Cambridge IGCSE Physics Fourth Edition PDF

The Cambridge IGCSE™ Physics series consists of a Student’s Book, Boost eBook, Workbooks and Teacher’s Guide with Boost Subscription. Cambridge Cambridge Cambridge Cambridge Cambridge IGCSE™ Physics IGCSE™ Physics IGCSE™ Physics IGCSE™ Physics...

The Cambridge IGCSE™ Physics series consists of a Student’s Book, Boost eBook, Workbooks and Teacher’s Guide with Boost Subscription. Cambridge Cambridge Cambridge Cambridge Cambridge IGCSE™ Physics IGCSE™ Physics IGCSE™ Physics IGCSE™ Physics IGCSE™ Physics Fourth Edition Fourth Edition Workbook Third Practical Skills Teacher’s Guide 9781398310544 Boost eBook Edition Workbook with Boost 9781398310841 9781398310575 9781398310551 Subscription 9781398310568 To explore the entire series, visit www.hoddereducation.com/cambridge-igcse-science Cambridge IGCSE™ Physics Teacher’s Guide with Boost Subscription Created with teachers and students in schools across the globe, Boost is the next generation in digital learning for schools and colleges, bringing quality content and new technology together in one interactive website. The Teacher’s Guide includes a print handbook and a subscription to Boost, where you will find a range of online resources to support your teaching. Confidently deliver the revised syllabus: guidance on how to approach the syllabus from experienced authors, practical support to help you work scientifically and safely, as well as lesson plans based on the provided scheme of work. Develop key concepts and skills: let students see how their skills are developing with a range of worksheets, formative knowledge tests and detailed answers to all the questions in the accompanying Student’s Book, Workbook and Practical Skills Workbook. Enhance learning: videos and animations on key concepts, mathematical skills and practicals plus audio of technical terms to support vocabulary flashcards. To purchase Cambridge IGCSE™ Physics Teacher’s Guide with Boost Subscription, visit www.hoddereducation.com/cambridge-igcse-science  Cambridge IGCSE™ Physics Fourth Edition 9781398310544.indb 1 19/02/21 8:12 PM This page intentionally left blank  Cambridge IGCSE™ Physics Fourth Edition Heather Kennett Tom Duncan 9781398310544.indb 3 19/02/21 8:12 PM  Cambridge International copyright material in this publication is reproduced under licence and remains the intellectual property of Cambridge Assessment International Education. Past paper questions reproduced by permission of Cambridge Assessment International Education. Exam-style questions [and sample answers] have been written by the authors. In examinations, the way marks are awarded may be different. References to assessment and/or assessment preparation are the publisher’s interpretation of the syllabus requirements and may not fully reflect the approach of Cambridge Assessment International Education. Cambridge Assessment International Education bears no responsibility for the example answers to questions taken from its past question papers which are contained in this publication. Although every effort has been made to ensure that website addresses are correct at time of going to press, Hodder Education cannot be held responsible for the content of any website mentioned in this book. It is sometimes possible to find a relocated web page by typing in the address of the home page for a website in the URL window of your browser. Third-party websites and resources referred to in this publication have not been endorsed by Cambridge Assessment International Education. We have carried out a health and safety check of this text and have attempted to identify all recognised hazards and suggest appropriate cautions. However, the Publishers and the authors accept no legal responsibility on any issue arising from this check; whilst every effort has been made to carefully check the instructions for practical work described in this book, it is still the duty and legal obligation of schools to carry out their own risk assessments for each practical in accordance with local health and safety requirements. For further health and safety information (e.g. Hazcards) please refer to CLEAPSS at www.cleapss.org.uk. Hachette UK’s policy is to use papers that are natural, renewable and recyclable products and made from wood grown in well-managed forests and other controlled sources. The logging and manufacturing processes are expected to conform to the environmental regulations of the country of origin. Orders: please contact Hachette UK Distribution, Hely Hutchinson Centre, Milton Road, Didcot, Oxfordshire, OX11 7HH. Telephone: +44 (0)1235 827827. Email [email protected] Lines are open from 9 a.m. to 5 p.m., Monday to Friday. You can also order through our website: www.hoddereducation.com ISBN: 978 1 3983 1054 4 © Tom Duncan and Heather Kennett 2021 First published in 2002 Second edition published in 2009 Third edition published in 2014 This fourth edition published in 2021 by Hodder Education, An Hachette UK Company Carmelite House 50 Victoria Embankment London EC4Y 0DZ www.hoddereducation.com Impression number 10 9 8 7 6 5 4 3 2 1 Year 2024 2023 2022 2021 All rights reserved. Apart from any use permitted under UK copyright law, no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or held within any information storage and retrieval system, without permission in writing from the publisher or under licence from the Copyright Licensing Agency Limited. Further details of such licences (for reprographic reproduction) may be obtained from the Copyright Licensing Agency Limited, www.cla.co.uk Cover photo © Zffoto – stock.adobe.com Illustrations by Fakenham Prepress Solutions, Wearset and Integra Software Services Pvt. Ltd., Pondicherry, India Typeset by Integra Software Services Pvt. Ltd., Pondicherry, India Printed in Slovenia A catalogue record for this title is available from the British Library. 