25 • As a car crashes into a wall, a force acts against its motion for a particular time. It quickly decelerates to rest (experiences an acceleration with a direction in opposition to its motion). (2nd law: F, = mal If the occupants are not wearing seatbelts, they will continue their motion (1st law: uniform velocity if F, = 0) until they collide with the windscreen, dashboard or some other object. An opposing force from the object then changes their motion, causing them to d ecelerate to rest. (2nd law: F, = ma l • As an aircraft accelerates along a runway, the backrest of a seat presses forward on its occupant. This, together with the forward forces of friction from the seat, armrest and carpet, on the person's body, produces a resultant force that causes the passenger to accelerate. (2nd law: F, = mal Each object producing a force on the passenger's body experiences an equal but oppositely directed reaction force from his/her body. For example, th e forward force of the seat on the passenger's back gives rise to a backward force from his/her back onto the seat. (3rd law: action = reaction) • If the aircraft moves at constant velocity, the resultant force on the passenger along the line of motion must be zero. The passenger will no longer feel the seat pushing on his/her back or friction at the arms. (1st law: uniform velocity if F, = 0) As the aircraft decelerates to rest due to the opposing force of the brakes on its wheels, the occupant also decelerates to rest due to the opposing resultant force experienced from the seatbelt, armrests and seat. (2nd law: F, = mal The forward force of the passenger's body on the seatbelt is equal in magnitude to the backward force of the seat belt on his/her body. (3rd law: action = reaction ) • A car uses a greater driving force from its engine to travel at a higher constant velocity. This is because the frictional force from the air is greater at higher velocity. The resultant force in each case is zero and hence the acceleration in each case is zero. (1st law: uniform velocity if F, = 0) • As a raindrop falls through the air, it qUickly attains a constant velocity. Initially, the only force on the drop is its weight (the force of gravity) which causes it to accelerate at approximately 10 m S-2 . (2nd law: F, = ma l As the velocity of the drop increases, the upward force of the air friction on it increases and hence the resultant downward force on the drop decreases. At some point the weight of the drop becomes equal in magnitude but opposite in direction to the opposing frictional force; the resultant force and acceleration are then zero and the velocity no longer increases. This maximum velocity reached is known as the terminal velocity. (1st law: uniform velocity if F, = 0) • As a child springs upward from a trampoline, an upward force acts on his/her feet resulting in an acceleration (2nd law: F, = mal. The force exerted by the child on the trampoline is equal but opposite in direction to the force exerted by the trampoline on the child. (3rd law: action = reaction) • As water spouts from a rotating garden sprinkler, the force of the device pushing on the water results in an equal but oppositely directed force from the water on the device. This causes the sprinkler arm to rotate. (3rd law: action = reaction) • An object being whirled in a circle at the end of a string is constantly changing direction and therefore its velocity is constantly changing, even if its speed is constant. It is accelerating under the influence of an external force from the tension in the string. (2nd law: F, = mal 26 7 Concise Revision Cou rse: CSEC· PhYSics Constant velocity implies zero resultant force From Newton 's 1st law, if the resultant force on a body is zero, th en one of the followin g is tru e: a) th e body is at rest, or b) the body is moving at constant velocity. The net force is th erefore zero in each of the following cases: . • a humming bird hovering above a flower • a raindrop falling at constant terminal velocity • a car moving at constant velocity (constant speed in a straight line). Abdul pulls a b lock of mass 8.0 kg by means of a horizontal string across a horizontal surface. The tension in the string is 29 N and the frictional force opposing the motion is 17 N. Determine the acceleration. F, = ma (29 -17) = 8.0 x a 12 8.0 -- =a a = 1.5 m S-2 Simran leapt into the air and spiked the ball horizontally. It rocketed away at 25 m s-, but found the palms of Zakira who struck it back along its path with the same speed. If the force exerted by Zakira was 1250 N and the mass of the ball was 500 g, determine the period of impact. Take the origina l direction of the bali's motion as positive. F = m(vR u) u = 25 m s-' ___ t - 1250 = 0.500(-25 - 25) v= -25 m s-' + - F, = -1250 N + - t t = 0.500(-50) -1250 t = 0.020 s Momentum The linear momentum of a body is the product of its mass and its velocity. momentum = mass x velocity The unit of momentum is kg m s-' . It may also be expressed as N s: From Newton's 2nd law, F= mv-mu t and therefore Ft = mv- mu (the change in momentum) The units on both sides of the equation must be equal and therefore, using the left side, the unit of momentum can be N s. Momentum is a VECTOR quantity and therefore its direction is significant. For motion along a straight line, positive valu es are assigned to one direction and negative values to the opposite direction. 7 Newton's laws and momentum Conservation of linear momentum The law of conservation of linear momentum states that, in the absence of extemal forces, Ihe lotal momentum of a s}'stem of bodIes is constant. • The greater the mass of the head of a golf club, the more momentum it has when swung at a given speed, and the greater is the momentum it will impart to the ball which it strikes. • When a bullet is fired, the forward momentum of the bullet is equal but oppositely directed to the backward (recoil) momentum of the gun. The total momentum after the exploSion is therefore zero, as it was before the shot was released. Tackling problems involving the conservation of linear momentum • Select one direction as positive and the opposite direction as negative. • Sketch a block diagram in equation form (see examples which follow), including all objects immediately before and after the collision or explosion, indicating the mass and velocity of each. Be very careful with the signs (+1- ) and arrows for each velocity. Do not place an arrow or - sign on any unknown velocity. • Use the conservation law and the diagram to formulate a numerical equation . • If the solution to the equation is a velocity or momentum, you should state its magnitude and its direction (obtained from its sign, +/-) . • Since 'mass x velocity' is the only quantity on each side of the conservation equation, any unit of mass or of velocity can be used, so long as it is applied consistently within the calculation. A car of mass 1000 kg travels north at 20 m S-1 and collides head-on with another car of mass 1500 kg, which is moving south at 18 m S-1. Determine the common velocity of the vehicles after the collision if they stick together. 20 m S-1_ ~ --18 m S-1 + ~ v ~ ~ v + Figure 7.1 Total momentum before collision ~ total momentum after collision (1000 x 20) + (1500 x -18) ~ 1000v + 1500v 20000 - 27000 ~ 2500v -7000 - 7000 2500 -2.8 ~ 2500v ~v v ~ The negative sign indicates the direction is south. Common velocity after collision v ~ 2.8 m S-1 towards south 7 Concise Revision Cou rse: CSEC· Physics ~ North + ) A body of mass 800 g moves to the right at 4.0 m s-' and collides head-on with a lighter body of mass 200 g which is moving to the left at 20 m s-' . After the collision, the heavier body rebounds at 5.6 m s-' . Determine the velocity of the lighter body immediately after the collision. 4.0 m s-, -+ right + --5.6 m s-, --20 m s-' v ) Figure 7.2 Total momentum before collision = total momentum after collision (800 x 4.0) + (200 x -20) = (800 x -5 .6) + 200v 3200 - 4000 = - 4480 + 200v -800 = -4480 + 200v -800 + 4480 = 200v 3680 = 200v 3680 --=v 200 18.4 = v Velocity of lighter object after collision v = 18 m s-' (to 2 sig. fig.) towards the right A stationary gun of mass 1.2 kg is loaded with a bullet of mass 20 g. Determine th e recoil velocity of the gun as the bullet leaves its nozzle at 200 m s-'. am 5- Om 1 ~ + ~ 200 m s-' 5- 1 • v l ~ + 0.020 kg ~ + ) l 0.020 kg Figure 7.3 Total momentum before collision = total momentum after collision (1.2 + 0.020) 0 = 1.2v + 0.020 x 200 0= 1.2v + 4.0 -4.0 = 1.2v -4.0 - - =v 1.2 -3.3 = v Recoil velocity of gun = 3.3 m s-' (in the opposite direction to the bullet) 7 Newton's laws and momentum f 29 Revision questions 1 State: a Aristotle's 'law of motion ' b the arguments he used to support his theory c one example that indicates that his belief was incorrect. 2 State Newton's three laws of motion, giving an example of each. 3 In which of the following is the resultant force on the ball zero? a A ball at rest on the ground b A ball moving to the right with uniform velocity of 4.0 m C S- I A ball rising vertically through the air after being shot from a spring gun d A ball, fastened to a strin g, and whirled in a circl e at constant speed 4 a Define momentum. b Give TWO units that can be used to express the momentum of a body. C State the law of conservation of linear momentum. d Is momentum a scalar or vector quantity? e How is it possible for two moving bodies to have a total momentum of zero? 5 Rikita of mass 40 kg steps from an initially stationary raft onto a nearby pier. Calculate the magnitude of her velocity if the raft is of mass 20 kg and moves away at 5.0 m s-' . 6 Omorade of mass 50 kg runs and jumps with a velocity of 4.0 m s-, onto a stationary trolley of mass 30 kg. Determine their common velocity immediately after they make contact. 7 Rasheed struck the ball straight into Akib's hands, but it was too hot to handle. The 500 g ball was travelling at 40 m s-, when it broke through his palms and co ntinu ed on in the same direction at 10 m s-' . Determine: a the deceleration of the ball, if the time of impact with Akib's hands was 0.020 s b the magnitude of the force on Akib's hands during the impact period. 30 7 Concise Revision Cou rse: CSEC' Physics 8 Energy Work is the producl of a force and lho distance moved by Its poult of applicaUon the force. 111 lhe dirocUon of Energy is lhc ability to do work. Power is the rale of doing work Of of uSlI1g energy. work = force x displacement W=Fxs energy = force x displacement E=Fxs work power=-.- P= W t tIme 1 jou le (1 J) of work is done when the point of application of a force of 1 N moves through a distance of 1 m in the direction of the force. 1 walt (1 W) is the power used in doing 1 J of work per 1 s. Some types of energy • mechanical energy: a) potential (gravitational or elastic) b) kinetic • e lectromagnetic energy (the energy of radio waves, microwaves, infrared waves, light waves, ultraviolet waves, X-waves and gamma waves; see Chapter 21) • chemica l energy (the energy stored in the bonds of chemical compounds) • sound energy (the energy transferred by vibrating particles of a sound wave) • thermal energy (the energy due to the motion of the particles of a body) • heat energy (thermal ene rgy in the process of being transferred from one point to a next, due to a temperature difference between them) • electrical energy (the energy resulting from charged particles being in electric fields) • nuclear potential energy (the energy binding the particles of the nucleus of an atom) Kinetic and potential energy Kinetic energy is the enNIlY a body has due 10 ils molion. Th e kinetic energy, E" of a body of mass m and speed v is given by: EK = lmv' 2 Potential energy is lh e energy a body has due 10: a) Il'i posllion in a force field, or bl Its slale (for example slrctchcdlcomprcsscdlchcl1l1ca/). The change in gravitational potential energy, I1E" of a body of mass m, as it moves through a height ch ange I1h in a gravitational field of strength g is given by: M p= mg I1h 8 Energy 31 I.....__ ... Examples of kin etic and potential energy • A fast-moving cricket bal/ has kinetic energy, mainly due to its high velocity. • A football kicked into the air has gravitational potential energy due to its position (height) in the gravitat io nal force field. • A stretched elastic band has elastic potential energy du e to its stretched state. • A compressed spring has elastic potential energy du e to its co mpressed state. • Gasoline, food and batteries have chemical potential energy due to their chemical state. The principle of conservation of energy The prin6pl<' of conservation of energy statc; tha t cneruy (al1l1ot bc created or destroyed but can be tram/o(med from one type to ano ther. Note that whenever energy is transform ed, an equal amount of work is done. Examples of energy transformations The tran sformation s li sted below show the MAIN energy changes in each situation. Note that kin etic energy is con stant when velocity is constant. If it is not increasing or d ecreas ing, it does no t take part in the transformation. • A cocon ut fal/ing from a tree and striking th e ground below (not rebounding): gravitational potential energy ---+- kinetic energy ---+- thermal energy + sound energy • A gasoline-fuel/ed car accelerating on a level road: chemical potential energy ---+- kinetic energy + thermal energy + sound energy • A gasoline-fuelled car moving at constant velocity on a level road: chemical potential energy ---+- thermal energy + sound energy • A boy running up stairs at constant velocity: chemical potential energy (from food)---+gravitational potential energy + thermal energy + sound energy • An aircraft taking off: chemical potential energy (from fuel)---+gravitational potential energy + kinetic energy + thermal energy + sound energy • A swinging pendulum, neglecting friction: gravitational potential energy ---+- kinetic energy ---+- gravitational potential energy---+kinetic energy and so on • A battery charging: electrical energy ---+- chemical potential energy • An electric fan: electrical energy ---+- kinetic energy • An electric oven: electrical energy ---+- thermal energy + electromagnetic (i nfrared and light) energy • An electric lamp: electrical energy ---+- thermal energy + electromagnetic (i nfrared and light) energy 32 1 8 Concise Revision Course: CSEC· Physics • A loudspeaker: electrical energy in speaker coil _ kinetic energy of speaker coil and cone_ kinetic energy of vibrating air layers (sound energy) • A microphone: kinetic energy of vibrating air of the sound wave_ kinetic energy of mi crophone coil and· diaphragm _ electrical energy in co il • Hydroelectric power: kin etic energy of falling water_ gravitational potential energy of water at top of falls _ kinetic energy of spinning generator turbine _ electrical energy in generator coil • A diesel-fuelled electrical power station: chemical potential energy of diesel_ thermal energy (to boil water to produce steam)_ kin etic energy of spinning generator turbine (t urned by steam pressure)_ electrical energy in generator coil • A battery used by a crane to lift an obj ect at constant velocity: electrical energy _ gravitational potential energy chemical potential energy _ Asabi pushes a block 25 m across a floor with a horizontal force of 20 N in a time of 4.0 s. Determine: a the work done a b the energy used c the power used. W=Fs W=20x25 W=500J b E=500J c p= W t p= 500 4.0 P=125W A bullet of mass 20 g is shot vertically into the air with a velocity of 200 m a S- I . Determine: the kinetic energy of the bullet on leaving the gun b the maximum potential energy gained by the bullet. mv' a EK =2. 2 1 x 0.020 2 EK = 400 J E, = - X 200' b The maximum EKof the bullet transforms completely to Ep at the maximum height. Therefore max. Ep = 400 J. 8 Energy Raveena grabs on to one of the vines in th e tree and starts to swing. She has a velocity of 6.0 m S-I at the lowest point of her motion. Determine the maximum change of height, I1h , she swings through. (Gravitational field strength = 10 N kg-I) The required height, I1h, is shown in Figure B.l. A I1Ep at the highest point transforms completely to EKat the lowest point. 1 2 -mv' = 1 - v' = g I1 h (m cancels) 2 ~6.0 2 ~ 2 2 k- mg I1h = 10 I1h 6.0' = I1h 10 R,,,en a , , L'l h ' , ..... J1 ------------- 6.0 m 5- 1 Figure B.l l1h=l.Bm If the block in Example 1 is being pushed at constant velocity across a horizontal floor, determine the thermal energy generated. 500 J of chemical potential energy stored in Asabi's muscles transforms into 500 J of thermal energy produced by friction between the block and floor. (Note that the kinetic energy and gravitational potential energy are unchanged since the velocity is constant and the floor is level.) Energy sources Renewable energy sources are those "hieh arc readily replaced. Examples are: solar, hydroelectric, geothermal, tidal, and wind energy. Wood and biomass (organic material ) may be considered renewable if the trees and crops are replanted . Non-renewable energy sources are those \.1.'hich are not readil}'" replaced and bccorne scarce With lime. Examples are fossil fuels (coal, oil and natural gas) and nuclear fuel. Prob lems associated with obtain ing electricity from foss il fuels • Limited reserves: Supplies are rapidly diminishing. • Pollution: Burning fossil fuels contaminates the environment with several pollutants including greenhouse gas emissions. • Fluctuating oil prices: The price has been low recently and this has highlighted the high risk of investing in crude oil companies. • Health care costs: Government funding is needed for health care facilities to deal with illnesses associated with pollutants from the burning of fossil fuels. Alternative sources of energy The Caribbean depends heavily on fossil fuels for the generation of electricity and there is an urgent need for utilising alternative sources of energy. Some possible sources are listed below. Solar energy: Solar water heaters heat water directly and are relatively cheap to install. Photovoltaic panels convert solar radiation into electrical energy. These have a relatively high installation cost but provide a clean source of electricity. The energy can be returned to the electricity grid or stored in p "_ _ _..;b ;,;a;,:tteries to be used at night. 8 Concise Revision Course: CSEC' Physics Hydroelectricity: Water is collected behind a dam in a river and then released. The kinetic energy of the water then turns the turbine of an electrical generator. Guyana has great potential for providing this form of energy, but the landscape of most Caribbean territories is unsuitable. Tidal energy: Water from the ocean can be collected at high tide and then released at low tide to produce powerful water pressure which can turn electrical generators. Alternatively, energy of wave motion and ocean currents can be harnessed to turn the generators. Geothermal energy: Thermal energy from the hot interior of the Earth can be brought to the surface as steam under pressure and released in hot water springs or geysers. Volcanic islands are capable of providing large amounts of this type of energy. Wind energy: Kinetic energy from the wind can be used to turn wind turbines. This form of energy generation, however, has the drawbacks of noise pollution, spoiling the scenery and being vulnerable to unpredictable stormy weather. Biomass energy: This is the energy obtained from plant or animal matter. • Biogas is obtained from the decay of animal wastes. It is comprised mainly of methane and is being used to drive e lectrical generators on farms that deal with livestock. • Wood can be used as a fuel for cooking. • Alcohol, produced from sugar cane, can be used to make gasohol, a useful fuel. Efficiency The efficiency ol a sy'stcm IS the ratIo of the useful energ} output to the l'nt:rg~ Input. It is commonly represented as a percentage. ' . useful work or ene rgy output 1000' eff ICiency = x /0 work or energy input It can also be calculated as the ratio of useful power output to power input. ' . e ff [clency = useful power . output x 1000'/0 power Input Thermal energy produced due to friction is the main reason for syst ems having low efficiency. The fuel tank of a toy car contains gasoline capable of releasing 3.0 kJ of energy. Calculate the efficiency of the conversion if the car moves 50 m, exe rting a driving force of 20 N before it is out of fuel. ' . e ff ICleney = useful energy . output x 1000'/0 energy Input .. Fxd 20x50 effiCiency = - - x 100% = x 100 = 33% E;c 3000 A mass of 200 kg is raised by an electric motor through a height of 25 m. Calculate the electrical energy used if the efficiency of the system is 80%. (Gravitational fie ld strength = 10 N kg-l) ' . useful energy output x 1000'/0 e ff IClency = . energy Input efficiency = mg I1h x 100 Em 80= 200x10x25 x100 f in E. = 5000000 In 80 62500 J 8 Energy , I 35 Revision questions Gravitational field strength = 10 N kg-' 1 Define: a work 2 b energy c power d potential energy e kinetic energy a State the principle of conservation of energy. b Describe the MAIN energy transformations occurring for each of the following situations. A gasoline-fuelled car accele rating along a level road ii A gaso line-fuelled bus driving along a level road at constant velocity iii The bob of a swinging pendu lum iv The generation of hydroelectricity v The generation of electricity from diesel vii A battery-powered motor of a c ran e lifting an object at constant ve locity 3 Mukesh, of weight 400 N, runs up a staircase of height 4.0 m at constant speed in a time of 2.5 s. Determine: a the energy transformation occu rrin g (neglect thermal and sound energy) b the energy used c the power used. 4 A bullet of mass 20 g and speed 400 m s-' embeds itself 12 cm into a block. Determine: a the kinetic energy of the bu ll et before entering the block b the energy transformed in boring th e hole c the work done in boring the hole d the average force of the bullet on the block as it bores th e hole. 5 List: a THREE problems associated with the use of fossil fuels b FOUR alternati ve sou rces of ene rgy. 6 36 Radiation from the Sun reaches the panel of a so lar water heater at a rate of 500 w. If the efficie ncy of the convers ion is 20%, calcu late the rate of energy supp lied to the water. 8 Concise Revision Cou rse: CSEC' Physics 9 Pressure and buoyancy Pressure is the force acting normall}' per unit area. force pressure = - area The 51 unit of pressure is N m ~2 which has been assigned the name pascal (Pa). Gravitational field strength = 10 N kg~ ' Determine the maximum pressure that can be exerted on a horizontal surface by a rectangular block of mass 50 kg and dimensions 20 cm x 50 cm x 1.2 m when resting on one of its faces. The maximum pressure is obtained when the block rests on its smallest face as shown in Figure 9.1. P = ~ / A 1.2 m / 50 kg P = !!2K (the force is the weight) A P 50 x 10 max 0.20 X 0.50 /o20m 0.50 m Figure 9.1 Pressure in fluids The pressure at a point in a fluid increases with increased depth and with increased density of the fluid. increase in pressure = tall can of water depth x density x gravitational field strength !;P = !;hpg Figure 9.2 shows a tall can of water with small holes in its sides at different depths. Water spouts with equal strength from holes on the same level, indicating that th e pressure is the same in all directions at a particular Figure 9.2 Pressure in a fluid increases with depth depth. Water spouts with greater force from holes at greater depth, indicating that the pressure increases with depth. Gravitational field strength = 10 N kg ~' Figure 9.3 shows a fish at a depth of h = 40 m in a lake where the density of the water is 1000 kg m ~ 3 Determine: a the pressure due to the water on the fish h b the total pressure on the fish if the atmospheric pressure is 1.0 x 10 5 Pa. Figure 9.3 a P water::; L::=========-J hpg P,,,,,, = 40 x 1000 x 10 = 400000 Pa b Ptot = Palmos +Pwater P'o< = 1.0 X 105 + 4.0 X 105 = 5.0 X 105 Pa 9 Pressure and buoyancy Archimedes' principle Archimedes' principle slates that "hcll" bod~ is comple/~' or partiall)' immer.sed in a fluid. il experiences an up,h",st equal 10 the Iveight of the !'lui" displaced. Figure 9.4 shows how the principle can be verified . • An object is first weighed in air and th en again when imm ersed in a displacement can filled to the spout with water. The difference between these weight s is the upthru st of th e water on th e immersed object. • The displaced water is collected in a beake r and weigh ed. The weight of th e em pty beaker is subtracted from the weight of th e beaker of water to fi nd the weight of water displaced. The readings verify that the upthru st is eq ual to the weight of the fluid displaced. w2 = WI =8N spring .--.. ba lanc~ ~ 5N !H • 'it '. ~ ~ j:j " () ? / object displacement can filled with water W4 =4 N W3= 7 N r ~ til , ~ , . 0 ~~ water W1 - W2", W3 - W4 8N-5N=7N -4N " , displaced upthrust = weight of fluid displaced displaced water in scale pan empty beaker in scale pan Figure 9.4 Verifying Archimedes' principle Floating A body floats if its own weight is equal to the upthrust on it (the weight of fluid displaced by it). A rectangul ar block of base dimensions 20 cm x 20 cm and weight 50 N floats as shown in Figure 9.5. Calculate the d epth, h, to which it is subme rged, given that the density of water is 1000 kg m-3 • (Gravitational field strength = 10 N kg-') ---- h water - block volume of water displaced - base dimensions 20cmx20 cm Figure 9.5 Since the block floats: weight of block = weight of water displaced weight of block = m"g weight of block = (vwp) g (since volume x density 50 = 0.20 x 0.20 x h x 1000 x 10 50 h 0.20 x 0.20 x 1000 x 10 h=0.125m 9 Concise Revision Course: CSEC· Physics = mass) Submari nes Figure 9.6 sh ows a toy su b marine that has a ball ast ta nk which ca n ho ld wate r. If wat e r is taken into the tank unti l th e submarine's weight exceeds th e w eight of wa te r d isp laced (up thru st). th e subma rin e w ill accelerate d ownwa rd s. The res ultant fo rce o n it is d ownwards. and it wi ll d escend without t he use of its e ngines. To acce lerate upward s. air und er press ure ex pe ls w ate r from th e ballast tank. d ecreas ing th e w e ight of the subm arin e. Wh en dec reased to a va lu e less than th e weigh t of water di sp laced (upth rust ). th e sub marin e wi ll acce le rate upwa rds. Fl oa tin g occu rs if the weight is equal to the weight o f wa ter disp laced (u pthru st ). u=7N u=12N I r u=12 N u= 12N h W=7N w=15N c. resultant for is 3 N downwards (accelerate downwards W=9N W=12N resultant force is 3 N upwards (accelerates upwards) resultant force is zero (either at rest or moving at constant velocity) resultant force is zero (remains at rest) Figure 9.6 Upthrust and submarines Balloons Figure 9.7(a) shows a ball oo n containin g air. If th e air in the ball oo n is heated. it will becom e less de nse and w i II expand . The upthrust o n th e balloo n will increase since it will now di splace m o re of the cool e r su rroundin g air. It w ill acce lera te upwards if its w eight p lus th e we ight o f its co ntents is less than th e w eight of th e air it di splaces (upthru st ). If t he balloo n contain s a gas of low d en sity such as helium. as in Figure 9.7(b ). it w ill accelerat e upwards eve n without its contents be ing heated. upthru sl (weight upthrust (weight of cool air displaced) of cool air displaced) t helium _____ warm air • weight of balloon and warm air 1 b weight of balloon and helium Figure 9.7 Upthrust and balloons Note th at air becomes less d e nse at hi gher altitudes and therefo re th e weight of th e air di spl aced (upthrust) becomes less. Wh en th e upthru st has d ec reased to th e w eight of th e balloon and its co ntents. t he res ultant force is zero and acce lerati o n ceases. Th e balloon co ntinu es upwards b ut th e re is then a net dow nward force sin ce th e upthru st is further reduce d. The ball oo n thu s begi ns to bob up and d own until it settl es at a height where th e net force o n it is zero. 9 Pressure and buoyancy 39 Measuring Pressure Example 4 metre rule Figure 9.8 shows a simple mercury barometer, an instrument used to measure the pressure of the atmosphere. The height, h, of the mercury column is proportional to the atmospheric pressure. Since there is a vacuum at the top of the tube, the pressure at Y is due only to the mercury above it. Given the following data, calculate the atmospheric pressure, PA, indicated by the barometer. density of mercury; 13 600 kg m-J , gravitational field strength; 10 N kg- I vacuum 75 em ----t" stout walled glass tube h; oem -i~ .;L ~ y ~X _ dish of mercury -j PA; pressure at X Figure 9.8 PA ; pressure at Y (since X and Yare at the same level in the mercury) (pressure at Y due to the column of mercury above it) PA ; hpg ; 0.75 x 13600 x 10 ;1.0xl0' P • Example 5 Figure 9.9 shows a manometer, an instrument used to measure the pressure of a gas. One arm of the U-tube is exposed to the atmosphere and the other is connected to the gas supply. The difference in the levels of the liquid in the arms of the tube indicates the difference in pressure between the gas and the atmosphere. Given the following data, calculate the pressure of the gas supply assuming the liquid in the manometer is mercury. atmospheric pressure; 1.0 x 105 Pa, h ; 20 em, density of mercury; 13600 kg m-J , gravitational field strength; 10 N kg-I gas pressure; pressure at X ; pressure at Y(since X and Yare at the same level in the fluid) metre rule atmospheric pressure fromgas supply gas pressure L X ..:h .t.. } t + (hpg) y liquid Figure 9.9 gas pressure; atmospheric pressure + excess pressure PG;PA+hpg ; 1.0 x 10' + (0.20 x 13 600 x 10) ;1.3xl0' P, Revision questions Acceleration due to gravity; 10 m S- 2 1 Shakira, of mass 40 kg, stands in soft mud in her garden. The sole of each of her shoes has an area of 140 em' . Determine the pressure she creates on the ground when standing on both feet. (1 m' ; 100 cm x 100 cm; 10 000 cm', therefore 140 cm' ; 0.0140 m' , i.e. divide by 10 000) 2 Determine the pressure at the bottom of a swimming pool of depth 2.0 m, on a day when the atmospheric pressure is 1.1 x la' Pa. The density of water is 1000 kg m-J . 3 a State the principle of Archimedes. b Write an equation showing the condition necessary for an object to float. 4 A raft of weight 500 N floats in water of density 1000 kg m-J • a What is the upthrust on the raft? b Calculate the volume of water displaced by the raft. 5 40 Explain, in terms of Archimedes' principle, why a hot air balloon rises. 9 Concise Revision Course: CSEC' Physics exce55 pressure Exam-style questions Chapters 1 to 9 Structured questions 1 a) Define EACH of the following terms. i) Scalar quantity (2 marks) ii) Vector quantity (2 marks) b) Complete Table 1 by placing EACH of the quantities listed below in the appropriate column. energy, force, displacement, pressure, momentum, power Table 1 Vector (3 marks) c) Komo's boat can travel across still water at 8.0 m s-' . He tries to cross a river which flows at 6.0 m s-' by directing the front of the boat perpendicular to the banks of the channel. Of course he ends up far downstream! i) ii) By means of a scale drawing, or otherwise, determine the magnitude of the resultant velocity of the boat and its direction in degrees measured from the bank of the river. (6 marks) Determine the actual distance travelled if the journey takes 5.0 minutes. (2 marks) Total 15 marks 2 a) Define EACH of the following terms. i) Displacement (2 marks) ii) Velocity (2 marks) iii) Acceleration (2 marks) b) A car starts from rest and accelerates uniformly for 4.0 s, reaching a maximum velocity of 20 m s-' . It remains at this velocity for the next 6.0 s and then uniformly comes to rest in a period of 8.0 s. i) Sketch a velocity-time graph of the motion. (3 marks) ii) Calculate the acceleration during the initial 4.0 s. (2 marks) iii) Determine, from your graph, the distance travelled in the first 10 s. c) Cite an example where an object accelerates although its speed is constant. (3 marks) (1 mark) Total 15 marks 3 a) Define EACH of the following terms. i) Moment of a force (2 marks) ii) Centre of gravity of a body (2 marks) State what is meant by the term 'the principle of moments'. (2 marks) b) i) ii) Write an SI unit to express the moment of a force. (1 ma Exam-style questions - Chapters 1 to 9 ~ r ;: k) _ _-I 41 c) Figure 1 shows a uniform cone of mass 2.0 kg and of height 40 cm, resting on its base, of width 30 cm. A • I I I 140 em I I I B ... -- -- --- - . C • 30 em Figure 1 Calculate: i) the weight, W, of the cone (2 marks) ii) the minimum horizontal pull, P, which can be applied at A to raise the edge, B, from the floor. (4 marks) d) Comment on the new value of P required if the height of the cone is doubled. (2 marks) (Gravitational field strength = 10 N kg-I) Total 15 marks Extended response questions 4 a) State Newton's three laws of motion. (6 marks) 4 b) A jet of m ass 4.0 x 10 kg accelerates at 3.6 m s-' along a runway. i) Determine the resultant force producing the acceleration. ii) Comment on the actual magnitude of the thrust (force) of the engines relative to the value calculated in (b)(i) . (2 marks) (2 marks) iii) Determine the work done along the runway by the resultant force if the length of the runway is 500 m. (3 marks) c) When the jet is in the air it moves at constant velocity for most of its journey but the engines must still provide a forward thrust. Deduce the resultant force on the jet at this time. (2 marks) Total 15 marks 5 a) Explain why it is necessary to use alternative sources of energy in the Ca ribbean, and describe how TWO such sources are being put to use today. (6 marks) b) Akuna drops a sharp stone of mass 500 g from a height of 30 m and it bores a hole of depth 20 cm into soft soil. Determine: i) the change in gravitational potential energy of the stone (2 marks) ii) the kinetic energy just befo re striking the ground (2 marks) iii) the work done in boring into the so il (1 mark) iv) the energy transformed as it bores the ho le (1 mark) v) the average force on the sto ne as it decele rates and comes to rest. (3 marks) (Acceleration due to gravity = 10 m s-') Total 15 marks Exam-style questions - Chapters 1 to 9 10 Nature of heat Caloric t heory The caloric theory of heat is an obsolete theory from the 18th century. Heat was believed to be an invisible fluid ca lled 'caloric ', which could combine with matter and raise its temperature. Argum ents for the caloric theory 1. Objects expand when heated because the increased 'caloric ' they contain causes them to occupy more space. 2. Heat flows from hotter to cooler bodies because 'ca loric ' particles repel each other. Argu ments against the caloric theory 1. When bodies are heated so that they change state (solid to liquid or liquid to gas), an increase in 'caloric' cannot be detected. 2. When different materials are given the same amount of heat ('ca loric'), their temperature s increase by different amounts, indicating that they receive different quantities of 'caloric'. 3. The weight of a body should increase as it is heated, because it should then contain more 'caloric '. However, the weight remains the same. Ru mford's cannon-boring experiment as evidence against caloric theory Count Rumford was an army officer responsible for the boring of cannons during the late 18th century. He realised that the heat energy transferred when a ca nnon was being bored was inexhaustible and depended only on the work done in boring the hole. The 'ca loric' theory was therefore not possible; if 'caloric ' was a material substance, there wou ld be a time when all of it had left the cannon. Ki netic theory The kinetic theory of matter states the following. • The particles of matter (atoms, molecules) are in constant motion of vibration, translation or rotation. The kinetic energy they possess is responsible for their temperature, or hotness (see Chapter 11 ). • There is space between the particles. Forces (bonds) pull them together when they are near to each other, and so the particles have potential energy. • When a substance is heated, the heat energy supplied could result in an increase in the kinetic energy of the particles of the substance, and hence in its thermal energy, causing the temperature to rise . • When a substance is heated so that it changes state, the heat energy supplied results in an increase in the spacing of the particles and hence an increase in their potential energy, allowing them to break bonds with their neighbours and to expand against any surrounding pressure. 10 Nature of heat Joule's role in establishing the principle of conservation of energy james joule proved experimentally that energy can be transformed from one type to another, but is always conserved (see Chapter 8). His experiment is outlined below. Two bodies, each of mass m, and attached to the ends of a string, were allowed to fall through a height h, as shown in Figure 10.1. As they descended, a pulley mechanism caused the strings to turn paddles in the water, of mass mw' On reaching the lowest point, the masses were quickly wound up to the starting position and then were allowed to fall again. This was repeated several times (n times). On analysing the results, joule concluded that the potential energy of the masses was transformed to kinetic energy of the paddles which then transformed to thermal energy of the water, causing the mass, temperature to rise by an amount tl T. The work done by the paddles in churning the water was equal to the gravitational potential energy of the falling masses which transformed to a rise in thermal energy of the water. n (2mgh) = mwc tl e (See Chapter 15 for calculations of thermal energy changes.) f -- m,ass" m F'-t-rl-- -- ~-:of a What was the 'caloric theory' of heat? b State TWO arguments for and TWO arguments against the caloric theory. c What evidence did Count Rumford use to indicate that the caloric theory was incorrect? 2 a What theory replaced the caloric theory? b Briefly describe this theory. 3 moving paddles Figure 10.1 Joule'S experiment, establishing the principle of conservation of energy Revision questions 1 fixed vane Describe the experiment of joule in establishing the principle of conservation of energy. 10 Concise Revision Cou rse: CSEC· Physics 11 Temperature and thermometers Temperature is the degree of hotness of a body. 4 thermometer is an instrument used to measure tempera ture . Units of temperature The kelvin (K) is the SI unit of temperature, but it is also common in science to express temperature in degrees Celsius (OC) . temperature T, in K = temperatu re Tc in °C + 273 This conversion wi ll be further discussed in Chapter 14. Designing a thermometer • Select a suitable thermometric property - a property of a material which varies with temperature (see Table 11.1 ). Table 11.1 Examples of thermometers and their thermometric properties Thermometer Thermometric property as temperature increases liquid-in-glass vo lum e of liquid increases constant-pressure gas thermometer vo lume of gas increases at constant pressure constant-volum e gas thermometer pressure of gas increases at constant vo lume thermoelectric thermometer (thermocouple) emf produced varies non-linearly resis tance thermometer resistance increases thermistor res istance usually decreases but increases for some types • Se lect a suitable range. A mercury-in-glass laboratory thermometer typically has a range from -10°C to 110 °C or O·C to 100 °C. A clinical thermometer typically has a range from about 34°C to 43 0C. A thermoelectric thermometer typically has a range from about -250°C to about 1500 0C. • Select a suitab le scale. The values of the thermometric property at upper and lower fixed points are found and marked on the th ermom eter (see Figure 11.1), and the interval between the fixed points is then calibrated. Fixed points on the Celsius scale • The upper fixed point (100 °C) is the temperature of steam from pure boiling water a t standard atmospheric pressure (Figu re 11.1 (a» . • The lower fixed point (0 °C) is the temperature of pure melting ice al standard atmosp heric pressure (Figure 11.1(b». 