9781398310544.indb 4 19/02/21 8:12 PM  Contents How to use this book vi Scientific enquiry vii 1 Motion, forces and energy 1 1.1 Physical quantities and measurement techniques 2 1.2 Motion 12 1.3 Mass and weight 25 1.4 Density 29 1.5 Forces 33 1.6 Momentum 55 1.7 Energy, work and power 60 1.8 Pressure 78 2 Thermal physics 85 2.1 Kinetic particle model of matter 86 2.2 Thermal properties and temperature 100 2.3 Transfer of thermal energy 115 3 Waves 127 3.1 General properties of waves 128 3.2 Light 136 3.3 Electromagnetic spectrum 160 3.4 Sound 167 4 Electricity and magnetism 175 4.1 Simple phenomena of magnetism 176 4.2 Electrical quantities 184 4.3 Electric circuits 209 4.4 Electrical safety 222 4.5 Electromagnetic effects 229 5 Nuclear physics 251 5.1 The nuclear model of the atom 252 5.2 Radioactivity 260 6 Space physics 275 6.1 Earth and the Solar System 276 6.2 Stars and the Universe 286 Mathematics for physics 295 Additional exam-style questions 299 Theory past paper questions 304 Practical Test past paper questions 324 Alternative to Practical past paper questions 331 List of equations 338 Symbols and units for physical quantities 339 Glossary 341 Acknowledgements 350 Index 351 9781398310544.indb 5 19/02/21 8:12 PM  How to use this book To make your study of Physics for Cambridge As well as these features, you will also see IGCSE™ as rewarding and successful as possible, additional support throughout the topic in the form this textbook, endorsed by Cambridge Assessment of: International Education, offers the following important features: Key definitions These provide explanations of the meanings of key words FOCUS POINTS as required by the syllabus. Each topic starts with a bullet point summary of what you will encounter within each topic. Practical work This is followed by a short outline of the topic These boxes identify the key practical skills so that you know what to expect over the next you need to be able to understand and apply as few pages. part of completing the course. Test yourself Worked example These questions appear regularly throughout the These boxes give step-by-step guidance on how to approach topic so you can check your understanding as you different sorts of calculations, with follow-up questions so progress. you can practise these skills. Revision checklist At the end of each topic, a revision checklist will Going further allow you to recap what you have learnt in each These boxes take your learning further than is topic and double check that you understand the key required by the Cambridge syllabus so that you have concepts before moving on. the opportunity to stretch yourself. A Mathematics for Physics section is provided for Exam-style questions reference. This covers many of the key mathematical skills you will need as you progress through Each topic is followed by exam-style questions to your course. If you feel you would benefit from help familiarise you with the style of questions further explanation and practice on a particular you may see in your examinations. These will also mathematical skill within this book, the prove useful in consolidating your learning. Past Mathematics for Physics section should be a useful paper questions are also provided in the back of resource. the book. Answers are provided online with the accompanying Cambridge IGCSE Physics Teacher’s Guide. A Practical Skills Workbook is also available As you read through the book, you will notice that to further support you in developing your practical some text is shaded yellow. This indicates that the skills as part of carrying out experiments. highlighted material is Supplement content only. Text that is not shaded covers the Core syllabus. If you are studying the Extended syllabus, you should look at both the Core and Supplement sections. vi 9781398310544.indb 6 19/02/21 8:12 PM  Scientific enquiry During your course you will have to carry out a few 3 Making and recording observations and experiments and investigations aimed at encouraging measurements – you need to obtain the you to develop some of the skills and abilities that necessary experimental data safely and scientists use to solve real-life problems. accurately. Before you start taking measurements Simple experiments may be designed to measure, familiarise yourself with the use of the apparatus. for example, the temperature of a liquid or the – Record your observations and readings in an electric current in a circuit. Longer investigations ordered way. If several measurements are may be designed to establish or verify a relationship to be made, draw up a table to record your between two or more physical quantities. results. Use the column headings, or start of Investigations may arise from the topic you are rows, to name the measurement and state its unit; for example ‘Mass of load/kg’. Repeat the currently studying in class, or your teacher may measurement of each observation; record each provide you with suggestions to choose from, or you value in your table, then calculate an average may have your own ideas. However an investigation value. Numerical values should be given to the arises, it will probably require at least one hour of number of significant figures appropriate to the laboratory time, but often longer. measuring device. Doing an investigation will involve the following – If you have decided to make a graph of your aspects. results you will need at least eight data points 1 Selecting and safely using suitable techniques, taken over as large a range as possible; be sure apparatus and materials – your choice of both to label each axis of a graph with the name and apparatus and techniques will depend on what unit of the quantity being plotted. you’re investigating. However, you must always – Do not dismantle the equipment until you have do a risk assessment of your investigation before completed your analysis and you are sure you do proceeding. Your teacher should help ensure that not need to repeat any of the measurements! all potential hazards are identified and addressed. 4 Interpreting and evaluating the observations 2 Planning your experiment – you need to think and data – this is important as doing it correctly about how you are going to find answers to the will allow you to establish relationships between questions regarding the problem posed. This will quantities. involve: – You may need to calculate specific values or – Making predictions and hypotheses (informed plot a graph of your results, then draw a line guesses); this may help you to focus on what is of best fit and calculate a gradient. Explain any required at this stage. anomalous results you obtained and how you – Identifying the variables in the investigation and dealt with them. Comment on any graph drawn, deciding which ones you will try to keep constant its shape and whether the graph points lie on the (controlled) so that they do not affect the line; mention any trend you noticed in the data. experimental results. The variable you change – Draw conclusions from the evidence that are is the independent variable and the variable you justified by the data. These can take the form will measure is the dependent variable. of a numerical value (and unit), the statement – Deciding on the range of values you will use for of a known law, a relationship between two the independent variable, how you will record quantities or a statement related to the aim of your results, and the analysis you will do to fulfil the experiment (sometimes experiments do not the aims of the investigation. achieve the intended objective). – The apparatus and materials you choose to – Comment on the quality of the data and whether use for the investigation need to have enough results are equal within the limits of the precision for the required use. For example accuracy of the experiment. Compare outcomes the smallest division on a metre ruler is 1 mm. with those expected. A measurement can be read to about half a scale 5 Evaluating methods and suggesting possible division so will have a precision of about 0.5 mm. improvements – not every experiment is flawless – Explaining your experimental procedure. and in fact, they rarely are. When looking at A clearly labelled diagram will be helpful here. evaluation you should: Any difficulties encountered or precautions taken – Identify possible sources of error in the to achieve accuracy should also be mentioned. experiment which could have affected the vii 9781398310544.indb 7 19/02/21 8:12 PM  accuracy of your results. These could include was at the centre of the planetary system, but a random and systematic errors as well as complex system of rotation was needed to match measurement errors. observations of the apparent movement of the – Mention any apparatus that turned out to be planets across the sky. In 1543, Nicolaus Copernicus unsuitable for the experiment. made the radical suggestion that all the planets – Discuss how the experiment might be modified revolved not around the Earth but around the Sun. to give more accurate results, for example in an (His book On the Revolutions of the Celestial Spheres electrical experiment by using an ammeter with a more appropriate scale. gave us the modern usage of the word ‘revolution’.) – Suggest possible improvements to the experiment. It took time for his ideas to gain acceptance. For example, efforts to reduce thermal energy The careful astronomical observations of planetary losses to the environment or changes in a control motion documented by Tycho Brahe were studied variable (such as temperature) in an experiment. by Johannes Kepler, who realised that the data could be explained if the planets moved in elliptical Suggestions for paths (not circular) with the Sun at one focus. Galileo’s observations of the moons of Jupiter with investigations the newly invented telescope led him to support this ‘Copernican view’ and to be imprisoned by the Some suggested investigations for practical work are Catholic Church in 1633 for disseminating heretical listed below: views. About 50 years later, Isaac Newton introduced 1 Stretching of a rubber band (Topic 1.5.1). the idea of gravity and was able to explain the 2 Stretching of a copper wire – wear eye motion of all bodies, whether on Earth or in the protection (Topic 1.5.1). heavens, which led to full acceptance of the 3 Toppling (Topic 1.5.1). Copernican model. Newton’s mechanics were refined 4 Friction – factors affecting (Topic 1.5.1). further at the beginning of the twentieth century 5 Model wind turbine design (Topic 1.7.3). when Einstein developed his theories of relativity. 6 Speed of a bicycle and its stopping distance Even today, data from the Hubble Space Telescope (Topic 1.7.1). is providing new evidence which confirms Einstein’s 7 Energy transfer using different insulating ideas. materials (Topic 2.3.1). Many other scientific theories have had to wait 8 Cooling and evaporation (Topic 2.2.3). for new data, technological inventions, or time and 9 Pitch of a note from a vibrating wire (Topic 3.4). the right social and intellectual climate for them 10 Variation of the resistance of a thermistor with to become accepted. In the field of health and temperature (Topic 4.2.4). medicine, for example, because cancer takes a long 11 Variation of the resistance of a wire with time to develop it was several years before people length (Topic 4.2.4) recognised that X-rays and radioactive materials 12 Heating effect of an electric current could be dangerous (Topic 5.2.5). (Topic 4.2.2). At the beginning of the twentieth century 13 Strength of an