11 Temperature and thermometers 1- 1\0-- smallI scratch made thermornet,,, -l ~ ": r: here (100 °C) r:r": steam exit (preventing increase in pressure) rr steam ttt a pure boiling water b heat thermomet" small scratch made here (O°C) pure melting ice funnel D molten ;ce collected in beaker Figure 11 .1 Determining (a) the upper and (b) the lower fixed points Laboratory mercury thermometer The laboratory thermometer is a 'Iiquid-in-glass' thermometer which utilises mercury as the liquid (Figure 11.2). • The bulb that holds the mercury has a thin wall so that heat can easily transfer through it. • The bore is very narrow so that any change in volume of the mercury will result in a noticeable change in the length of the mercury thread. • The bulb is relatively large so that th e corresponding expansion or contraction of the mercury it contains is noti ceabl e for small changes in temperature. The larger the bulb, th e longer must be the stem and bore; the separation of the intervals on the scale is then greater and it is easier to read. • The scale is positioned very close to the bore to reduc e parallax error (see Chapter 1). o mercury glass stem thread thin walled bulb I 9 , o ~I I ~/ / narrow bore o, o, , o <»-'" o, , 0 0--- 0 '? n intervals on scale are 1°C Figure 11.2 Liquid-in-glass laboratory thermometer Advantages of a mercury thermometer • Mercury is a metal so it has a high conductivity and a low specific heat capacity (see Chapter 15). This means its temperature quickly adjusts to the t e mperature it is measuring. • The boiling point of mercury is 357 °C and therefore the thermometer is suitable for most laboratory experiments done at school. If alcohol was used as the liquid, it would evaporate and distil on the upper part of the bore. • Mercury is bright silver and can easily be seen . • The thermometer has a linear scale which is easy to read. 11 Concise Revision Course: CSEC· Physics Disadvantages of a mercury thermometer • It can not be used to measure very cold temperatures because merc ury freezes at -39°C. • It is expensive. • Mercury is poisonou s. Clinical mercury thermometer A clini cal thermometer (Figure 11.3) can also be of the liquid-in-glass type. It therefore has many of th e feat ures and properties of the laboratory thermometer. However, the following shou ld be noted. • The scale ranges only from 34°C or 35 °C to 43°C because the normal body t empe rature of a human is 37 0C. • The interval between markings on the scale is 0.1 °C so th at a very precise reading is obtained. • There is a narrow co nstriction in the bore. When the thermometer is removed from the patient, the sudden change in temperature causes a rapid contraction of th e mercury. As th e mercury rus hes toward the bulb, the thread breaks at the constriction, leaving the thread above it to be read. • Mereu ry is poisonous. • This type of clini cal thermometer is rapidly being replaced by an electron ic, digital thermometer. thin walled thread bulb mercury average body temperature glass stem constriction intervals on scale are 0. 1°C Figure 11.3 Liquid-in-glass clinical thermometer Thermocouple A thermocouple (Figure 11.4) is simply a pair of dissimilar metal wires, A and B, joined at their ends. On heating one of the junctions, an emf is produced which varies with the temperature difference between the junctions. By connecting a voltmeter between the junctions, the emf (see Chapter 28) can be detected. The scale of the voltmeter can be calibrated in units of temperature. Si nce the thermometer depends on tem perature difference, the reference junction must always be at the same tem perature it had at ca libration . The cold junction is generally the reference junction. voltmeter calibrated with respect to the cold junction B warm junction (in liquid) cold junction (in pure, melting ice at Q"C) Figure 11.4 Thermocouple 11 Temperature and thermometers Advantages of a thermocouple • It responds quickly to temperature changes because metals have high conductivities and low specific heat capacities. It is therefore useful for measuring rapidly changing temperatures. • It takes very little heat from the body it is measuring and is therefore capable of determining the temperature of a small body without noticeably altering its temperature. • It can withstand very low and very high temperatures and is therefore useful for measuring temperatures in freezers and in furnaces. • Since it is electrical, it can be connected to digital displays and computer systems. Disadvantages of a thermocouple • Large temperature differences produce only small changes in emf. It is therefore not useful for detecting small changes in temperature. • The measuring instrument used with a thermocouple must be sensitive to small changes in emf and this can be expensive. • The scale is non-linear and is the refore difficult to read . Revision questions 1 a Define temperature. b What is meant by the ' upper fixed point' on the Celsius scale? 2 list TWO types of thermometer together with the thermometric property they each utilise. 3 list TWO advantages and TWO disadvantages of a liquid-in-glass mercury thermometer. 4 State THREE ways that a laboratory mercury thermometer differs from a clinical mercury thermometer. 5 a Describe how a thermocouple can be used as a thermometer. b list TWO advantages and TWO disadvantages of this type of thermometer. 11 Concise Revision Course: CSEC· Physics 12 States of matter Solids, liquids and gases are all composed of t iny atoms o r molecules. Figure 12.1 shows the relative positioning of the particles, and Tab le 12.1 shows howthe forces and distances between these particles can be used to explain their physical properties. . Solids The attractive forces between the particles of a solid are strong, bringing them very close together. However, at even closer distances, these forces are repulsive. The atoms or mo lecules therefore con stantly vibrate about some mean position, while being bonded in a fixed lattice. Liquids The forces between the part icles of a liquid are weaker than in solids. The molecules have more energy and the weaker forces are not enough to make the bonds rigid. They separate slight ly more than in solids and are able to translate relative to each other. Gases Except at times of collision, the particles of a gas are far apart and the forces between the particles are negl igible. They therefore translate freely, filling the conta iner in which they are enclosed. solid u liquid Figure 12.1 Particles of a solid, a liquid and a gas Table 12.1 Physical properties of matter explained in terms of forces between particles Solids Liquids Gases Density High since the particles are tightly packed High since the particles are tightly packed - almost as close as in solids Very low since the particles are far apart Shape Fixed since there are rigid bonds due to strong forces between the particles The bonds are not rigid and therefore liquids take the shape of their container. However, the forces between the particles still cause liquids to have a fixed volume The forces between the particles only exist at the time of collision and therefore gases spread out to fill the container which encloses them Ability to flow The rigid bonds between particles prevent solids from flowing The weaker forces between the particles cannot form rigid bonds and therefore liquids can flow The very weak forces between the particles cannot form rigid bonds and therefore gases can flow 12 States of matter Table 12.1 Physical properties of matter explained in terms of forces between particles continued Ability to be compressed Solids Liquids Gases Not easily compressed since th e particles are tightly packed, making it difficult to push th em closer Not easi ly compressed since the particles are tightly packed, making it difficu lt to push them closer Easy to compress since there is much space between the particles The particles translate Main motion The particles vibrate about The particles vibrate and translate, constantly chang ing freely, having neighbours of particles a mean position, always adjacent to the same set neighbours only at the time of collision of particles Revision questions 1 Describe solids, liquids and gases in terms of the separation and motion of their particles, and th e forces between those particles. 2 Explain the following properties of a LIQUID in terms of your description in question 1. a density b shape c ability to be compressed d abi lity to flow 12 Concise Revision Course: CSEC· Physics 13 Expansion Expan sion in terms of the kinetic theory of matter Solids: Whe n a solid is heated, the heat energy supplied converts into kinetic energy of its particles (which we call thermal energy). The molecules of the solid vibrate faster and with greater amplitude and therefore occupy more space. Liquids and gases: When a liquid or gas is heated, the heat energy supplied conve rts to kinetic energy of its particles. The molecules of the liquid or gas translate faster and therefore occupy more space. Demonstrating expansion Simple experiments to show expansion in solids, liquids and gases are shown in Figure 13.1. Solid: At room temperature, th e hammer is just able to fit into the space and the ball can just fit throug h the hole. However, when the hammer or ball is heated, this fit is no longer possible. Liquid: The flask expands slightly when heated, causing the liquid level to drop initially. With conti nued heating, however, the liquid expands up the tube. With a narrow tube, th e rise is very noticeable. Gas: The air expands when heated, producing bubbles in the water. It---narrow tube fhammer air air bubbles ~ cork space ~ bal l flask of liquid ~hOle .' ~ L{] ttt heat SOLID LIQUID GAS Figure 13.1 Demonstrating expansion in solids, liquids and gases Utilising expansion • liquid -in-glass thermometers (see Chapter 11). • Applications of the bimetallic strip (considered later in this chapter) . • M etal plates joined with the use of hot rivets; on cooling, the rivets contract and bind the plates firmly. Avoiding problems due to expansion • Conc rete surfaces are laid in slabs (Figure 13.2(a)) and the spaces between them are filled with pitch. During expansion of the surface, the soft pitch is compressed, avoiding strong forces in the concrete which would otherwise produce c racks. • Ra ilway lines are laid in short lengths with their ends bevelled and overlapping (Figure 13.2(b)). This prevents warping because it allows them to freely slide over each other when they expand and co ntract. 13 Expansion • Pipelines in deserts, or those which ca rry steam, are laid in a zig-zag formation (Figure 13.2(c)) with fl ex ible joints. On expansion or contraction, these fl ex without the pipeline being subjected to strong forces. • Large structures such as bridges ca n be made with one end on rollers (Figure 13.2(d)). This allows them to expand and contract freely without producing strong forces which co uld weaken the assembly. • Baking di shes w hich undergo large tem perature differences are made of materials that expand and contract very little with temperatu re change. Thi s prevents them from c racking when removed from the oven into the much cooler environment. • Power lines must be laid slack in su mm er, so that strong tension forces are not produced when they contract in winter. concrete slabs a b bevelled ends where the rails join free end bridge Figure 13.2 Some ways of dealing with expansion Other phenomena involving expansion • Roofs shrink at night as the temperature falls. Contraction of the wood causes the joints to move relative to each other, producing a creaking sound. • A tight metal lid on a glass jar is easi ly removed by running hot water onto it. The lid rapidly expands due to its high thermal conductivity, and beco mes loose. The bimetallic strip A bimetallic strip consists of two metal strips riveted together (Figure 13.3). The strips bend on heating such that the metal that expands more is on the outer side of the curve. Brass expands much more than invar when heated and so this combination forms a good bimetallic strip. Brass will also contract more on cooling. ~ brass invar invar 20°C 50°C brass ~ Figure 13.3, The bimetallic strip 13 Concise Revision Course: CSEC· Physics 80 °C 1 Sim ple fire a larm A simple f ire alarm is shown in Figure 13.4. Heat from the fire causes the bimetallic strip to bend upwa rd and closes the contacts. This completes the circuit and sounds the alarm. (See Chapter 29 for interpreting circuit symbols.) ...."'t~- graphite ~i= contacts insulating mount Ele ct ric thermostat An electric thermostat is shown in Figure 13.5. This type may control the temperature of an oven. With the switch on, the heater warms the oven. The bimetallic strip then bends causing the sliding contacts to separate and break the circuit. With the heater disconnected, the oven cools, the co ntacts reconnect, and the process repeats. The te mperature control knob is an adjusting screw that can be advanced so that it forces the sliding co ntacts further over each other. The bimetallic st rip must then bend more in order to break the circuit. By switching the position of the brass and invar, the thermostat can be used to prevent a fridge from becoming too cold. Figure 13.4 A simple fire alarm using a bimetallic strip "v )-------, heater insulating mount -~rl ~ Invar brass 1-+1+- flexible metal strip screw )I~. W- graphite contacts Figure 13.5 An electric thermostat connected to a heating element Revision questions --- 1 Explain, in terms of the kinetic theory, why matter expands when heated. 2 Describe how you can show that solids expand when heated. 3 State TWO problems associated with expansion and how they may be avoided. 4 Describe and explain the function of a simple fire alarm which utilises a bimetallic strip. 13 Expansion 14 The ideal gas laws Temperature scales Two important temperature sca les are the Celsius scale and th e kelvin scale. The kelvin scale is also known as the thermodynamic temperature scale o r absolute temperature scale. The relation between the Celsius and the kelvin sca les is sh own in Figure 14.1. Note that the intervals of1 K and 1 °C are equal. Examples of converting between °C and K are shown in Table 14.1. Table 14.1 Converting °C to K 200 27 o -20 273 273 273 273 + 200 = 473 + 27 = 300 + 0 = 273 - 20 = 253 IHK "" lOOK absolute l ero ~I I a - 273 ~ I K 373 M e = 100 °c .----------------. I C ( i -273 temperature TK in K = temperature Te in °C + 27 3 Q a 100 Figure 14.1 Temperature scales The ideal gas laws 1. Boyle's law: For a fixed mass of gas at constant temperature, the pressure is inversely proportional to its volume. P ex - 1 V PV = co nstant (when T co nstant) or 2. Charles' law: For a fixed mass of gas at constant pressure, the volume is directly proportional to its absolute temperature. V ex T o r - V = constant (when P constant) T 3. Pressure la w: For a fixed mass of gas at constant volume, the pressure is directly proportional to its absolute temperature. P ex T o r - P T = constant (when V constant) Combining the th ree laws: For a fixed mass of an ideal gas cha nging from state 1 to state 2, the fo llowing holds: P, V, P,V, T, T, -- =-Note th e following: • P and V may be in any unit of pressure and volume, respectively. • T must be measured on the KELVIN scale. • In problems where one of the variables is constant, it may be omitted from the equation. There is no such thing as an idea l gas but many gases behave approximate ly as an ideal gas at eas ily reached temperatures and pressures. An important ass umption of ideal gas theory is that there are no intermolecular forces between its molecules. Constant temperature If the ves sel is a very good conductor (poor insulator), any instantaneous rise or fall in temperature will quickly readjust to that of the environme nt. It can therefore be ass umed that temperature is constant. 14 Concise Revision Course: CSEC· Physics Constant pressure If the vessel is freely expandable, it can be assumed that the pressure is constant. Should the pressure instantaneously rise or fall, the vessel will expand or contract so that its contents have the same press ure as the environment (usually atmospheric pressure). Such is the case with a gas trapped in a syringe with a well oiled piston. Co nstant volume If the co ntainer is a strong, solid vessel, it can be assumed that the volume is constant. An increase in tempe rature will cause a slight increase in volume of the vessel but this is insignificant when compared to the increase that would have occurred if the gas had freely expanded. Verifying the gas laws To verify Boyle's law Boyle's law can be verified using the apparatus shown in Figure 14.2. The pressure, P, and volume, V, are measured and recorded. The pressure is increased by use of the pump, and the new pressure an d volume readings are taken. This is repeated until a total of six pairs of readings are obtained and tabulated . + is calculated and re co rded for each value of V, and a graph of P agamst + IS plotted. o The scale could be of length instead of volume. Since the tube is of uniform cross-sectional area, any change in length will produce a proportional change in volume. o Increasing the pressure will also increase the temperature. Before taking readings, a short period should be allowed after increasing the pressure for the air to return to room temperature. o The straight line through the origin of the graph verifies the law. em 3 Pressure - r---- volume scale PI P. Volume V/cm 3 0- - r--- air trapped in glass tube 1- pressure gauge 2- P 3- 4- -5 ~=t-, '--_-'I oil o l/V Figure 14.2 Experimental verification of Boyle's law To verify Charles' law Charles' law can be verified using the apparatus shown in Figure 14.3. The volume, V, of the air trapped by the bead of sulfuric acid is measured and recorded together with the temperature, T(' The temperature is then increased several times by about 10 degrees Celsius, each time taking a new pair of readings of Vand T(' The temperatures are converted to kelvin temperatures, TK, and a graph is plotted of Vagainst TK• o The scale behind the tube could be of length instead of volume. Since the tube is of uniform crosssectional area, any change in length will produce a proportional change in volume. o Readi ngs are only taken when the bead of sulfuric acid is steady, indicating that the pressure of the gas is back to its initial value. o The straight line through the origin of the graph verifies the law. 14 The ideal gas laws Note that zero on the kelvin scale is th e temperature at which an ideal gas will occupy no space. This point of absolute zero is used in the establishment of the kelvin temperature scale. thermometer \ - em 3 r- - r-- volume scale Volume 54- Temperature Temperature Tere V/cm 3 TK/K - sulfuric acid 3- 21- 0- v - air trapped in glass tube /// - water bath o T, Figure 14.3 Experimental verification of Charles' law To verify the pressure law The pressure law ca n be verified using the apparatus shown in Figure 14.4. The pressure, P, and temperature, TO' of the gas trapped in the spherical flask is measured and recorded. The temperature is increased several times by intervals of about 10 degrees Celsius, each time taking a new pair of readings of P and Tc The temperatures are converted to kelvin temperatures, TK, and a graph is plotted of P against TK• o It is assumed that the expansion of the vessel is negligibl e and that the volume of the gas is therefore constant. o The straight line through the origin of the graph verifies the law. Zero on the kelvin scale is the temperature at which an ideal gas will exert no pressure. This point of absolute zero is used in the establishment of the kelvin temperature scale. ID- - - - -- thermometer Pressure PjPa pressure Temperature re TC gauge p - "'r-+-- air trapped in glass vessel /./ ... water bath ttt o HEAT Figure 14.4 Experimental verification of the pressure law 14 Concise Revision Course: CSEC· Physics T, Temperature T,/K Figure 14.5 shows some other important graphs illustrating gas law relationships. v p p P constant Tconstant v o a Boyle's law o ~273 V constant ~273 TIC b Charles' law o TIC c Pressure law Figure 14.5 Other important graphs Gases and the kinetic theory The molecules, of mass m, of a gas, bombard each other and the walls of their container. As they rebound, in a short time t, their velocity changes from u to v and they impart forces, F, in accordance wi th Newton's second law of motion (see Chapter 7). F= m(v- u) t This force creates a pressure, P, on the area, A, of the walls. F P=A At higher temperatures, molecules translate at higher velocities and therefore the rate of change in mo mentum (the force) on collision is greater. The pressure therefore increases. The three gas laws are individually explained in terms of the kinetic theory, as follows. Kinetic theory and Boyle's law As a gas is compressed at constant temperature, the speed of its molecules is unchanged and the refore the force exerted by its molecules on the walls remains constant. However, since the vo lume decreases, the collisions are on a smaller area. The force per unit area (pressure) therefore inc reases. See Figure 14.6(a). Ki netic theory and Charles' law As t he temperature of a gas rises, the average speed of its molecules increases and therefore the force exerted by its molecules on the walls is greater. If the vessel is freely expandable, the volume will increase, and therefore the area of the walls will also increase. The force and area increase by the same facto r and therefore the pressure remains the same. See Figure 14.6(b). Ki net ic theory and the pressure law As the temperature of a gas ris es, the average speed of its molecules increases and therefore th e force exerted by its molecules on the walls is greater. If the volume remains constant, the area of the walls is constant. Since the force increases as the area remains co nstant, the pressure on the walls increases. See Figure 14.6(c). 14 The id eal gas laws htl\11 before F p,~ P'A P'-ia Boyle's law (T constant) p ""' ~ F P'A [XXII ::3Q] after htl\11 h ~ /\ 1 ~~ A b Charles' law V"" TK (P constant) I P,~ p,[ c P Pressure law TK (V constant) Qo'; A longer arrow implies greater speed and therefore greater rate of change of momentum (Le. force) on collision. Figure 14.6 Kinetic theory and the gas laws Revision questions 1 Make a sketch comparing the Celsius temperature scale and the kelvin temperature scale. Indicate values on each scale for absolute zero, the melting point of ice and the boiling point of water. 2 Describe an experiment to verify Boyle's law. Your account should include any precautions taken and a statement as to how the law is verified. 3 Explain the following, in terms of the kinetic theory of matter. a A gas creates a pressure on the walls of its containing vessel. b The pressure in a car tyre increases as the air in it becomes hotter. 4 40 em] of an ideal gas at a temperature of 27 'c is heated to 227 expandable vessel. Determine the new volume of the gas. 14 Concise Revision Course: CSEC· Physics 'c in a freely 15 Heat and temperature change Heat is thermal energy in the process of transfer from a point of higher temperature to one of lower temperature, due to the temperature difference between them. Note that a body possesses thermal energy, but not heat energy. The thermal energy of a body can ri se or fall, for example by the abso rption or emission of heat. Th e specific heat capacity Ic) of a substance is the heat needed to change unit mass of the substance by unit temperature. It is the property of a SUBSTANCE. Th e heat capacity (C) of a body is the heat needed to change the body by unit temperature. It is the p roperty of a BODY. Calculations • When heat energy is supplied to a body its tempera ture may rise. The increase in temperature is the result of an increase in the KINETIC ENERGY of the particles of the substance. The following relation then applies: E=mctJ.T E= heat energy supplied m = mass c = specific heat capacity tJ.T = temperature change • The heat capacity, C, of a body is related to the specific heat capacity, c, of the materia l from which it is made, by: C=mc • The unit of specific heat capacity is obtained as follows. Since mc tJ. T = E E mtJ.T C=-- so the unit of cis _J_ or _J_ kg K kg 'C • The unit of heat capacity is obtained as follows. Since mc tJ.T = E E mc=-tJ.T so the unit of C is _J_ or _J_ 'C K • Values of specific heat capacity of some substances are given in Table 15.1. Note that the values for metals are lower than those for non-metals, and that water has the highest value in this list. Table 15.1 Specific heat capacity of several substances • ethanol water ice wood lead copper . . . .. 2400 4200 2100 1700 130 390 15 Heat and temperature change Tackling problems involving heat and temperature change • Always draw a temperature diagram before you formulate your equation. This is illustrated in Figures 15.1 to 15.3, in the three Examples below. • Place hotter bodies on the right and cooler bodies on the left. • Temperature change, {, T, is calculated as 'warmer subtract cooler'. • For situations where heat gain and heat loss are equated, your diagram should show each chain of arrows having all bodies meeting at a common temperature. Determine the heat energy required to change the temperature of a block, of mass 4.0 kg and specific heat capacity 400 J kg-' 0C-', from 20°C to 60 0c. E=mc{,T E = 4.0 x 400 x (60 - 20) = 64000 J Figure 15.1 Determine the thermal energy released when the temperature of water, of mass 2.0 kg and specific heat capacity 4200 J kg-' 0C-', cools from 60°C to 20 0c. E=mc{,T E = 2.0 x 4200 x (60 - 20) = 336000 J Figure 15.2 A copper block of mass 2.0 kg cools from 120°C to X °C as it is immersed in water of mass 3.0 kg, initially at 25°C. Determine the final temperature, X 0C. (Specific heat capacity of water = 4200 J kg-' 0C-'; specific heat capacity of copper = 390 J kg~ ' 0C-') 3.0 kg 3.0 kg Figure 15.3 heat gain of water = heat loss of coppe r mwcw{,Tw =m,c, {'T, 3.0 x 4 200 x (X - 25) = 2.0 x 390 x (120 - X) 12600 (X - 25) = 780(120 - X) 12 600X - 315 000 = 93 600 - 780X 12 600X + 780X = 93 600 + 315 000 13 380X = 408 600 X = 408 600 =30.5 13 380 Fin~1 temperature = 30.5 °C (31°C to 2 sig. fig.) 15 Concise Revision Course: CSEC· Physics .... Determining specific heat capacity The spe cific heat capacity of a metal by the method of mixtures • The mass, m" of a polystyrene cup is measured and recorded. Water is poured into the cup and the new mass, m eWI is measured and recorded. • The mass of water, mw' is then calculated from m ew - m c' • The mass, m m' of the metal object is measu red and recorded. • The temperature, T" of the cool water in the cu p is measured and recorded. • The metal object is heated in boiling water for a few minutes so that it acquires the tempe rature of the hot water. This temperature, TI , is measured and recorded. • The hot meta l is removed from the water bath by holding the string; it is quickly shaken and put into the coo l water. • The water is stirred using the thermometer and the high est temperature reached, T" is measured and re co rd ed. Figure 15.4 illu strates the process. Assume that all the thermal energy lost by the metal is gained by the water. thermal energy gained by water = thermal energy lost by metal mwe)T) - T2 ) = m Jw( T, - T,) m m( T, - T,) retort stand - beaker of - --ti- --I 61 f - - -T, thermometer - Bunsen burner cm --ti- - - ---i water tripod and gauze T3 ) thermometer and clamp string suspending metal in water bath mmcm( T1 - --ti--- 1/ --ti- --i/-- -1n cup of cool - water ~ hot object placed into cool water T, - 6 I r-- thermometer metal and cup of water at final temperature Figure 15.4 Determining the specific heat capacity of a metal by the method of mixtures ' Precautions to minimise errors • Some energy from the hot metal is lost to the surrounding air. To keep this to a minimum, the hot metal object is quickly transferred to the cool water. • The object is briefly shaken to remove water from its surface since this water is not considered in the calculation . • The water is stirred with the thermometer to ensure that the temperature recorded is the mean tem perature reached. Sources of error • Thermal energy is transferred by conduction to th e cu p and to the bench top. Thermal energy is also tra nsferred by radiation to the surrounding air. 15 Heat and temperature change • Evaporation of water from the surface of the metal on tran sferring it to the cool water removes latent heat of vaporisation (see Chapter 16). The temperature of the metal on reaching the cool water is therefore less than T,. The specific heat capacity of a liquid by the method of mixtures • The mass, m ", of a beaker and the mass, m" of a polystyrene cup are measured and recorded. • The liquid being investigated is poured into the beaker and water is poured into the cup, and the new masses, mbl and m O."" are measured and recorded. • The mass, m L' of the liquid, and the mass, m w ' of the water in the cup are calculated from m bL - mb = m l and mew- me = mw' • The temperature, T" of the cool water in the cup is measured and recorded. • The liquid is heated for a few minutes and its temperature, T is then measured and recorded. " • The hot liquid is quickly poured into the cool water. • The mixture is stirred using the thermometer and the highest temperature reached, TJ' is measured and recorded. Figure 15.5 illustrates the process. Assuming that all the thermal energy lost by the metal is gained by the water: thermal energy gained by water = thermal energy lost by liquid mwc)TJ - T,) = mLcL(T, - T,I m wcw( TJ - T2 ) m L(T, - TJ ) thermometer - - - - - - - 1 8 beaker of - - - -- I liquid 'it=~ thermometer tripod and - - - - -1/ T2 ~ T, - - - thermometer gauze Bunsen burner - - - ---il-- -t1 cup of cool water - cup of water and liquid at final temperature Figure 15.5 Determining the specific heat capacity of a liquid by the method of mixtures Precautions to minimise errors • Some thermal energy from the hot liquid is lost to the surrounding air. To keep this to a minimum, the hot liquid is quickly poured into the cool water. • The mixture is stirred with the thermometer to ensure that the temperature recorded is the mean temperature reached. Sources of error • Thermal energy is transferred by conduction to the cup and to the bench top. Thermal energy is also tra",sferred by radiation to the surrounding air. • Evaporation from the warm mixture will absorb latent heat of vaporisation from it (see Chapter 16). 15 Concise Revision Course: CSEC· Physics .... The specific heat capacity of a metal by an electrical method • A metal block having slots to fit a heater and thermometer is used. The mass, m, of the block is measured and recorded. • The apparatus is th en set up as shown in Figure 15.6 and the heate r is switched on. • After a short while, th e initial temperature, T of the block is measured and a stop watch is started " t. simu ltaneously to measure the time of heating, • The current is kept constant by adjusting the rheostat. Readings of the current, I, and th e voltage, V, are meas ured and recorded. • When the temperature has risen by abo ut 20 degrees Celsius, the new temperature, T" is meas ured and recorded, and the heater is switched off. Assum ing that all of th e electrical energy is responsible for the in crease in th ermal energy of the block, the specific heat capacity, c, of the metal can be calculated from: electri ca l energy; increase in thermal energy of block Vlt ; mc(T, - TTl / Oil, placed around the thermometer and heater. improves conduction with the block. insulating material The block is surrounded by an insulating material to reduce outward conduction. A polished silver jacket (foil paper) surrounds the insulator to reduce radiation to the air. --:\H-- heating element (surrounded by oil) 1+-- 1-+-- thermometer (surrounded by oil) I..,. -++--- metal block ~=:'-poliShed outer jacket Figure 15.6 Determining the specific heat capacity of a metal by an electrical meth od Precaution to minimise errors • It is ensured that th e current remains co nstant during the expe riment by adju sting th e rheostat. So urce of error • The rmal energy is transferred to the oil, to the surrounding air and to the bench top . The specific heat capacity of a liquid by an electrical method • The mass, m, of th e liqu id is measured and reco rded. • The apparatu s is th en set up as shown in Figure 15.7 and the heate r is switched on. • Afte r a short while, the initial temperature, TI' of the liquid is measured and th e stop watch is sta rted simultaneously to measure th e time of heating, t. • The current is kept constant by adjusting the rheostat. Readings of the current, I, and the voltage, V, are measured and recorded. • When the temperat ure has risen by about 20 degrees Celsius, the new temperature, T" is measu red and reco rded, and the heater is switched off. 15 Heat and temperature change Assuming that all of the electrica l energy is responsible for the increase in thermal energy of the liquid, the specific heat capacity, c, can be calculated from: electrical energy = increase in thermal energy of liquid Vlt = mc(T, - T,l The container of liquid is surrounded by an insulating materia! to reduce outward conduction. A polished silver jacket (foil paper) surrounds the insulator to reduce radiation to the air. ,---{ A insulating material 11 \--++-- thermometer stirrer liquid _1Ii- -+l~ L':=~- heating element polished outer jacket Figure 15.7 Determining the specific heat capacity of a liquid by an electrical method Precautions to minimise errors • The liquid is stirred before measuring the temperature to ensure that the mean temperature is detected. • It is ensured that the current remains constant during the experiment by adjusting the rheostat. Source of error • Thermal energy is transferred to the surrounding air and to the bench top. Revision questions 1 Define: a heat 2 b specific heat capacity c heat capacity State 51 units for: a specific heat capacity b heat capacity 3 Using data from Table 15.1, determine the heat energy required to change the temperature of 250 g of ethanol from 15 'C to 65 'c. 4 Using the data in Table 15.1, determine the initial temperature of a lump of lead of mass 300 g which when immersed in 400 g of water raises the temperature of the water from 20 'C to 22 'c. 5 Describe how the specific heat capacity of a metal can be found using an electrical method. 15 Concise Revision Course: CSEC· Physics 1 16 Heat and state change The te mperature remains constant during a change of state. Demonstrating a change of state Liquid to gas • A beaker of water is heated until about one quarter of it boils away (Figure 16.1). Several readings of temperature and corresponding time are measured and recorded. • A graph is plotted of temperature against time (a heating curve) . This reveals that the temperature increases steadily until the water begins to boil, but then remains constant as it changes state. thermometer li temperature boiling point steady temperature wate r u ttt tiJ'e HEAT Figure 16.1 The temperature is constant during boiling Liquid to solid • Figure 16.2 shows wax being heated in a boiling tube by means of a water bath. The w ate r is allowed to boil for a few minutes. • The wax melts and a thermometer is placed at its centre. • The tube and th e thermometer are removed from the water bath and the wax is allowed to cool. • Readings of temperature and corresponding time are taken every minute as the wax cools, solidifies, and then cools further. • A graph is plotted of temperature against time (a cooling curve). This reveals that the te mperature remains constant as th e liquid solidifies. retort stand and clamp 11-- - thermometer temperature --==jr-- melted wax in boiling tube - ttt HEAT - meltin~ water bath r-- melting ---iI " " - - - -_ point ,---:-_ steady temperature time wax cooling Figure 16.2 The tempera ture is constant d uring solidification 16 Heat and state change Latent heat Latent heat is the heat energy necessary to change the state of a body without a change of temperature. The specific latent heat of fusion (/ ~ of a SUBSTANCE is the heat energy needed to change unit mass of the substance from solid to liquid without a change of temperature. The specific latent heat of vaporisation (/) of a SUBSTANCE is the heat energy needed to change unit mass of the substance from liquid to gas without a change of temperature. Table 16.1 Specific latent heat of ice and water Specific latent heal of fusion of ice 3.4 X 105 J kg-1 = 3.4 X 10' J g_' Specific lalenl heat of vaporisalion of waler 2.3 X 10' J kg-' = 2.3 X 103 J g-' Calculations • When a substance changes from solid to liquid or from liquid to gas, latent heat provides the necessary increase in POTENTIAL ENERGY of the particles of the substance. The following relation then app li es: E= ml E = heat energy supplied m = mass I = specific heat of fusion or vaporisation • The latent heat of fusion is necessary to provide potential energy in order to: a) do internal work in breaking the bonds between the particles of a solid b) do external work as the particles' spacing expands slightly against the atmospheric pressure. • The latent heat of vaporisation is necessary to provide potential energy in order to: a) do internal work in overcoming the attractive forces between the particles of a liquid b) do external work as the particles' spacing expands significantly against the atmospheric pressure • As substances change to a higher energy state, they absorb latent heat, and as they change to a lower energy state, they release latent heat (Figure 16.3). latent heat of vaporisation absorbed lalenl heat of fusion absorbed i i8 ! GAS ! Iatent heat of vaporisation released lat~n heat of IUSlon released INCREASED ENERGY L ........] Figure 16.3 Latent heat and state changes Heating curves Heating curves indicate when the substance changes state (Figure 16.4). • The kinetic energy of the particles increases as the temperature increases. • The potential energy of the particles increases as the state changes from solid to liquid or from liqUid to gas. 16 Concise Revision Course: CSEC· Physics temperature b.p. ml - - - - - - - - -, -....:::;- -" mC,1,T ml time Figure 16.4 Heating curve showing the changes in internal energy of a substance as it changes state Tackling problems involving heat and state change • Always draw a temp erature diagram (like that in Figure 16.5) before you formulate your equation. mC,1,T ml, OOG Figure 16.5 mC,1,T 100°C lOC°C 110°C Temperature diagram showing conversion of ice at - 5 'C to steam at 170 'C • Place hotter bodies on the right and cooler bodies on the left. Temperature change, !J.T, is ca lculated as 'wa rmer subtract cooler'. • A change of state and a change in temperature cannot occur at the same time. Th ey mu st be represented as separate changes in th e diagram. • Fo r situations where heat gain and heat loss are equ ated, your diagram sho uld show each chain of arrows having all bodies meeting at a common temperature. Refe r to data in Table 16.1. Determine the power of a heater which takes 15 minutes to convert 2.0 kg of water at 100 'C to stea m at 100 'c. E ml P = -=-' t t G;J-.::m,,-I,- P = 2.0 x 2.3 x 10' 15 x 60 P =5 .1 x l0' W 2.0 kg 100 °C 100°C Figure 16.6 Refer to data in Tab le 16.1. Determin e the heat released when 500 g of water at 0 'C converts to ice at 0 'c. E= ml, E = 0.500 x 3.4 x 10' = 1.7 x 10' J _ ~ O°C _m -,\ -a O°C Figure 16.7 16 Heat and state change Refer to data in Table 16.1. Th e specifi c heat capacity of water = 4200 J kg-' °C ' . A mass of 400 g of ice at _10 °C is placed into 5.0 kg of water at 60°C. Determine th e final temperature of the mixture, given that all th e ice melts. 0.400 kg mCIl. T mctJ.T 0.400 kg 5.0 kg x·c Each arrow represents EITHER a change of temperature OR a change of state. The same mass is at each end of any particular arrow. Figure 16.8 Heat gained by ice and molten ice = heat lost by warm water (00400 x 2100 x 10) + (00400 x 304 x 105) + (00400 x 4200 x X) = 5.0 x 4200 x (60 - X) 8400 + 136 000 + 1680X = 21 000(60 - X) 144 400 + 1680X = 1 260 000 - 21 OOOX 22680X=1115600 X= 49 Final temperatu re = 49°C Determining specific latent heat The specific latent heat of fusion of ice by an electrical method • The mass, m b, of an empty beaker is measured and record ed. • The apparatus is set up as shown in Figure 16.9 and the heater is switch ed on. • Ice chips are packed around th e heater element in a funn el so that the heater el ement is completely immersed, and a stop watch is simultaneously started. Th e melted ice is collected in the beaker. • The readings of voltage, V, across the heater, and current, I, through it, are measured and recorded. • As th e ice melts, more is added so that the heater is always submerged. • After about 10 minutes, the funnel is removed, the watch stopped, and the time, t, measured and recorded. "'"J ( -7"'</I l - - 1 L- • The mass, m bw' of the beaker and water is measu red and the mass of water, m w ' calculated from m w ;;;; m bw - m b, Assum e that all the electrical en ergy is used in melting the ice. electrical energy = heat energy supplied to melt ice Vlt = mwI, Vlt =I mw ' 16 Concise Revision Course: CSEC· Physics 1!.2: !~ g = ~ I f--- ;ce ch;ps ;n funnel heater element beaker collect;ng melted ice electronic scale Figure 16.9 Determining the specific latent heat of fusion of ice by an electrical method Precaut ions to minimise error • Sma ll chips of ice are used so that we can assume their temperature is 0 colder temperatures at their centres). 0c. (Larger chips may have • Befo re putting the ice in the funnel, it is quickly dabbed in a tissue so as to remove water from its surface. • The heater element is always completely submerged so that it transfers thermal energy only to the ice. • The current is kept cons tant during the experiment by adjusting the rheostat. Source of error • Thermal energy wi ll be transferred to the ice from the atmosphere and the funnel. The specific latent heat of vaporisation of water by an electrical method • The appa ratus is set up as shown in Figure 16.10 and the heater is switched on. • When the water is boiling, the initial mass, m 11 is measured and recorded, and the stop watch is started. • The readings of voltage, V, across the heater, and curren t, I, through it, are taken. • After a few minutes, the new mass, m 21 and the time, t, are measu red and recorded. l I I L- Assuming that all the electrical energy is used in boiling the water, the specific latent heat of vaporisation can be calcu lated from: ii" electri cal energy = heat energy supplied to boil water ~ g ~ ~ beaker of water heatr element electronic scale Vlt = m w,I Vlt = (m, - m 2) I, _--.:V.:o't_ = I (m - m ) v 1 2 Figure 16.10 Determining the specific latent heat of vaporisation of water by an electrical method Precautions to minimise error • The water is allowed to boil for a few minutes before the mass measurement is made and the stop watch started, to ensure that all of it has reached boiling point. • The heater is placed near the bottom of the water in order to produce convection currents which transfer thermal energy to the entire mass. • The beaker can be lagged to prevent conduction of thermal energy to the surroundings. • The beaker can be wrapped in shiny silver foil to prevent radiation of thermal energy to the atmosphere. Source of error • The re will be thermal energy transferred to the environment. 16 Heat and state change Revision questions 1 Define: a latent heat b specific latent heat of fusion. 2 Describe a simple experiment to verify that the temperature of a liqu id remains steady when it changes to a gas. 3 Sketch a temperature- time graph showing the conversion of ice at -4 °C to steam at 105 Indicate on th e graph where there are changes in the kin etic ene rgy and potential energy of th e mol ecules. 4 Using data from Table 15.1 and Table 16.1, determine the heat released when 2.0 kg of steam at 100 °C converts to water at 90 5 Describe how the specific laten t heat of fusion of ice can be found using an electrical method. 0c. 0c. 16 Concise Revision Course: CSEC· Physics 17 Evaporation and boiling Evaporation is th e escape of m olecules from th e sur face of a liquid. Boiling is th e escap e of m olecules from th e bod y of a liquid and occurs only at a particular temperature fo r a given pressure. Table 17.1 Differences between boiling and evaporation Occurs over a range of temperatures lEoes not require an external heat source Occurs at one temperature for a given pressure Requires an external heat source Cooling due to evaporation During evaporation, the faster molecules escape from the surface of the liquid at a rate dependent on the temperature. Some may return to the liquid after rebounding from other molecules above the surface, but most will escape completely. The remaining liquid becomes cooler since the more energetic molecules absorb latent heat of vaporisation from the less energetic ones as they eva porate. Factors affecting the rate of evaporation The factors affecting the rate of evaporation can be explained by the kinetic theory, as follows. 1. Temperature: Molecules move faster at higher temperature and therefore possess more kinetic energy. They have a better chance of overcoming the attractive forces of the neighbouring molecules so that they may escape as a gas. 2. Humidity: If the humidity is high, molecules escaping from the surface are more likely to crash into other molecules and rebound to the liquid, thereby reducing the rate of evaporation. If the air becomes saturated with vapour, the rate of molecules entering the liquid is equal to the rate escaping from it. 3. Wind: The moving air removes evaporated molecules from above the surface, allowing other evaporating molecules to have a better chance of escaping completely without colliding and rebounding to the liquid. 4. Surface area: Evaporation is a surface phenomenon and therefore the larger the surface area, the greater is the chance for molecules of the liquid to escape. Demonstrating cooling due to evaporation A beaker of ether is allowed to rest in a small pool of water, as shown in Figure 17.1. Ether is a volatile liq uid - it evaporates very eaSily. When the air above the liquid is saturated with vapour from the ether, there is less chance of evaporation occurring. However, by pumping dry air through the body of the ether, the following conditions for evaporation ryai become favou rable: • the surface area between the liquid and the air is increased • the air bubbling through the ether is unsaturated. As the ether evaporates, it draws latent heat of vaporisation from the water around the beaker, causi ng the pool of water to rapidly freeze. J1\~ £:::l"':'::::;beaker of ether freezing water Figure 17.1 Demonstrating cooling due to evaporation 17 Evaporation and boiling Refrigerator At the evaporator A volatile liquid - the refrigerant - is pumped up to an expansion valve, where it evaporates as it is sprayed through a fine nozzle (Figure 17.2). The latent heat necessary for evaporation of the refrigerant is absorbed by conduction from the food in th e fridge. At the condenser The refrigerant gas is th en pumped to the condenser wh ere it is compressed and condenses back to a liquid, releasing the latent heat energy previously absorbed. Copper or aluminium fin s are connected to the condenser so that the heat can quickly be conducted from the refrigerant and radiated to th e surrounding air. The condenser should be in a well ventilated area so that the thermal radiation emitted can easily dissipate to the environment. EVAPORATOR (latent heat absorbed) / / .. . • • • • • • • •• ••••••• ••• +------- refrigerant (gas) .., ... -----·• ·.•.•........ • • expansion valve ~ - - refrigerant (liquid) •• • • • • -radiator (copper or aluminium grill) - - CONDENSER (latent heat released) t J - refrigerant ....J (compressed gas) pump Figure 17.2 A refrigerato r Air conditioner At the evaporator Air from th e room is circ ulated through the evaporator and then return ed to the room by means of a fan (Figure 17.3). The liquid refrigerant is pumped to an expansion valve where it evaporates, removing latent heat from th e surrounding air in the process. At the condenser The refrigerant gas is then pumped to the condenser where it is compressed and condenses back to a liquid, releasing the latent heat en ergy previously absorbed. This heat energy is conducted to th e aluminium gri ll and then radiates to the surro undings. A fan produces forced convection of the hot air away from th e unit, to the outside. 17 Concise Revision Course: CSEC· Physics It is co mmo n to have th e evapo rator installed in th e room and the condenser installed as a separate unit o utside the building. EVAPORATOR Oatent heat absorbed) , expansion valve I I air sucked in by fan I I partition I cool air out through vents ~" A"~ \ ~ I I air sucked .- ) ~ j/"7tI refrigerant (liquid) '\ ~: -I- '-r-oo CONDENSER (latent heat released) in by fan -- -. • I I ~ I I I I I I : radiator ..---I I I / - (aluminium grill) refrigerant (compressed gas) / refrigerant (gas) hot air blown out by fan pump Figure 17.3 An air conditioner Other phenomena involving latent heat • Earthenware vessels: An earthenware vessel has very narrow cal'iliary bores within its structure. Water placed in such a vessel is attracted through the capillari es to the outer surface where it evaporates, drawing latent heat from the container and its contents in th e proce ss. • Hurricanes: The Sun provides energy for water to evaporate from the ocean and produce clouds. As the vapour condenses, the latent heat relea sed powers the storm, driving the winds faster and faster towards the storm's eye and increasing the rate of evaporation. The region becomes covered in cloud and, as the large amount of condensation occurs, a tremendous amount of energy is released, producing hurricane-force winds. • Perspiration: When we use excessive power, for example, when running or lifting heavy weights, our body temperature rises due to the higher rate of conversion of chemical energy. We then sec rete perspiration which evaporates from our bodies, removin g latent heat of vaporisation and cooling us. Dogs and cats also cool by evaporation, but since their bodies are almost totally covered by hair, they have wet nostrils and thick wet tongues to provide the cooling effect. • Spraying aerosols: A can of insecticide, for example, becomes cold as its liquid co ntents are sprayed through the fine nozzle of the expansion valve. On expanding into the atmosphere under reduced pressure the liquid changes to gas, absorbing latent heat from the can and its remaining co ntents in the process. Revision questions 1 State THREE differences between evaporation and boiling. 2 Use the kinetic theory to explain how th e following affect the rat e of evaporation of a liquid. temperature 3 humidity wind surface area Briefly describ e and explain how the refrigerant of an air conditioner removes heat energy from the air in a room and then releases it to the air outside. 17 Evaporation and boiling 18 Thermal energy transfer Processes of thermal energy transfer Conduction: The transfer of thermal energy between two points in a medium by the relaying of energy between adjacent particles of the medium, with no net displacement of the particles. Convection: The transfer of thermal energy between two points in a medium by the movement of the particles of the medium due to existing regions of different density. Radiation: The transfer of thermal energy by means of electromagnetic waves. These processes occur to a greater or lesser degree in different media - see Table 18.1 . Table 18.1 Thermal energy transfer through solids, liquids, gases and a vacuum Occurs significantly in so lids (to a greater extent in metals than in non-metals), less in liquid s, and very little in gases. Cannot occur through a vacuum. Conduction -Convection -----Radiation Occurs in liquids and gases. Cannot occur through a vacuum. Occurs readily through gases and through a vacuum . Conduction Conduction and th e kinetic theory Non-metals: Figure 18.1(a) shows what happens when one end of a non-metallic bar is warmed. The heat energy supplied converts to kinetic energy of the molecules which causes them to VIBRATE faster and with greater amplitude than before. They bombard their neighbours with greater force and higher frequency than befo re, passing on the increased vibration. In this manner, thermal energy is re layed between adjacent molecu les to the other end of the bar. Th e temperature of a substance is proportional to the kinetic energy of its particles and therefore the temperature at the coo ler end of the bar increases. Metals: A similar process occurs in metals (Figure 18.1(b)). The cat ion s (positively charged ion s) receive the heat energy and VIBRATE faster and with greater amp litude than before, bombarding their neighbours with greater force and higher frequency, and so passing the vibration from particl e to particle. Metals, however, also contain a 'sea' of free electrons which TRANSLATE between the cations. When th ese electrons are supplied with heat energy their kinetic energy increases, causing them to translate faster. On co lli sion with a cation, the energy is transferred to it, increasing its vibration. Si nce metals have two modes of co nductio n, w hereas non-metals have on ly one, metals are better cond uctor s. ~ I~ ~.I -'11 _ ~ ...- ..A-'I""..- :~ NON·METAL HEAT HEAT • b METAL ~ I vibrating molecule ~ vibrating cation ---'" translating free electron Figure 18.1 Conduction in non-metals and metals Demonstrating conduction Figure 18.2 shows rods of different materials, initially covered in wax, being heated by a water bath. The wax quickly melts from the copper, not as fast from the iron, and very slowly from the wood, indicating that copper is a very good conductor, but wood a good insulator (poor conductor). 18 Concise Revision Cou rse: CSEC· PhYSics Figu re 18.3 shows a piece of ice wrapped in copper mes h and submerged in a te st tube of water. The weight of the mesh keeps the ice at the bottom of the tub e. The water, heated at the top to avoid convection, rapidly comes to a boil, but the ice rema in s so lid for quite some time. Thi s demonstrates that wate r is a very poor conductor. f-/_I _ _-{/ boiling water hot water bath - ~-/ wood -'"/ iron copper ------- ice wrapped in copper mesh wax Figure 18.2 Demonstrating conduction in solids Figure 18.3 Demonstrating that water is a poor conductor Convection Convection and the kinetic theory Figure 18.4 illu strates the process of co nvection. On wa rmin g a liquid or gas from below, th e increase in thermal energy in its lower reg ion gives the molecules increased ki netic energy, ca using them to TRANSLATE mo re vigorously and to take up more space. The region therefore becomes less dense, res ulting in its molecules ri sing and allowing cooler molecul es from denser regions to fall in and take their place. ...... . . . .. -:- . .e. : . .. :. ~ :;- ·........ . :~. . •• ·:· :*.... .,,* • ( . .. . ~: • "'. . i .·: .... ..... . • .•.•. * •*•• •~ :. . •"*. ". •• :.::.'::...m... •• _ :. *: :.. hotter, less dense regIon of molecules (r;s;ngl cooler, more dense region of molecules (falling) HEAT from below Figure 18.4 Convection in liquids and gases Demonstrating convection In liquids: Figure 18.5(a) shows a crystal of potassium permanganate (which is purple) added to a beaker of water. Th e beaker is heated from below the crystal and the coloured solution formed shows the path of the co nvection current. Alternatively, tiny flakes of aluminium can be used instead of the crystal. Th e flakes will be seen glittering as th ey travel the path of the convection cu rrent. In gases: Heating the air below the hand-held fan of Figure 18.5(b) produces a convection current wh ich causes it to spin. fan spins due to upward air current purple solution showing the path of the current beaker of water - --1 crystal of potassium permanganate a -'< t ? t' ~ ' t - -' HEAT from below HEAT b from below Figure 18.5 Demonstrating convection in a liquid and in a gas 18 Thermal energy transfer Land and sea breezes During the day: The Sun's radiation warms the land more than it warms the sea. Th e air above the land is then heated by conduction, becomes less dense and rises, allowing cool air from over the sea to take its place (Figure 18.6(a)). This creates a convection current and causes a cool onshore breeze from the sea. Coastal regions therefo re do not experience extremely high temperatures during the day. The air in contact with the ground further inland also becomes hot during the day but cannot rise because there is no cooler air nearby that can take its place. For this reason, deserts are usually found away from the coast, and during the day they experience very high temperatures. During the night: The land loses heat by radiation at a higher rate than the sea. The surface of the land therefore becomes cooler than that of the sea. Air in contact with the sea is warmed by conduction. Warm convection currents rise from over the sea and cause a cool breeze to blow offshore from the land (Figure 18.6(b)). Coastal regions therefore do not experience extremely low temperatures during the night. The air in contact with the land further inland also becomes cool during the night but cannot flow since there is no nearby warmer air rising that it may take the place of. For this reason, desert areas away from the coast experience very low temperatures during the night. DAY hot air cannot rise very hot inland region hot air rises ~ HOT LAND • NIGHT cool air cannot flow very cold Inland region cool onshore breeze s COOL SEA C =:tt cool offshore breeze - . . COOL lAND warm air rises S WARMSEA b Figure 18.6 Convection currents causing onshore and offshore breezes Radiation • All bodies emit infrared radiation. This is a type of electromagnetic wave with wavelength greater (and frequency smaller) than light waves. • Hotter bodies emit more infrared radiation than cooler bodies. The radiation is called thermal radiation or 'radiant energy'. • Our bodies detect infrared radiation as warmth. • Electromagnetic waves provide the only method of thermal energy transfer that can occur through a vacuum. • The energy that an electromagnetic wave transmits is proportional to its frequency. 18 Concise Revision Course: CSEC· Physics Demonstrating that radiant energy can propagate through a vacuum The appa ratus shown in Figure 18.7 demo nstrates that infrared radiation can pass through a vacuum. The jar is first evacuated by means of the pump and the heate r is then switched on. The coil begins to glow, and shortly after, the walls of the jar become warm . The energy therefore radiates through the vacuum, is absorbed by the glass, and is conducted through its wall to th e outer surface. f-- - - - connecting leads bung of poor conducting material ~-. ~ heater coil pressure gauge to power supply _ g l asSj" .r ~ '" air pumped out ____ stop cock Figure 18.7 Demonstrating that radiant energy can propagate through a vacuum Em itters and absorbers of thermal radiation Al l bodies emit and absorb infrared radiation. Figure 18.8 illustrates that the temperature of a body relative to its surroundings determines whether it is a net emitter or net absorber at any particular time. • Bodies that are hotter than their surroundings are net emitters of thermal radiation - they emit more radiant energy than they absorb. • Bodies that are cooler than their surroundings are net absorbers of thermal radiation - they absorb more radiant energy than they emit. • The surface of a body will reflect some of the radiation . A good absorber is a poor reflector, and a poor absorber is a good reflector. cool surroundings warm surroundings reflection 100% emission o 1100- , )% absorption (X%) O COOL HOT Figure 18.8 Emitters and absorbers of radiation Factors affecting the absorption or emission of radiation 1. Texture of surface (rough, matt, dull/smooth, shiny, polished) 2. Colour of surface 3. Area of surface Surfaces that are good absorbers are also good emitters. See Table 18.2. Table 18.2 Good absorbers and good emitters good emitters poor emitters It is important to note that texture and colour do not determine whether a body is a net absorber or a net emitter. This depends on its temperature relative to the surroundings at the time. • First determine if the body is a net absorber or net emitter by considering its temperature relative to surrounding bodies. • Then examine the physical properties of its surface to determine how good an absorber or emitter it is. A black surface is a better emitter of radiation than a white or silver surface. Figure 18.9 shows two detectors of thermal radiation placed at equal distances from the su rfaces being investigated. Both surfaces are at the temperature of the hot water. The detector fac ing the black surface gives a higher reading, ind icating that the black surface is the better emitter of radiation. white or silver radiation detector C] black \---oor--I radiation detector ~ D Figure 18.9 Showing that a black surface is a better emitter than a white or silver surface 18 Thermal energy transfer A black surface is a better absorber of radiation than a white or reflection silver surface. absorption Figure 18.10 shows an arrangement where an equal amount of radiant energy is incident on a black and on a white or silver surface. Corks are initially stuck to the outside of each plate with wax. The cork falls first from the plate which has its inner surface painted black; th e wax there rapidly becomes hot and melts. The black surface is therefore the better absorber of radiation. The experiment also shows that the white or silver surface is the better reflector, since less energy is transferred onto the white or silver plate to be conducted to the wax. Examp les Figure 18.10 Showing that a black surface is a better absorber of radiation than a white or silver surface • Two metal cans, one black and the other white, are filled with cool water and left in the yard exposed to the Sun's radiation . The cans are both net absorbers since they are cooler than their surroundings. The water in the black can warms up faster since the black surface is the better absorber of radiation. • The cans are filled with boiling water and placed in the shade. They are now both net emitters since they are much hotter than their surroundings. The temperature of the water in the black can falls faster since the black surface is a better emitter of radiation. Applications of thermal energy transfer processes The vacuum flask A vacuum flask has several features that reduce thermal e nergy transfer. See Figure lB.ll. • The vacuum prevents transfer of thermal energy by conduction and convection. • The double-walled container which holds the food or drink is made of glass. Thermal energy transfer by conduction through the walls is therefore reduced because glass is a poor conductor. • The inner, facing walls of the vacuum region are silver. If the contents of the flask are hot, thermal radiation will be emitted through the vacuum from th e wall touching the conte nts. Since silver is a poor emitter, the extent of this radiation is minimised. On reaching the other silvered surface on the opposite side of the vacuum, the radiation will be strongly insulating cover reflected. If the contents of the flask are cold, thermal polished cap energy entering the system will be similarly minimised. .--- • The cover, case and shock pads are made of good insulating material to prevent transfer of thermal energy by conduction. • The outer wall of the case is polished. If the contents are hot, the thermal radiation emitted would be minimised since shiny surfaces are poor emitters of radiation. If the contents are cold, the radiation absorbed would be minimised since shiny surfaces are also poor absorbers of radiation. --U . --- polished exterior vacuum prevents conduction and convection silver , polished inner walls prevent radiation - insulating case insulating shock pads Figure 18.11 The vacuum flask The glass greenhouse The Sun's surface temperature is in excess of 6000 K and therefore it emits a large amount of highfrequency (short-wavelength) electromagnetic waves. This is mostly visible light, ultraviolet and shortwavelength infrared radiation. These waves are very energetic and easily enter a greenhouse through the glass walls, as shown in Figure 18.12(a). The contents of the greenhouse are then warmed and emit their own radiation. However, since their temperature is much lower than that of the Sun, the waves emitted are longer-wavelength infrared radiation. This is reflected by glass, so the greenhouse acts as a heat trap. 18 Concise Revision Cou rse: CSEC· Physics Another impo rtant feature o f the greenho use is that its roof and sides prevent th e hot air from leaving by natural convection. The greenhouse effect The Earth's atmosph e re be haves like th e gl ass of t he gree nh o use, as shown in Fi gure 18.12(b ). Hi ghfrequency radiat ion is emitted f ro m th e ve ry hot surfa ce of th e Sun. Thi s includes sh o rt -wavele ngth infrared waves and th ese easily pe net rate th e Ea rt h's atm os ph e re and w arm t he planet. The Earth's surface th e n emits its ow n radiation, but of longe r w avel ength, m ainly lo nger-w avele ngth infrared. These waves are absorbed by ce rtain gases in the atmosphe re, called greenhouse gases particu larly carbon dioxide, wa te r vapour and meth ane. When thes e gases are w armed th ey emit their own infrared radiation, mu ch of it returning t o Earth to produ ce global warming. high-frequency carbon dioxide water vapour methane waves / glass plants ~ IR Earth ---'-';;0... GREENHOUSE GREENHOUSE EFFECT b Carbon dioxide, water vapour and methane allow high-frequency radiation to enter but prevent low-frequency infrared radiation from leaving. a Glass allows high-frequency radiation to enter but prevents low-frequency infrared radiation from leaving. Figure 18.12 Th e greenhouse and the greenhouse effect The solar water heater The fe atures of a so lar w ate r heate r are illu strated in Figure 18.13. silver to reduce lagged to reduce outward conduction from tank radiation emitted connected to water mains \ COOL WATER STORAGE TANK glass cover traps outgoing copper surface readily conducts heat to copper tubes infrared radiation black surface increases absorption of solar radiation / ....... ~=:IHEATER PANEL hot tap f§ slanted to allow for natural convection of the heated water small diameter copper tubes ensure that the poorly conducting water is near to the hot walls to be easily heated by conduction Figure 18.13 The solar water heater 18 Thermal ene rgy t ransf e r A black surface is a better absorber of radiation than a white or silver surface. Figure 18.10 shows an arrangement where an equal amount of radiant energy is incident on a black and on a white or silve r surface. Corks are initially stuck to the outside of each plate with wax. The cork falls first from the plate which has its inner surface painted black; the wax there rapidly becomes hot and melts. The black surface is therefore the better absorber of radiation. The experiment also shows that the white or silver surface is the better reflector, since less energy is transferred onto the white or silver plate to be conducted to the wax. Examples f11 reflection absorption ~ II white wax melts lJucork or;lblad Figure 18.10 Showing that a black surface is a better absorber of radiation than a white or silver surface • Two metal cans, one black and the other white, are filled with cool water and left in the yard exposed to the Sun's radiation. The cans are both net absorbers since they are cooler than their surroundings. The water in th e black can warms up faster since the black surface is the better absorber of radiation. • The cans are filled with boiling water and placed in the shade. They are now both net emitters since they are much hotter than their surroundings. The temperature of the water in the black can falls faster since the black surface is a bette r emitter of radiation. Applications of thermal energy transfer processes The vacuum flask A vacuum flask has several features that reduce thermal energy transfer. See Figure 18.11. • The vacuum prevents transfer of thermal energy by conduction and convection. • The double-walled container which holds the food or drink is made of glass. Thermal energy transfer by conduction through the walls is therefore reduced because glass is a poor conductor. • The inner, facing walls of the vacuum region are silver. If the contents of the flask are hot, thermal radiation will be emitted through the vacuum from the wall touching the contents. Since silver is a poor emitter, the extent of this radiation is minimised. On reaching the other silvered surface on the opposite side of the vacuum, the radiation will be strongly insulating cover reflected. If the contents of the flask are cold, thermal polished cap ,-./ energy entering the system will be Similarly minimised. • The cover, case and shock pads are made of good insulating material to prevent transfer of thermal energy by conduction. • The outer wall of the case is polished. If the contents are hot, the thermal radiation emitted would be minimised since shiny surfaces are poor emitters of radiation. If the contents are cold, the radiation absorbed would be minimised since shiny surfaces are also poor absorbers of radiation. U . ,-- polished exterior l - vacuum prevents conduction and convection silver, polished inner walls prevent radiation I - insulating case "- insulating shock pads Figure 18.11 Th e vacuum flask The glass greenhouse The Sun's surface temperature is in excess of 6000 K and therefore it emits a large amount of highfrequency (short-wavelength) electromagnetic waves. This is mostly visible light, ultraviolet and shortwavelength infrared radiation. These waves are very energetic and easily enter a greenhouse through the glass walls, as shown in Figure lB.12 (a). The contents of the greenhouse are then warmed and emit their own radit~on. However, since their temperature is much lower than that of the Sun, the waves emitted are longer-wavelength infrared radiation. This is reflected by glass, so the greenhouse acts as a heat trap. 1 B Concise Revision Course: CSEC' Physics Another important feature of the greenhouse is that its roof and sides prevent the hot air from leaving by natural convection. The greenhouse effect The Earth's atmosphere behaves like the glass of the greenhouse, as shown in Figure lB.12(b). Highfrequency radiation is emitted from the very hot surface of the Sun. This includes short-wavelength infrared waves and these easily penetrate the Earth's atmosphere and warm the planet. The Earth's surface then emits its own radiation, but of longer wavelength, mainly longer-wavelength infrared. These waves are absorbed by certain gases in the atmosphere, called greenhouse gasesparticularly carbon dioxide, water vapour and methane. When these gases are warmed they emit their own infrared radiation, much of it returning to Earth to produce global warming. high-frequency waves carbon dioxide water vapour ~ methane ~~ glass plants / . Earth GREENHOUSE ~ ~ IR ' GREENHOUSE EFFECT b Carbon dioxide, water vapour and methane allow high·frequency radiation to enter but prevent low-frequency infrared radiation from leaving . a Glass allows high·frequency radiation to enter but prevents low-frequency infrared radiation from leaving. Figure 18.12 The greenhouse and the greenhouse effect The solar water heater The features of a solar water heater are illustrated in Figure 18.13. silver to reduce radiation emitted \ connected to water mains \ I, ~ =. _I :H~OT lagged to reduce outward conduction from tank W~ATER I COOL WATER ==:::J'I..II •• STORAGE TANK glass cover traps outgoing infrared radiation copper surface readily conducts heat to copper tubes black surface increases absorption of solar radiation ...... r hot tap "8 slanted to allow for natural convection of the heated water r=~:.tHEATER PANEL small diameter copper tubes ensure that the poorly conducting water is near to the hot walls to be easily heated by conduction Figure 18.13 The solar water heater 18 Thermal energy transfer Note the following about the solar water heater shown in Figure 18.13: • All hot water exits and entries are at the top, and all cold water exits and entries are at the bottom of the tank or panel. • Water is a poor conductor of thermal energy and therefore the hot water in the tank remains hot although it rests on the cooler water below. • If the tank is too heavy for the roof, it may be placed on the ground. An electric pump will then be necessary to force the hot water downward from the heater panel. Revision questions 1 Define: a conduction 2 b convection c radiation Use the kinetic theory to explain: a conduction in metals b convection in liquids. 3 Describe experiments to demonstrate each of the following. a Convection currents occur in a liquid. b Black surfaces are better absorbers of thermal radiation than white surfaces. c Thermal radiation can pass through a vacuum. 4 a State THREE features of a vacuum flask that prevent thermal energy transfer. b Explain how each feature mentioned in part a achieves its purpose. 5 Describe and explain the greenhouse effect. 6 For EACH of the features (i to vi) of the solar water heater listed below: a state the PROCESS of thermal energy transfer involved b explain how the feature makes the associated process more efficient. Glass cover on the heater panel " Copper tubes in the heater to contain the water iii Matt black surface in contact with the tubes in the panel iv Storage tank placed above the heater panel v Lagging around the storage tank vi Silver outer surface of the storage tank 18 Con cise Revision Course: CSEC' Physics Exam-style questions Chapters 10 to 18 Structured questions 1 a) Distinguish between the heat capacity of a body and the specific heat capacity of a substance. (2 marks) b) An immersion heater of power 600 W provides energy to 500 g of water initially at 30°C until 200 g of it converts to steam. Calculate: i) the heat capacity of the water (2 marks) ii) the time taken to bring the water to boiling point (2 marks) iii) the latent heat supplied (2 marks) iv) the time for which the water was boiling. (2 marks) (Specific heat capacity of water = 4200 J kg- ' K-I; specific latent heat of vaporisation of water = 2.3 x 10" J kg-I) Define temperature. c) i) ii) (1 mark) Name 1WO types of thermometer and state the thermometric property that each utilises. (4 marks) Total 15 marks 2 a) Complete Table 1 by giving the name of the law that corresponds to the relation outlined in the first column between the pressure (P), volume (V) and absolute temperature (T) of a fixed mass of gas. Table 1 V IX T (P constant) 1 P IX - (T constant) V b) i) ii) P '" T (V constant) (3 marks) 10 cm ' of air in a syringe is at a temperature of 30°C and a pressure of 8.0 x 10' Pa. Calculate the new pressure if the air is compressed to 5.0 cm ' and the temperature is kept constant. (2 marks) Use the kinetic theory of matter to explain the increase in pressure in part b) i). (2 marks) iii) Use Newton's second law of motion to explain why the molecules of a gas exert a force on the walls of the container that encloses them. (2 marks) c) The graph shown in Figure 1 shows the temperatu re of a mass, m, of water as it is heated. "~ ~ I vi 100 30 B I I o 200 time / s Figure 1 Exam-style questions - Chapters 10 to 18 i) ii) Calculate the mass, m, given that the power of the heater is 300 Wand the specific heat capacity of water is 4200 ) kg- ' °C-' . (3 marks) Calculate the time for the same heater to melt 400 g of ice at 0 °C if the specific latent heat of fusion of ice is 3.4 x 10' ) kg-I. (3 marks) Total 15 marks Extended response questions 3 a) Describe an experiment to determine the specific latent heat of vaporisation of water using the apparatus shown in Figure 2. You must indicate by means of an equation how you would arrive at your result. (6 marks) stop ~ watch ~ 1---- beaker of water r7~ ~ - heater element electronic scale Figure 2 b) In an experiment like that in part a), a power of 1.0 kW was supplied and it took 10 minutes to boil off 250 g of water, when at 100°C. Determine: i) th e specific latent heat of vaporisation of water (3 marks) ii) the latent heat supplied. (3 marks) c) The value calculated in part b) i) would be different from the true value. i) Suggest a reason why this may be so. ii) Deduce whether the calculated value is greater or lesser than the true value. (1 mark) (2 marks) Total 15 marks 4 a) Coastal regions generally have their temperatures moderated during the day by cool onshore breezes. Explain this phenomenon. (6 marks) b) Solar radiation reaches the panels of a water heater system at an average rate of 800 W m-' between 6am and 6pm . The system has 8 panels, each with an area of 0.50 m' , and is capable of transferring 60% of the received radiation to the water. Determine: i) the total receiving area of the panels ii) the solar power reaching the system 's panels between 6am and 6pm. (1 mark) (2 marks) iii) the solar power transferred to the water (2 marks) iv) the time taken to raise the temperature of 250 kg of water by 40 °C. (4 marks) (Specific heat capacity of water ~ 4200 J kg-I K- ' ) Total 15 marks Exam-style questions - Chapters 10 to 18 19 Wave motion Types of waves A pul.. e IS d ... inglt' disturoancl ~hat rl()f'd~, ....... I{ un me Joint to 11lt' f. As the pulse passes, as in the rope o r slinky spring in Figure 19.1, for example, each particle mimics the vibration at the source. propagation single vibration of rope left H r.or_;g_hl_ _...Jf\ - rope propagation push single vibration of slinky ...... pull ---.. ~ +- WJJJ.JJJ.J.JIII S1i nk y Figure 19.1 A pulse in a rope and in a slinky A waH' IS a continuous !;tream or regular disturbance.s . Transverse and longitudinal waves Waves may be classified as being eithe r transverse or longitudinal. '\ lransrer-se wave is one that has vibrations perpendicular to its direction of propagation. Examples of t ransverse waves • The wave produced in a rope or slinky lying on a horizontal surface and vibrated from one end, perpendicularly to its length (see Figures 19.2 and 19.3). • The wave produced in water by an object vibrated perpendicularly into and out of its su rface. • An electromagnetic wave, for example light. source vibration I before after particle motion Figure 19.2 Particle motion in a transverse wave source vibration I rlWfU}J-I.\4mn1"· ·~ "' fixed end Figure 19.3 Transverse wave in a slinky " longitudinal wa" e is olle th,ll has vibratIOns parallcl to its direction ofpropagaUon. Longitudinal waves are characterised by regions of high pressure (compressions) and regions of low pressure (rarefactions), indicated by C and R in Figures 19.4 and 19.5. 19 Wave motion 83 Examples of longit udinal wave s • The so und wave produced in a solid, liquid or gas (see Figure 19.4). • The wave produced in a slinky lying straight on a horizontal surface and vibrated parallel to its length from one end (see Figure 19.5). Figure 19.4 Particle motion and pressure variation in a longitudinal sound wave -- propagation source vibration +--+- c R c R c Figure 19.5 Longitudinal wave in a slinky Progressive and stationary waves Waves may also be classified is either being progressive or stationary. Pro g r e ~f.,iI 'e wd,"'es JfC those th tran<;fer energr from une point to th( next Stationary waves do not transfer energy. These waves are not on the CSEC syllabus . Wave parameters • Amplitude, a: The alnplituc/t of a wa\'( is the maximum displacement of the \.'ibr,llIon or ()~uJlaon '-,om Its mean posItion. See Figure 19.6. If the amplitude of a light wave increases, the light becomes brighter. If the amplitude of a sound wave increases, the sound becomes louder. displacement Figure 19.6 Amplitude, a • Phase: 'OIfHS pronre..,. \.1\ eo arC' in pha se 'f thf' d/~t.1n( (' b( In ('en them along the dllPctlOn of propagation is equal to a whole number of wa l'elengths, A: IJA, 1A, 2,1, and so on. See Figure 19.7, --- , When points are in phase in a progressive wave they have the same displacement, direction and speed in their vibrations. 84 19 Concise Revision Course: CSEC· Physics ,..... 10'nl ... C" ~\d!.( Ie in anlip"~e (( \:.1c'fy ovt 0f phase of prop.jll ." "1 'S ('qUdl to A 1 A ) 1 A nrl ~fJ In ,/!(., \\he I, chp dl f ,f, If t ~ bt "~\(cn tl en aI, Illj 't,( A I , I in phase : (A, F and K), (B. G and l). (e and HI, (0 and I), (E and J) antiphase: (B and DJ, (B and 1), (e and El. (e and J), (0 and Gl. etc. In Figure 19.7 Phase and antiphase • Wavelength, A: disPlacement r ,. \ I\,.{( I1gll , p o ----- - --,, -- ~ - - - , .~ ""=7 ~L'fl llthet du'("",( , position J({e' ~('flrt I ~ i - l t GljJ c J 1 1~lrn c R R n' , c R L(I'nc1\\'IV T II position Figure 19.8 The wavelength A of a transverse and a longitudinal wave • Peri od, T: Till In Figure 19.9 the period is 200 ms = 0.2 s. Fre quency, f: I' " f T =..!.. and f Tm ust be in seco nds (s) for fto be in hertz (Hz). If T = 0.2 s then f dis P l acemnt~ o~ 'II/i), 1" I r (nd 1 f=T =_1_ =5 Hz. 0.2 10~O . 300 tlms Figure 19.9 A displacement-time graph for a wave Th e frequency of a light wave determin es its colour. Red has the lowest frequency and violet the hig hest frequency of the visible spectrum. The frequency of a so und wave determ in es its pitch. A bass note has a low frequency and a treble not e has a high frequency. • Wavefront: This is a line perpendicular to the propagation of a wave on which all points are in p hase. Wavefronts are generally taken through crests of transverse waves and through co mpressions of longitud inal waves, as illustrated in Figure 19.10. Figure 19.11(a) shows the refl ection of plane wavefrants at a barrier. ,, , Figure 19.10 Wavefronts of transverse and longitudinal waves 19 Wave motion 85 • Speed, v: This is the rate at which the wavefronts of a wave propagate, and it depends on the medium of propagation. At a boundary between media the speed changes and the wave undergoes refraction (Figure 19.11 (b)). plane plane source source x a b speed of waves in Y < speed of waves in X Figure 19.11 Reflection and refraction of plane wavefronts Variation of the speed of waves The speed of light is greater in media of lesser density. Light therefore travels fastest in a vacuum or in air and slower in water or glass. The speed of sound is greater through gases of lesser density. Molecules of lesser mass respond more readily to vibrations than those of greater mass. Sound therefore travels faster through air than through carbon dioxide. The speed of sound is greatest through solids, less in liquids and least in gases. The closer packing of the particles and the rigidity of the bonds in a solid allows vibrations to transfer more readily. See Table 19.1. The speed of sound through gases is greater at higher temperatures because the increased kinetic energy allows the vibrations to be passed on more readily. The speed of a water wave is greater across a deeper region. Table 19.1 Speed of sound in steel, water and air Speed/m 330 S-1 General wave equations A v = Af ~=A; V1 V=- T Al = sin 81 sin 82 1}2 =-:ry; where 71 represents the refractive index of a medium (see Chapter 24), and 8, and 8, are as shown in Figure 19.12. Figure 19.12 shows in detail the change in direction of wavefronts when the wave is refracted. Note the following: • 8, and 8, are the angles (of incidence and refraction respectively) between RAYS and the NORMAL or between WAVEFRONTS and the INTERFACE. 