electromagnet (Topic 4.1). scientists were trying to reconcile the wave theory 14 Efficiency of an electric motor (Topic 4.2.5). and the particle theory of light by means of the new ideas of quantum mechanics. Ideas and evidence in Today we are collecting evidence on possible health risks from microwaves used in mobile phone science networks. The cheapness and popularity of mobile In some of the investigations you perform in the phones may make the public and manufacturers school laboratory, you may find that you do not reluctant to accept adverse findings, even if interpret your data in the same way as your friends risks are made widely known in the press and on do; perhaps you will argue with them as to the best television. Although scientists can provide evidence way to explain your results and try to convince and evaluation of that evidence, there may still be them that your interpretation is right. Scientific room for controversy and a reluctance to accept controversy frequently arises through people scientific findings, particularly if there are vested interpreting evidence differently. social or economic interests to contend with. This Observations of the heavens led the ancient is most clearly shown today in the issue of global Greek philosophers to believe that the Earth warming. viii 9781398310544.indb 8 19/02/21 8:12 PM  SECTION 1 Motion, forces and energy Topics 1.1 Physical quantities and measurement techniques 1.2 Motion 1.3 Mass and weight 1.4 Density 1.5 Forces 1.6 Momentum 1.7 Energy, work and power 1.8 Pressure 9781398310544.indb 1 19/02/21 8:12 PM  1.1 Physical quantities and measurement techniques FOCUS POINTS ★ Describe how to measure length, volume and time intervals using simple devices. ★ Know how to determine the average value for a small distance and a short time interval. ★ Understand the difference between scalar and vector quantities, and give examples of each. ★ Calculate or determine graphically the resultant of two perpendicular vectors. This topic introduces the concept of describing space and time in terms of numbers together with some of the basic units used in physics. You will learn how to use simple devices to measure or calculate the quantities of length, area and volume. Accurate measurements of time will be needed frequently in the practical work in later topics and you will discover how to choose the appropriate clock or timer for the measurement of a time interval. Any single measurement will not be entirely accurate and will have an error associated with it. Taking the average of several measurements, or measuring multiples, reduces the size of the error. Many physical quantities, such as force and velocity, have both magnitude and direction; they are termed vectors. When combining two vectors to find their resultant, as well as their size, you need to take into account any difference in their directions. Units and basic quantities Before a measurement can be made, a standard or unit must be chosen. The size of the quantity to be measured is then found with an instrument having a ▲ Figure 1.1.1 Aircraft flight deck scale marked in the unit. Three basic quantities we measure in physics are length, mass and time. Units for other quantities Powers of ten shorthand are based on them. The SI (Système International This is a neat way of writing numbers, especially if d’Unités) system is a set of metric units now used they are large or small. The example below shows in many countries. It is a decimal system in which how it works. units are divided or multiplied by 10 to give smaller 4000 = 4 × 10 × 10 × 10 = 4 × 103 or larger units. 400 = 4 × 10 × 10 = 4 × 102 Measuring instruments on the flight deck of a passenger jet provide the crew with information about 40 = 4 × 10 = 4 × 101 the performance of the aircraft (see Figure 1.1.1). 4=4×1 = 4 × 100 0.4 = 4/10 = 4/101 = 4 × 10 −1 0.04 = 4/100 = 4/102 = 4 × 10 −2 0.004 = 4/1000 = 4/103 = 4 × 10 −3 2 9781398310544.indb 2 19/02/21 8:12 PM  Significant figures The small figures 1, 2, 3, etc. are called powers of To obtain an average value for a small distance, ten. The power shows how many times the number multiples can be measured. For example, in ripple has to be multiplied by 10 if the power is greater tank experiments (Topic 3.1), measure the distance than 0 or divided by 10 if the power is less than 0. occupied by five waves, then divide by 5 to obtain Note that 1 is written as 100. the average wavelength. This way of writing numbers is called standard notation. Significant figures Every measurement of a quantity is an attempt Length to find its true value and is subject to errors The unit of length is the metre (m) and is the arising from limitations of the apparatus and distance travelled by light in a vacuum during the experimenter. The number of figures, called a specific time interval. At one time it was the significant figures, given for a measurement distance between two marks on a certain metal bar. indicates how accurate we think it is and more Submultiples are: figures should not be given than are justified. 