19 Concise Revision Course: CSEC· Physics ME DIUM 1 interface MEDIUM 2 Figure 19.12 Change in direction of waves on refraction • Th e speed, v, wavelength, A, and sin 8, all change by the same proportion when the wave goes into a new medium. If v doubles, then A and sin 8 also double. The angle e will not double, but will increase. • T and f do not change when a wave passes from one medium to the next. • When using the equations in calculations it is a good idea to use relevant letters as subscripts rather than numbers - for example, Vw for the speed in water and Vg for the speed in glass. This reduces errors due to incorrect substitution into an otherwise correct equation. • In the third equation above, the ratio of refractive indices has its subscripts inverted relative to the other three ratios. Calculate the wavelength of the broadcast from a radio station which emits waves of frequency 104.1 MHz, given that the speed of the wave is 3.0 x 108 m S ~I . V= Af 3.0 10' = A x 104.1 X X 106 3.0 X 10' = A 104.1 X 106 2.9m = A A water wave has a speed of 3.0 m S~1 and its crests are 5.0 m apart. It approaches a reef at an angle of incidence of 60°. On passing over it, the distance between its crests reduces to 4.0 m. Determine for the wave: a the frequency in the deeper water b the period in the deeper water c the frequency as it passes over the reef (shallow) d the period as it passes over the reef e the speed as it passes over the reef f the angle of refraction on reaching the reef g the refractive index on travelling from the deep to the shallow. V = Af a 3.0 = S.Of 3.0 = f 5.0 0.60 Hz = f b T=2.=_1_ f 0.60 T = 1.67 s (1.7 s to 2 sig. fig.) c 0.60 Hz (frequency does not change) d 1.7 s (period does not change) e Using s for 'shallow' and d for 'deep': ~= Vd Ad v, 4.0 3.0 = 5.0 v , =~x3.0 5.0 v; = 2.4 m S~1 19 Wave motion , 87 sin 8s As sin 0d ; Ad f sin 0, ; 4.0 sin 60 5.0 s:o . 0s :::: 4.0 Sin . 60 x Sin 0;44° , g When referring to refractive index of one medium relative to the next, the second medium must be in the numerator. ~= Ad A, '7d '7, 5.0 '7d ; 4.0 '7, ; 1.25 '7d Graphs of waves Displacement-position graph A displacement-position graph relates the displacement of each point in a wave to the distance or position from some reference point at ONE INSTANT IN TIME (the time is held fixed). See Example 3. Figure 19.13 shows a wave of speed 32 m a the amplitude S-1 at an instant in time. Determine: b the wavelength The x·axis gives the wavelength . displacemenVmm speed 32ms- 1 5.0 o +-- ---'1<--- -,1'-- --+-+ position/em - 5.0 Figure 19.13 a Amplitude; 5.0 mm b Wavelength ; 80 cm or 0.80 m c Frequency f: v; Af v 32 f 40 f; - ; - - ; 40 Hz A 0.80 d Period T: 1 1 T; - ; ; 0.D25 s 19 Concise Revision Course: CSEC' Physics c the frequency d the period Displacement-time graph A displacement-time graph relates the displacement of ONE POINT in the wave as time continues (the position is held fixed) . See Example 4. Figure 19.14 shows a wave of speed 40 m s-'. Determine: a the amplitude of particle P b the displacemen( of particle P d the f requency e the wavelength c the period di splacementjmm speed 40 ms- 1 10.0 5.0 of-- --\--- -J-- -t----+ time/ ms - 5.0 -10. 0 Figure 19.14 a Amplitude of P = 10.0 mm b D isplacement of P = -5 .0 mm c Pe riod = 200 ms or 0.200 s d Frequency f: 1 1 f = - = -=5 .00 Hz T 0.200 e Wavelength A: v= Af v 40 A= - = -- = B.O m f 5.00 Important notes • Displacement- position and displacement-time graphs of waves have the shape of transverse waves, but they can represent both transverse and longitudinal waves. Recall that graphs are a mathematical means of relating two variables - they are not pictures. • Pressure-position and pressure-time graphs always represent longitudinal waves. Recall that these waves have regions of high and low pressure - compressions and rarefactions. • The mean value on the vertical axis of a pressure- time graph of a sound wave (see Figure 19.15) is not zero, as it is with a graph of displacement. pressure/ Pa pressure at compression atmospher ic pressu re pressure at rarefaction 1.1 x 10 5 1.0x105 time/ms 0.9 x 105 Figure 19.15 Pressure-time graph of a sound wave 19 Wave motion 89 Revision questions 1 What is meant by each of the following terms describing waves? a longitudinal wave b transverse wave C progressive wave 2 Give TWO examples of a transverse wave and TWO examples of a longitudinal wave. 3 Define the following terms associated with waves: a wavelength 4 b amplitude c frequency e wavefront d period How does the speed of the wave change in each of the following situat ions? a light wave travels from glass to air. b Water wave travels from a deep region to a shallow region. c Sound wave travels from air to a denser gas. d Sound wave travels from air to water. 5 Give reasons for you r answers to 4c and 4d above. 6 Calculate the frequency of blue light in air given that its wavelength and speed are 4.0 x 10-7 m and 3.0 x 108 m S-1 respectively. 7 The speed of a wave reduces from 40 m S- 1 to 32 m S-1 on entering a second medium. The angle of incidence is 30° and the period of vibration is 0.40 s. Determine for the wave: a the frequency b the wavelength in the first medium c the wavelength in the second medium d the angle of refraction. 8 The wave shown in the graph of Figure 19.16 has a speed of 4.0 m b its frequency a its period C displacement/em 5.0 0 1'-- ---'......- --,/'------'1---+ time j ms - 5.0 Figure 19.16 19 Concise Revision Course: CSEC· Physics its amplitude S- I. Determine: d its wavelength 20 Sound waves Production and propagation Production: Sound waves are produced by mechanical vibrations. Propagation: They can only travel through a material medium (solid, liquid or gas). Each particle of the medium passes on the vibration to the one adjacent to it. Sound cannot propagate through a vacuum. Figure 20.1 shows an electric bell suspended in a sealed glass jar. With the bell switched on, observers can see it and hear it ringing. As the air is pumped out, the sound level diminishes to almost zero, but the bell is still seen to be functioning. This occurs because there is no material medium .between the bell and the glass jar to transmit the vibrations. wlres~,o ~= =n = power supply :- -l c:=J-- -- rubber bung .I!lI- - - elastic bands electric bell---+ 'O hammer---oI gong _ _ _-'l~ - glass jar A slight ringing may still be heard since small vibrations may be transmitted by the rubber bands and wires that suspend the bell. pumped oul lap ~ kr Figure 20.1 Sound cannot propagate through a vacuum Pitch and loudness (volume) Figure 20.2 shows three sound waves, A, Band C. They have the same speed because they are in the same medium. A greater frequency wave produces a sound of higher pitch . • A and B have the same wavelength and the same speed, so they must also have the same frequency and pitch. f =.!... ,\ • A has a smaller wavelength than C but the same speed, so the frequency and pitch of A must be greater. a b c IIII 11111111111 1111111 II/II 1111111 1111111 I I I 1111111 Figure 20.2 Comparing pitch and volume from wavefront diagrams 20 Sound waves 91 A tuning fork (Figure 20.3) gives a sound of a fixed frequency and pitch, dependent on its dimen sions and on th e material from which it is made. .. air vibrating tuning fork C R C R C Figure 20.3 A tuning fork is a two pronged, U-shaped fork made of an elastic metal. When struck, it vibrates with a particular frequency, creating compressions and rarefactions in the air. A greater amplitude wave gives a high er volume (louder) sound. • In Figure 20.2, the volume of B is greater than that of A. The compressions and rarefactions of B have greater and lesser pressures respectively than those of A. This greater change in pressure between the compressions and rarefactions of B causes the ear drum to be pushed and pulled with greater amplitude, and therefore produces a louder sound. Pitch and loudness (volume) from a displacement-time graph The graph of Figure 20.4 shows a varying sound produced by a signal generator. Recall that amplitude governs the volume and frequency governs the pitch. displacement Volume A High B C D Low High Low Pitch Low High High Low D Figure 20.4 Comparing pitch and volume from a graph Classification of frequencies of sound Frequency below 20 Hz: infrasound. Frequency 20 Hz to 20 kHz: the audible range of the average human. As one grows older the upper limit gradually reduces to about 16 kHz. Frequency above 20 kHz: ultrasound. Uses of ultrasound • Communicating: Dolphins communicate by emitting and receiving ultrasonic vibrations. • Measuring distance: Bats determine distances by emitting ultrasound and assessing the time in which the echoes return. Depth sounding (see the next page) uses a similar technique. • Diagnostic imaging: Ultrasound is partly reflected when it strikes the boundary between different materials. Doctors use a probe to direct ultrasonic waves into the patient. The reflected waves, received by the same probe, are analysed by a computer to produce an image on a screen. Pre-nataj scanning, as well as the examination of internal organs, can be carried out by this technique. Ultrasonic waves are relatively safe in comparison to X-rays, which have the risk of producing cancer. 92 20 Concise Revision Cou rse: CSEC· Physics • Materials testing: Flaws in solid objects such as metal castings can also be detected by ultrasound probes . • Cleaning: Small objects such as electronic components may be sprayed with a cleanser and then subjected to ultrasonic waves. The vibrations easily remove the dirt and grease. Estimating the speed of sound in air using echoes Observers, A and B, stand about 50 m from a tall, hard, smooth, vertical wall (Figure 20.5). Observer A claps two blocks of wood at such a rate that the returning echo coincides with each succeeding clap. Observer B measures the time, t, for the sound to go to the wall and back 20 tim es. The velocity of sound is found from: d V=- t 20(2x) v = -- t Note: The error due to reaction time is greatly reduced by measuring the total time for 20 echoes to return. The featu res of the wall produce a strong, undiffused echo. The observers should not be too close to the wall because it would then be difficult to differentiate between a clap and its succeeding echo. stop watch tall. smooth, hard, vertical wall ~ \...:J B &A blocks afwood ( / x Figure 20.5 Estimating the speed of sound using echoes Other uses of echoes Thunder cloud proximity Thunder and lightning occur simultaneously. Due to the extremely high speed of light it can be assumed that an observer sees lightning as soon as it is produced. Sound travels much slower and it generally takes a few seconds for us to hear the thunder. The speed of sound is approximately 330 m s·', so it takes about 3 seconds to travel 1 km. An observer who counts the seconds between see ing the flash and hearing the sound can estimate the distance from the thunder cloud (in km) by dividing the count by 3. p <;0 nd ng Ul trasonic waves are used to determine the depth of water. Pulses of ultrasound are emitted by a tra nsmitter, T, as shown in Figure 20.6, and a timer is started Simu ltaneously. A receiver, R, detects the reflected pulses and record s the time. A computer then calcu lates the depth, x, of the water from: 2x v=- t whe re t is the measured time and v is the velocity of soun d in water, which is 1500 m s· ' . 1500 = E.. t 1500t x - - =X 2 750t = x Figure 20.6 Depth sounding using echoes .-----., 20 Sound waves 93 Behaviour of sound waves Evidence that sound waves reflect The echo produced when a loud sound is made in front of a cliff is evidence that sound waves reflect. Evidence that sound waves refract Sounds are more audible at night. The air in contact with the ground is cooler at this time. A sound wave travelling upwards will increase in speed as it enters layers of warmer air (see Chapter 19). The wavefronts therefore separate more, taking up the shape shown in Figure 20.7. Since rays (lines of propagation ) are always perpendicular to wavefronts, the sound ray refracts along a curved path, returning to the surface of the Earth and allowing more sound energy to reach the observer. less dense / warmer faster , therefore wavelength denser leaaler slower, therefore shorter wavelength source near observer ground level Figure 20.7 Evidence that sound waves refract Evidence that sound waves diffract A sound-proof cabin Figure 20.8 shows a small sound-proof cabin, initially completely closed, and in the middle of a large open region of flat land. The music from a loudspeaker in the cabin will not be heard outside. If a window is opened, an observer at A will hear the music even if he/she is not in the direct line of sight of the loudspeaker. It is not possible for the sound to reflect to the observer from objects outside, since the land is flat. The direction of the sound wave spreads as it passes through the window, a phenomenon known as diffraction. Diffraction is discussed in Chapter 22. loudspeaker ) window Figure 20.8 Evidence that sound waves diffract Evidence that sound waves interfere 8 A Signal generator, connected to loudspeakers as shown in Figure 20.9, emits a note of constant frequency. Speakers S, and S2are coherent sources, meaning they emit waves in phase or with some constant phase difference. An experimenter walking along the line AB will observe alternate points where he/she hears no sound and then a loud sound. Where the waves from S, and S, meet the experimenter in phase, a loud note is heard, and where they meet exactly out of phase, nothing is heard. Sound waves therefore exhibit the phenomenon of interference. I nterference is discussed in Chapter 22. 94 20 Concise Revision Course: CSEC· Physics A Figure 20.9 Demonstrating that sound waves interfere A thunder clap is heard 5.0 s after the flash of lightning is seen. How far away is the thunder cloud, if the speed of sound is 350 m s· ' ? d v=t d 350=5.0 350 x 5.0 = d 1750m=d A man standing 700 m from the face of a tall cliff fires a rifle. He hears the returning echo 4.0 s later. Determine the speed of sound in the region. d v::;- t 2x v = -t- (distance to cliff and back is 2x) 2(700) 4.0 v = 350 m s· ' v= Observers A and B stand together in front of a tall, smooth, vertical wall. Person A claps two blocks of wood at such a rate that each returning echo is synchronised with the succeeding clap. Person B starts a stop watch and times the period for the return of 20 echoes. If the speed of sound is 350 m s· ', and B records a time of 8.0 s, determine the distance of the observers from the wall. d v=v= t 20(2x) t 40x (distance to wall and back (2x) is travelled 20 times) 350=-8.0 350 x 8.0 =X 40 70m =X 20 Sound waves 95 Revision questions 96 1 Describe how sound propagates through a medium. 2 What can be said of the volume and the pitch of note A relative to note B, if A has a lesser frequency but greater amplitude than B? 3 Construct a table to contrast the frequencies associated with ultrasound, th e audible range of sound, and infrasound. 4 State TWO uses of ultrasound. 5 A pulse of ultrasound is transmitted from beneath a boat and the echo returns after 0.20 s. What is the depth of the ocean at the location, if the speed of sound in water is 1500 m s-' ? 6 A crash of thunder is heard 3.0 s after a flash of lightning is seen. Determine the distance from the thunder cloud, if the speed of sound in air is 350 m s-' . 7 Explain, with the aid of a diagram, why sounds emitted at ground level are more aud ible at night. 8 Desc ribe, with the aid of a diagram, how you could demonstrate that sou nd waves can exhibit interference. 20 Concise Revision Course: CSEC· Physics 21 Electromagnetic waves ,--------------------------, "~ f/rc(roma,£:nl'lit w.n cs an... ~r( up of tnt Yo;;( waves U)t1S1S 1[! 01 I l ('c'r;( 11/'leI lnd ...., . I r tIl (1(" J "'( hI Ii)f P{ r{J("'1dic ',1< r to t .lCh Jthef IIJ!J () thclfcJm'(l1on o(,)(O/Jd!;d/lOn . Thi s is depicted in Figure 21.1. • propagation magnetic field Figure 21.1 An electromagnetic wave General properties of electromagnetic waves • They are all transverse waves. • They travel at the same speed of 3.0 x 108 m S· 1 through a vacuum or through air. • They can propagate through a vacuum. • They consists of varying elect ric and magnetic fields. As for all waves, electromagnetic waves can: • reflect • refract • diffract • ex hibit the phenomenon of interference • transfe r energy. Wavelengths and frequencies of the electromagnetic spectrum Each category of electromagnetic energy co ntains waves of a particu lar frequency range and wave length range. Together they make up the electromagnetic spectrum, as shown in Figure 21.2. Their production is outlined in Table 21.1. Within the category of visible light, each smaller frequency range is detected as a different colour. In orde r of in creas ing frequency, these co lours of the visible spectrum are red, orange, yellow, green, blue, indigo, violet (ROYGBIV). frequency 1Hz 0( 10 19 .."ays 10 17 -I X-rays 10- 13 10- 11 .1 .:: W 10-9 10 13 10 15 E " ,10- 5 I E V 4 x 1O-7 m 1,_. IR IO-}' ' 109 l Oll 10-' 10 7 10' radio 10 1 101 10' w3lJelength/ m 7 x lO-7m Figure 21.2 Wavelengths and frequencies of the electromagnetic spectrum 21 Electromagnetic waves 97 Table 21.1 Production of electromagnetic waves radio Radio tran smitters - metal rods (aerials) that emit radio waves when electric current oscillates within them infrared All bodies above temperature 0 K (-273 0c) visible light (ROYGBIV) Bodies above 1100 °c ultraviolet Very hot bodies, such as the Sun (6000 °C), welding torches, electric spa rk s, lightning ./\./VV'\/\. X and gamma x- High-speed electrons bombarding metal targets Gamma - Changes in nuclei of unstable atoms Uses of electromagnetic waves Radio waves and microwaves • Radio and television broadcasting • Cell phone communication • Warming food Infrared radiation (IR) • Ovens, toasters and heat radiators: IR is detected by our nerves as heat. • Remote controls: When a button on the control is pressed, an IR beam pulses with a unique code to carry out a particular function. • Fibre-optic cables in telecommunication systems including the internet: IR is absorbed less than visible light by the glass fibres and can therefore transmit information over longer distances before the need for amplification. • Heat-seeking missiles: These are able to follow aircraft by using sensors to detect the IR emi tted from engines. • Treatment of certain muscular disorders. • In frared cameras: These produce images showing regions of different temperatures. Bodies at higher temperatures emit higher-frequency waves. The radiation is detected by infrared sensors and passed to a computer program which produces a visible image of the variations in temperature. • Some animals can detect IR emitted from the bodies of their prey and can therefore hunt in the dark. 98 21 Concise Revision Course: CSEC' Physics Ultraviolet radiation (UV) fluOft'''i U 'n n'J",'h P/(I(,-., ...... \\/1((,/)\ ( / 'f ,<. high f/{(111I11(\' ,f111/{ l 1 1(1 '( • Detergen ts co ntain fluorescent substances so that cloth es washed with them look 'whiter than white' - they absorb UV from the Sun and th en emit the energy as visible light waves. • Bank notes have a marking made from a fluorescent substance which becomes visibl e when UV is incide nt on them. This helps to discourage th e circulation of fraudulent bank notes. • Fluo rescent lighting tubes contain mercury vapour which emits UV radiation when a current is passed through it. The UV is absorbed by a fluorescent coating on the inside of th e tube which then emits the energy as visible light. See Figure 21.3. light emitted t~ UV absorbed by fluorescent coating ~ electrode mercury vapour emits LN UV electrode Figure 21.3 A fluorescent lighting tube X-rays • Medical imaging of dense materials such as bones or tumours within flesh • Security scanning of passengers and luggage X-ray crystallography: a method of investigating the structure of crystals Gamma-rays • Cancer therapy Imaging using a gamma camera Tracers Sterilisation See also Chapter 34. Revision questions 1 State FOUR properties of electromagnetic waves. 2 Five groups of electromagnetic waves are: visible light X and gamma infrared ultraviolet radio and microwaves a List th e groups in order of increasing frequency. b What is the range of wavelength s of the visible spectrum? c Which colour has the shortest wavelength? d Which GROUP has the longest wavelength ? e State ONE source and ONE use of EACH group. 21 Electromagnetic waves 99 22 Light waves Rival t heori es of light At the beginning of the 18th century there were two rival classical theories of the nature of light - the wave theory and the corpuscular (particle) theory. W ave the o ry - Huygen s In 1690 Huygens suggested that light was a longitudinal wave, capable of propagating through a material called the aether which he believed filled all space. This material medium justified why light can pass through a vacuum despite the fact that it was supposedly a longitudinal wave, as is sound. Huygens proposed that each point along a wavefront, such as A in Figure 22.1, acts as a so urce of new 'wavelets'. After a short time, t, each of these secondary wavelets has advanced by the sam e amount and a new wavefront, B, is formed from the envelope of the individual wavelets from sources on wavefront A. After a time 2t, the wavefront C is the envelope of all the wavel ets produced from sources on wavefront B. The advancing wavefront is therefore always perpendicular to the direction of propagation of the wave. wavefronts A B c wavelet source of wavelet Figure 22.1 Huygens ' wave theory Particle (corpuscular) theory - Newton Newton proposed in 1704 that light was 'shot out' from a source as particles. He believed that the mass of th e source diminished as it releases these particles . • At that time, the diffraction of light had not been observed and Newton argued that since light does not diffract, it cannot be a wave. Also at that time, it was not known that light trave ls faster in air than in water. Newton 's corpuscular theory suggested that it should be faster in water. His argument could not explain why the velocity of light is not higher when coming from bodies of higher temperature. According to accepted theory, higher temperature suggests that the ' particles' should have more kinetic energy. Wave theory - Young Young showed experimentally in 1802 that light from two very narrow slits can produce a pattern of bright and dark fringes on a screen (see later in the chapter). He argued that this was the result of the 'principle of superposition' of light acting as waves. However, Newton's corpuscular theory still lived on, mainly due to his reputation as a dominant physicist and mathematician. Wave theory - Foucault Foucault showed experimentally in 1850 that light travelled faster in air th an in water, contrary to what Newton 's corpuscu lar theory suggested. This seemed at the time to be the deciding factor that tilted the balance in favour of the wave nature of light. 100 22 Concise Revision Cou rse: CSEC· Physics Wave-particle duality - Planck and Einstein M ax Planck in 1900 put forward the quantum theory which combined the wave and particle theories. In 1905 Einstein showed that the phenomenon of photoelectric emission cannot be explained by wave theory, but only by particle theory. On the other hand, particle theory could not explain ph enome na such as diffraction and interference, which wereclearly due to waves. Ein stein had also shown that there is an equivalence between matter and energy in accordance with hi s famo us equation, />,E = />'mc' (see Chapter 34). Today we accept the quantum theory which considers light as particle-like as well as wave-like in nature - each wave pulse is a packet (particle) of energy, known as a photon. Diffraction and interference Diffract ion Diffra<lion I' tl" 'P" "d"'l l\ <II '(> a~ It p, .,s( an edf.!,( (), '()( thruugh J 10. Speed, wavelength, frequency and period do not change as a result of d iffraction. The smaller the wavelength relative to the gap, the lesser is the diffraction (Figure 22.2). The wave length of light waves is extremely small- approximately 5 x 10-7 m for yellow light. This is much smaller than most gaps commonly encountered and therefore the diffraction of light is not usually obse rved - we say that 'light travels in a straight line'. Light will diffract, however, if it passes through an extreme ly small gap. I Small gap Larger gap Edge Figure 22.2 Diffraction through gaps and around edges • Radio waves have the largest wave lengths of the electromagnetic wave group and the refore diffract considerably. This makes them suitable for radio, television and cel l phone communication as well as for radar t racking, because they can diffract around hills and buildings on their route to and from receivers and transmitters . • In the case of sound waves, bass notes have larger wavelengths than t reble notes and therefore diffract more. Similarly, red light has a larger wavelength than blue light and diffracts more. Interference i nterfer ('nlf! i'i the phen()m~{J whirh Ol(UrS <it a point \,h('((' fwo or n'/n(l' \V.JW S "ul)(-'rpos( U/1 each other ladd I to produ( c a comiJlnr>d vlbr.Jl1()n of dt1lplJlude /(l!)!:}er or ~rcat(' than ~HJV uf the indiVidual Wdves, Constructive interference occurs where two or more waves superpose in phase to create a vibration greater than that of either of the individual waves. For a transverse wave, this is can be where two crests or two troughs meet; for a longitudinal wave, it can be where two compressions or two ra refactions meet. 22 Light waves 101 Destructive interference occurs where two or more waves superpose out of phase to create a vibration less than either of the individual waves. For a transverse wave, this can be where a crest meets a trough; for a longitudinal wave, it can be where a compressio n meets a rarefaction. • The resulting displacement at the point of constructive or destructive interference is the sum of the displacements of the individua l waves at that point. • Displacement is a vector quantity and can have positive and negative va lu es. Each wave shown in Figure 22.3 has an amplitude of 5.0 mm. The plane wavefronts represent crests of identical water waves (transverse waves) produced by plane sources 5, and 5, . The circular wavefronts represent compressions of identical sound waves (longitudinal waves) produced by point sources 53 and 5,. Determine the displacement, s, of each of the marked points A to F at the instant shown. Figure 22.3 A: Constructive interference; crest meets crest s; 5.0 mm + 5.0 mm; 10.0 mm B: Const ructive interference; trough meets trough s; -5.0 mm + -5.0 mm; -10.0 mm C: Destructive interference; crest meets trough s; 5.0 mm + -5.0 mm; 0 mm 0: Constructive interference; compression meets comp ression s; 5.0 mm + 5.0 mm ; 10.0 mm E: Constructive interference; rarefaction meets rarefaction s ; - 5.0 mm + -5.0 mm ; -10.0 mm F: Destructive interference; compression meets rarefaction s ; 5.0 mm + -5.0 mm ; 0 mm Coherence Vibrations are coherent if they are in phase or have a constant phase difference . They must therefore have the same frequency. To produce a pattern that demonstrates complete constructive and destructive interference, the following conditions must be met: • The sources must be coherent. • The waves produced must have the same amplitude and shape . . - - -... 102 22 Concise Revision Course: C5EC· Physics To produce an interference pattern for light waves, a single lamp must be used in front of two narrow gaps (5, and 52' as shown in Figure 22.4). If two bulbs were used, they would emit waves randomly and disarra nge the pattern. However, If the smgle source emits randomly, sources 5, and 52 will still be coherent. Young 's double-slit experiment demonstrating the interference of light waves Fig ure 22.4 shows waves from a monochromatic source diffracting through a narrow slit, S, and th en undergoing further diffraction through two other narrow slits, 5, and 5" about 0.5 mm apart. The emerging wavefronts progress towards a translucent screen where they superpose and form an inte rference pattern of bright and dark fringes. The experiment should be performed in a poorly lit roo m. path difference ()..) screen - - - - - . I + 2ie ~ 11/2}. 2nd dark fringe :: ~ monochromatic 1A source \ -,~ - -- - -------- --'- ... ~- ----- S21 +----- 1 m~.- 1st bright fringe '1M 1st dark fringe 0.5 mm 1 2nd bright fringe -- : "::. +-------------2m-------------.1 Die central bright fringe 1/ 2). 1st dark fringe U 1st bright fringe }1/2). 2nd dark fringe 2A 2nd bright fringe Figure 22.4 Young's double-slit experiment A sodium vapour lamp emits only yellow light and is a suitable monochromatic source. Alternatively, a fil ament lamp emitting white light can be used if a colour filter is placed in front of it. Without the fi lte r, however, the various frequencies would produce overlapping fringes and the uniform pattern will not be observed. 5, and 5, are coherent sources since they depend on a common primary source, 5. They emit waves which are in phase, or have some constant phase difference, to produce the pattern of bright and dark fringes observed. Brig ht fringes When the waves from 5, and 5, meet the screen in phase, their path difference is a whole number of wave lengths, 0,1, 1,\, 2,1, 3,1, and so on. They undergo constructive interference and a bright fringe is formed. Dark f ringes When the waves from 5, and 5, meetthe screen exactly out of phase, their path difference is :!- A, 1:!- A, 2:!-A, an d so on. They undergo destructive interference and a dark fringe is formed. 22 Light waves 103 Evidence for the wave nature of light Young's double-slit experiment provides evidence for the wave nature of light, since interference is a phenomenon of waves. Young's e' periment in relation to sound waves The experiment can be carried out using sound waves as shown in Chapter 20, Figure 20.9. Revision questions 1 Briefly describe Huygens' wave theory of light. 2 Which scientist proposed a particle theory of light? 3 a Which theory of light was backed by the experiment performed by Young? b How does Young's experiment support the theory mentioned in part a? 4 a Which theory was backed by the experiment performed by Foucault? b How does Foucault's experiment support the theory mentioned in part a? 5 a Name TWO 20th century scientists responsible for the quantum theory. b What does the quantum theory suggest? 6 a What is meant by the term diffraction? b What condition is required for strong diffraction? c Why is the diffraction of light waves not generally observed? 7 a What is meant by the term interference? b Sketch wavefronts to show how waves from two plane sources can interfere. Mark a point C and a point D where there is constructive and destructive interference, respectively. C If the amplitude of each wave in part b is 2 mm, what is the amplitude at each marked point? 8 This question is about Young's double-slit experiment. a Why is it not possible to use two separate lamps as the light sources? b Why is it not possible to use a source of white light without a colour filter if complete destructive interference is to be observed? c What can you say about the path difference between waves that produce a bright fringe on the screen? 104 22 Concise Revision Course: CSEC' Physics I""" 23 Light rays and rectilinear propagation I I A r(l,~ uf /Jf!,ht A 1)('.1 m )/ II) 'he lir(>('lnt In 1if!,'lt , ... tr ~1, (I I \1 I I/~n 'ei, IIJ.;ht pr }Ila' (I (f afL c; \ Sha dows Sh a dow produced by a point source of light Light travels in straight lines and therefore a shadow is formed when an opaque object obstruct its path (Figure 23.1). white screen 1rJ ~ L8J : l=J ~ : object A umbra - total shadow of uniform obscurity and sharp edge, indicating that light travels in straight lines B bright front view point souree of Ii ght of screen Figure 23.1 Shadow produced by a point source of light Sha dow produced by an extended source of light Alam p in a box with a large hole acts as an extended source of light. The hole can be interpreted as seve ral point sources, each casting a shadow which overlaps with the shadows from the other neigh bouring point sou rces. There is an umbra and a penumbra, as shown in Figure 23.2. white screen ~ ~ :;r "l ~d r extended source of tight - -----. - -- -- · A umbra - total shadow of uniform obscurity A B B penumbra - partial shadow gradually becoming fainter towards its outer edge C bright C front view of screen Figure 23.2 Shadow produced by an extended source of light Ecli pse of the Moon The Moon is a non-luminous body and is the refo re seen from the Earth by reflection of lig ht from the Sun. The orbit of the Moon usuall y passes outside of the Earth's shadow, but at times it travels through the cone of shado w, as shown in Figure 23 .3. When this hap pens, light from the Sun can no longer reach the Moon and there is a lunar eclipse. The f ull Moon is eclipsed (obscured). It can take more than l V, hours before it emerges fro m the other edge of the shadow. -., MOON EARTH " .... \ eclipsed Moon SUN ,, umbra Moon's orbit Diagram not to scale Figure 23.3 Eclipse of the Moon 23 Light rays and rectilinear propagation 105 Eclipse of the Sun At tim es the o rbit of th e Moon ca n pass directl y thro ugh th e lin e joining th e Sun to the Earth, as in Figure 23.4. When thi s occ urs, th e M oo n's umb ra reaches the Earth 's surface ove r a small reg io n, fro m whi ch a to tal solar eclipse can be obse rved . People in th e penumbra will obse rve a p artial ecl ipse. The Sun as viewed from POints on Earth: A no eclipse umbr SUN ~ ~a ~ " =: ~ penumbra B A B partial eclipse C total eclipse MOONQ C D partial eclipse E EARTH E no eclipse Diagram not to scale Figure 23.4 Eclipse of the Sun The pinhole camera When an o bj ect is placed in front of th e pinhole camera show n in Figure 23.5, an inve rted image is fo rm ed o n th e translucent screen. Sin ce light travels in a straight line, rays f rom any po int o n th e o bject have o nly one possible path into th e box, and consequently only one po int at whi ch th ey meet th e sc reen. A focused, real, inverted im age is th erefo re always produced . small hole in front face of box ~ <r translucent screen focused, reat, inverted image object Figure 23.5 Formation of an image b y a pinho le ca m era • Th e image becomes smaller on increas ing the di stance of the object from th e box, beca use th e rays enter at a smaller angle. • Th e image becomes larger on increas in g th e depth of the box, because the rays spread mo re before reaching the screen . • If th e ho le in the front face is made large r, th e image becomes: a blurred due to the formation of several overl apping images b brighter due to th e increased light intensity entering the box. 106 ""'" 23 Concise Revision Course: CSEC· Phys ics Revision questions 1 Define: a a ray of light b a beam of light 2 State the property of light responsible for the formation of shadows. 3 Draw ray diagrams to represent the formation of each of the following. a The shadow produced by a point source of light b An eclipse of the Moon (lunar eclipse) C 4 An eclipse of the Sun (solar eclipse) Draw ray diagrams to show the formation of the image in a pinhole camera for each of the following cases. a The camera focusing an image of an object b The effect on the image of increasing the size of the hole c The effect on the image of moving the object further from the camera d The effect on the image of making the box deeper 23 Light rays and rectilinear propagation 107 24 Reflection and refraction Reflection Laws of reflection • TIn· 111( pO ll It ident ra}~ fhe rc{/(!{ ted r.n .mel lIu· (1ort"al at (d inc ic/('ncc are 01. the ~am(' rh!' plan('. • The an~ :It ()f lI1odC'ncc /s equal to the angh' of rC'fll'cif()n (Figure 24.1) . Characteristics of the image formed a plane mirror In Figure 24.1 The laws of reflection 1. Same size as object 2. Same distance perpendicularly behind the mirror as the object is in front 3. Virtual 4. Laterally inverted Virtual means not real- the image cannot be formed on a screen, and light does not come from where the image appears to be. Laterally inverted means reversed side to side, so that the image of a word placed to face a mirror is reversed as shown: Reflection ray d iagrams us ng point objects • Draw a line to represent the mirror and place a small dot to represent the point object in its correct position to scale on the diagram. • Place the point image in the diagram the same distance perpendicularly behind th e mirror as the point object is in front. A faint construction line, perpendicular to the mirror, is useful here. image image ~ ~ ." - ~ - ~ ~ object "'::.::::: ;? eye mirror mirror eye image object ...,-- - - - - - - - :7' ' ~: • Draw an eye at the location from which the image is viewed. .. "':::::.: • Draw two rays from the image to the edges of the eye (use broken lines behind the mirror). eye • Draw two more rays, this time from the object, to where the first two rays intersect the mirror. See Figu<e 24.2 for mirror Figure 24.2 Examples of reflection ray diagrams some examples. 108 24 Concise Revision Course: CSEC' Physics ~_ '" object Refraction La ws of refraction • The InCIdent fa}" the (('{ra( led ny and the • The ratIO sm f is d cOJ1."tanllOi d nOfmd/, gll.'('n [Jdlr 0/ al the pOint media, \vhl'(e j r angle of refraclion. This is Snell's law, see Figure 24.3. IS or in( 1(}(,I1C(> are on Ih, ' ~am( f}lanp Ih( dnb /( oj Inu(/encc Jnd r I" the S1I1 medium 1 ~= sin r ......... constant medium 2 ........................ Figure 24.3 Snell's law of refraction Refractive index, 7) F"Jf light trJ\'( WrIt} from on( mcdlUn 1 to another, thp (dUO ~;s ~ I }('UlUm relalll·" lu the 11f,1 the refrJu;" e indcli 01 (hi '!,('(ond ~In liJ)T12 r sin i 711 sin r Fo r light travelling from one medium to another, the ratio speed in medium of incidence speed in medium of refraction is also equal to the refractive index of the second medium relative to the first: 1J1 vr Table 24.1 Refractive indices of common materials w ater 1.3 glass 1.5 Deviation on passing from one medium to another Wh en light enters a second medium perpendicular to its interface (Figure 24.4(a)): • it does not deviate - the angles of incidence and refraction are both zero • its speed is greater in the less optically dense medium. Whe n light ente rs a more optically dense medium other than perpendicularly (Figure 24.4(b)): • it refracts towards the normal, that is the angle between the ray and the normal decreases • its speed decreases. 24 Reflection and refraction 109 When light enters a less optically dense medium other than perpendicularly (Figure 24.4(c)): • it refracts away from the normal, that is the angle between the ray and th e normal increases • its speed increases. Figure 24.5 shows light being deviated as it passes through triangu lar prisms. denser medium denser medium a b denser medium c 60' Figure 24.5 Deviation through triangular prisms Figure 24.4 Deviation of light passing between media of different optical density Refraction ray diagrams using point objects in the denser medium The rules for drawing these ray diagrams are baSical ly the same as for reflection diagrams. Figure 24.6 shows how they ca n be applied. • Drawa line to represe nt the interface between the media and place a sma ll dot to represent th e point object in its correct position on the diagram. • Place the point image in the diagram. An estim ate will be sufficient here unless the exact position is given. An imaginary lin e connecting the object and the image is perpendicular to the interface. The image is closer to the interface than is the object. • Draw an eye at the locati on from which the im age is viewed. • Draw two rays from the image to the edges of the eye (use broken lines before they reach the interface). • Draw two more rays, this time from the object, to w here the first two rays intersect the interface. straight rod appears crooked 7 r- ~ -_I image _