1 decimetre (dm) = 10 −1 m For example, a value of 4.5 for a measurement has two significant figures; 0.0385 has three 1 centimetre (cm) = 10 −2 m significant figures, 3 being the most significant and 1 millimetre (mm) = 10 −3 m 5 the least, i.e. it is the one we are least sure about since it might be 4 or it might be 6. Perhaps it had 1 micrometre (µm) = 10 −6 m to be estimated by the experimenter because the 1 nanometre (nm) = 10 −9 m reading was between two marks on a scale. When doing a calculation your answer should A multiple for large distances is have the same number of significant figures as the 5 measurements used in the calculation. For example, 1 kilometre (km) = 103 m ( mile approx.) if your calculator gave an answer of 3.4185062, this 8 would be written as 3.4 if the measurements had 1 gigametre (Gm) = 109 m = 1 billion metres two significant figures. It would be written as 3.42 for three significant figures. Note that in deciding Many length measurements are made with rulers; the least significant figure you look at the next the correct way to read one is shown in Figure 1.1.2. figure to the right. If it is less than 5, you leave the The reading is 76 mm or 7.6 cm. Your eye must be least significant figure as it is (hence 3.41 becomes directly over the mark on the scale or the thickness 3.4), but if it equals or is greater than 5 you increase of the ruler causes a parallax error. the least significant figure by 1 (round it up) (hence 3.418 becomes 3.42). If a number is expressed in standard notation, correct wrong the number of significant figures is the number of digits before the power of ten. For example, 2.73 × 103 has three significant figures. 70 80 object ▲ Figure 1.1.2 The correct way to measure with a ruler 3 9781398310544.indb 3 19/02/21 8:12 PM  1.1 Physical quantities and measurement techniques Sometimes we need to know the area of a triangle. Test yourself It is given by 1 How many millimetres are there in these 1 area of triangle = 2 × base × height measurements? a 1 cm The area of a circle of radius r is π r2 where b 4 cm π = 22/7 or 3.14; its circumference is 2πr. c 0.5 cm d 6.7 cm e 1m Worked example 2 What are these lengths in metres? a 300 cm Calculate the area of the triangles shown in Figure 1.1.4. b 550 cm c 870 cm a area of triangle = 1 × base × height 2 d 43 cm so area of triangle ABC = 1 × AB × AC e 100 mm 2 3 a Write the following as powers of ten with one = 1 × 4 cm × 6 cm = 12 cm 2 figure before the decimal point: 2 100 000 3500 428 000 000 504 27 056 1 b area of triangle PQR = × PQ × SR b Write out the following in full: 2 10 3 2 × 106 6.92 × 10 4 1.34 × 102 109 1 = × 5 cm × 4 cm = 10 cm 2 4 a Write these fractions as powers of ten: 2 1/1000 7/100 000 1/10 000 000 3/60 000 C b Express the following decimals as powers of R ten with one figure before the decimal point: 0.5   0.084     0.000 36     0.001 04 6 cm 4 cm 90° Area A 4 cm B P S Q The area of the square in Figure 1.1.3a with 5 cm sides 1 cm long is 1 square centimetre (1 cm2). ▲ Figure 1.1.4 In Figure 1.1.3b the rectangle measures 4 cm by 3 cm and has an area of 4 × 3 = 12 cm2 since it has Now put this into practice the same area as twelve squares each of area 1 cm2. 1 Calculate the area of a triangle whose base is 8 cm and The area of a square or rectangle is given by height is 12 cm. 2 Calculate the circumference of a circle of radius 6 cm. area = length × breadth The SI unit of area is the square metre (m2) which is the area of a square with sides 1 m long. Note that Volume 1 cm 2 = 1 m × 1 m = 1 m 2 = 10−4 m 2 Volume is the amount of space occupied. The unit of 100 100 10000 volume is the cubic metre (m3) but as this is rather large, for most purposes the cubic centimetre (cm3) is used. The volume of a cube with 1 cm edges is a 1 cm 1 cm3. Note that 1 cm 1 1 1 3 cm 1 cm 3 = m× m× m 100 100 100 1 = m 3 = 10−6 m 3 1000 000 b 4 cm ▲ Figure 1.1.3 4 9781398310544.indb 4 19/02/21 8:12 PM  Volume For a regularly shaped object such as a rectangular block, Figure 1.1.5 shows that volume = length × breadth × height 5 cm meniscus 3 cm 4 cm ▲ Figure 1.1.6 A measuring cylinder Worked example a Calculate the volume of a block of wood which is 40 cm long, 12 cm wide and 5 cm high in cubic metres. volume V = length × breadth × height = 40 cm × 12 cm × 5 cm = 2400 cm3 = 2400 × 10 −6 m3 = 2.4 × 10 −3 m3 3  4  5 cubes b Calculate the volume of a cylinder of radius 10 mm and ▲ Figure 1.1.5 height 5.0 cm in cubic metres. volume of cylinder V = πr 2h The volume of a cylinder of radius r and height h is πr 2h. r = 10 mm = 1.0 cm and h = 5.0 cm The volume of a liquid may be obtained by so V = πr 2h pouring it into a measuring cylinder (Figure 1.1.6). = π × (1.0 cm)2 × 5.0 cm When making a reading the cylinder must be = 16 cm3 = 16 × 10 −6 m3 = 1.6 × 10 −5 m3 upright and your eye must be level with the bottom of the curved liquid surface, i.e. the meniscus. Now put this into practice The meniscus formed by mercury is curved 1 Calculate the volume of a rectangular box which is 30 cm oppositely to that of other liquids and the top long, 25 cm wide and 15 cm high in cubic metres. is read. 2 Calculate the volume of a cylinder of radius 50 mm and Measuring cylinders are often marked in millilitres height 25 cm in cubic metres. (ml) where 1 ml = 1 cm3; note that 1000 cm3 = 1 dm3 (= 1 litre). 5 9781398310544.indb 5 19/02/21 8:12 PM  1.1 Physical quantities and measurement techniques Time or mechanical switch is useful. Tickertape timers or dataloggers are often used to record short time The unit of time is the second (s), which used to be intervals in motion experiments. Accuracy can be based on the length of a day, this being the time improved by measuring longer time intervals. Several for the Earth to revolve once on its axis. However, oscillations (rather than just one) are timed to find days are not all of exactly the same duration and the period of a pendulum; the average value for the the second is now defined as the time interval for period is found by dividing the time by the number a certain number of energy changes to occur in the of oscillations. Ten ticks, rather than single ticks, are caesium atom. used in tickertape timers. Time-measuring devices rely on some kind of constantly repeating oscillation. In traditional clocks and watches a small wheel (the balance Test yourself wheel) oscillates to and fro; in digital clocks and 5 The pages of a book are numbered 1 to 200 and watches the oscillations are produced by a tiny each leaf is 0.10 mm thick. If each cover is 0.20 mm quartz