object Figure 24.6 Examples of refraction ray diagrams Refraction through a rectangular glass block Figu re 24.7 shows the path of a ray through a rectangular glass block. The net deviation, D , is zero sin ce the clockwise deviation, d is equal " in magnitude to the anticlockwise deviation, d,. The emergent ray is parallel to the incident ray and th erefore the angle of emergence is equa l to the ar;gle of incidence. There is a lateral displacement, x. 110 24 Concise Revision Course: CSEC' Physics AIR transparent medium , deviation D = dl - d2 = 0 'V' , Figure 24.7 Refraction through a rectangular transparent block Ca lculations Figure 24.8 shows th e typ e of diagram th at is he lpf ul when tackling a refracti o n problem. e, medium 1 fJ = refractive index (J == '" medium 2 0, v == angle between the RAY and NORMAL speed 112 ~= sin 0 1 Vj si n 8 r = V. v, Figure 24.8 The re lation shown in Figure 24.8 can also be written as: 1Jy sin Ox 17: = sin v, By = ~ w here x and y represent the two media. It is helpful to use subscripts relevant to the media in order to re duce errors of substitution, for exampl e Vg for th e speed in glass or '1" for th e refractive ind ex of wate r. Note that the ratio of refracti ve ind ex has it s subscript s reve rs ed wh en compared with the othe rs ratios. (Speed of light in air = 3.0 x 10' m s· '; use the data for refractive indices from Table 24.1.) Light enters water from the air above at an angle of incidence of 60°. Determin e: the angle of refraction a b the speed of light in water. e sin e, sin e sin a w w sin 60 '1, '1w 1 1.3 sin 60 b ~3;-.0:xc,1" Vw 1 B = -1.-3 3.0 x 10' 2.3 X 10' m S· l 24 Refl ection and refraction 111 Determine the angle of inci dence o n the glass su rface shown in Figure 24.9. (Use th e data for refractive indices from Tabl e 24.1.) .-, ~- You must use the angle between the ray and the normal T GLASS Figure 24.9 sin 0, 1.5 - -- = sin40 1.0 sin 0, = 1.5 sin 40 °, = 75° Dispersion The di"iperslOIJ (d \\ 'lite hgh IS the s(!/ }(,lllon 0'- \\'17,((' flrhl mlo ib (on! iruL'nl c%urs. Figure 24.10(a) shows the set-up of an expe riment originally done by Newton. A narrow beam of wh ite light from a double slit co llim ator is incident on a glass prism. On entering the prism, the light waves refract and each colour is deviated differently. Red refract s least, and vio let most. The beam therefo re sepa rates, and th e emerging light forms a visible spectrum on a w hite screen: red, orange, yellow, green, blue, indigo, violet (ROYGBIV). Newton was first to dem o nstrate that white light can be separated in this manner. Note that a wide incident beam will produce seve ral ove rlapping spectra which will recombine to form white light. A rainbow is produced when white light is dispersed in this way by water droplets in the sky. narrow beam of white light visible spectrum on a white screen '" double slit collimator source of white light ~ "-\ \ \\ a Separating the colours b Individual colours cannot be further separated AU corou.rs erner.ge in a parallel beam } recombining to produce white light white light white screen c Recombining the colours • Figure 24 .10 Newton's experimen ts with white light and prisms 112 24 Concise Revision Course: CSEC· Physics Newton made a number of changes to the expe rim ent in order to prove that th e origin of the coloured light was not within the prism. He: • changed the size of the slits of the co llimato r • used prisms of different types • altered the distance between the light sou rce and the prism • isolated a colo ur and showed that it was not affected by another pri sm (Figure 24.10(b)) • added a second prism to show that the co lours can be recombined (Figure 24.10(c) ). Newton's experim ents proved that white light was a co mbination of light of different co lours. Hi s approach is to be co mmended since he experim ented rath er than simply th eorised. I Critical angle and total internal reflection Figure 24.11 shows that light directed into a medium of lesse r o ptica l density (s mall er refractive index) is partl y reflected and partly refracted. At small angles of incidence the reflected ray is wea k and th e refracted ray is strong. As th e angle of incidence in creases, th e angle of refraction also in creases, and the reflected ray becomes slightly stronger. At a ce rtain angle of in cidence, c, th e refracted ray passes just along th e surface, and for angles greater than thi s critical angle, there is total internal reflection. LESS DENSE MEDIUM (smaller refractive IndeK/greater speed) strong C total internal reflection C -', .~ . ". x>c weak DENSER MEDIUM Figure 24.11 Critical angle, c, and total internal reflection for incident angles greater than c Two ways to define critical angle • The critic .JI angle l11prlll.lfl , 0/.1 In oj ... mall ~r lenal is 'he Iclr~t·_ .. t .In,~/f'l \\/1/(1I (dV (,If Ipproac/-' :Jn mtcli1(C \ /111 d rl'llcl( 1/\ ( rndl:\ and /)( ref, (ted mto JI • hf~T (rit;ccll angft' of I m,JtcfI. 'i.., OH sfl)JiI ~ , aT .,/t .• If \\ 'lI' h d r.'\ <- n apr: r). mCdlll11l oj smallt" n fr~(l\ E mdl,( and hl (01<111\ Ifllcrna/ly It flec' ,i 1)\ it. (11 , tnt 1<1( \\ IC 1 a Conditions necessary for total internal reflection • The ray must approach the second medium from one of greater refractive index, that is from one in w hich its speed is less. • The angl e of approach mu st be greater than the criti ca l angle. 24 Reflection and refraction 113 The mirage During the day the temperature of the air directly above the surface of a road increases due to conduction of heat from th e asphalt. A ray of light from low in th e sky will refract away from the normal as it enters the hotter, less dense air (Figure 24.12). The deviation continues until the ray is totally reflected just above the road. It is then continuously refracted towards the normal as it enters the cooler, denser, air above. An observer receiving this ray will see a virtual image of the sky and may interpret it as a pool of water. blue sky cool air less dense hot air --- ---~ ~ hot road surface virtual , inverted image of blue sky Figure 24.12 Formation of a mirage Viewing from above a water surface Figure 24.13 shows a light source at the bottom of a large swimming pool. When viewed from above, one would see light leaving the water from within a circle of a certain diameter, d. Rays reaching the surface outside of this circl e are totally internally reflected, because their angles of incidence are greater than the c ritical angle (x > c and y> c). reflection from surface reflection from floor light bulb Figure 24.13 Viewing a light on a swimming pool floor from above the water surface Relation between critical angle and refractive index If one of the media is air, as in Figure 24.14, then the relation is: sin sin ex 7J a sine a ==11; sin c sin 90 == 1 IJ; 1 C = - 1) AIR I s;nc 1 = 1 n, I c MEDIUM X Figure 24.14 Relation between critical angle and refractive index If neither medium is air, or if the question involves wavelength or velocity, then this general relation is used: sin , v, e sin ey 114 1 24 Concise Revision Course: CSEC· Physics One of the angles is 90° and the other is the critical angle, c. The critical angle is always in the medium in wh ich the wave travels with lesser speed - for light, thi s is th e more optically dense medium. Note that, if the critical angle or the refractive index of a materia l is referred to without mention of the second medium, it can be assumed that it is relative to air. The light bulb under the water in Figure 24.15 produces an illuminated disc on the water su rface of diam eter 20 m. The refractive index of water is 1.33. AIR r;lOm -- -------- ,. c h WATER Figure 24.15 Calculate: a the critical angle of water a . b the depth of the water 1 Sin C = - '7 . 1 Sin C= - - 1.33 c = 48.8' = 49° to 2 sig. fig. b r h tan c = - 10 tan 48.8 =h' 10 tan 48.8 h = --=-=- h = 8.8 m Applications of total internal reflection Optical fibres light entering through one end of a thin, transparent, glass fibre will mainly be totally internally reflected until it emerges from the other end (Figure 24.16(a)). This is the principle of an optical fibre. Scratc hes on the outside of the fibre could cause light to exit through the sides. A cladding of a different type of glass is placed around the core in order to protect it (Figure 24.16(b)). Since the light is transmitted through the core, scratches on the outside of the cladding are unimportant. For total inte rnal reflection, the refractive index of the cladding must be less than that of the core. @= light thin. flexible, fibre a of pure glass b claddin g core (greater refractive index) cross-section through cladded fibre Figure 24.16 An optical fibre 24 Reflection and refraction I 115 Optical fibres have the following uses: • Telecommunications: Electro ni c communications for cable TV, telephone and th e internet are largely transmitted by mea ns of light pulses in fibre-optic cables. • Endoscopes 1. Diagnostic imaging: Light is transmitted into th e pati ent through a bundle of optical fibres. The reflected light then returns throu gh anoth er bundl e of fibres connected to a video ca mera whi ch displays th e image on a screen . 2. Therapy: Tumours in solid organs are difficult to remove by surgery. A laser beam can be directed to destroy such tumours by means of o ptical fibres. Reflecting prisms A mirror reflects only about 90% of the light incident on it. Utilising total internal reflection in o ptica l devices allows 100% of the radi ation to be reflected and therefo re produ ces a stronger image. Rightangled, isosce les-triangular glass prisms are used in many optical instrum ents, such as periscopes and binoculars, to refl ect light (see Figure 24.17). When light enters the prism perp endicularly through one of th e shorter sides, it meets th e opposite wall at 45°. This is more than th e c ritical angle of glass (42°), and therefore there is total internal reflection . In Figure 24.17, all angles angles are either 90° or 45°. The medium around the prism s is air. turning through 90 Q turning through 180 0 turning through 180 0 periscope Inverting prism used in binoculars . Note how the incident rays are flipped when they emerge from the prism . Figure 24.17 Reflecting prisms 116 24 Concise Revision Course: CSEC· Physics Revision questions Use this data: speed of light in air = 3.0 x 108 m s-' speed of light in water = 2.3 x 10 m s-' 8 refractive index of glass =1.5 refractive index of air = 1.0 refractive index of water = 1.3 1 State the laws of reflection. 2 A point object is 3.0 cm in front of a plane mirror. Sketch a ray diagram using TWO rays from the object to indicate how an eye can view the image in the mirror. 3 State FOUR characteristics of the image formed in a plane mirror. 4 State the laws of refraction. 5 Light enters water from air at an angle of incidence of 40°. Determine the angle of refraction. 6 What phenomenon of light is associated with each of the following? a Glare is produced by the white sands of Caribbean beaches. b The depth of the water above a coral reef appears less than it actually is when viewed from a fishing boat above. 7 Light travelling in air enters a liquid of refractive index 1.4. Determine its speed in the liquid. 8 Sketch a diagram to show a ray of light passing obliquely through opposite faces of a rectangular glass block. Indicate the angle of deviation as it enters and leaves the block and comment on the net deviation and the lateral displacement of the ray. 9 With the aid of a diagram, explain the formation of a mirage. 10 Sketch a ray diagram to show why a straight pencil appears crooked when partly immersed in a bowl of water. Your diagram should include TWO rays from the lowest point on the pencil. 11 Sketch a diagram to show how white light can be dispersed using a triangular glass prism. 12 State a natural phenomenon that demonstrates the dispersion of white light. 13 Name the scientist who concluded that white light is a mixture of several colours. 14 Determine the critical angle of glass of refractive index 1.5. 15 Determine the refractive index of a material that has a critical angle of 35°. 16 For light travelling in glass towards water, calculate the maximum angle of approach for which there can be refraction into the water. 17 The speed of light in medium M is 1.8 medium M with respect to air. 18 A bright bulb is at the bottom of a swimming pool of depth 2.0 m. Calculate the diameter of the disc through which light emerges at the surface. (HINT: First calculate the critical angle of water.) 19 State TWO uses of optical fibres. 20 Sketch a diagram showing how a ray of light can be reflected by a single right-angled isosceles glass prism (critical angle 42°), through a 90° X 108 m s-' . Determine the critical angle of b 180° 24 Reflection and refraction I 117 25 Lenses • A l ens I .... .1/1/('( (' (),- .... I){'cial~ ··.hl/l( (Ilr In"part'nt mal('/it/lt}),}l (.In !fJrm f(JC lJ':i{ (/ fln.~'S • i\ ('011\'(>,\ Of nmH·rJ.: ;ng /(.n.... I' one th.ill . . . thicker.1l pr()c/un c1 j"(·lll/nl,lg('. Ih «'ntre It (.Ill ()fJ\;'I~ • r\ (O'K,1\.'(' ()t dh'erging len ... '." onr" fry, produ( ( \ ir lhlllt1.d,gf' It, ('/I'I'( It • I I" tIJ1f11H r ell {he' op tical «('111ft', O. ( i.l 1{>11 .... '",PC /1J!.un· 1.3.1, IS the pOInt 1111 fav . . p,/~ . . \\'lIhnut r/{'\-;dflOfL at C.1Il ril\ (,['( p.l/.ilh e)J {)iJjcof ''\. I rar" f)llighl tf) !"l{aIILI (ws ( f Iigl ! 'n the ('Ill .....• of It,( lens thr )u,r,h 1\ /l1d, • The principal (ui ,-; o{ a lens IS tilt' /in{' tlld! p<l . . .'iv ... tllIllugh IC"" optlc,)1 «(,flln mel I.') f1erpencli( tll.1I tf) the I~l( (,s o{ til(' len ... • Thc ' pr;no'pcJl fo (u\ , I; of a /el S I.'" tIl( [)(lint Of rh(" print '/J,tf <lX/S thr~(lb 1\ hit/, .tli r..J\'\ p.1rc,//p/.lf1rt c/()~ 10 tilt' ,ni", (rJI1VL'/gt', Of irUln \'\ hfch the) ...1fJfJ( 'f to (JJ\ '('fl:!C', 'j('ef pa')sin u throug,h tin I('nt.;_ len.;:, i, til(' di . . tanc(' bel ~\ • The inca/length, f. ()i~., • The focal plane ()j" c/ /('n~ principal {oc t/,C;. i~ ('('11 t/)( ,"'lIr/~t()fJ1 II .. uptical c('nln' ,}f)d if pflf1(Jpall()[ 'J':,. ul.1f to it<, principdl ,Hi.'" .uHI «()n/cllning itt.; ,,-, focal plane focal plane / principal axis I .... ! principal aXIS \1 focal length focal length • CONVEX LENS b CONCAVE LENS Figure 25 .1 Terms used with lenses Parallel rays focus on the focal plane even if they are not parallel to the principal axis - see Figure 25.2. In order to determine where the rays focus, draw an in ciden t ray straight through the optical ce ntre to a point on the focal plane. Then connect the other parallel rays, after passing through the lens, to the same point. focal plane ~ Incident parallel rays ,, ,,, , principal axis focal length Figure 25.2 Parallel rays focus on the focal plane 118 25 Concise Revision Course: CSEC· Physics Magnification Magnifica tion, rn, is Ihe ratIO of tIl(' 'i/ze oltho imJMc (0 fl1ec;lLc or the nhjccl. magm'f'lea t'Ion = image height object height I m =- magnl.f"Icatlon = ..cd".i'-st'-'.a'--n..cc-'e_o"f,-i...,m_a.....g"e"f,-r-'o_m---:-Iec..n-,s,distance of object from lens o v m =u Th erefore I v u -=- o An object of height 2.0 cm, placed 40 cm in front of a convex lens, produces an image of height 8.0 cm. Det ermine: a a the magnification b the distance of the image from the lens I m=- o 8.0cm m=--2.0cm m=4.0 b v m=u 4.0=_v_ 40cm v = 4.0 x 40 cm = 160 cm Determ ining the focal length of a converging lens A converging lens is mounted as shown in Figure 25.3. The distance between the lens and the object (a small gap with crossed wires) is altered until a sharp image is observed next to the object. Light from the object almost retraces its path after reflection from th e mirror, and the parallel beam focuses at the principal focus. The distance between the centre of the lens and the object is therefore the focal length of the lens. object (gap with crossed wires) image of crossed wires mirror focal length Figure 25.3 Determining the focal length of a converging lens 25 Lenses 119 Real and virtual images Rt,tll imag(" It 1'1')5(' prOdULC c t I pC" # I.) \\ I lell "[,1)( rd\ <;; con\ (r ~( See Tables 25.1 and 25.2. Table 2S.1 Examples of real and virtual images Examples of real images ••• image produced on the retina image produced in a mirror image produced in a camera image produced by a convex lens acting as a magnifying glass image produced on the screen at the cinema image produced by a concave lens Table 2S.2 Features of real and virtual images of real objects produced by a lens .. • •• Virtual images formed by lenses can be formed on a screen cannot be formed on a screen are produced by the convergence of rays are produced due to the divergence of rays are located on the side of the lens opposite to the object are located on the same side of the lens as the object are inverted are erect Constructing scale diagrams Convex lenses 1. Draw two perpendicular lines to represent the principal axis and the lens. 2. Place points, F, to scale in pOSition, to represent the principal foci. 3. Draw the object to scale, in size and position, to stand on the principal axis. 4. Draw lines to represent the following rays from the top of the object: • parallel to the principal axis, and then through F after passing through the lens • straight through the optical centre. S. Where the rays cross represents the top of the image. Draw the image from the principal axis to this point. See the examples in Figure 25.4. The points 2F have been included in these diagrams to provide a better understanding of how the position of the object affects the characteristics of the image. These points, however, are unnecessary for the construction of the scale drawing. 120 2S Concise Revision Course: CSEC· PhYSics CAMERAjEYE o 2F object distance"" image distance object height = image height o 2F 2F F PROJECTOR o F 2F 2F o 2F " 2F F ' ~ ~, I I I I I no localised image: image at infinity , , '''', " " MAGNIFYING GLASS ", I I I 2F This is the only case where the image is virtual and erect. 2F The distance of 0 from the lens must be less than the focal length . eye Figure 25.4 Ray diagrams for several object positions relative to a convex lens Concave lenses The method used is similar to that for convex lenses with one exception; the ray which is parallel to the pri ncipal axis until reaching the lens is then divergent, appearing to come from F on the same side of the lens as the object. See the examples in Figure 25.5. 25 Lenses 121 Characteristics of the image formed in a concave lens • Smaller than the object • Closer to the lens than is the object • Virtual • Erect F Figure 25.5 Ray diagrams with a concave lens Important rays for lens diagrams Figure 25.6 summarises the rays used to construct image positions. CONVEX ~ . ---<1>---+--=-0F CONCAVE F I F----::::::::::: ~ •f -F F F Figure 25.6 Important rays for lens diagrams The lens formula 1 1 1 -+-=- u v f u = distance of object from lens: + if real, - if vi rtual v = distance of image from lens: + if real, - if virtual f = focal length: + for convex, - for concave Look back to Table 25.2 for features of real and virtual images of real objects produced by a lens. 122 25 Concise Revision Course: CSEC· Physics A need le is placed with its length perpendicular to the principal axis of a convex lens of focal length 10 cm. Determine the nature and orientation of the image, as well as its position relative to the lens, when it is placed at each of the fo ll owing points: a 25 cm from the lens a 1 b 4.0 cm from the lens 1 1 u v f 1 1 1 -+-=25 v 10 1 1 1 -=--v 10 25 -+- =- 2. = 0.060 v 1 . f. v=--= 16.7 cm = 17 cm to 2 slg. Ig. 0.060 Since v is positive, the image is real, inverted and on th e side of th e lens opposite to that of the object. 1 1 1 - + - =u v f 1 1 1 - +-=4.0 v 10 1 1 1 -=- - v 10 4.0 1 - = - 0.15 v 1 v= - - =-6.7 cm - 0.15 Since v is negative, the image is virtual, erect and on the sa me sid e of the lens as the object. b A concave lens of focal length 12 cm is placed 16 cm in front of a thin rod placed perpendicular to its principal axis. Determine the nature, orientation and position relative to the lens, of the image it produces. 1 1 U v 1 f -+- =- ...:!... + 2. = _1_ (focal length of concave lens is negative) 16 v -12 111 -=-+-v -12 -16 1 7 =- v 48 v = - 6.9 cm to 2 sig. fig. Since v is negative, the image is vi rtual, erect and on the same side of the lens as the object. 25 Lenses 123 Revision questions 1 Define each of the following with respect to lenses: a convex lens b concave lens C focal length d principal focus e optical centre. 2 Draw ray diagrams to show how an image is formed by PARALLEL RAYS on the focal plane of a converging lens for each of the following situations. a Rays parallel to the principal axis b Rays not parallel to the principal axis 3 An object of height 5.0 cm is placed 20 cm in front of a converging lens and produces an image which is 50 cm from the other side of the lens. Determine: a the height of the image 4 Define the following, giving TWO examples of how each may be formed: a a real image b a virtual image 5 State TWO differences between the properties of the images produced by an object placed in front of a convex lens at a distance greater than its focal length and closer than its focal length. 6 An object of height 2.0 cm is placed in front of a convex lens of focal length 20 cm. Construct scale diagrams to determine the nature, size and position of the image when the object stands perpendicular to the principal axis at the following distances from the lens. (The vertical and horizontal scales in your diagrams may be different.) a 50 cm 124 b the magnification b 10 cm 7 An object of height 3.0 cm stands perpendicular to the principal axis, 7.0 cm in front of a concave lens of focal length 10 cm. Construct a scale diagram to determine the nature, size and position of the image. 8 An ant is 5.0 cm in front of a convex lens of focal length 12 cm. State the nature of the image formed and determine its position. 9 If the lens in question 8 is replaced by a concave one, what is the new nature and position of the image? 25 Concise Revision Course: CSEC· Physics Exam-style questions Chapters 19 to 25 Structured questions 1 a) i) List FOUR types of electromagnetic wave, in order of increasing wavelength. (2 marks) ii) Complete Table 1 of the sources and uses of two types of electromagnetic wave. Table 1 Type of wave Source radio gamma (4 marks) iii) Which of the waves in Table 1 diffracts least? (1 mark) b) Calculate the wavelength, in a vacuum, of X-rays of frequency 1.5 x 10" Hz. (Velocity of electromagnetic waves in a vacuum (2 marks) = 3.0 x 108 m s-' ) c) A ray of yellow light from a sodium vapour lamp travels in air until it enters a prism of critical angle 39°. The angle of refraction in the prism is 33°. Determine: i) the refractive index of the material of the prism with respect to yellow light (3 marks) ii) the angle of incidence on the prism . (3 marks) Total 15 marks 2 (2 marks) a) i) State the laws of reflection of light. ii) List THREE characteristics of the image formed in a plane mirror. (3 marks) b) The wave shown in Figure 1 has a velocity of 4.0 m s-' . Determine its: i) amplitude (1 mark) ii) period (1 mark) iii) frequency (2 marks) iv) wavelength. (2 marks) v) Comment on whether the wave would diffract slightly or extensively when passing through a gap of widt h 25 m. (2 marks) displacement/m '"P o ~V o A 120 time/s Figure 1 c) Sketch a diagram showing the form of a transverse water wave. Identify the following on the diagram: i) the direction of vibration of the water particles (1 mark) ii) the d irection of progression of the wave. (1 mark) Total 15 marks Exam -style questions - Chapters 19 to 25 __- --I 125 I I Extended response questions 3 a) Describe, with the aid of a diagram, the Young's double slit experiment which produces an interference pattern of light waves. (6 marks) b) Rihanna and Mechka, two dedicated CSEC students, stand 60 m in front of a tali, vertical cliff of rock. Rihanna claps two wooden blocks at such a rate that the returning echo coincides with each succeeding clap. Mechka times the interval for 20 echoes to return and finds it to be 7.0 s. (5 marks) i) Determine the speed of sound from this data. ii) Predict how this result would change if the blocks were clapped with greater force, producing a louder sound. (1 mark) iii) The teenagers then see a flash of lightning, and 6.0 seconds later a loud crash of thunder startles them. How far are the girls from the thunder cloud? (3 marks) Total 15 marks 4 a) Describe an experiment to determine the focal length of a converging lens. (6 marks) b) A thin nail is placed 20 cm in front of the plane of a converging lens of focal length 15 cm. The nail stands perpendicular to the principal axis of the lens. i) Determine the distance from the lens at which a screen can be placed to produce a focused image of the nail. (3 marks) ii) Is the image real or virtual? (1 mark) iii) Is the image erect or inverted? (1 mark) The height of the nail is 5.0 cm. Calculate: iv) the magnification (2 marks) v) the height of the image. (2 marks) Total 15 marks 126 Exam-style questions - Chapters 19 to 25 26 Static electricity Introduction to electric charges • All matter contains positive and negative electric charges. • In liquids and gases, the positive and negative charges can be mobile. • In metals, the negative charges (electrons) can be mobile and the positive charges remain fixed. • Neutral bodies have the same amount of positive and negative charge and these therefore cancel. When sketching diagrams of charged bodies, usually only the excess charge of any region is shown. • Electron flow is opposite in direction to conventional current flow (see Chapter 27). • The term earth refers to a large body that can provide electrons to, or take electrons from, another body and still be considered neutral. • Electrostatic induction is the process by which electrical properties are transferred from one body to another without physical contact. Charging by friction Figure 26.1 shows a glass rod and a polythene rod being rubbed by a dry cloth. Electrons transfer from the surface of the glass rod onto the cloth, leaving the glass with excess positive charge and the cloth with excess negative charge. Electrons transfer from the cloth onto the surface of the polythene rod leaving the polythene with excess negative charge and the cloth with excess positive charge. glass rod polythene rod Figure 26.1 Charging by friction Demonstrating attraction and repulsion Two balls, each about 6 mm in diameter and made of compressed aluminium foil, are each suspended by a thin nylon thread. O ne ball is allowed to momentarily touch the positive terminal, and the other, the negative terminal, of a battery. The balls become charged, positively and negatively respectively, by contact. A glass rod, charged positively by friction, is brought near to each of the balls (Figure 26.2). It will be observed that the pos itive rod attracts the negative ball but repels the positive one. Similar charges repel. Unlike charges attract. charged glass ro d charged glass ro d + + + + + + + + + attraction repulsion Figure 26.2 Similar charges repel and unlike charges attract 26 Static electricity f 127 A charged body can attract an uncharged one A charged polythene rod brought near to a sma ll piece of paper wi ll attract th e paper as shown in Figure 26.3. Electrons in the paper are repelled by the negative ly charged polyth ene, leaving a net positive charge o n the side o f th e paper nearest to the rod. Since th e positive charges of the paper are close to the negative polythene, the attraction is stro ng and the paper jumps onto the rod. In humid Caribbean regions th e paper will not stick to the rod fo r long. Electrons from the rod will condu ct to the paper through th e layer of moisture that coats the rod, and th e positive charge on the paper reduces so that the attraction is insufficient to support its weight. charged polythene rod \ ++ + + + + paper jumps onto rod Figure 26.3 A charged body can attract an uncharged one Charging a metal dome by induction A metal dome can be charged negatively by induction usin g a positively charged rod. See Figure 26.4. 1 3 2 4 + 5 + t electrons A neutral metal dome rests on an insulating stand. A positively charged rod brought The dome is earthed, allowing NEAR to the dome attracts electrons, leaving excess positive charge on the opposite side. electrons from earth to cancel the positive charge on it. The negative charges are held fixed by the rod. The earth wire is removed without moving the rod. The rod is removed, allowing the electrons to repel each other and to spread out uniformly. Figure 26.4 Charging a metal dome by induction The final charge on the dome is opposite to the inducing charge. By a simi lar procedure, a negatively charged rod ca n be used to charge the dome p os itively. This is d iffere nt from cha rgin g a metal dome by contact - see Figure 26.5. 1 2 3 The contact method produces a charge of the same sign to the charge producing it. A neutral metal dome rests on an insulating stand. A negatively charged rod is rolled over the dome. The repulsive force between the electrons within it causes them to transfer onto the dome. Figure 26.5 Charging a metal dome by con tact .... 128 26 Concise Revision Course: CSEC· Physics The rod is removed. Hazards of static charge Lightning A cloud becomes charged due to friction between layers of air and water molecules rising and falling within it. The base of the cloud usually becomes negatively charged and the top positively cha rged, as shown in Figure 26.6. Sparks occur between opposite charges within the cloud. The negative charge on the base of the cloud repels electrons further into the ground below, resulting in a net positive charge accumulating at the surface of the Earth. When the potential difference (see Chapter 27) between the base of the cloud and the surface of the Earth is sufficiently large, electrons and negatively charged ions (heavier charged particles) will rush from the cloud to the ground. These high· speed particles crash into air molecules, knocking electrons o ut of them and creating pairs of oppositely charged ions. The result is an avalanche of positive and negative ions, which rush to the cloud and the Earth respectively. The discharge current can be as high as 20 000 A. Electrical energy transforms into heat and light energy (lightning) which transforms further into sound energy as the air rapidly expands, increasing the pressure and producing a sonic shock wave - thunder. + + + + + riSing and falling air within cloud - ai r molecules ionised on collision + t - + + - +- l EARTH + ~ -_ ++++++++ t electrons Figure 26.6 Lightning Charges from fabric in the seats of vehicles The occupants of a vehicle usually become charged by friction with the fabric of the seats, especia lly in dry regions. When someone gets out of a vehicle to operate a gasoline pump, a spark may jump between the person's body and the metal nozzle of the hose, producing a flash fire through the flammable vapour. It is therefore advisable to discharge oneself immediately on exiting the vehicle by touching the metal body of the car. Useful applications of static charge Lightning conductors Figure 26.7 shows a lightning conductor protecting a tall building from the danger of a lightning strike. The negative charge on the base of a nearby cloud induces opposite charge at the spikes, by repelling electrons down the copper str ip and into the ground. The positive charge at the spikes is very concentrated due to their sharp curvature and this ionises nearby air molecules by ripping electrons from them. The positive and negative ions produced, rush to the base of the cloud and to the sp ikes respectively, cancelling the charges there, and reducing the potential difference to a safe value. CJ ++++ - ~ _ - - _ - - charged thunder cloud tt, + + ii~. + + air ionised by high concentration of charge at spikes + + ++ metal spike s ~ thick copper strip on side of tall building Even if the cloud did spark to the rods, th e discharge would be less violent and would pass readil y to the ground through the thick copper strip, instead of through the building. thick metal plate Figure 26.7 A lightning conductor 26 Static electricity (._---1 129 Dust precipitators gases free of dust Fi gure 26.8 shows how an electrostatic precipitator prevents smoke, conta ining du st and carbon parti cles, from pollutin g th e environment. A cathode in the form o f an electri c grid at a potential of abo ut -40 kV io ni ses the gases in th e chim ney. As th e ri si ng smoke passes through th e io ni sed regio n, elect ro ns stick to th e smoke parti cles, making them negati ve. Th ey are then attracted to a positive metal anode on th e side of the chimn ey. Th e anode is periodi cally stru ck so that th e du st particl es can fall into a tro ugh and be collected fo r di sposal. chimney wall . . . . . . . ' I' negatively charged dust particles attracted to anode ( + ) I -I " .~ • _ _ anode plate (+l -. •• __ . ..... ......... t r o u gh ~. waste collection _ _ _ ___ _ ¥- ~ ~- • ca th odeg r idH _ gases containing dust Figure 26.8 Electrostatic dust precipitator Electrostatic spraying Spray painting, fo r exa mple of ve hicles, ca n take advantage of electro static chargin g. As the paint passes through a nozzle (Figure 26.9) it becomes charged po sitively by fri cti o n. The pos itive drop lets th en induce o ppos ite charge o n the metal to be pai nted and are att racted to it. To increase th e attraction, th e metal ca n be connected to a negative potential. + - + + + - spray nozzle cl negatively charged metal 0+: - f-----, If-+ ---- paint droplets + + Figure 26.9 Electrostatic spray painting Advantages: • Similarly charged drops rep el each oth er, spreadin g uni fo rml y and givin g good coverage. • The drops are o pposite in charge to th e metal and th erefo re stick well to it. • Shadow regio ns also receive the paint since the electric fi eld can red i rect the drops. In secticid es, herbi ci des and fertili sers can be appli ed in a similar way. The chemical is charged and sprayed as a fin e mi st onto th e plants, where it sticks firml y to th e leaves and stem s due to th e o pposite ch arge it induces. Photocopiers Figure 26.10 illu strates th e rol e of electrostatic charge in the action of a ph otocopier. DRUM A shadow image of the printed item to be copied is cast by a beam of light onto a positively charged plate (dru m). Charge leaks from the plate where light is reflected to it from the white parts of the paper, leaving a positively charged image on the drum. Figure 26.10 Ho w a photocopier works 26 Con cise Revision Course: CSEC· Physics Negatively charged toner is attracted to the positive image . The drum rotates and presses onto a sheet of paper. Heat and pressure are then applied to fuse the toner firmly onto the surface. Electric fields 4 declric field is the (('M/on In !""hfCh a hod}' ['.\perH'f)CCS c1 force cluc tu its dlcll).W. The direction of an electric field at a point is the direction of the force caused by the field on a positive charge placed at the point. Fie ld lines Field lines may be used to represent the strength and direction of electric (or magnetic) fields. Important properties of field lines: -" metal plates • The lines never touch. • There is a longitudinal tension within a line. + • The field is uniform where the lines are evenly spaced and parallel. • Electric field lines are directed from positive charge to negative charge. Obtaining a uniform electric f ield - - + I r- - I A uniform electric field will exist in the central region between ch arged metal plates, as shown in Figure 26.11. The field lines there are evenly spaced and parallel. Figure 26.11 A uniform electric field in the central region between charged metal plates Near to the edges of th e region, the field is not uniform. Field lines near to the top will be pushed upward due to the lateral repulsion from lines below, and field lines near to the bottom will be pu shed downward due to the lateral repulsion from lines above. Figures 26.12 and 26.13 illustrate electric fields for several arrangements of charges. '--' + + -+ + + + • There is a lateral repulsion between lines that are close to each other. Electric fields around and between charged bodies /_--" --" ** isolated 1solated positive charge negative charge Figure 26.12 Electric field lin es aro und isolated point charges F F - l-J......-1 _ charged plate a F is a force of repulsion, due to the lateral push between field lines. b F is a force of attraction, due to the longitudinal tension within field lines. c F is a force of attraction. due to the longitudinal tension within the field lines joining the point charge to the plate. Figure 26.13 Electric field lines around and between charged bodies 26 Static electri city 131 • The point X in Figure 26.13(a) is a neutral point - th e field strength there is zero . • Field lin es do not necessarily point along the direction of force. In Figure 26.13(b) two opposite ly directed forces are along the same field lin e. Revision questions 1 Describe and explain w hat happens, in terms of the movement of cha rges, in each of th e following cases. a A glass rod is rubb ed with a cloth. b The rod in part a is then brought nea r to a small piece of uncharged paper. 2 A neutral metal dom e supported by an insulated stand can be charg ed using a polythene rod whi ch has been rubbed by a cloth. Describe and exp lain, in terms of the movement of charges, how thi s may be done by each of the following methods: a induction method 3 b co ntact method Describe and explain : a the fo rmation of li ghtning b how a lightning conductor can protect a tall building. 4 Draw diagrams to show the electric field in the following regio ns: a between two oppositely charged parallel plates b aro und a negatively charged particle c between and around two oppos itely charged particles d between and around two simi larly charged particles. 26 Concise Revision Course: CSEC' Physics 27 Current electricity Conductors and insulators Conduc tors arc matcria/<; through which e/celf/cal charges can /10\\ Ireel}>, • Metals contain free electrons which have broken away from their atomic orbits and are not bound to any particular atom. • Graphite (a non-metal) is a good conductor and is widely used for 'make and break' contacts in electrical circuits. As in metals, the mobile free charges are electrons. • Solutions of ionic substances, as well as molten ionic substances, have mobile positive and negative ions, which move in opposite directions when connected in an electrical circuit. /1I,u/ators are materials In which electrical charges do not flo \\ freel)· • Non-metallic solids are usually good insulators, because most of them do not contain free charges. Sf'miconductors arc a class of ma terials vl/ith conducti\'ity in a range between that of good conductors ,nd good Insulators. An understanding of charge carriers in semiconductors is beyond the scope of this syllabus. Table 27_1 Examples of conductors, semiconductors and insulators Semiconductors silver, gold, copper, aluminium, graphite silicon, germanium glass, mica, quartz, rubber, plastic Conventional current and electron flow Current 15 the rate of flo\\' of charge. Q t 1=1= cu rrent, Q = charge, t = time Q = It The coulomb, C, is the 51 unit of charge. The ampere, A, is the 51 unit of current. '1(> current is 1 ampere when the rate uf {Im\ of charge is 1 (ou/omb per second through J point Since Q = It, lC=lAxls lC=lAs Note that if the number of particles (N) is known, together with the charge on each particle (q), then the total charge Q is given by Q = Nq. (,JIl Hm(;onal current J.'" in the directIOn If 'direction 01 the electriC field. In \\hich a POSITI \'[ chart;(' \\'Quld fl10\C Ii {ree to do 5(1. It I~ Electron flow is the flow of NEGATIVE charge and is therefore opposite to the direction of conventional flow. 27 Cu rrent electricity ( 133 A charge o f 20 flC flows past a point in a time of 4.0 m s. Determine: a the c urrent b the numbe r of electrons that flow past the point, given that the charge on an electron is -1.6 x 10- 19 C. a / =.Q t / =20x 10- 6 4.0 X 10-] / = 5.0 X 10-] A or 5.0 mA Note that the negative sign in front of the charge of the electron is ignored in calculating the size of the current. b Q=Nq 20 X 10-6 = N x 1.6 X 10- 19 20 x 10-' 1.6x10- 19 1.25 X N 10 14 = N Alternating and direct current An alternating current (ac) is a current that repeatcd/), r('versc' dircclion wllh timc. A direct current (de) is a current that does not change direction with lime. The voltage, V (see Chapter 28), follows a similar patte rn to th e current. Figure 27.1 shows som e examples o f how the voltage might vary with time, t. ac output from ac generator square wave ac sawtoothed ac de rectified from ac using a diode de output from de generator de output from battery Figure 27.1 Exa mples of ac and dc voltage variation For ac: • thc frequency, f, (1 Hz = 1 s-' ) IS thc number or complcte aSCII/at 10m or cycles per second. Its unit is Hz • the period. 1, ;, the limc taken for one complcte oscil/alion or cycle. Its unit is s. f = _1 T Determin e th e period of a 50 Hz ac electrical mains supply. 1 1 T=- = - = 0.02 s f 50 Hz 27 Concise Revision Course: CS EC· Physics Revision questions 1 Define the following electrical terms: a conductor 2 C current Give TWO examples of each of the following: a conductors 3 b insulator b insulators c semiconductors Differentiate between each of the following: a alternating current and direct current b conventional current and electron flow. 4 Sketch V-t graphs of each of the following: a output from an ac generator b output from a battery. 5 Calculate the frequency of an ac supply whose period is 16.7 ms. 6 Calculate the current in a discharge of 8.0 x 103 C that occurs during a time of 4.0 ms. 27 Cu rrent electricity 135 28 Electrical quantities Table 28.1 Common electrical quantities " watt W power P energy E joule voltage V volt V ampere A current charge Q coulomb C time t second s Electromotive force and potential difference in a circuit The electromotil-'c force (emf) ol a cel/ i~ the cncQj\' used (or \,vork. done) in transferring unit charge around a complett..' CIrcuit. including through the rell ihc/f electromotive force = energy charge Electrical components offer resistance and therefore energy is needed to drive charges through them. The pot('ntial diffcr c-nce Ipd between tHO POll1ts in a CIrcuit I... the cnerg}' used or \tor/.;. done in transferring unit charge between those point~. potential difference = energy charge Since potential difference and electromotive force are both voltages, we can write in symbols (see Table 28.1) for each : where E is the electrical potential energy. Th( \.'olt \, is the 51 unit of \'oitagc. 1 \ I!' the potential difference exislmg between t\\'o points -, I or cnergr i.') required per 7 C of charge lran . . icrred betH'ecn those point ..... Current flows from points of higher potential to points of lower potential through the circu it outside the cell. Chemical reactions of the cell then enable it to return to the higher potential. See Figure 28.1, where X and Y are components in the circuit. A cell of emf 1.5 V raises the potential at one end of the string of components such that it is 1.5 V higher than at the other end of the components. The greater the emf, the high er the potential would be raised, and the greater would be the rate of flow of charge through the components, X and Y. Figure 28.1 shows that: The emf in a circuit is equal to the sum of pds in the circuit. 111 . J. '~ 28 Concise Revision Course: CSEC' Physics 1.5 V ----- ~ - - - - -- -- - - - emf hell -1;dl~50V6 V -- ------- - 0.9V 1.5V Y OV H L -_ _ _ _ _ _~ -~ Ipd ~0.9V - -ov current 1.5 V~ 0.6 V+ 0.9 V emf = sum of pds Figure 28.1 The relationship between emf and pd in a circuit Electrical power fJ (trical pmier /,I;j the' ralc of transfer of ('Icclflcal ('nerli~. energy power; time p; .i... t p; VQ (s ince E ; VQ) t p; VI (since ~; t I) The unit of power is the watt, W, and 1 W; 1 J S-1. A current of 4.0 mA flows in a resistor for a time of 48 ~ s . There is a pd of 4.0 kV between the ends of th e resistor. Determine: a the charge that passes through th e res isto r b the energy used by the resistor c the power used by the resistor. a Q; It 10-' x 48 X 10-6 1.92 X 10- 7 C X 10' x 1.92 X 10- 7 ; 7.68 X 10-4 X 10' x 4.0 Q; 4.0 b X ; E; VQ E; 4.0 c p; VI p; 4.0 X J 10-' ; 16 W Alternatively: p;.i... t p; 7.68 48 10-4 10- 6 X X 4.0 X 10" electrons flow between two electrodes in a discharge tube in a time of 5.0 ms. (Electron charge; -1.6 x 10- 19 C; electron mass; 9.1 x 10-31 kg.) Determine: a the total charge that flows b the cu rrent c the energy used if the pd between the electrodes is 2.0 kV d the energy transformation occurring as the electrons leave the cathode, accelerate across the tube, and strike the anode e the electrical potential energy of a single electron leaving the cathode f the maximum kinetic energy acquired by an electron on reaching the anode g the maximum speed acquired by a single electron in the tube. 28 Electrical quantities j 137 a Q=Nq Q = 4.0 x 10" x -1.6 10- 19 = -6.4 x 10-' C X b Q = It I=!l t 1= 6.4 x 10-' 5.0 x 10-' 1= 1.28 X 10-4 A = 1.3 X 10-4 A to 2 sig. fig. In calculating the size of the current, or energy, the negative sign on the charge is ignored. c E=QV E = 6.4 x 10-' x 2.0 x 10' E = 1.28 X 10-' J = 1.3 X 10-' J to 2 sig. fig. d electrical potential energy -+ kinetic energy -+ thermal energy e For ONE electron: E= qV E = 1.6 X 10- 19 x 2.0 X 10' = 3.2 X 10- 16 J For ONE electron, electrical potential energy transforms to kinetic energy, so maximum kinetic energy = 3.2 x 10- 16 J. f g Kinetic energy Ek = ~ mY', so 2Ek = v' m 2(3.2 x 10- 16 ) 9.1 X lO-JI v=2.7xl0' ms- 1 Importance of conserving electrical energy Electricity plays an important role in our everyday lifestyle. • It can readily be transformed into other types of energy such as heat, light, sound and kinetic. • It can be transmitted easily over long distances. Caribbean territories depend heavily on energy from fossil fuels. Due to pollution (i ncluding greenhouse gas emissions that lead to global warming - see Chapter 18), limited oil reserves, fluctuating fuel costs and rising health care costs, it is important that we utilise alternative sources of energy and become more energy efficient. Alternative sources of energy are discussed in Chapter 8. '- Becoming more energy efficient at home • Install high-efficiency, certified electrical appliances and LED lighting. • Install photovoltaic (PV) panels to produce electrical energy from solar radiation. • Install solar water heaters to produce thermal energy from solar radiation. • Only wash full load s in the washing machine. • Dry clothes by hanging on lines or racks rather than by using electric dryers. • Switch off electrical equipment when not in use. • Save on gasoline by car-pooling and ensuring that the engine is tuned. 28 Concise Revision Course: CSEC' Physics • Ensure that your home is designed for efficiency, by having a) double glazed windows, especia lly in rooms that use air condit ioning b) proper insulation of roofs and cei lin gs c) wa ll s built with hollow blocks (air is a poor thermal conductor) d) hoods on windows and curtains to block excessive solar radiation e) walls painted white to reflect excessive so lar radiation. Revision questions 1 Define: a electromotive force 2 b potential difference 20} of energy transfers 80 mC of charge between two points in a time of 5.0 ms. Calculate: a the pd between the points b the current c the power used d the number of charged particles transferred (the charge on each particle is 1.6 x 10-19 C). 3 a State TWO reasons why electrica l energy is such an impo rtant type of energy in our everyday lives. b State FOUR ways by which we can be more energy efficient at home. 28 Electrical quantities f 139 29 Circuits and components Fi gure 29.1 sh ow s th e c ircuit symbol s for some co mmon co mpon ents. + -l~ -l~ ~ ---l f - ~ + f- -0 + 0- -o'"Vo- battery pack of cell battery of 3 cells several cells ac supply de supply -e- -0- -B- -0- -<Dvoltmeter ----c:::=J-- ammeter galvanometer ---¢- -y6- ac supply galvanometer ~ o- -!- variable resistor resistor or rheostat thermistor switch earth =1l] Ct= conducting wire + T (not connected) connected wires speaker microphone --0- --0- =CJ =D filament lamp lamp electric buzzer electric bell crossing wires ~ -00- push button switch ] [ 0- transformer motor c::=J ---G><O-- Bgenerator JfJf -f>I- light-emitting fuse fuse diode (LED) diode --=- --@",,,, fight-dependent resistor ---t>!- For symbols used electrolytic cell in electronic circuits see Chapter 30. or voltameter Figure 29.1 Common circuit symbols Some important electrical components • Voltmeter: A device that measures the potential difference between two points • Ammeter: A device that measures the current flowing through a point • Galvanometer: A device that detects, measures, and determin es th e direction of very small electric currents , • ReSIstor: A compon ent that opposes th e flow of current • Rheostat: A variabl e resi sto r whos e resi stance can be altered, usually by means of a slider control A.,...r - - - _ 29 Conc ise Revision Co urse: CSEC' Physics • Light-dependent resistor (LOR): A resistor whose resistance decreases with increased light intensity • Thermistor: A resistor whose resistance changes with temperature (generally decreases with in creased temperature) • Diode: A device that normally allows current to flow through it in one direction only • Light-emitting diode (LED): A diode that emits light when a current flows through it in a particular d irection • Fuse: A metallic resistance wire placed in series with a device, which protects a circuit from excess ive current by becoming hot, melting and disconnecting it • Circuit breaker: An electromagnetic switch which protects a circuit from excessive current by disconnecting it • Transformer: A device that increases (steps up) or decreases (steps down) an alternating voltage Series and parallel circuits Figure 29.2(a) shows a series circuil. The ammeter AI is measuring the current through the diode, lamp and variable resistor. Figure 29.2(b) shows a parallel circuil. Ammeter A, is measuring the current through the diode only. Part of the current from the cell is passing through the thermistor. For some components, such as ammeters, voltmeters and d iodes, the polarity of their terminals must be considered when connecting a circuit. The + terminals are marked in Figure 29.2. The + terminal (or pole) of the battery must always connect with the + marking on the instrument or component. • • SERIES CIRCUIT b PARALLEL CIRCUIT Figure 29 .2 Series and parallel circuits Cells Primary and secondary cells A primary cell is a source that converts chemical energy to electrical energy by a non -reversible chemical reaction. A + B_ C + D + electrical energy A secondary cell (also known as an accumulator or storage cell) is a source that converts chemical energy to electrical energy, and electrical energy to chemical energy, by a reversible chemical reaction. A + B_ electrica l energy + C + D _ C + D + electrical energy A+B To charge a secondary cell, current must flow through it in a direction opposite to that in which it no rmally delivers current during discharge. discharging: chemical energy _ electrical energy charging: electrical energy _ chemical energy 29 Circuits and components f 141 The zinc-carbon dry cell - a primary cell Figure 29.3 shows a zi nc-carbo n dry cell. • Ammoni um chloride (the electrolyte) reacts with the zin c, producing electricity. • The manga nese oxide and carbon mi xture is used to prevent polarisation . Polarisation causes the co llection of hydrogen bubbles around the ca rbon rod, and these bubbles wou ld add to th e unwanted internal resistance of th e ce ll . + _______ protective metal cap insulating seal prevents evaporation of electrolyte ~ - - graphite rod (positive pole) ~ ammonium chloride paste or jelly (electrolyte) mixture of manganese ~ oxide and carbon, enclosed by a paper separator zinc case (negative pole) :...--- cardboard or metal ~ case with advertising label Figure 29.3 Th e zinc·carbon dry cell The lead-acid accumulator - a secondary cell Thi s type of ce ll is rechargeable and is capable of delivering higher currents than the zinc·carbon ce ll. Its st ru ct ure is not a requirement of th e CSEC syllabus. Advantages of zinc-carbon dry cell over lead-acid accumulator 1. Sma ll and li ght, whereas the accumulator is large and heavy. 2. Can be inve rt ed w ithout spillage because its electrolyte is in the form of a paste. 3. Batteries of various vo ltages can eas ily be made by packing the cells in seri es or in parallel. 4. Less cos tl y. Advantages of lead-acid accumulator over zinc-carbon dry cell 1. Can produce mu ch larger currents beca use th e electro lyte is liquid and the elect rode plates have large surface areas for reaction . 2. Has a much lower internal resistan ce. 3. Can be recharged. Table 29.1 summarises the features of the two types of ce ll . ... Table 29.1 Comparison of zinc·carbon cell and lead·acid cell Rechargeability not rechargeab le rechargeable Terminal voltage 1.5 V 2.0 V I nternal resistance high (0.5!1) low (0.01 !1) Maximum current a few amps (works well up to abo ut 1 A) > 400 A Electrolyte ammonium chloride paste dilute sulfuri c ac id Portability small and li ght large and heavy • 29 Concise Revision Course: CSEC· Physics Other types of cell • Alkaline cells have potassium hydroxid e as their el ectrolyte. They are not gen e rally re charg,:,abl e . • Lithium-ion cells are rechargeable cells used in laptop computers, cell phones and digital cameras. Charging an accumulator from the ac mains Figu re 29.4 shows how an accumulator can be charged from the ac mains supply. • The charging current must be driven into the positive terminal of the accumulator. • A step-down transformer is used to reduce the voltage (see Chapter 32). • The variable resistor adjusts the pd across the battery to be just above 12 V. • A diode is used to rectify the ac to dc (see Chapter 30). - -12 ~ -vb; t~ry ~ : to be charged : mains] , + ' r--r--t ~ f- 1 !------:-"'I ,' f-/<j-- , _____ _ _ _ .J supply l lO V A Figure 29.4 Charging an accumulator Amp-hours (A h) The CHARGE stored in a cell or battery is sometimes stated, usually given in the unit A h. Since Q = It, 1 A h = 1 A (60 x 60) s = 3600 A s = 3600 C Creating a battery by joining cells 1.5 V 1.5V 1. 5 V -llillf- Series connection emf=4 .5V If each cell has an emf of 1.5 V, total emf of battery = 1.5 V + 1.5 V + 1.5 V = 4.5 V -r: ~ 1.5V Pa rallel connection If e ach cell has an emf of 1.5 V, total emf of battery = 1.5 V emf= 1. 5V 1.5V The advantage of connecting similar cells in parallel is that they will last longe r, because each has to produce only a portion of the total current output of the battery. Figure 29.5 Combined emf of cells in series and in parallel 29 Circuits and components C 143 A 12 V battery storing a charge of 80 A h is connected to a lamp that uses 6.0 W. Determine: a the charge sto red, in cou lombs b the current c the maximum t ime for which the ave rage current calculated in part b can flow. a Q = It = 80 b x 60 x 60 = 288 000 C = 288 kC P= VI 6.0 = 121 1 = 6.0 12 1 = 0.5 A c Q = It 288 000 = O.5t t = _2-'-,88:...,0",00,-- 0.5 t = 576 000 s or 576000 -i- (60 x 60)= 160 hours Alternatively, using charge in A h, Q = It 80 = 0.5t 80 -=t 0.5 t = 160 hours Resistance IS a measure of the opposition prO\·ided to an electrical current; it a conductor to the current through it Resista nce acr()~!l IS the ratio of the pd A resistor is a device having resistance. Explanation of resistance When electron s flow through a condu ctor, they are obstructed by vibrating atoms in their paths. These atoms th erefore decrease th e rate of flow of the electrons and hence the current. Effect of length and cross-sectional area on resistance Th e res istance, R, of a conducting wire is proportional to its length, I, and inversely proportional to its cross-sectional area, A: I R "' A Adding resistors In series R = R, + R, + R, .... In p arallel 1 1 1 1 /i = /f +/f+/f .... I 29 Co ncise Revision Course: CSEC· Physics , , In th e special case of TWO resistors in parallel: R = product sum • W hen resistors are connected in parallel, their total resistance is less than any of the resistors. • If two identical resistors are placed in parallel, their combined resistance is half the value of either of the individual resistors. If each is of resistance 5.0 0, then the total resistance is 2.5 O. Find the combined resis tance of each of the following. a 30 and 2 0 in series c 20,40 and 8 0 in parallel b 30 and 2 0 in parallel a R=3+2=SO b R=3x2~ c 3+2 R = 1.2 0 5 1 1 1 1 7 R 2 4 8 8 R= ~ -=-+-+- = - 0 (invert) Find the combined resistance between X and Y in each arrangement in Figure 29.6. ~ 20 20 20 ~ 20 X60a:::D20 Y X a -y X 30 Y b c Figure 29.6 R a 3x2 = 3+2 R = 1.2 0 2x3 2+3 c R=2+--=2+1.2 R= 3.20 Ideal ammeters and voltmeters • Ammeters are connected in series with a component in order to measure the current through it. They must therefore have negligible resistance so as not to affect the very curre nt they are measuring. An ideal ammeter has zero resistance. • Voltmeters are connected in parallel with a component in order to measure the potential difference across it. Current will divert and flow through the voltmeter, leaving a smaller curren t through the component. The voltmeter shou ld therefore have a very high resistance to keep thi's diversion to a minimum. An ideal voltmeter has infinite resistance. 29 Circuits and components Ohm 's law and I-V characteristic curves Ohm 's law Pro\'lcicd the lernperature and other phvt;ical conditions remain constant, the current I. through a I; bct\\ccn ito cnd,. conductor" proportional to the pd, V = IR The equation shows that V is proportional to I, and the constant of proportionality is R, the resistance of the conductor. I-V relationships If a material is an ohmic conductor, a graph of I against V, or Vagainst I, is a straight line through the origin. The relationship between the current, I, through a component such as a resistor and the potential difference, V, across it, can be investigated using the circuit shown in Figure 29.7(a). The more complex circuit of Figure 29.7(b) may be used by your teacher for investigating filament lamps and diodes. (Lamps and diodes behave differently at low voltages from how they behave at higher voltages and th e circuit of Figure 29.7(a) is unable to produce voltages across the component close to zero.) • An initial pair of readings of I and V is taken. • By adjusting the rheostat (variable resistor), other pairs of values of I and V are obtained. • The co nnection between the terminal s of th e battery and the circuit is then reversed and the process is repeated. • A graph of I against V is plotted. component under study component under study • b Figure 29.7 Investigating I-V relationships Graphs of I against V, called 'I-V characteristics' are shown in Figure 29.8 for a metallic conductor, a filament lamp, a semiconductor diode, and an aqueous solution of copper sulfate with copper electrodes. forward bias v -v v -v v -v -v reverse bias -/ a metaUic conductor b filament lamp -/ c semiconductor diode Figure 29.8 I-V characteristics for different components 146 1 29 Concise Revision Course: CSEC· Physics d aqueous solution of copper sulfate with copper electrodes v • Figure 29.8(a) and (d): For conductors that obey Ohm's law, the gradient of an I-V graph is the inverse of the resistance. (The gradient of a V-I graph is the resistance.) • Figure 29.8(b): As the voltage is increased across the lamp, the electrons are pulled with greater force and collide more vigorously with the cations of the metallic filament. Their kinetic energy transforms in to thermal energy, causing the vibration of the cations to increase. The increased vibration blocks the path of the electrons to a greater extent than previously and the resistance rises. • Figure 29.8(c): When the diode is forward biased (its polarity such that it conducts), a small initial vo ltage is needed before a current flows. When it is reverse biased, conduction is almost zero. Current and voltage in complete circuits The following rules apply. Cu rrent 1. Se ries circuit (Figure 29.9(a)): The current is the same at all points in the circuit. 2. Parallel circuit (Figure 29.9(b)): The sum of the currents in the branches is equal to the total current outside the branch. a b Figure 29.9 Current in series and parallel circuits Voltage (potential difference) 3. Series circuit (Figure 29.10(a)): The sum of the potential differences across the individual resistors is equal to the total potential difference across the group. 4. Pa rallel circuit (Figure 29.10(b)): The potential difference across each resistor is the same, and this is equal to the potential difference across the group. V3 \-- --" a Figure 29.10 Voltage in series and parallel circuits 29 Circuits and components j 147 Calculations on complete circuits • When using formulae, V, 1 and R must pertain to the same component or group of components. Subscripts may be used to identify the components. In the Examples that follow, if no subscript is used, V, 1 and R pertain to totals. • emf = sum of pds in the circuit • A double-ended arrow (see the following Examples) should be placed across ALL the resistors as a reminder of the components that can be used in a formula involving the emf or total pd. Determine for the circuit in Figure 29.11: emf == 3.0V a the cu rrent from the battery b the pd across A c II ~ the pd across B RA = 3.0n Rs = 2.0n A d the pd between X and Y. • pd d .OV Figure 29.11 a V= IR c 3.0 = 1(3.0 + 2.0) V,=I,R, VB = 0.60 x 2.0 = 1.2 V 3.0 = 5.01 3.0 =1 5.0 1 = 0.60 A VXY = 0.60 x 0 = 0 V VA= 0.60 x 3.0 = 1.8 V Determine for the circuit in Figure 29.12: em;d.O V a the total resistance III· b the current from the battery c RA = 6.0 n r---.--, the pd between X and Y d the pd across A e the pd across B f X~ I~ the cu rrent in A g the cu rrent in B. a R = product sum R = 6.0 x 2.0 6.0 + 2.0 R = 12.0 8.0 b = 1 5 fl . V= IR 3.0 = 1 x 1.5 3.0 = 1 1.5 1 = 2.0 A c VXY = 3.0 V (emf = total pd) 29 Concise Revision Course: CSEC· Physics Figure 29 .12 y y •X d VA= 3.0 V (see rule 4 for pd in parallel circuits) e V, = 3.0 V (see rule 4 for pd in parallel circuits) f g VB= I, R, 3.0 = I, x 2.0 =, 3.0 2.0 ' · I,= 1.5A VA='ARA Alternatively: 3.0 = ' A X 6.0 '='A+" 3.0 = 6.0/ A 3.0 6.0 =, 2.0 = 0.50 + " A ', = 1.5A 'A= 0.50 A Calculate the current in resistor B of Figure 29.13. emf = 1.5 V ~_-1 1 'I- I _~ Figure 29.13 Note that the 1.5 V cannot be used with the 10 n, because 1.5 V is the total voltage but 10 n is not the total resistance. Using 1.5 V with the total resistance of 30 n will give the total current. Since this is a series circuit, the current is the same everywhere, I = fA= 's' V = IR 1.5 = /(20+10) 1.5=/x30 22 =, 30 I, =,= 0.05 A Determine for the circuit in Figure 29.14: a the total resistance b the cu rrent from the battery c the pd between X and Y emf=3.0V d the pd between Y and Z e the pd across A f :II X RA= 10.4 n A yl the pd across B g the pd across C R,=8 .0 n Rc = 2.0 n I Z' pd=3.0V h the current in A the c urrent in B Figure 29.14 th e current in C. 29 Circuits and components I 149 a R 8.0 x 2.0 = 10.4 + 8.0 + 2.0 16 = 2.6 V f VB= VyZ = 0.4 V g V, = VyZ = 0.4 V R = 10.4 + 1.6 = 12 n h IA = I = 0.25 A (total current) VB= I, R, V= IR ~=I 3.0 = I x 12 0.4 = I, x 8.0 12 0.4 = I 8.0 B I, = 0.05 A 1= 0.25 A VXY :;; I XyR XY Ve = leRe V" = 0.25 x 10.4 = 2.6 V d VA= V" R = 10.4 + 10.0 b c e 0.4 = le x 2.0 V= VXy + Vy Z 0.4 = I 2.0 e 3.0 = 2.6 + VyZ le = 0.2 A 3.0 - 2.6 = VyZ VyZ = 0.4 V Energy and power in complete circuits Table 29.2 shows the equations used to calculate these quantities. Table 29.2 Energy and power in complete circuits energy Power = -.-lime . Energy = power x lime P= VI E = Vlt P = I'R E = I'Rt V' V' t E=R P=R Determine for the circuit in Figure 29.15: a emf ", 5.0 V the power used by resistor A I, I' b the energy used by resistor B in 5 minutes c the power delivered by the battery. RA =6.0n RB= 4.0n A • pd = 5.0V Figure 29.15 150 29 Concise Revision Course: CSEC' Physics • a Note that the 5.0 V is not the pd across A and therefore cannot be used with the resistance of A. V= IR b E, = 1,' R,t E, = 0.50' x 4.0 x (5 x 60) = 300 J c P = VI P= 5.0 x 0.50 = 2.5 W 5.0 = I x (6.0 + 4.0) 5.0 = I 10.0 1= 0.50 A PA = (ly RA PA = 0.50' x 6.0 = 1.5 W Determine for the circuit in Figure 29.16: a emf = 3.0 V the pd across A ill b the current in B RA = 6.on c the power used by A A d the power used by B I e the total power used by both resistors f R,.2.0 Q Y X • the power delivered by the battery pd -3.0 V • g the energy used by B in 3.0 minutes Figure 29.16 h the energy delivered by battery in 10 minutes. a VA= 3.0 V e P = 1.5 W + 4.5 W = 6.0 W b V, = I, R, f 3.0=I,x2.0 3.0 = I 2.0 ' 1,=l.5A V' c PA=iA 3.0' PA = 6.0 =1 .5W d P, Power delivered by battery = power used by resistors = 6.0 W V 't g E,= i - , E = 3.0' (3 x 60) , 2.0 E h P=T 810 J :. E= Pt E = 6.0 x (lOx 60) = 3600 J V' =' R, 3.0' P, = 2.0 =4.5W Electricity in the home Advantages of parallel connection of domestic appliances • Appliances can be switched on and off without affecting each other. If, instead, they were connected in seri es, switching off one would switch off all. • Appliances can be designed to operate on a single voltage. This voltage is about 115 V in Barbados and Trinidad. If appliances were connected in series, they would have to share the 115 V and would each have a smaller pd across their terminals. 29 Circuits and components 151 Fuses A fuse is a short piece of thin wire which is placed in a circuit in series with one or more devices. When too high a current flows, it melts and breaks the circuit, preventing damage to the devices. An appropriate fuse should melt at a current slightly greater than that which the circuit takes under normal operation. This value is known as the current rating, in A, of the fuse. See also 'Fuses in plugs or appliances' below. Thickness of wires High-powered electrical appliances, such as water heaters, fridges, cookers and washing machines, should use thick wires because they need high currents - the currents they draw are proportional to the power they consume. Distribution box • A LIVE and a NEUTRAL wire enter the distribution box from the electrical power company, delivering alternating current. There is a fuse or circuit breaker in each live wire. The international colour code is shown in Figure 29.17, together with a distribution box. • If the supply voltage is 115 V, there is a pd of 115 V between each live and neutral wire leaving the box. • The rating of the fuse or breaker depends on the total possible current that should flow when all the lights or appliances connected to it are being used . • Since cookers and water heaters usually take large currents they have a fuse or breaker specially assigned to them in the distribution box. • An actual distribution box usually has many more wires exiting. A separate fuse or circuit breaker may be connected to the supply for each room in the building. lights sockets cooker heater socket 15 A 20 A 15 A 15 A electrical supply International colour code Live - BROWN Neutral - BLUE Earth - GREEN or GREEN/fELLOW -wires fr om distribution box earthed in the yard Figure 29. 17 Distribution box and colour code for wiring Figure 29.18 Ring-mains circuit with sockets Ring-mains circuit (socket circuit) This is illustrated in Figure 29.18. • The circuit uses thick wires because they carry current to several sockets. • If the supply voltage is 115 V, each socket will provide a pd of 115 V because they are all in parallel. • If the socket is viewed with the EARTH at the top and centred, then the LIVE is on the right. Function of the earth wire A short circuit can occur if a piece of metal bridges the gap between a circuit and the metal case of a device. If there is no earth wire and the case is touched, current may pass from it through the perso n to the ground. Since some of the resistance is now bypassed, the curren t is larger than before, so th e person will receive an electrical shock and the fuse will blow. ,....----152 29 Concise Revision Course: CSEC· Physics Figure 29.19 shows an electric toaster re sting on insulating supports. To avoid electrical shock, an earth wire is connected between the case of the toaster and the ground in the yard (see Figure 29.17). Under normal conditions (Figure 29.19(a» current flows in the live and neutral wires only. If there is a short circuit inside th e toaster and some of the resistance is bypassed, a large current will flow via the live and earth wires (Figure 29.19(b», and the fuse (or breaker) will blow (or trip). • No current flows in the earth wire unless a malfunction occurs. • When current flows in the earth wire, the neutral wire is bypassed. • The short circuit should be fixed before the fuse is replaced (or the breaker reset) . metal causing toaster short circuit heater resistor a normal working, no short circuit b short circuit Figure 29.19 The function of the earth wire Placement of fuses, breakers and switches in the live wire • Fuses 'blow' or breakers 'trip' when there is a) a short circuit in the appliance so that current flows in the live and earth wires, or b) a power surge for reasons external to the appliance so that excess current flows in the live and neutral wires. By placing fuses or breakers in the live wire, the appliance is protected for both situations . Switches should also always be placed in the live wire. If a switch in the 'off' position is in the neutra l wire connected to a lamp, of course no current can flow. If, however, an attempt is made to change the lamp and the live terminal is touched, the person can receive an electric shock. By placing the switch in the live wire, once it is in the 'off' position, no cu rrent can reach any of the terminals of the appliance. Fuses in plugs or appliances A fuse in the plug of the appliance or in the appliance itself can offer better protection than the fuse in the distribution box. Its rating should only be slightly higher than the current normally taken by the appliance. Say the device requires 2.5 A for normal operation, a fuse with a rating of 3 A will be more suitable than the larger fuse in the distribution box, which will not blow unless the current rises to a much higher value. A dverse effects of connect ing electrical appliances to an incorrect or fluctuating supply . • Appliances are normally designed to operate on ac frequ encies of either 50 Hz or 60 Hz. If operated on an incorrect frequency they are likely to malfunction or even be damaged . • If an appliance is supplied with a voltage higher than it is designed for, overheating due to excess ive current may result in it being destroyed. • If a motor is supplied with a voltage that is too low, the current in its coils will ri se (due to reasons beyond the scope of this syllabus) and the device can be damaged due to overheating. 29 Circuits and components 153 Revision questions 1 Sketch a circuit diagram containing a switch, a battery of two cells in series, and a LDR in series with two lamps which are in parallel. Insert a voltmeter to measure the pd across the LDR, and an ammeter to measure the current through one of the lamps. 2 a What is the difference between a primary cell and a secondary cell? b Drawa diagram of a zinc-carbon dry cell. e How are hydrogen bubbles prevented from accumulating around the anode of a zinc-carbon dry cell? d List THREE advantages and THREE disadvantages of the zinc-carbon dry cell relative to a lead-acid accumulator. e Construct a table showing the differences between a zinc-carbon dry cell and a lead-acid accumulator with respect to the following: terminal voltage v rechargeability ii maximum current iii internal resistance iv portability vi electro lyte 3 Draw a circuit diagram illustrating how a 12 V accumulator may be charged by a 120 V ac supply. 4 A battery storing a charge of 60 A h discharges completely with an average current of 5.0 A. a How much charge in coulombs is stored before discharge? b How long does the discharge take? 5 a Define resistance. b How does the length and cross-sectional area of a resistor affect its resistance? e Determine the total resistance of each of the following arrangements: iii four 2 fl resistors in parallel. two 8 fl resistors in series ii two 8 fl resistors in parallel 6 a Sketch graphs of current against voltage for each of the following: a metallic resistor at consta nt temperature iii a semiconductor diode. ii a filament lamp b State which of the components in part a are ohmic conductors. e State how the resistance of the filament lamp changes with increasing voltage, and give an exp lanation of the cha nge in terms of the kinetic theory. 7 8 Two 10 fl bulbs connected in parallel are joined in series to a 5.0 fl resistor. A 5.0 V battery is connected across the arrangement. Draw a diagram of the circuit and determine the following: a the total resistance d b the current from the battery e the power used by the 5.0 fl resistor e the pd across the 5.0 fl resistor f the pd across the parallel sectio n the power used by each bulb. a State TWO reasons for using parallel connection of domestic appliances. b What is the purpose of a fuse or circuit breaker? e In which wire from an ac supply should a fuse always be placed? d In which wire from an ac supp ly should a switch always be placed? e Describe and explain the function of an earth wire in a domestically wired system. f Describe the adverse effects of connecting elect ri cal app liances to incorrect or fluctuating vo ltages. 154 29 Concise Revision Cou rse: CsEC· Physics 30 Electronics Rectification Rectific,lIion IS the process of converling alternating current ( 1C) to direct current (dc ). H,,'f-wave r ectification IS the process of connHtll1g ac to dc by prc\'enling one half of edch c\'ele from being applied to the load. An oscilloscope is an instrument that produces graphs of voltage against time, allowing the observation and measurement of varying electrical signals (Figure 30.1). ae ~ load +---+ • V half-wave rectified ac de load 00 oscilloscope +---+ V b 00 oscilloscope 00 c L __-'===::::J oscilloscope Figure 30.1 Displaying voltages using an oscilloscope • In Figure 30.1 (a ) an alternating voltage is applied to a load. • In Figure 30.1(b) a diode is placed in the circuit. The diode allows current to flow through it in only o ne direction. In the half of the cycle when there is no current in the load resistor, there can be no potential difference across it (V = IR). • Note how ac rectified to dc by a diode differs from the dc of a battery shown in Figure 30.1(c). Logic gates Digital electronics is based on circuits that can exist in one of two possible states. The two possible states can be represented by the numbers (digits) 1 and O. Electronic systems represent these two logic states as a ' high' and a 'low' voltage, respectively, by the use of electronic pulses. Si nce there are only two states, 1 and 0, the circuits function on binary decision making. An example of a decision making situation could be an AND decision . Imagine that your mother says you will be rewa rded if you are polite AND helpful; we specify that polite ! helpful! rewarded are each represented by 1 impolite! unhelpful! not rewarded are each represented by 0 The possible outcomes are shown in a truth table (Table 30.1). Table 30.1 Truth table for AND decision A- po'ite? D B - helpful? 1 _~.; 1 _...I Q - rewarded? . Figure 30.2 AND gate 30 Electronics f 155 A logic gate IS an Idealised or physical electronic devIce that processes one or more input statcs lIow or high, logic states 0 or 1 to produce a smgle output state (low or high, logic slates nor I). Figure 30.2 summarises the AND decision making, using the symbol for an AND gate - a logic gate used in electronic circuitry for carrying out an AND decision. It has two inputs (A and B) and a single output (Q). Table 30.2 shows a range of different logic gates and their corresponding truth tables. The inputs to the gates are on the left of the symbol, and the output at the right. Table 30.2 Logic gates and their truth tables Doutput input ° ° ° ° ° ° ° ° 1 1 1 1 1 1 1 Note that: AND: output r>- Dinput output input 1 output input output 1 ° 1 ° ° ° ° ° ° ° ° ° ° ° ° ° ° 1 1 1 1 1 1 1 1 1 1 1 1 --{>o- 0 1 1 ° This gate simply switches the logic state TWO 1s produce a 1; OTHERWISE, the output is NAND: TWO 1s produce a 0; OTHERWISE, the output is 1 OR: ANY 1s produce a 1; OTHERWISE, the output is NOR: ANY 1s produce a 0; OTHERWISE, the output is 1 NOT: 1 produces a 0; ° produces a 1 Constructing truth tables for a combination of gates The following Example shows the construction of a truth table for a combination of logic gates. The number of inputs determines the number of possible combinations of input states to the circuit. For example: TWO inputs _ THREE inputs _ 2' = 4 different combinations (4 rows in truth table) 23 = 8 different combinations (8 rows in truth table, as in the following Example) An easy way to set up the input part of the table is shown in Table 30.3. • The least significant input column (P in this case) has its values alternating 0, 1, 0, 1, 0, 1, 0, 1. • The column immediately preceding it (F) has its values changing 0,0,1,1,0,0,1,1. • The third column (T) has its values changing 0, 0, 0, 0, 1, 1, 1, 1. The output from each gate is determined by considering its inputs together with the rule for that gate. 30 Concise Revision Cou rse: CSEC· Physics An alarm (A) is to sound (logic 1) if the temperature (T) in a piece of machinery rise s above 500 'c (logic 1) while its pistons are oscillating with a frequency (F) greater than 20 Hz (logic 1). It is also to sound if the oi l pressure (P) is low (logic 1). Draw a truth table and a suitable circuit. The combination of gates will have inputs T, F and P, and output A. The requirement is that if (T ~ 1 AND F ~ 1) OR P ~ 1 then A ~ 1 This can be written as: (T AND F) OR P~A Table 30.3 shows all combi nati ons of inputs and the re sulting o utputs. The X column holds the value of the output of the AND gate which then acts, together with P, as the input to the OR gate. The logic circuit is shown in Figure 30.3. Table 30.3 T F P 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 :2 F alarm X Figure 30.3 Impact of electronic and technological advances in society Pros • Businesses get a competitive edge when they use advanced technologies. • The global pooling of information increases the rate of research and development. • Improved transport through airplanes and train s, as well as better communicating devices such as cell phones and computers, has led to more efficient business transactions and to an increase in social contact. • Better machinery leads to increased and improved productivity. • Electronic banking has facilitated the process of financial transactions. Cons • Incorrect information is common on the internet. • In dividuals can be addicted to social networking to such an extent that th eir productivity decreases. • Excessive virtual communicati on may lead to lack of real communication and to a fall in social ski lls. • Exposure to movies with immoral sexual content and violence can eventually lead to some persons accepting these acts as the norm. • Hackers can intrude on computers and manipulate information such as bank accounts. • M ore efficient machinery can result in a decrease in ava ilabl e jobs. 30 Electronics 157 Revision questions 1 a What is meant by half-wave rectification? b Describe how ac can be converted to dc using half-wave rectification. C Sketch graphs to show how each of the following vary with time: domestic supply ac voltage ii domestic supply ac voltage converted to dc by a diode iii voltage output from a battery. 2 Draw the truth table for each of th e following logic gates. a AND 158 , 1 b OR c NAND d NOT 3 A warning light is to glow on a motor cycle if the key is placed in the ignition (logic 1) while either the tyre pressure is below 80 PSI (logic 1) or the oil level is low (logic 1). The warning light glows when logic 1 is input to it. Draw a truth table and a circuit appropriate to this application . 4 Discuss the pros and cons of the impact of electronic and technological advances on society today. 30 Concise Revision Course: CSEC· Physics 31 Magnetism Magnetic materials are those which are attracted or repelled by magnets. Examples are iron, nickel an d cobalt, and some materials containing th ese elements, such as steel and magnadur. A bar of magnetic material is comprised of tiny atomic magnetic dipoles (atoms that behave as magnets, having a north pole and a south pole) . If the bar is unmagnetised, these dipol es are arranged in such a way that their associated magnetic fields are not experienced outsid e the material. In the presence of a strong magnetic field, however, the dipoles align with it, and the bar becomes magnetised with a north pole (N) and a south pole (5). Forces between magnetic poles • Similar magnetic poles repel and unlike magnetic poles attract. • The force between magnets diminishes rapidly with increased separation of the magnets. Magnetic induction Magnetic induction is the process by which magnetic p roperties are tran sferred from one body to anoth er w ithout physical contact. Figure 31.1 shows th e arrangement of atomic dipoles as a bar magnet is placed onto the door of a fridge (N poles represented by arrow heads). The dipoles of the fridge door are initially disarranged, but when a pole o f the magnet is brought near, it attracts opposite poles. Th e induced 5 pole c reated on the fridge then attracts the N pole of the magnet. part of fridge door ~ "'~< ~ ~.i ~tj ~ ¥ ..{ -." ,~ mag n et }-!:I! !n ¥jt~ k dipoles in door are initially bar magnet brought disarranged near to door Figure 31.1 Magnetic induction Testing for polarity A magnet is freely suspended by means of a string (Figure 31.2). One end of the body (X) under test is brought close to one of the known poles of the magnet. If there is attraction, X may be either of the following: a) a previously unmagnetised piece of magnetic material whose nearby end has been magnetised by induction, with opposite polarity to the indUCing pole b) a magnet whose nearby pole is of opposite polarity to that of the suspended magnetic pole attracting it. If there is repulSion, X must be a magnet whose nearby pole is of similar polarity to that of the suspended magnetic pole repelling it. The only true test for the polarity of a magnet is REPULSION. J2 ATTRACTION I string REPULSION =:X:======i'IiJ held fixed ( X held fixed Figure 31.2 Tes ting for polarity 31 Magnetism , I 159 Permanent and temporary magnets Steel forms permanent magnets ('hard magnets' ). Other permanent magnetic materials are magnadur, alnico, ticonal and alcomax. Permanent magnets are used in directional compasses and in loudspeakers. Iron forms temporary magnets ('soft magnets'). Other temporary magnetic materials are mumetal and stalloy. Temporary magnetic materials are used in electromagnets (see Chapter 32), which are used for lifting metal objects and are also important components in electric bells, magnetic relays and electromagnetic circuit breakers. Magnetic fields A magnetic field IS the region in which a body expericnccs a force due to its magnetic po/arily The direction of a magnetic field is the direction of motion of a free N pole placed in the field. Magnetic fields lines A magnetic field is a vector quantity and can be represented by lines labelled with arrows to indicate its direction. Important features of magnetic field lines are: • They never cross or touch. • There is a longitudinal tension within each line, causing it to behave as a stretched elastic band. • There is a lateral repulsion between lines that are close ' side by side'. • The field is uniform where the lines are parallel, in the same direction, and evenly spaced. • The field is stronger where the lines are more concentrated. • They are directed from a N pole to a 5 pole. Forces between bar magnets explained in terms of magnetic field lines Forces of attraction exist between dissimilar poles due to the longitudinal tension within the field lines joining them (Figure 31.3). -F --F Figure 31.3 Longitudinal tension within field lines Forces of repulsion exist between similar poles due to the lateral push between the field lines passing close to each other (Figure 31.4). 