crystal. A swinging pendulum controls a thick, what is the thickness of the book? 6 How many significant figures are there in a length pendulum clock. measurement of To measure an interval of time in an experiment, a 2.5 cm first choose a timer that is precise enough for the b 5.32 cm task. A stopwatch is adequate for finding the period c 7.180 cm in seconds of a pendulum (see Figure 1.1.7 opposite), d 0.042 cm? but to measure the speed of sound (Topic 3.4), 7 A rectangular block measures 4.1 cm by 2.8 cm by 2.1 cm. Calculate its volume giving your answer to a clock that can time in milliseconds is needed. an appropriate number of significant figures. To measure very short time intervals, a digital 8 What type of timer would you use to measure clock that can be triggered to start and stop by the period of a simple pendulum? How many an electronic signal from a microphone, photogate oscillations would you time? Practical work Period of a simple pendulum A to O to B to O to A (Figure 1.1.7). Repeat the For safe experiments/demonstrations related timing a few times for the same number of to this topic, please refer to the Cambridge oscillations and work out the average. IGCSE Physics Practical Skills Workbook that 1 The time for one oscillation is the period T. is also part of this series. Determine the period of your pendulum. In this investigation you have to make time 2 The frequency f of the oscillations is the measurements using a stopwatch or clock. number of complete oscillations per second A motion sensor connected to a datalogger and and equals 1/T. Calculate a value for f for your computer could be used instead of a stopwatch pendulum. for these investigations. 3 Comment on how the amplitude of the oscillations changes with time. Attach a small metal ball (called a bob) to a piece 4 Plan an investigation into the effect on T of of string, and suspend it as shown in Figure 1.1.7 (i) a longer string and (ii) a larger bob. opposite. Pull the bob a small distance to one 5 What procedure would you use to determine side, and then release it so that it oscillates to and the period of a simple pendulum? fro through a small angle. 6 In Figure 1.1.7 if the bob is first released Find the time for the bob to make several at B, give the sequence of letters which complete oscillations; one oscillation is from corresponds to one complete oscillation. 6 9781398310544.indb 6 19/02/21 8:12 PM  Systematic errors is given by the scale reading added to the value of x. 7 Explain where you would take The equation for the height is measurements from to determine the length of the pendulum shown in Figure 1.1.7. height = scale reading + x height = 5.9 + x metal plates By itself the scale reading is not equal to the height. It is too small by the value of x. This type of error is known as a systematic error. The error is introduced by the system. A half-metre string ruler has the zero at the end of the ruler and so can support be used without introducing a systematic error. stand When using a ruler to determine a height, the ruler must be held so that it is vertical. If the ruler is at an angle to the vertical, a systematic error is introduced. 8 7 pendulum bob P 6 B O A 5 ▲ Figure 1.1.7 4 3 Systematic errors 2 Figure 1.1.8 shows a part of a ruler used to measure 1 the height of a point P above the bench. The ruler chosen has a space before the zero of the scale. This 0 x is shown as the length x. The height of the point P bench ▲ Figure 1.1.8 Going further Vernier scales and micrometers Lengths can be measured with a ruler to a precision of about 0.5 mm. Some investigations may need a more precise measurement of length, which can be achieved by using vernier calipers (Figure 1.1.9) or a micrometer screw gauge. ▲ Figure 1.1.9 Vernier calipers in use 7 9781398310544.indb 7 19/02/21 8:12 PM  1.1 Physical quantities and measurement techniques Vernier scale Micrometer screw gauge The calipers shown in Figure 1.1.9 use a vernier scale. This measures very small objects to 0.001 cm. One The simplest type enables a length to be measured to revolution of the drum opens the flat, parallel jaws 0.01 cm. It is a small sliding scale which is 9 mm long by one division on the scale on the shaft of the gauge; but divided into ten equal divisions (Figure 1.1.10a) so this is usually mm, i.e. 0.05 cm. If the drum has a scale of 50 divisions round it, then rotation of the drum by 1 vernier division = 9 mm one division opens the jaws by 0.05/50 = 0.001 cm 10 (Figure1.1.11). A friction clutch ensures that the jaws = 0.9 mm exert the same force when the object is gripped. = 0.09 cm jaws shaft drum One end of the length to be measured is made to coincide with the zero of the millimetre scale and the other end with the zero of the vernier scale. The length of the object in Figure 1.1.10b is between 1.3 cm and 0 1 2 35 1.4 cm. The reading to the second place of decimals is obtained by finding the vernier mark which is exactly mm 30 opposite (or nearest to) a mark on the millimetre scale. In this case it is the 6th mark and the length is 1.36 cm, since object friction clutch OA = OB − AB OA = (1.90 cm) − (6 vernier divisions) ▲ Figure 1.1.11 Micrometer screw gauge = 1.90 cm − 6(0.09) cm The object shown in Figure 1.1.11 has a length of = (1.90 − 0.54) cm 2.5 mm on the shaft scale + 33 divisions on the drum = 1.36 cm scale Vernier scales are also used on barometers, travelling = 0.25 cm + 33(0.001) cm microscopes and spectrometers. = 0.283 cm a Before making a measurement, check to ensure that vernier scale mm scale the reading is zero when the jaws are closed. Otherwise the zero error must be allowed for when the reading is 5 taken. 