160 31 Concise Revision Course: CSEC· Physics -F F Figure 31.4 Lateral repulsion between field lines Mapping the magnetic field of a bar magnet using a plotting compass plotting compass The magnet is placed at the centre of a large sheet of paper and its perimeter is outl in ed. The ends of the magnet are marked and a plotting compass is positioned near to the N po le. The positions of the head and tail of its magnetised needle are marked by dots on the paper, as shown in Figure 31.5. The compass is advanced such that its tail now lies over the dot where the head was previously, and the new position of t he head is marked. This is continued until the dots reach th e other end of the magnet or extend off the paper. The dots are jo ined by a smooth line with an arrow to indicate the direction of the field. The process is repeated to produce several other field lines. • • Figure 31.5 Plotting the magnetic field of a bar magnet Mapping the magnetic field of a bar magnet using iron filings The magnet is stuck to the work bench by a piece of tape and a sheet of card is placed over it. Iron filings are sprink led onto the ca rd. When the card is tapped gently, the fi lings indicate the pattern of the magnetic field, as shown in Figure 31.6. Figure 31.6 Magnetic field shown by iron filings A uniform magnetic field A uniform magnetic field exists in the central region between plane, facing magnetic poles, as shown in Figure 31.7. The field lines there are evenly spaced and parallel. Near the edges of the poles, the fi eld lin es curve due to lateral repulsion from lines closer to the centre. Figure 31.7 Uniform magnetic field 31 Magnetism 161 The Earth's magnetic field The core of the Earth contains iron and nickel and therefore behaves as a magnet. A directional compass will point along the magn et ic field lines towards the north pole of the Earth, w hich is towards th e S pole of th e magnet within the co re (Figure 31.8). geographic north pole Figure 31.8 The Earth's magnetic field Identifying the poles of a magnet using the Earth's magnetic field If a magnet is hung from a string it will align itself with the Earth's magn etic field, as shown in Figure 31.9. It behaves as a compass, with its N pole facing north. In the northern hemisphere, the N pole declines (points down) toward s the Earth; in the southern hemisphere, the N pole inclines (points up) away from the Earth. You can see that this is following the direction of the fi eld lines in Figure 31.8. Earth's magnetic field Figure 31.9 Identifying the poles of a magnet using the Earth's magnetic field Revision questions 1 State how a magnetic material may be identified. 2 When the pole of a magnet is placed next to a body X, there is attraction. What does this indicate about the nature of X? 3 When the pole of a magnet is placed next to a body Y, there is repulsion. What does this indicate about the nature of Y? 4 State TWO temporary magnetic materials and TWO permanent magnetic materials. 5 Define: a a magnetic field 6 Draw magnetic field diagrams to show two bar magnets: a attracting each other 162 b the direction of a magnetic field b repelling each other 7 Draw an arrangement that may be used to set up a uniform magnetic field. Your diagram should include magnetic field lines. 8 Describe how the poles of a bar magnet may be identified using the Earth's magnetic field. 31 Concise Revision Course: CSEC· Physics 32 Electromagnetism Magnetic fields and electric currents Electric cu rrent s create magnetic fields. The patterns of these fields may be invest igated by sprinkling iro n filings in the region around the conductors, as in the experiments outlined in Figure 32.1 . key: I ® o 0:: current into plane of paper = current out of plane of paper I field of a straight current-carrying conductor c-- t I I ~ // I \ __ - - - -~' .... _-:-::-_, I ( .. ....) ,; , ......... - ___ / ', ..... / . cardW.ilhhOleallOWin g " ------_ ......... --------- wire to pass through I I / iron filings showing pattern of magnetic field plan view of card field of a short current-carrying coil /I~: """"-.. \\ ,.. [] _ ~, ~ --....... ,; / .... ',--'; \ '" . . :t---/ card with two holes _- - - ."1)/' ,"// ! t'l~, 'r - ..... , ~;:/ -- : I ,/ I I I I L - - _-101 •I I \ I \ -.... - j - -___ \ \ allowing wires 10 pass Ih raug h iron filings showing pattern of magnetic field I plan view of card field of a long current-carrying coil (solenoid) card with slots allowing wires to pass through iron filings showing pattern of magnetic field ' -- 1 1 I I plan view of card Figure 32.1 Magnetic fields produced by electric currents Note the following: • The magnetic field associated with the current in a solenoid is identical to that of a bar magnet. • Magnetic fi eld lines are directed out of the north pole and into the south pole of a current-carrying coil. • The direction of the field can be obtained by using the right-hand grip rule described next . 32 Electromagnetism , I 163 Right-hand grip rule current 1. For a straight conductor: Imagine gripping the wire with the right hand such that the thumb is in the direction of the current; the fingers will then be in the direction of th e magnetic field. 2. For a coil: Imagine gripping the coil with the fingers of the right hand in the direction of the current; the thumb will then indicate the direction of the magnetic field (th e end of the coil which acts as a north pole). Applying the right-hand grip rule to each of the experiments in Figure 32.1 results in the field directions shown in th e plan views. s N Magnetic fields of two parallel wires carrying current Figure 32.2 The right-hand grip rule The force s on the wires produced by the interacting magnetic fields are equal, in accordance with Newton's 3rd law (see Chapter 7) . • In Figure 32.3(a) the forces (F) of attraction are due to the longitudinal tension within the field lines . • In Figure 32.3(b) the forces (F) of repulsion are due to the lateral push between the field lines. ~ I , I I , '-:c~ side view . I~;O I f It..... I ·~ plan view offield a currents in same direction _ ~ . f /' ,-:~\ '" I r /~-, , 1/' ... --.... ... __ .... \ \ I ,\\1, r. .. , \ ~ ...... / ..... __ - 1 ' 1 \ " - - - ', ... ,./ .... - ___ ... insulating supports /~ I I / I r T \ .... \ .... - ___ - I ,,/ '. b currents in opposite directions Figure 32.3 Magnetic fields associated with parallel wires carrying currents Electromagnets An electromagnet is an electrical coil wound on a softiron core (Figure 32.4). The core significantly increases the strength of the magnetic field when the current flows. Electromagnetic relay ~ soft iron ~ iron being attracted iron being attracted Figure 32.4 Electromagnets Figure 32.6 shows another type of relay. When 5, is closed, the current in the coil magnetises the electromagnet, causing it to attract the soft-iron armature. The armature then rocks on its pivot and closes the graphite contacts, completing the circuit connected to terminals T, and T,. """"'.....-..... 164 , 32 Concise Revision Cou rse: C5EC' Physics \ .jo. I plan view of field One application of an electromagnet is an electromagnetic relay. Figu re 32.5 shows one type. When switch 5, is closed the current in the coil creates a magnetic field which magnetises the two soft-iron 'reeds'. The adjacent ends of the reeds beco me opposite magnetic poles and attract each other, completing the circuit connected to terminals, T, and T,. The reeds are protected from the environment by the inert gas in the glass enclosure. \ A ~ I , " ,,- ...... I':-"~ ... " '- ' c0 }:71T~ ~ \ .. \,':.-...;, I ': \ \ ~_\ 'I' \ "- side view , , These can be connected to a vehicle starter motor. When the ignition key,S " is turned on, the lowcurrent circuit of the solenoid switches on the high-current circuit to the starter motor. Note that the wires in the high-current circuit must be thick. T, inert gas in glass enclosure N ~ , , ~ metal graphite strips contacts _\ N S soft-iron thick wires 5 armature soft~rn reed soft-iron core of electromagnet -, I 1 Figure 32.5 Electromagnetic relay Figure 32.6 Another type of electromagnetic relay Force on a current-carrying conductor in a magnetic field Fig ure 32.7 shows a stiff wire hanging from a metal loop and immersed in a magnetic field. The lower end of the wire just touches the surface of mercury contained in a dish below. A force acts on the wire in accordance with Fleming's left-hand rule (described below), which pushes it out of the mercury and breaks the circuit. The current then diminishes to zero, the wire falls back into the mercury, and the process repeats. support plan view of magnetic field thrust or motion mercury in dish current Figure 32.7 Demonstrating the force on a current-carrying conductor in a magnetic field Flem ing's left-hand rule If t he first finger, the second finger and the thumb of the left-hand are placed mutually at right angles to each other (Figure 32.8), with the First finger in the direction of the magnetic Field and the seCond in the direction of the Current, then the ThuMb will be in the di rection of the Thrust or Motion. Th e strength of the thrust (force) Th e force is proportional to: a) the magnitude of the current b) the strength of the magnetic field. thrust or motion i First SeCond ThuMb ~curent /field ---+- Field ---+---+- Current Thrust or Motion Figure 32.8 Fleming's left-hand rule 32 Electromagnetism Use Fleming's left-hand rule to verify that the THRUST or FORCE on the current-carrying conductors in Figure 32.9 is as shown. to top of page perpendicularly out of page no THRUST or FORC E to the left Figure 32.9 Deflection of charged particles entering a magnetic field Moving charged particles that enter a magnetic field which is at right angles to their motion travel in a circular path (Figure 32.10), in accordance with Fleming's left-hand rul e. X := magnetic field into paper ~ Note the following: • The direction of current for the flow of negative charges is opposite to the direction of motion. Recall that the direction of an electrical current is the direction of flow of POSITIVE charge. t h,"st X -----.. X motion + X X X X X X X X deflection of positive charge • No work is done since the force (thrust) is always perpendicular to the displacement. 166 X X X X X X X curreffl ~ x motion X thrust axle fixed graphite brushes ;o J'. : ~.:- - 32 Concise Revision Cou rse: CSEC· Physics X X deflection of negative charge ,oct'"O"," coil commutator (split-ring) The left-hand side of the coil in Figure 32.11 (a) has a downward force on it, causing anti clockwise rotation. Half a revolution later (Figure 32.11(b)) it is on the right-hand side and requires an upward force to maintain the rotation. The split-ring is fixed to the axle and allows this to happen by switching connection between the a anti-clockwise rotation coil and battery every half revolution viewed from commutator as it rotates and rubs against the fixed graphite brushes (contacts). Figure 32.11 Simple de motor I:. X Figure 32.10 Deflection of positive and negative charged particles by a magnetic field Simple dc motor Current through a coil which is immersed in a magnetic field produces forces in accordance with Fleming's left-hand rule. Since the current flows in opposite directions in either side of the coil, the forces are in opposite directions, and the coil rotates about the axle. X current b anti·dockwise rotation viewed from commutator Fo r a motor, the strength of the thrust (force) is proportional to: a) the magnitude of the current b) th e strength of the magnetic field c) the number of turns of the coil (each turn of coil produces its own force). Electromagnetic induction Two impo rta nt laws 1. Whenever there is relative motion of magnetic flux (field lines) linked with a conductor, an em f is induced, which is proportional to the rate of cutting of flux (Farada y's law). If the circuit is complete, this emf will produce a current. 2. The induced current is always such as to oppose the motion creating it (Lenz's law). Figure 32.12 shows a metal rod being pushed downwards through a magnetic field. • As the conductor cuts through the magnetic field, an emf is induced which drives a current through the centre-zero galvanometer. The positive pole of the rod is the end which drives the current into the external circuit. This can be compared with a cell or battery - the rod is acting as a source of electricity. • If the rod is now pulled upwards, the induced current is in the opposite direction. • Moving the rod faster increases the magnitude of the current. metal rod centre-zero galvanometer -f field a ~ motion b Figure 32.12 Induced current in a metal rod Figure 32.13 shows a pole of a magnet being pushed into a coil. • An induced current is detected by the galvanometer. • Pulling the magnet out results in a current in the opposite direction. • Keeping the magnet stationary in the coil produces no current. • Increasing the speed of the magnet increases the magnitude of the current. • Increasing the strength of the magnet increases the magnitude of the current. induced N pole NI -- magnet pushed into coil Is induced S pole NI -- magnet pulled out of coil Is galvanometer Figure 32.13 Induced current in a coil 32 Electromagnetism f 167 As the rod in Figure 32.12 is moved through the magnetic field, and as the magnet in Figure 32.13 is moved into and out of the coil, the experimenter will experience a force opposing the motion. The opposition to the motion is in agreement with the principle of conservation of energy. The mechanical energy used to push against the opposing force converts to electrical energy induced in the conductor. Direction of emf and current The direction of the emf for the rod in Figure 32.12 can be obtained by the use of Fleming's righthand rule, in which the fingers and thumb represent the same as they do in Fleming's left-hand rule (Figure 32.8). Apply the rule to Figure 32.12(b) to confirm that the induced current direction shown is correct. The direction of the current in the coil in Figure 32.13 can be obtained by applying Lenz's law. If the N pole of a magnet is pushed into the coil it induces a N pole at that end of the coil, which opposes its motion. If the N pole of a magnet is pulled out of the coil it induces a 5 pole at that end of the coil, which opposes its motion. Then using the right-hand grip rule with the polarity of the coil gives the direction of the current. Transferring electrical energy between coils • Figure 32.14(a): On closing the switch, the current in coil A rapidly rises to some maximum value and then remains constant. In this time, the magnetic field associated with this current also grows to a maximum value and then remains constant. As it grows, the flux (field lines) enters coil B and induces a current in it. The magnetic poles induced in B are such as to oppose the entry of the magnetic field of A. • Figure 32.14(b): When the current in A reaches its maximum value and remains constant, the magnetic field associated with it no longer grows, but remains stationary. No current is therefore induced in B at this time. • Figure 32.14(c): If the switch in IVs circuit is now opened, the current will rapidly fall to zero. The magnetic field associated with this current therefore also diminishes to zero. As it does so, the flux withdraws from B and once more induces a current there. The magnetic poles induced in B are now such as to oppose the withdrawal of the magnetic field of A. Use the right-hand grip rule to confirm that the directions of current in coil B of Figure 32.14(a) and (c) are correct. • switch closed b switch remains closed c switch opened Figure 32.14 Transferring electrical energy between coils Simple ac generator A simple ac generator is shown in Figure 32.15. The coil is rotated with the sides P and Q cutting through the magnetic field. This induces an emf which drives current around the circuit in accordance with Fleming's right-hand rule. After every half revolution, the side of the coil which was moving downwards then moves upwards through the field, reversing the direction of the emf and producing an alternating voltage. The altern~ig voltage is transferred to the external circuit by a pair of slip rings which rub on a pair of fixed graphite brushes as the coil rotates. This ensures that each side of the coil is always 168 . 32 Concise Revision Course: CSEC· Physics connected to th e same output terminal for any coil position, allowing the ac generated in the co il to be transferred to the external circui t. Note that the slip rings are rigidly connected to the shaft and coi l and therefore rotate together. They are necessary so as to prevent tangling of the wi res con nected to the external circuit. motion motion motion motion coil viewed from slip rings coil viewed from slip rings Figure 32.15 The ac generator Ass uming clockwise rotation, use Fleming's righthand rule to ve rify that the currents in P and Q are as shown in Figure 32.15. The variation in the emf produced during one revo lutio n of the co il is illustrated in Figure 32.16. Use Flem ing's ri ght-hand rule with respect to the ' red' si de of the co il for the positions shown to verify that the current alternates as illustrated by the graph. E O ~ -T ~ -T ~ IT ~ I Figure 32.16 Output of ac generator Transformer 4 transform er is a device that increases or decreases an alternating voltage. Figure 32.17 shows a si mple transformer. The pri mary co il is co nnected to an ac supply of voltage Vp and the seco ndary coil delivers a voltage Vs to the device to be operated. Th e changing current in the primary coil produ ces a changing magnetic field w hich repeated ly grows into, and diminishes from, th e secondary co il, thereby induci ng an alternating vo ltage within it. ( primary coil (input)~ '\ /~:;-\' 6 I I , I I I IA v, rv I 'i' VC~.:->' secondary coil (output) V " rv v, c;> I I I I .I J I I I I I I \ ,./ soft-iron core magnetic flux passing from primary to secondary coit Figure 32.17 A transformer 32 Electromagnetism 169 • The soft-iron core allows the magnetic flux to easily pass from the primary to the secondary coil. • Direct current is not input to a transformer because it cannot produce a changing magnetic field. • Placing a fuse in the primary coil protects both coils from high currents, because current can only flow in the secondary if there is current in the primary. • Step-up transformers increase an alternating voltage and step-down transformers decrease it. • A transformer that increases the voltage decreases the current (see 'Calculations involving transformers' below). • The coil with the least number of turns carries the lower voltage and therefore the greater current. It should be of thicker wire to increase its conduction and prevent overheating. Long-distance ac distribution Power stations generate electrical energy at alternating voltages, which has to be transmitted over long distances to the city where it is consumed. The power lost as heat in the electrical cables is given by P = PR. In order to prevent large amounts of energy wastage, the transmission current (I) and the resistance of the cables (R) should be kept to a minimum. A step-up transformer at the power company increases the voltage and hence decreases the current. Where the electricity is to be consumed, a step-down transformer decreases the voltage to an appropriate value to be delivered to factories, homes and so on. Advantages of using ac for transferring electrical energy • Consumer appliances operate on several different voltages, which can easily be obtained from an ac mains supply by use of a transformer. • Transformers step up and down ac with minimum energy loss. • The ac can be transferred from the power station at small currents, resulting in minimum energy being wasted as heat in the resistance of the transmitting cables. • By stepping down the transmission current from the power station, thinner cables can be used and therefore the material cost is reduced. Calculations involving transformers vpand V, = voltage across the primary and secondary coils Np and N, = number of turns in the primary and secondary coils Ip and I, = current in the primary and secondary coils Pp and P, = power in primary and secondary coils • For an ideal transformer (which is 100% efficient) the following holds: Pp = P, V - p V, N I =-'=' N 1 , p Important note The current ratio is inverted compared with the ratios for voltage and turns. 32 Concise Revision Course: CSEC· Physics The primary coil of an ideal transformer is connected to a 120 V mains supply and is used to operate a 60 W 12 V device (F igure 32.18) . The primary coil is wound with 4000 turns of wire. Dete rmine: a the number ofturns on the secondary coi l b the current in the secondary coi l c the current in the primary coil. output (secondary) Input (primary) soft iron Figure 32.18 Ns Np a ~ 4000 Vs = v;- = ~ 120 12 N, = 120 x 4000 = 400 b P, = V"I 60 = 12/, I = 60 = 5.0 A , 12 Ip Vs c -=I, Vp Ip 12 5.0 = 120 12 Ip = 120 x 5.0 = 0.50 A (Note that as the transformer reduces the voltage, it increases the current.) Revision questions 1 Describe, with the aid of diagrams, experiments to investigate the magnetic fie ld patterns around each of the following current-carrying conductors: a straight wire b so lenoid Your diagrams should clearly indicate the direction of the current and the field. 2 Describe, with the aid of a diagram, one commercial application of an electromagnet. 3 Describe an experiment which indicates that there is a force on a curren t-carrying conductor placed in a magnetic fie ld. 32 Electromagnetism I 171 4 Figure 32.19 show s electrical currents flowing through magnetic fields. Determine th e direction of the thrust on the conductors in each case . o • b Figure 32.19 5 Sketch the magnetic field diagram for Figure 32.19(a). 6 With the aid of a diagram, explain the functioning of a simple de motor. 7 Describe how an induced current can be produced in a metal rod. 8 Redraw Figure 32.20, showing the current direction in the solenoid and the magnetic polarity at its ends, for each of the following cas es: a The N pole of the magnet is pushed into the coil. b The N pole of the magnet is left at rest in the coil. e The N pole of the magnet is withdrawn from the coil. solenoid magnet N ,--I_ _ _--"I s galvanometer Figure 32.20 9 State THREE ways by which the current produced in question 8 may be increased. 10 Sketch a diagram of a simple ac generator. 11 With the aid of a diagram, explain how a transformer can transfer electrical energy from its primary coil to its secondary coil. 12 State TWO advantages of using ac for the long·distance transmission of electricity. 13 An ideal transform e r has 4000 turns on its primary coil and 200 turns on its secondary coil. The primary coil is connected to a 120 V ac mains supply and the secondary to a 4.0 fl device. Draw a circuit diagram of the arrangement, and determine: a the voltage across the 4.0 fl device b the current through the secondary coil (and through the device) e the current in the primary coil d the power input and the power output. 172 32 Concise Revision Course: CSEC· Physics Exam-style questions Chapters 26 to 32 Structured questions 1 a) Complete Table 1 to compare the properties of the zinc-carbon cell and the leadacid accumulator. Table 1 Terminal voltage L Maximum current [ Internal resistance b) i) ii) >400 A 0.01 n (4 marks) Distinguish between the directions of conventional current and electron flow. (2 marks) State a type of conductor in which both positive and negative charges translate freely. c) A charge of 480 ~C (1 mark) flows through a resistor of resistance 500 n in a period of 12 ms. Determine: i) the cu rrent (2 marks) ii) the potential difference across the resistor (2 marks) iii) the number of electrons which flow (the charge on each electron is -1.6 x 10-19 C) (2 marks) iv) the electrical energy transformed. (2 marks) Total 15 marks 2 a) Figure 1 shows two oppositely charged particles and Figure 2 shows a current flowing in a wire perpendicularly into the plane of the paper between two magnetic poles. - - o s N - - Figure 1 Figure 2 i) Sketch the electric field lines between and around the particles of Figure 1 and the magnetic field lines associated with the current and magnetic poles of Figure 2. ii) By means of an arrow labelled F, show the direction of the force on the current-carrying conductor in Figure 2. (6 marks) r (1 mark) Exam -style questions - Chapters 26 to 32 ~-., 173 b) i) Determine the combined resistance between X and Y of Figure 3(a) and between P and Q of Figure 3(b). (4 marks) A current of 1 A flows in the 4 fl resistor of Figure 3(b). Determine: ii) (2 marks) the potential difference across the parallel section of the circuit (2 marks) iii) the total power used by the three resistors. ~ 5.0<> I ~ 2.0 <> x I ~ 4<> p -Q 2 <> y bl al Figure 3 Total 15 marks Extended response questions 3 a) Sketch graphs of current against voltage for each of th e following components when the potential difference is varied across them. Both graphs should have positive and negative axes. i) Filament lamp (3 marks) ii) Semiconductor diode (3 marks) A graph of current against potential difference for a particular component is a straight line and passes through the origin. (1 mark) iii) What can you dedu ce about the res istance of the co mponent ? b) The variable resistor (rh eostat) shown in Figure 4 has a maximum resistance of 10 fl. emfj 5.0V I' .1f / RA= 10 n A Figure 4 The rheostat is initially set to 0 fl . Determine: i) the current in the circuit. (2 marks) The rheostat is adjusted to have its maximum resistance. Determine: ii) the new cu rrent iii) the potential difference across resistor A iv) the power used by A. (2 marks) (2 marks) (2 marks) Total 15 marks 174 Exam-style questions - Chapters 26 to 32 4 a) i) ii) b) i) ii) Explain how a transformer can alter the value of an alternating voltage. (3 marks) State THREE advan tages of using ac for transferring electri cal energy. (3 marks) Indi cate, by means of arrows, the directions of th e cu rrent induced in th e metal rod and in the coil of Figure 5. (3 marks) (1 mark) Mark th e indu ce d north pole of the coil with th e letter N. iii) Indi cate the polarity of the rod by marking + at the co rrect end. lJ t ~LC (1 mark) metal magnet pulled out of coil -. motion Figure 5 c) An ideal transformer has 6000 turns and 1000 turns on its primary and secondary co ils re spectively. It is used to operate a 100 W 20 V devi ce. Determine: i) th e input voltage (2 marks) ii) th e c urrent in the secondary coi l. (2 marks) Total 15 marks Exam-styl e questions - Chapters 26 to 32 175 33 The atom Models of the atom Evolution of the concept of the atom z400BC The Greek philosopher, Democritus, suggested that matter consisted of small indivisible particles. He called these particles 'atomos', from the Greek word for indivisible. 1897 Joseph John Thomson viewed the atom as a positively charged sphere with smaller, negatively charged, fixed particles (electrons) interspersed within it, the resultant charge being zero. This is known as the plum pudding model of the atom. 1911 Ernest Rutherford proposed that most of the atom is empty space and that it contains a nucleus of very concentrated positive charge. He suggested that small negatively charged particles exist in a surrounding 'electron cloud', making the net charge zero. 1913 Niels Boh r suggested that the negatively charged electrons orbit the nucleus in particular shells. A unique energy value is required by an electron to exist within any shell. 1932 James Chadwick discovered neutrons, uncharged particles that exist together with protons within the nucleus of an atom . Neutrons were difficu lt to detect because, unlike protons and electrons, they have no charge, and are therefore unaffected by electric and magnetic field s. positive sphere - 'pudding' negative charges - 'plums' @ electrons scattered in region of mainly empty space electrons I- - "-'>-+-r concentrated n.-I--t-, concentrated nucleus of protons and neutrons positive nucleus concentrated positive nucleus J. J. Thomson electrons in shells in shells E. Rutherford J. Chadwick N. Bohr (H. Geiger & E. Marsden) Figure 33.1 Successive models of the atom The Geiger-Marsden (or 'Rutherford scattering') experiment Ernest Rutherford worked with Hans Geiger, investigating the behaviour of alpha particles when fired through metals. In 1911, Geiger, together with a student, Ernest Marsden, carried out a research proj ect in Rutherford's laboratory, measuring the angles of deflection of the alpha particles (Figure 33.2). They shot alpha particles through a thin sheet of gold foil and observed the scintillations produced as the particles struck a zinc sulfide screen. The chamber was evacuated because alpha particles are stopped by just a few centimetres of air. The microscope could be rotated to observe the scintillations received at any angle. vacuum gold atoms gold foil (1 11m thick) \ scintillations seen 't t. on zinc sulfide screen ./ ~: . i, microscope rotates .- ./'1 .1: ~ey alpha source i lead castle ! The arrows indicate the paths of the alpha particles. Very few were deflected. Figure 33.2 The Gieger-Marsden (or 'Rutherford scattering') experiment Rutherford analysed the observations and made his conclusions. 33 Concise Revision Course: CSEC' Physics Observations 1. Most of the particles passed straight through the foil without deflection. 2. Very few were deflected, but those that were, did so with extremely high speeds, even at large angles of deflection. Conclu sions 1. Most of the atom is empty space. 2. The nucleus is extremely dense, and consists of positive charges which repelled the positively cha rged alpha particles. Stru cture of the atom Th e Periodic Table is a table of elem ents of increasing proton number, arranged so as to categorise their electronic configurations and chemical properties. Groups III 1 ~ • . ."• 0 N V VI 0 VlI H 2 Li 3 Be 4 B 3 N, 11 Mg 12 AI 4 K 19 C, 20 He Ne 5 F 9 13 CI 17 Ar 2 10 IB Figure 33.3 The first 20 elements of the Periodic Table: their symbols and their proton numbers • The I'roton number or atomic number, Z, of an element is the number of protons contained in the nucleus of an atom of the element. Neutral atoms have the same number of protons as electrons. • The neutron number, N, of an element is the number of neutrons contained in the nucleus of an atom of the element. • The mass number or nucleon number, A, of an element is the SUM of the numbers of protons and neutrons contained in the nucleus of an atom of the element. A=Z+N Isotopes of an element have the same atomic num ber but different mass numbers. Table 33.1 Mass and charge of sub-atomic particles 1 1 1 1840 Relative charge +1 0 -1 Actual mass/kg 1.7x 10-27 1.7x 10-27 9.1 x 10-31 Actual charge/C 1.6x10-19 0 -1.6 x 10-19 Relative mass Representation of a nuclide A nuclide is a nucleus with a particular number of protons and neutrons. It is represented by: AX Z wh ere X is the symbol of the element. For example: ~i Na: this nuclide contains 11 protons and 13 neutrons ~ Na : th is nuclide contains 11 protons and 12 neutrons 33 The atom Representation of a subatomic particle N+Z y relative charge where Y is the symbol for th e particle. For example: ~ p: ~ n: proton _ ~e neutron : electron Electron configuration An electron configuration shows the number of electrons in each shell. See Figure 33.4. 24 Na 1 23 Na ~ 1 3 177CI ~ isotopes of Na same period (3) 3 shells same atomic number different mass number 19r ~ 9 same group (VII) 7 electrons in outer shell Figure 33.4 Electron configurations For the first 20 elements of th e Periodic Table, the shells can hold thes e maximum numbers of electrons: 2nd shell: 8 electrons 1 st shell: 2 electrons 3rd shell: 8 electrons Meaning of the periods and groups of the Periodic Table Period: Th e period number indicates the number of shells of the atom. Groul': The group number indicates the number of electrons in the outer shell of the atom. See Figure 33.4. Revision questions 1 State the contribution made by each of the following in the evolving theories of the structure of the atom: Thomson, Rutherford, Bohr, Chadwick. 2 a) Describe, with the aid of a diagram, the important experiment of Geiger and Marsden. b) State the observations made in the Geiger-Marsden experiment, and the conclusions drawn from those observations. c) What made the neutron so difficult to discover? 3 a) Sketch the structure of the following atoms, showing, for each, the numbers and positions of its sub-atomic particles. ;;Mg ~ Ca 1:F b) Using the same notation, state a possible isotope of ;:;Ca. c) Represent the proton, neutron and electron using this notation. 4 Construct a table showing the mass and charge of the neutron and the electron, relative to the proton. a) If the electron has a mass of 1 unit, what would be the mass of a proton? b) What can be said of the numbers of protons and electrons in a neutral atom? 5 Define each of the following: a atomic number b mass number 33 Concise Revision Course: CSEC· Physics C isotopes 34 Radioactivity Rad ioactive emissions Marie Curie's work in the field of radioactivity Marie Curie was born in Poland in 1867. Following up on Henri Becquerel's work on the radiation emitted from uranium, she realised that the intensity of the rays was dependent only on the mass of th e emitting sample. Since no environmental conditions could alter the intensity, she concluded that radioactivity is an atomic phenomenon. In 1903 Marie and Pierre, her husband, shared the Nobel Prize in Physics with Henri Becquerel for their work on radioactivity, and in 1911 she was awarded another Nobel Prize, this time for the isolation of the elements polonium and radium. Her work opened the field of radiotherapy and nuclear medicine. She died in 1934 from the cumulative effects of the radiation that she encountered during her investigations. The nature of radioactivity Radioactivity is the spontaneous disintegration ('decay') of unstable atomic nuclei. The nucleus becomes more stable by emitting alpha particles, beta particles andlor gamma waves. Some of the properties of these types of emissions are outlined in Table 34.1. . . ,. .. Table 34.1 Properties of radioactive emissions . Nature 2 protons and 2 neutrons tightly bound Symbol Relative mass Beta particle ([3) Gamma wave ("'I) 1 electron High-frequency electromagnetic wave _ ~ [3 4 1 zero 1840 Relative charge +2 -1 Speed (in air or vacuum)/m S-1 2 x 10' Up to almost the speed of light Ionisation of the air strongly ionising on collision with neutral air molecules Absorbed by a thin sheet of paper or about 5 cm of air Detection of presence by GM tube and accessories zero 3 X 10' weakly ionising on very weakly ionising collision with neutral air when the wave energy molecules is absorbed by air molecules a few m of air or about 3-5 mm of aluminium several m of concrete (4 cm of lead absorbs 90%) GM tube and GMtube and accessories accessories Background radiation is the ionising radiation within our environment arising from radioactive elements in the Earth and its surrounding atmosphere, plus X-rays from medical equipment and highspeed charged particles from the cosmos. 34 Radioactivity Detection using the Geiger-Muller tube Radioactive emissions may be detected by a Geiger-Miiller tube (G M tube) and accessories. Radi atio n entering the tube produces a current which may be passed to one of the following: • a rate meter, which gives the rate at which emissions occur o a loudspeaker, which produces a sound whenever the GM tube detects an emission • a scalar, which counts the emissions. The activity of a sample of radioactive material is the rate at which the nuclei decay. The unit of activity, the becquerel (Bq), is the rate of one nuclear disintegration per second. Received count rate The received count rate detected by a GM tube depends on the distance from the source to the detector. Experiments investigating the activity of a source should therefore maintain a constant distance between it and the detector. The count rate observed will also include that due to background radiation. This must be subtracted from the received count rate to obtain the correct portion detected from the source being investigated. Testing for the type of radiation 1. Absorption test (Figure 34.1) o The background count rate is measured . o The source is then placed in front of the GM tube and the count rate is again measured . o A thin sheet of paper is placed between the source and detector and the count rate is measured. If the activity is reduced to the background count rate, then the source is an a-emitter. o If the activity is unaffected, then the source is eithe r a i3-emitter or a "I-emitter. The paper is replaced by an aluminium sheet of thickness 5 mm. If the activity now returns to the background count rate, then the source is a l3-emitter; otherwise, it is a "I-em itte r. source absorber (paper or aluminium) In VL:\=J rn ~ lead castle ~M detector Figure 34.1 Absorption test Alpha particles are readily stopped by air, and therefore for experiments where there is the poss ibility of a -emission, either the source must be placed very close to the detector or the apparatus should be set up in a vacuum. 2. Electric field deflection test (Figu re 34.2) o The count rate is taken with the electric field switched off. o The electric field is then switched on. a) If the count rate is unaffected, the source is a "I-em itte r. b) If the count rate falls and only returns to its initial value when the detector is shifted towards the positive plate, then the source is a i3-emitter. The positive plate will attract the negative i3-particles. c) If the count rate falls and only returns to its initial value when the detector is shifted towards the negative plate, then the source is an a-emitter. The negative plate will attract the positive a-particles. 34 Concise Revision Course: CSEC' Physics metal plates source In lead castle GM detector Figure 34.2 Electric field deflection test 3. Mag netic field deflect ion t est (Figure 34.3) • The count rate is taken in the absence of the magnetic field. • The magnetic field is then directed perpendicular to the path of the rays as shown in Figure 34.3 . a) If t he count rate is unaffected, th e source is a "I-emitter. b) If the count-rate falls, the detector should be shifted until it returns t o its previous value. Current is a flow of charge and therefore a - and l3-particles will experience forces in accordance with Fleming's left-hand rule (see Chapter 32). Remember that the direction of the current is the direction of flow of positive charge. Apply Fleming's left-hand rule to Figure 34.3. Although an a-particle has twice the charge of a l3-particle, it is deflected less, because its mass is much greater than that of the l3-particle (see Table 34.1). x source in x x x lead castle ~-D .:-:: .. X represents X ~ on on .. X magnetic field into plane of paper x _ .. -I 1 Y X GM detector X X Figure 34.3 Magnetic field deflection test 4. The diffusion cloud chamber test Rad ioactive sources produce cloud tracks in a device known as a cloud chamber. The tracks become visi ble as condensation occurs on ions created by the radiation, and are characteristic of the type of rad iation as illustrated in Figure 34.4. • a tracks: An a-particle has a mass of more than 7000 times that of a l3-particle. The a-particles are strongly ionising on collision with other particles and produce thick tracks. The tracks are straight because a -particles are not eaSily deviated on collision with other particles. • 13 tracks: l3-particles are only weakly ionising, d ue to their relatively small mass, and produce weak tracks. The tracks are randomly directed because these particles deviate readily on collision with other particles. • "I tracks: These tracks are extremely weak and dispersed. The ions in this case are produced when a "I-wave is absorbed by an atom, resulting in the ejection of an electron. i'.J " Ptracks a. tracks ytracks Figure 34.4 Tracks produced in a cloud chamber Beta emission Beta particles (electrons) are emitted from the nucleus of an atom. During beta emission, a neutron in the nucleus decays into a proton and an electron. The electron shoots out of the atom as a high-velocity l3-particle, leaving the newly formed p ro ton within the nucleus (Figure 34.5) . o -. neutron + proton !}particle Figure 34.5 Neutron decay and beta emission Equations of radioactive decay Table 34.2 Common symbols used in nuclear equations Neutron • When an isotope emits an a-particle it becomes an element two places back in the Periodic Table. 