1 2 mm b O object A B 5 10 1 2 mm ▲ Figure 1.1.10 Vernier scale 8 9781398310544.indb 8 19/02/21 8:12 PM  Scalars and vectors Scalars and vectors A vector can be represented by a straight line whose length represents the magnitude of the Length and time can be described by a single quantity and whose direction gives its line of number specifying size, but many physical action. An arrow on the line shows which way quantities have a directional character. along the line it acts. A scalar quantity has magnitude (size) only. Scalars are added by ordinary arithmetic; Time is a scalar and is completely described when vectors are added geometrically, taking account its value is known. Other examples of scalars are of their directions as well as their magnitudes. In distance, speed, time, mass, pressure, energy and the case of two vectors FX and FY acting at right temperature. angles to each other at a point, the magnitude of A vector quantity is one such as force which is the resultant F, and the angle θ between FX and F described completely only if both its size (magnitude) can be calculated from the following equations: and direction are stated. It is not enough to say, FY for example, a force of 10 N, but rather a force of F= FX 2 + FY 2 , tan θ = 10 N acting vertically downwards. Gravitational field FX strength and electric field strength are vectors, as The resultant of two vectors acting at right angles are weight, velocity, acceleration and momentum. to each other can also be obtained graphically. Worked example Calculate the resultant of two forces of 3.0 N and 4.0 N Graphical method acting at right angles to each other. The values for F and θ can be found graphically by drawing Let FX = 3.0 N and FY = 4.0 N as shown in Figure 1.1.12. the vectors to scale on a piece of graph paper as shown in Figure 1.1.12. scale 1 cm = 1 N F First choose a scale to represent the size of the vectors (1 cm could be used to represent 1.0 N). Draw the vectors at right angles to each other. Complete the rectangle as shown in Figure 1.1.12 and draw the diagonal from the origin as shown. The diagonal then represents the 4.0 N resultant force, F. Measure the length of F with a ruler and use the scale you have chosen to determine its size. Measure the angle θ, the direction of the resultant, with a protractor. Check that the values for F and θ you obtain are the same θ as those found using the algebraic method. 3.0 N Now put this into practice ▲ Figure 1.1.12 Addition of two perpendicular vectors 1 Calculate the following square roots. a 62 + 82 Then b 52 + 72 F= FX2 + FY2 = 3.02 + 4.02 = 9 + 16 = 25 = 5.0 N c 22 + 92 FY 2 Calculate and tan θ = 4.0 = = 1.3 a tan 30° FX 3.0 b tan 45° so θ = 53º. c tan 60°. 3 Calculate the resultant of two forces of 5.0 N and 7.0 N The resultant is a force of 5.0 N acting at 53° to the force which are at right angles to each other. of 3.0 N. 4 At a certain instant a projectile has a horizontal velocity of 6 m/s and a vertical velocity of 8 m/s. a Calculate the resultant velocity of the projectile at that instant. b Check your answer to a by a graphical method. 9 9781398310544.indb 9 19/02/21 8:12 PM  1.1 Physical quantities and measurement techniques Revision checklist After studying Topic 1.1 you should know and After studying Topic 1.1 you should be able to: understand the following: ✓ write a number in powers of ten (standard ✓ how to make measurements of length and time notation) and recall the meaning of standard intervals, minimise the associated errors and use prefixes multiple measurements to obtain average values ✓ measure and calculate lengths, areas and volumes of regular objects and give a result with ✓ the difference between scalars and vectors and the correct units and an appropriate number of recall examples of each. significant figures ✓ determine by calculation or graphically the resultant of two vectors at right angles. 10 9781398310544.indb 10 19/02/21 8:12 PM  Exam-style questions Exam-style questions 1 A chocolate bar measures 10 cm long by 2 cm c Write down expressions for wide and is 2 cm thick. i the area of a circle a Calculate the volume of one bar. ii the circumference of a circle b How many bars each 2 cm long, 2 cm iii the volume of a cylinder. wide and 2 cm thick have the same total [Total: 7] volume? c A pendulum makes 10 complete oscillations in 8 seconds. Calculate the time period of Going further the pendulum. 5 What are the readings on the micrometer screw [Total: 8] gauges in Figures 1.1.14a and 1.1.14b? 2 a A pile of 60 sheets of paper is 6 mm high. Calculate the average thickness of a sheet a of the paper. b Calculate how many blocks of ice cream each 0 1 2 35 10 cm long, 10 cm wide and 4 cm thick can mm 30 be stored in the compartment of a freezer measuring 40 cm deep, 40 cm wide and 25 20 cm high. [Total: 7] b 3 A Perspex container has a 6 cm square base and contains water to a height of 7 cm 11 12 13 14 0 (Figure 1.1.13). a Calculate the volume of the water. mm 45 b A stone is lowered into the water so as to be completely covered and the water rises 40 to a height of 9 cm. Calculate the volume of the stone. [Total: 7] ▲ Figure 1.1.14 [Total: 4] 6 a Select which of the following quantities is a vector. A length 7 cm B temperature C force D time b Two forces of 5 N and 12 N act at right 6 cm angles to each other. 