2~ Ra ---+- ; He + 2~ Rn 34 Radioactivity • When an isotope emits a [3-particle it becomes an element one place forward in the Periodic Tab le. The mass number is unchanged. He - . {, °e+ 147 N -1 • When an isotope emits a 'I-photon its atomic number and mass number remain unchanged. ~ Pa --+- ~ Pa + "Y Some nucl ei may remain in an excited state (more energetic state) after emitting an n- or [3-particle. A 'I-photon is then emitted, returning the nucleus to its more stable, ground state. 2~ U ---+ 2~ ~ Sr + Th ;a+ "y ---+- ~ y + _~ ~ + 'Y During radioactive decay, the decaying nuclide is called the parent and the new nuclide produced is the daughter. The nature of the radioactive decay process Radioactive decay is random. This can be compared to throwing dice, tossing a coin or shooting at a target. If a radioactive source is placed in front of a GM detector the following will occur, depending on the instrument connected to the GM tube: • the ratemeter needle will flicker • the 'cl icks ' from the loud speake r will be heard at a random rate • the scalar will indicate a random increment of the detected emissions. Although the activity of a radionuclide is random, there is a definite period for half of a given sampl e to decay. The half-life of a radioisotope is the time taken for the mass (or activity) of a given sample of it to decay to half of its value. The half life of a radioactive material is not affected by conditions external to th e nucleus. This includes: a) physical conditions such as temperature and pressure b) chemical conditions such as whether or not the isotope is in its pure state or chemically combined with some other element in a compound. Graphs showing exponential decay Figure 34.6 shows that radioactive decay is exponential with time. Note that the curve never meets the time axis but gets close r and closer to it. The activity (the rate of decay) is measured by the count rate, and is proportional to the number of atomic nuclei remaining at any particular time. It is therefore proportional to the mass at that time. The vertical axis of the graph can show mass, count rate (or activity), or number of nuclei remaining. The half-life is found by choosing any point on the graph and finding the time for its mass, count rate, or number of nuclei remaining, to fall to half of its value at that point. An average from THREE decay periods gives a more accurate result. 34 Concise Revision Cou rse: CSEC· Physics x ~ ", a u " x/2 ~ ~ m E x/ 4 x/8 I I I I 8 16 ---1--- o 24 36 time/days Figure 34_6 Graph showing exponential decay and half-life Simulating radioactive decay • About 300 dice are placed in a bucket. The number of dice, 0, is recorded. • The bucket is em ptied (the dice 'thrown ') and the dice with the value 6 facing upward are removed. The new value of 0 is recorded. • Th e process is repeated using the remaining dice, recording the number of throws, N, and the new valu e of 0, until fewer than 25 dice remain. • A graph is plotted of 0 against N, as shown in Figure 34.7. D Note: • Th e points on the graph are not exactly on the smooth curve drawn through them because the generation of the value 6 occurs at random. x half-life x/2 • The exponential nature is indicated by the curve. • • As 0 decreases, the outcome of each throw becomes statistically less accurate. • • The ' half-life' of this decay can be found by reading from the graph THREE values of 0 and determining the co rresponding time taken for 0 to fall to half of its value. These three half-lives can then be averaged. o N Figure 34.7 Simulating radioactive decay: dice remaining versus number of throws Calculations involving half-life The following Examples illustrate these two methods: Arrow method • Each arrow represents a half-life transition and points to half the value it originates at. • The total time of decay is the sum of the half-lives. Tab le method • Particularly useful if a graph is to be plotted. • The 'Time' column always starts at 0 and increases by one half-life for each new row. • The 'Activity' or 'Mass remaining' column decreases to half its value for every new row. A radioisotope gives a count rate of 50.0 Bq. Determine the count rate after 40 years if its half-life is 20 years. Arrow method: 50.0 Bq -+- 25.0 Bq -+- 12.5 Bq 20 Y 20 Y After 40 years, the count rate is 12.5 Bq. Table method: Activity/Bq Timely 50.0 o 25.0 20 12.5 40 34 Radioactivity A radioisotope has a mass of 200 g and a half-life of 25 ms. Determine the time taken for it to decay to a mass of 25 g. Arrow method: 200g --+ 100g --+ 50g --+ 25g 25 ms Time taken to decay to 25 g Table method: 25 ms 25 ms = 3 x 25 ms = 75 ms Mass/g Time/ms 200 0 100 25 50 50 25 75 A radioisotope decays to":!" of its mass in 12 weeks. Determine its half-life. 8 Arrow method: With fractions, start with 1. So 12 weeks represents 3 half-lives. One half-life =12 weeks =4 weeks 3 Table method: 1 o i 4 4 1 8 1 12 "8 A radioisotope of mass 80 g has a half-life of 5700 yea rs. Determine its mass 17 100 years ago. Arrow method: 17100 = 3 5700 So it has decayed for 3 half-lives. Work backwards from 80 g for 3 half-lives: 640g --+ 320g --+ 160g --+ 80g 17100 years ago, the mass was 640 g. Table method: Mass/g 640 Timely 0 320 5700 160 _---C..: 11400 80 17100 34 Concise Revision Course: C5EC· Physics II1I A radioisotope has a half-life of 30 days. How long will it take for its mass to fall by 87.5%? Arrow method: With percentages, start with 100%. It falls BY 87.5% and therefore falls TO 12.5%. 100% _ 50% _ 30 d 25%' _ 12.5% 30 d 30d It takes 3 half-lives, so 3 x 30 days = 90 days, to fa ll by 87.5%. Tab le method: 50 30 25 60 12.5 90 Radio-carbon dating W hen an animal or a plant dies, its decaying C-14 (radioisotope carbon-14, or " C) is no longer replaced, so the ratio of C-14 to non-radioactive C-12 decreases with time. Every 5730 years the amo unt of C-14 in a dead specimen falls to half the mass it had at the beginning of that period. If the amount of C-14 per gram of carbon in a living organism is known, together with the amount fou nd per gram of carbon in an old specimen, the age of the specimen can be calculated . In natural carbon there is only one atom of C-14 with every 8 x 10" atoms of carbon. Due to this very small proportion of C-14 in a sample of carbon, even from a living organism, the count rate obtained fro m very old specimens is very low. This type of dating is therefore not useful for determining the age of samples which have been dead for over 60 000 years (about 10 half-lives). A mass of 1.0 g of carbon from a living plant gives a count rate of 19.0 min-'. An extremely o ld specimen is found and 6.0 g of carbon is extracted from it. The count rate produced by this sample is 28.5 min-' . Given that the half-life of C-14 is 5730 years, determine the age of the old specimen. We need to compare equal masses of the living organism and the old specimen. For the old specimen: 6.0 g gives a count rate of 28.5 min-' . 28.5 48 . , . 1.O g gives a count rate 0 f - = . mln6.0 The activity of 1.0 g has reduced from 19.0 min-' since the plant died. Arrow method: 19.0 min-' _ 9.5 min-' _ 5730 Y 4.8 min-' 5730 Y So the age of the old specimen is 2 x 5730 = 11460 years. Table method: 19.0 o 9.5 5730 4.8 11460 34 Radioactivity Uses of radioisotopes Medical uses - cancer therapy 1. Externa l beam radiotherapy Gamma radiation from cobalt·60 can be used to destroy malignant growths (cancerous tumours). The treatment is only useful if the cancer is localised in a small region, because the radiation also destroys good cells. This type of therapy has its problems. a) Normal tissue is irradiated between the surface and the tumour. b) The beam cannot be sharply focused so tissue surrounding the target can be affected. c) Bone may shield the tumour from receiving radiation. The use of Co·60 for external beam radiotherapy is no longer common. It has been replaced by highenergy X-rays, because the X-ray beam is much easier to control and a sharper focus can be obtained. 2. Surface and implant radiotherapy Radioactive sou rces may be a) st uck to the patient's skin to treat skin disorders b) placed in a tumour in the form of needles, as in the treatment of breast cancer c) placed into capsules and inserted into body cavities, as in the treatment of cervical cancer. The sou rces used can have short or long half-lives because they can be removed from the patient at any time. Short-range radiations (oc, 13 and low-energy "I) are used so that they are totally absorbed by the malignant region. 3. Radiopharmaceut ical therapy This form of treatment is used when a pharmaceutical (drug) can carry the radioactive source to the target site. An example is in the treatment of thyroid cancer. The thyroid uses iodine so if a patient is given a dose of iodine, it is targeted there. lodine-131 emits 13- as well as "I-radiation. Its l3-radiation is particularly useful in destroying cancer cells. In order to protect others, patients should remain in th e hospital until a safety level of radiation is reached. It is important that for this form of therapy the sources have short half-lives so as not to expose the patients to excessive doses of radiation for long periods. Medical uses - d ia g nost ic Radioisotopes used for diagnosis are preferably "I-emitters, because "I-radiation is least absorbed by the body. 1. Rad ioactive tracing A radioactive tracer is a chemical compound in which one or more elements have been replaced by radioisotopes, used to investigate chemical reactions by tracking the path it follows. In medical diagnosis a suitable tracer is given to the patient orally or as an injection, and a detector is used to follow its path through the body. lodine-123 is used as a tracer to investigate the functioning of the thyroid. 34 Concise Revision Course: CSEC· Physics 2. Photography Th e patient is given a "V-emitting radioisotope which can be targeted to a particular region within the body. A scanner or gamma camera is positioned outside the patient to detect the emitted radiation. Tu mours present will show up as a shadow in the image, since they will absorb th e radiation. lodine-123 can be used for thyroid scans. It only emits "V-radiation, unlike 1-131 which also em its the stro nger [3-radiation . . Techne tium-99m (Te-99m), also a "V-emitter, joins to phosphate compounds which collect in bones, so th is is therefore important for bone scans. Non-medical uses Ot her photography Gamma radiation is used in the photography of metal castings to investigate weak areas. Other tracers Wate r containing a "V-sou rce can be pumped below the ground. Engineers then use detectors to trace its flow as it seeps through cracks to the surface. This gives them information of th e strength of the fo undations for potential building sites. Radio-carbon dating The age of an o ld organic specimen can be calcu lated by measuring the amount of ca rbon-14 it contains, as discussed ea rlier in the chapter. Sterilisation The objects to be sterilised are packed and sealed in plastic containe rs which are then irradiated by "V-radiation from cobalt-60 to kill bacteria. Some foodstuffs are also sterilised in this way. Thickness measurements Beta or gamma radiation may be passed through va rious materials, and by examining the amount of radiation that penetrates, the thicknesses of the samples can be determined. Strontium-90, a "V-e mitter, is used for measuring the t hi ckness of meta l sheets (Figure 34.8). material under 0-- beta source 0- GM detector Figure 34.8 Thickness measurement Choice of half-life in applications Long half-life Sources used for thickness measurements should have long half-lives so that their activity remains steady during the measurement. Sources used in dating must have very long half-lives so that they still emit, even after thousands of years. Radioisotopes used for external beam, surface or implant radiotherapy can have long or short half-lives because they may be removed from the patient's en vironment at any time. Short ha lf-life Sou rces given to patients orally or by injection should have short half-lives so that they are not in the patient at dangerous levels for long periods. The half-life, however, cannot be too short, because tim e is needed for th e radioisotope to be transported by the blood to the target site. The half-lives of some radioisotopes used in the medical field are: technetium-99m (Te-99m) - "V-emitter - half-life 6 hou rs iodine-131 (1-131) - [3- and "V-emitter - half-life 8 days iodi ne-123 (1-123) - "V-emitter - half-life 13.2 hours 34 Radioactivity Nuclear fission and fusion Nuclear fission is the splitting of a large atomic nucleus into two nearly equal parts, resulting in a large output of energy and a decrease in mass. heavy nucleus + + ENERGY OUTPUT (loss in mass) Figure 34.9 Nuclear fission Nuclear power plants produce electricity by nuclear fission in controlled reactors. The 'atomic bomb' also utilises nuclear fission. Two possible fission reactions of uranium-235 (U-235) are shown below. A stray, high-speed neutron penetrates the uranium nucleus and triggers the reaction. 235U + 1n ---+- 141Ba + 92Kr + 31n + energy 92 2~ 0 U +~ n 56 36 0 ';:Ba + ~ Kr + 2 ~ n + energy Nuclear fusion is the ioining of two small atomic nuclei to produce a larger nucleus, resulting in a large output of energy and a decrease in mass . ---+- light nuclei + + ENERGY OUTPUT (loss in mass) Figure 34.10 Nuclear fusion Nuclear fusion is the process by which radiant energy is produced by the Sun - in the core of the Sun, energy is generated by two hydrogen nuclei as they join to form a single helium nucleus. The ' hydrogen bomb' also utilises nuclear fusion. Two ways by which hydrogen nuclei fuse to helium : ~ H +~ H ---+-- ~ He + ~ n + energy ~H +~ H ---+-- ~He + ~ n + energy These reactions require temperatures in excess of 10' K to allow the positive hydrogen nuclei to travel fast enough to ove rcom e the very strong electrical repulsion that exists between them. The difficulty of maintaining these extremely high temperatures has been the main obstacle in the design of fusion reactors. Einstein's equation of mass-energy equivalence When nucl ei undergo fission or fusion the resulting nuclei are, as in radioactive decay, more stable, and energy is released. The energy output by a nucl eus during radioactivity, nuclear fission and nuclear fusion is obtained by a reduction in its mass. Th e mass defect is directly related to the energy output: tlE = tlmc' This equation was famously proposed by Albert Einstein. tlE = energy output tlm = mass defect c = speed of light in a vacuum 34 Concise Revision Course: CSEC' Physics The Sun radiates energy at a rate of 3.6 x 10" J S-1. This energy originates from nuclear fusion reactions. Determine the loss in mass each second. In 1 s, 3.6 X 10" J is converted from mass to energy. tlE; tlmc' M - ;tlm c;2 3.6 x 1023 (3.0 X 10')' tlm 4.0xl0'kg;tlm The nuclide ';:Po emits an ex-particle to form '~ Pb. a Write an equation for the reaction. b Determine the energy released by an atom of ' ~Po as it undergoes nuclear decay. Atomic mass of Po-21 0 ; 209.9829 u Atomic mass of He-4; 4.0026 u Atomic mass of Pb-206; 205.9745 u 1 atomic mass unit, u; 1.66 x 10-" kg Speed of light in a vacuum; 3.0 x 10' m a 2~ PO ----. ~ He +~ Pb S-1 + energy b Step 1: Find the mass defect, 11m, in atomic mass units, u. 210PO; 'He + "'Pb + energy 84 2 82 209.9829 u ; 4.0026 u + 205.9745 u + tlm 5.8 x 10-3 u ; tlm Step 2: Convert u to kg. 5.8 X 10-3 x 1.66 9.63 x 10-30 X 10-" ; tlm kg; tlm Step 3: Calculate M. M; tlmc;2 M; 9.63 x 10-30 (3.0 x 10')'; 8.7 x 10-13 J Pros and cons of nuclear power stations Ad va ntages 1. In the absence of natural disasters, they do not contaminate the environment if carefully managed. They do not produce greenhouse gases such as methane or carbon dioxide, or other hazardous gases such as sulfur dioxide or carbon monoxide. 2. When compared to obtaining energy from fossil fuels, fewer lives are lost each year per unit of energy produced. 3. Many radioactive materials used in medicine are produced at nuclear power plants. 34 Radioactivity 4. A small amount of nuclear fuel produces an enormous amount of electricity, and therefore delivery and storage of the fuel is relatively cheap. 5. A large supply of U-235 is available. D isadva nt ag e s 1. Nuclear radiation can destroy or damage living organisms. It can alter the DNA of cells and can produce cancers and other abnormal growths. 2. Staff working with radioactive material are irradiated by radioisotopes which contaminate their surroundings, and may be contaminated themselves if they ingest the material. 3. Used radioactive fuel still contains radioactive material and is hazardous to the environment. It is usually stored under water in order to remove the excessive heat it produces. The water also acts as a radiation shield for the surroundings . 4. There is the possibility of a catastrophic effect if there is a critical malfunction at the plant. Huge explosions can spread the radioactive material over large areas and the radiation could impact heavily on the planet. 5. Nuclear power stations have to be shut down after several years because the plant and machinery become heavily contaminated. This is very costly and hazardous. Hazards of ionising radiations • Radiation ' burns' can be obtained by those receiving high doses. • DNA may be damaged. This can cause changes which may lead to cancer or to genetic mutations. Sources outside the body: If the source is several metres away, only "I-radiation is dangerous, because a- and i3-particles cannot travel this distance in air. Sources inside the body: If the source has been ingested or inhaled, a- and i3-radiation are very dangerous, because the emissions will be heavily absorbed by the body cells. Gamma radiation is not as dangerous since much of it passes through the body and only a portion of the electromagnetic energy is transferred to the cells. The tri-foil, the international hazard symbol for ionising radiation, is shown in Figure 34.11. It has a yellow background. Figure 34.11 The hazard symbol for ionising radiation Safety precautions against the hazards of ionising radiations • The tri-foil hazard sign must be visible wherever ionising radiation is hazardous. • All radioactive samples should be labelled by name, and as being radioactive and dangerous. • The use of robotic arms, tongs or gloves should be employed when handling radioisotopes. • One should never consume food or drink when in a location where there is radioactive material. • Radioactive samples should be stored in lead containers. • One should wear lead-lined clothing or stand behind lead-lined walls when working with radioisotopes. • One should comply with current regulations on the disposal of radioactive waste. • Nuclear weapon testing must be done underground. 34 Concise Revision Course: CsEC· Physics Revision questions 1 Marie Curi e realised that the intensity of radiation from uran ium was proportional only to th e mass of the emitting sample and that nothing cou ld be done to change this. a What important conclusion did she make from thi s obse rvation? b State the reason she was awarded EACH of her two Nobel prizes. c What important field did her work open for others to develop? 2 Define the following with respect to nuclear emissions: a radioactivity 3 b activity of a sample C becquerel The cloud chamber can be used to identify radioactive emissions. a Draw diagrams to illustrate the tracks associated with each type of emission. b Briefly describe and explain these tracks in terms of strength and direction. 4 a State the nature of each of the following: a-particle ii i3-particle iii 'I-wave b For each of the following, state the type of radiation (a, i3 or 'I) th at has the particu lar characteristic. Has the strongest ionising capabi lity ii Is stopped by a thin sheet of paper or a few cm of air iii Has the strongest penetrating capabi lity iv Cannot be deflected by an electric or a magnetic field v Is deflected most by an electric or a magnetic field vi Can penetrate no more than a few mm of aluminium vii Is a particle of relative charge +2 viii Is a particle of charge - 1.6 x 10-" C 5 ix Is comprised of particles of tota l charge +3.2 x 10-19 C x Is comprised of particles of total mass more than 7000 times that of an electron a What is meant by background radiation? b Id entify THREE sources of background radiation. 6 Describe an experiment, using EACH of the methods listed below, to determine the type of radiation being emitted by a radioactive source. a absorption test b electric field deflection test c magnetic fi eld deflection test 7 State the numbers that sho uld replace the boxes in the following nuclear equat ions. a 214 PO _ a + O Pb b O Pb _ i3 + 21° Bi C 99mTc _ 'I + O Tc 8 A mass of4.0 g of iodine-131 (1-131), of half-life 8 days, decays for a period of 24 days. o 82 82 0 0 43 a Define the term half-life. b What mass of 1-131 remains after this time? C 9 Sketch a graph of mass against time for the decay. A samp le of the metal sod ium-24 (Na-24) at a temperature of 20 °C is left for a period of 30 hours. After this time its activity falls by 75%. a Determine the half-life of Na-24. b What wou ld be the half-life if the temperature was 40 °0 C Would the half-life be affected if the sample was in the form of the compound NaCI? 34 Radioactivity 10 It is said that radioactivity is a random process. a How can the use of a Geiger tube and accessories be used to verify this random nature ? b How can an experimental plot of count rate against time illustrate th e random nature? 11 A sample of 1.0 g of carbon from a live plant gives a count rate of 20 min-' . The same mass of carbon is analysed from an old relic and gives a count rate of 5 min-' . a Assuming the half-life of C-14 to be 5700 years, determine the age of the relic. b Why is C-14 dating not useful for ageing specimens over 60 000 years old? 12 a Briefly describe the use of the following in the medical field, stating a suitable radionuclide in each case: ii tracers external beam radiotherapy b State TWO problems with the use of external beam radiotherapy. 13 The following is about radioisotopes used in the medical field. a Explain why the half-life of a radioisotope given orally or by injection to a patient must be short, but not too short. b Name the type of radioactive emission that is least absorbed by the body. In questions 14, 15 and 16 use: speed of light in a vacuum = 3.0 x 10' m sol. 14 1 g of matter is completely transformed into energy. a Write the equation needed to calculate the amount of energy produced. b Identify each quantity in the equation. C Name the scientist associated with this equation. d Calculate the energy derived from the mass. 15 A certain star is losing mass at a rate of 2.0 x 10' kg So, . Determine its power output. 16 Determine the energy released during the fusion of the hydrogen nuclei shown below. ;H+;H ----... (; H = 3.345 x 10-27 kg, ; H ~ He = 5.008 x 10-27 kg, ; n +~ n = 1.675 x lo-27 kg) 17 Briefly describe TWO advantages and TWO disadvantages of obtaining electricity from nuclear energy. 18 Alpha, beta and gamma radiation are ionising radiations. a Briefly describe the effects of ionising radiation on body cells. b Suggest a reason why a gamma source is usually less dangerous than an alpha or beta source when ingested or inhaled. c State THREE precautions that can be taken as protection against the hazards of ionising radiations. 19 a Define: ii nuclear fusion nuclear fission b Why do nuclei undergo fission? c Name the process by which the Sun liberates energy. d Name the process by which today's nuclear power stations generate electricity. ,20 State the numbers that should replace the boxes in this nuclear equation. 235 U + 1n D o ---.. 139Ba + D Kr + 310 n + energy S6 36 34 Concise Revision Course: CSEC· Physics Exam-style questions Chapters 33 to 34 Structured questions 1 a) Complete Table 1 with reference to the nucleus of a carbon atom, ':c. Table 1 T Mass number Atomic number An isotope (represented in a similar manner) Number of electron shells in its atom Number of electrons in its neutral atom (5 marks) b) Complete Table 2 to show the mass and charge of the neutron and the electron relative to that of the proton. Table 2 Relative charge:._ _ _.:. + 1_ _~_ (2 marks) c) Carbon-14 is used to determine the age of old organic material. It has a half-life of 5700 years. In natural carbon there is ONE atom of C-14 with every 8 x 10" atoms of carbon. i) What percentage of a sample of the isotope remains after a period of17100 years? (2 marks) ii) Predict whether or not the isotope would be useful in determining the age of a specimen older than 60 000 years. iii) A sample of carbon-14 is heated in a furnace so that its constituent atoms obtain increased kinetic energy. By applying your knowledge of nuclear processes, predict how the half-life of the isotope is affected. iv) C-14 decays by emission of a beta particle to form N-14. Write a nuclear equation for the decay. 2 (2 marks) (2 marks) (2 marks) Total 15 marks a) Complete Table 3 with reference to the properties of radioactive emissions. Table 3 Tracks produced in a cloud chamber are thick and straight Travels at the speed of light in a vacuum Strongly ionises the air it passes through Penetrates up to a few mm of aluminium Is deflected most by magnetic fields On emission, produces an element one place ahead in the Periodic Table Is el ectromagnetic in nature (7 marks) Exam-style questions - Chapters 33 to 34 b} Calculate the values of p, q, r, sand t in the following nuclear disintegrations, and rewrite the equations. 210Pb 82 Bi P q °e + PBi q ~ ~ -1 0e+ '5 Po -1 ; Po _ ~ He + '';' Pb (4 marks) c} A ratemeter detects a background count rate of 5 Bq. When a radioactive source is placed close to its detecting window, it detects a count rate of 85 Bq. If the half-life of the source is 20 minutes, what will be the count rate received after a period of 1 hour? (4 marks) Total 15 marks Extended response questions 3 a} The 'gold-foil' experiment carried out by Geiger and Marsden revealed a better understanding of the structure of an atomic nucleus. i} Briefly describe the procedu reo ii} Stete TWO important observations of the experiment. iii} State TWO conclusions drawn from the observations. (6 marks) b} lodine-131 (I-131) has an atomic number of 53 and is a beta-emitter with a half-life of 8 days. It decays to the element xenon, Xe. i} Write a nuclear equation for its decay. (3 marks) ii} 160 g of iodine-131 is left in a sealed container in the laboratory. Calculate the mass of the sample remaining after a period of 40 days. (3 marks) (3 marks) iii} Sketch a graph of mass against count rate for the first 24 days. Total 15 marks 4 a} State THREE advantages and THREE di sadvantages of generating electricity in nuclear power stations. b} i} (6 marks) The equation of the fusion reaction of deuterium, an isotope of hydrogen, is shown below. Table 4 indicates the atomic masses of the particles involved in the reaction. ~ H +~H ---+- ~ He + ~ n + energy Table 4 .,. 3.017 1.009 Calculate the energy released by the fusion reaction of two deuterium nuclei. (5 marks) (1 u = 1.66 X 10-27 kg, c = 3.0 X 10' m s-' ) ii} Determine the number of neutrons released in the nuclear reaction shown below. (1 mark) 235U + 'n ---+- 146la + 85Br + neutrons 9205735 c} A certain star loses mass at a rate of 5.0 x 10' kg s-'. Calculate its power output. (Speed of light in a vacuum = 3.0 x 10' m s-') (3 marks) Total 15 marks Exam-style questions - Chapters 33 to 34 Index A absorplion test, 180 accu mulator, 141 charging. 143 lead-acid, 142 ac generator, 168-169 air cond itioner, n-73 alkali ne cel ls, 143 alternating cu rrent (ac), 134 ammeters, 140, 145 am pere (unit of current), 133 am plitude, 84 AND decision, 155-156 anode, 130 ant i-parallel vectors, 11 Archim edes' principle, 38 Aris totle, 25 atom concept, evolution of, 176 model s of, 176-177 structure of, 177-178 ato mic number, 177 B background radia tion, 179 ba lloons, upth ru st and,39 barometer, mercury, 40 beam, light, 105 becquerel (Bq ), 180 bel a em issio n, 181 bimetall ic strip, 52-53 biomass energy, 35 Bohr, Nie ls, 176 boili ng defined, 71 evaporat io n vs., 71 Boy le's law, 54, 55 kinetic theory an d, 57 breakers, place ment of,153 convect ion defined,74 demonstrating. 75 and kinetic theory, 75 conven tional curren t, 133 convex/converging lens, 11 8 focal length of, 119 and scale diagrams construction, 120-121 cooling, evaporation and, 71 coulomb (unit of cha rge), 133 critical angle, 113- 115 and refractive index, 114-115 Curie, Marie, 179 current in complete circu its, 147 defined, "133 current electricity, 133-135 current rating, 152 D dc motor, 166-167 deformation, 16-20. see also Hooke's law Democritus, 176 density, 8 dependent va riable, 1 destructive i nterference, 102 diffra ction, 94, 101 di ffu sion cloud cham ber test, 181 digital electron ics, 155 diode, 141 dipoles, 159 direct current (dc), 134 displacement-posi tion graph, 88 di splacement- time (5-1) graph s, 21 , 89 distance- time graph, 22 di stribution box, electri city, 152 double-slit experiment (Young), 102 dust precipitators, 130 ca loric theory of heat, 43 cancer therapy, radi oisotopes in, 186 cathode, 130 cells alkal ine, 143 lithium·ion, 143 primary, 141 secondary, 141 zi nc-carbon dry, 141 Celsius, 45 Celsius scale, 54 centre of gravity, 15-16 Chadwick, James, 176 Cha rles' law, 54, 55-56 kine tic th eory and,57 chem ical energy, 31 circuit brea ker, 141 circuits parallel, 141 se ries, 141 sym bois, 140 clinica l therm ometer, 47 cloud chamber, 181 coherence, 102-103 coherent sources, 94 coils, transferring electrical energy between, 168 compression s, 83 concave/diverging lens, 118 and scale diagrams construction, 121-122 Cond uCl ion defined,74 demonstrat ing, 74-75 and kinetic theory, 74 conductors, 133 lightning, 129 constructive interference, 101 cont rol variable, 1 earthenware vessel s, 73 Earth's magnetic field, 162 earth wire, 153 echoes, uses of, 93 eclipse lunar, 105 solar, 106 efficiency, system, 35 Einstein's equation (mass-energy equivalence),188 Einstein' wave theor y, 101 elastic deformation, 18 elastic forces, 13 elastic limit, 18 electrical components, 140-141 electrical energy, 31 electrical potential energy, 136 electrical power, 137 electrical quantities, 136-139 electric charges, static, 127 applications of, 129-130 by friction, 127 hazards of, 129 metal dome by induction, 128 electric cu rrents, magnetiC fields and,163-164 electric field deflection test, lao electric fields defined, 131 Jines, 131 un iform, 131 electricity current, 133-135 in home, 151-153 static, 127-132 electric thermostat, 53 electromagnetic energy, 31 electromagnetic induction, 167-168 electromagnetic rela y, 164-165 elect romagnetic waves, 76, 97-99 produ ction of, 98 properties of, 97 uses of, 96-99 electromagnetism, 163-171 electromagn.ets, 160, 164-165 electromotive force (emf), 136 directio n of, 168 electron configuration, 178 electrons, 176 elect ro sta tic forces, 13 electrostatic induction , 127 electrostatic precipitator, 130 elect rostatic spraying, 130 energy alternative so urces of, 34- 35 in complete circu its, 150 defined,31 principle of conservation, 32-33, 44 sou rce s of, 34-35 types of, 31-32. see also specific types eq ui librium, bodies calculations on, 14-15 neutral,16 stable, 16 unstable, 16 errors minim ise, precau tions to, 18 parallax, 4 random, 4 systematic, 4 ze ro, 4 evaporation boiling vs., 71 and cool ing, 71 defin ed , 71 factors affecting, 71 expa nsion, 51-53 F fi re alarm, 53 1st Newton's law, 25, 27 Fleming's left-hand rule, 165, 181 Fleming's right-hand rule, 168 floating, 38 fluids, pressu re in, 37 fl uorescence, 99 focal length, 118 convex/converging lens, 119 focal plane, of lens, 118 force constant, 18 force-extension graph s, 13-19 forces, 13. see also specific types forward biased, diode, 147 fossil fuel s, eleCl ricity obtaining from, 34 Foucau lt' wave theory, 100 free electro ns, 133 frequency, wave, 85, 92 of electromagnetic spectrum, 97-98 friction, 13 fringes, 103 fu ses, 141, 152 placeme nt of, 153 in plu gs/applian ces, 153 1 , Cali lei, Galileo, 1 galvanometer, 140 gamma-rays, 99 gases, 49 expansion in, 51 and kinetic theory, 57-58 laws. see gas laws state change from liquids to, 65 gas laws ideal,54-55 verify ing. 55-57 Geiger-Marsdenl'Ruth erford scattering' experiment, 176-177 Geiger-Muller tube, 180 geothermal energy, 35 glass greenhou se, 73-79 global warm ing, 79 graphs displacement·position,88 di splacement-t ime, 21, 89 distance-time, 22 drawing, 1-2 exponential d ecay, 182 force-extension, 18-19 speed-lime, 22 st rai ght- li ne, gradienlls lope of,3 velocity-time, 21-22 of waves, 88-89 gravitational fi eld strength, 13 gravitationa l force s, 13 gravitational potential energy, 31 greenhou se effeCl, 79 gree nhouse gases, 79 ... half-life, of radioi sotope, 182 half-wave recti ficat ion, 155 heat calculation s, 59-60 caloric theory, 43 and change of state, 65-69 defined,59 kinetic theory, 43 latent. see latent heat heat ca pacit y, 59 heat en ergy, 31 healing curves, 66--67 home, elect ri city in, 151-153 Hoo ke's law defined, 18 verifying, 18 hurricanes, 73 Huygens' wave th eory, 100 hydroeleClricity,35 ideal gas laws, 54-55 ideal tran sformer, 170 independent variable, 1 index notation, 7 induction, electromagnetic, 167-168 infrared radiation (lR), 76, 98 instruments, measurements. see also specific in strum ents reading. 4-5 suitability of, 5-6 insulators, 133 interference, 94, 101-102 isotopes, 177 I-V relation ships, 146-147 Joule, James, 43 K kelvin, 45 kelvin scale, 54 kinematics variab les in, 21 kinetic energy defined,31 exam pies, 32 kinetic theory, 43 conduction and, 74 convection and, 75 gases and, 57-58 L latent heat calculat ion s, 66 defined,66 phenomena involving. 73 specific, determination of, 68-69 law of conservation of linear momentum, 28 Index 195 laws of reflection, 108 laws of refraction, 109-111 lead-acid accumulator, 142 lenses defined,118 formula, 122 magnification, 119 light-dependent resistor (LOR), 141 light-emitting diode (LED), 141 lightning, 129 light waves, 100-104 linear momentum conservation of, 28 defined,27 liquids, 49 expansion in, 51 to gas, state change, 65 specific heat capacity of, 62, 63-64 state change to solid, 65 lithium-ion cells, 143 logic gates, 155-156 truth tables, 156 longitudinal wave, 83-84 loudness, sound waves, 91 - 92 lower fixed point, 45 lunar eclipse, 105 M magnetic fields, 160-162 deflection of charged particles entering, 166 Earth's, 162 and electric currents, 163-164 lines, 160 mapping, 161 uniform, 161 magnetic forces, 13 magnetic induction, 159 magnetism, 159-162 magnification, 119 manometer, 40 mass, defined, 13 mass defect, 188 mass-energy equivalence, Einstein's equation, 188 mass number, 177 matter, states of, 49-50 mechanical energy, 31 mechanical forces, 13 mercury barometer, 40 mercury thermometer, 46 advantages of, 46 disadvantages of, 47 metal dome, charges by induction, 128 metals conduction in, 74 specific heat capacity of, 61-62 micrometer screw gauge,S moments defined,14 principle of, devices utilising, 17 tackling problems involving, 14 momentum, 27- 29 N neutral equilibrium, 16 neutral point, 132 neutron number, 177 neutrons, 176 Newton's corpuscular theory, 1()(} Newton's laws of motion, 25. see also specific laws applications of, 25- 27 non-renewable energy sources, 34 nuclear fission, 188 nuclear forces, 13 nuclear fusion, 188 nuclear potential energy, 31 nuclear povJer, 188 nuclear power stations, pros/ cons of, 189-190 196 nucleon number, 177 nucleus, atom, 176 nuclide, 177 o oblique vectors, 10 ohmic conductor, 146 Ohm's law, 146--147 optical centre, of len s, 118 optical fibres, 115-116 oscilloscope, 155 p parallax errors, 4 parallel circuits, 141 paral lelogram method, 10 paral lel vectors, 11 parameters, waves, 84-86 particle (co rpuscular) theory, 1()(} pascal (pa), 37 penumbra, 105 period, wave, 85 Periodic Table, 177 permanent magnets, 160 perpendicular vectors, 11 -12 perspiration, 73 phase, as wave parameter, 84-85 photocopiers, 130 photon, 101 photovoltaic panels, 34 pinhole camera, 106 pitch, sound waves, 9-1 - 92 Planck' wave theory, 101 plastic deformation, 18 plum pudding model, 176 polarity, testing for, 159 polygon method, 10 potential difference (pd), 136 potential energy defined,31 examples, 32 power in complete circuits, 150 defined,31 electrical,137 prefixes, 7 pressure constant, 55 defined,37 in fluids, 37 pressure law, 54, 56-57 kinetic theory and, 57- 58 primary cell, 141-142 principal axis, of lens, 118 principal focus, of lens, 118 principle of conservation of energy, 32-33, 44 prisms, 116 progressive waves, 84 proportional lim it, 18 proton number, 177 protons, 176 pulse, defined, 83 Q quantities, and 51 units, 6-7 quantum theory, 101 R radiations, 76-78 defined,74 ionising, hazards of, 190 testing, 180-181_ see also specific tests radioactive decay equations, 181-182 process, nature of, 182 simulating, 183 radioactive tracer, 186 radioactivity, 179-190 defined,179 nature of, 179 radio-carbon dating, 185 radioisotopes, uses of, 186-187 random errors, 4 rarefactions, 83 rate meter, 180 rays, light, 105 Concise Revision Cou rse: CSEC· Physics real i mages, 120 rectification, 155 reflection, laws of, 108 refraction, 86 laws of, 109-111 refractive index, 109 critical angle and, 114-115 refrigerator, 72 relay, electromagnetic, 164--165 renewable energy sources, 34 repulsion, 127 resistance, 144-145 defined,144 resistors, 140 adding in circuits, 144-145 defined,144 reverse biased, diode, 147 rheostat, 140 right-hand grip rule, 168 ring-main s ci rcuits, 152 Rumford, Count, 43 Rutherford, Ernest, 176 'Rutherford scattering' experiment, 176-177 5 scalars, 180 defined, 10 scientific method, 1-8 secondary cell, 141-142 2nd Newton's law, 25 semiconductors, 133 series circuit s, 141 shadows, 105 shells, 176 short circuit, 152 51 units, quantities and, 6-7 5nel l's law, 109 solar eclipse, 106 solar energy, 34 solar water heater, 79-80 solids, 49 expansion in, 51 state change from liquids to,65 sound energy, 31 sound waves, 91-95 behaviour of, 94 specific heat capacity, 59 determination, 61-64 specific latent heat of fUSion, 66, 6....9 specific latent heat of vaporisation, 66, 69 speed, waves, 86 speed-time graphs, 22 spraying aerosols, 73 stable equilibri um, 16 standard form, number, 7 static electricity, 127-132 applications of, 129-130 hazards of, 129 stationary waves, 84 straight-line graphs gradienVslope of, 3 submarine, upthrust and, 39 switches, placement of, 153 symbols, circuits, 140 systematic errors, 4 T temperature constant, 54 defined,45 scales, 54 units of, 45 temporary magnets, 160 terminal velocity, 26 thermal energy, 31 thermal energy transfer applications of, 78-80 processes, 74-78. see also conduction; convection; radiation thermal radiation, 76 thermistor, 141 thermocouple, 47 advantages of, 48 disadvantages of, 48 thermometers clinical, 47 defined,45 designing, 45-47 examples of, 45 laboratory, 46 thermometric property, 45 thermostat, 53 3rd Newton's law, 25, 164 Thomson, Joseph John, 176 tidal energy, 35 total internal reflection applications of, 115- 116 conditions necessary for, 113 transformer, 141, -169-170 transverse wave, 83 truth tables, 156 AND decision, 155 ultrasound, uses of, 92-93 ultraviolet radiation (UV), 99 umbra, 105 uniform electric field, 131 uniform magnetic fields, 161 unstable equilibrium, 16 upper fixed point, 45 upthrust and balloons, 39 and floating, 38 and submari ne, 39 V vacuum flask, 78 variables independent, 1 in kinematics, 21 vectors anti-parallel,11 defi ned,10 oblique, 10 parallel,11 perpendicular, 11-12 velocity, 21 terminal,26 velocity-time (v-t) graphs, 21-22 vernier calliper, 5 vernier scale, 5 virtual images, 120 volt (V), 136 voltage, in complete circuits, 147 voltmeters, 140, -145 W wavefront, 85 wavelength,85 of electromagnetic spectrum, 97- 98 waves coherence, 102- 103 defined,83 diffraction, 101 electromagnetic, 97-99 general equations, 86-87 graphs of, 88-89 interference, 101-102 light, 100-104 longitudinal,83-84 parameters, 84-86 progressive, 84 sound,91-95 stationary, 84 transverse, 83 weight, defined, 13 wind energy, 35 work, defined, 31 X x-rays, 99 y Young' wave theory, 1()(} Z zero error, 4 zinc-carbon dry cell, 141 Collins CSEC® REVISION GUIDE Get ready to succeed in CSEC ® Physics with this full-colour Concise Revision text. Written by an experienced teacher and author, this book offers complete course coverage and is packed with illustrations, revision questions and exam practice to ensure that you are fully prepared for the exam. • Comprehensive coveroge of the CSEC ® Physics course, presented in an engaging, full-colour format • Revision questions at the end of each topic help to secure knowledge and understanding • Exom-style questions at the end of each section provide effective practice for the actuol e,xom • Answers are available for free at www_collins_co.uk/caribbeanschools About the author Peter Defreitas is an experienced author and tutor and teaches Physics at St Winifred's School, Barbados. CSEC · revision guide ronge CONCISE REV ISK>N COURSE CONCISE REVI5ION COURSE CONCISE REVISION CSEC" Biology . CSEC" Chemistry CSEC \ Physics ? ~ft ~ ~ -! 41 ~ - ~ 978-0-00-815787-6 ~ - 978-0-00-815788-3 978-0-00-815789-0