6 cm Using a piece of graph paper determine the magnitude and direction of the resultant ▲ Figure 1.1.13 force graphically. State the scale you use 4 a State the standard units of length to represent each vector. You will need and time. a protractor to measure the angle the b A measurement is stated as 0.0125 mm. resultant makes with the 5 N force. State the number of significant figures. [Total: 8] 11 9781398310544.indb 11 19/02/21 8:12 PM  1.2 Motion FOCUS POINTS ★ Define speed and velocity and use the appropriate equations to calculate these and average speed. ★ Draw, plot and interpret distance–time or speed–time graphs for objects at different speeds and use the graphs to calculate speed or distance travelled. ★ Define acceleration and use the shape of a speed–time graph to determine constant or changing acceleration and calculate the acceleration from the gradient of the graph. ★ Know the approximate value of the acceleration of freefall, g, for an object close to the Earth’s surface. ★ Describe the motion of objects falling with and without air/liquid resistance. The concepts of speed and acceleration are encountered every day, whether it be television monitoring of the speed of a cricket or tennis ball as it soars towards the opposition or the acceleration achieved by an athlete or racing car. In this topic you will learn how to define speed in terms of distance and time. Graphs of distance against time will enable you to calculate speed and determine how it changes with time; graphs of speed against time allow acceleration to be studied. Acceleration is also experienced by falling objects as a result of gravitational attraction. All objects near the Earth’s surface experience the force of gravity, which produces a constant acceleration directed towards the centre of the Earth. Speed To find the actual speed at any instant we would need to know the distance moved in a very short The speed of a body is the distance that it has interval of time. This can be done by multiflash travelled in unit time. When the distance travelled photography. In Figure 1.2.1 the golfer is is s over a short time period t, the speed v is photographed while a flashing lamp illuminates him given by 100 times a second. The speed of the club-head as it v=s hits the ball is about 200 km/h. t Key definition Speed distance travelled per unit time If a car travels 300 km in five hours, its average speed is 300 km/5 h = 60 km/h. The speedometer would certainly not read 60 km/h for the whole journey and might vary considerably from this value. That is why we state the average speed. If a car could travel at a constant speed of 60 km/h for 5 hours, the distance covered would still be 300 km. It is always true that total distance travelled average speed = total time taken ▲ Figure 1.2.1 Multiflash photograph of a golf swing 12 9781398310544.indb 12 19/02/21 8:12 PM  Acceleration Velocity For a steady increase of velocity from 20 m/s to Speed is the distance travelled in unit time; velocity is 50 m/s in 5 s the distance travelled in unit time in a given direction. (50 − 20) m/s acceleration = = 6 m/s2 If two trains travel due north at 20 m/s, they have the 5s same speed of 20 m/s and the same velocity of 20 m/s due north. If one travels north and the other south, Acceleration is also a vector and both its their speeds are the same but not their velocities since magnitude and direction should be stated. their directions of motion are different. However, at present we will consider only motion in a straight line and so the magnitude of the distance moved in a given direction velocity will equal the speed, and the magnitude velocity = time taken of the acceleration will equal the change of speed = speed in a given direction in unit time. The speeds of a car accelerating on a straight Key definition road are shown below. Velocity change in displacement per unit time Time/s 0 1 2 3 4 5 6 The velocity of a body is uniform or constant if it Speed/m/s 0 5 10 15 20 25 30 moves with a steady speed in a straight line. It is not uniform if it moves in a curved path. Why? The speed increases by 5 m/s every second and The units of speed and velocity are the same, the acceleration of 5 m/s2 is constant. km/h, m/s. An acceleration is positive if the velocity increases, and negative if it decreases. A negative 60 000 m 60 km/h = = 17 m/s acceleration is also called a deceleration or 3600 s retardation. Distance moved in a stated direction is called the displacement. Velocity may also be defined as change in displacement velocity = Test yourself time taken 1 What is the average speed of Speed is a scalar quantity and velocity a vector a a car that travels 400 m in 20 s quantity. Displacement is a vector, unlike distance b an athlete who runs 1500 m in 4 minutes? which is a scalar. 2 A train increases its speed steadily from 10 m/s to 20 m/s in 1 minute. a What is its average speed during this time, in m/s? Acceleration b How far does it travel while increasing its speed? When the velocity of an object changes, we say the object accelerates. If a car starts from rest 3 a A motorcyclist starts from rest and reaches and moving due north has velocity 2 m/s after a speed of 6 m/s after travelling with 1 second, its velocity has increased by 2 m/s in constant acceleration for 3 s. What is his 1 s and its acceleration is 2 m/s per second due acceleration? north. We write this as 2 m/s2. b The motorcyclist then decelerates at a constant rate for 2 s. What is his Acceleration is defined as the change of acceleration? velocity in unit time, or 4 An aircraft travelling at 600 km/h accelerates change of velocity v steadily at 10 km/h per second. Taking the acceleration = = Δ speed of sound as 1100 km/h at the aircraft’s time taken for change Δt altitude, how long will it take to reach the ‘sound barrier’? Key definition Acceleration change in velocity per unit time 13 9781398310544.indb 13 19/02/21 8:12 PM  1.2 Motion Speed–time graphs Values for the speed of the object at 1 s intervals can be read from the graph and are given in Table If the speed of an object is plotted against the 1.2.2. The data shows that the speed increases by time, the graph obtained is a speed–time graph. the same amount (4 m/s) every second. It provides a way of solving motion problems. ▼ Table 1.2.2 In Figure 1.2.2, AB is the speed–time graph for an object moving with a constant speed of Speed/m/s 20 24 28 32 36 40 20 m/s. Time/s 0 1 2 3 4 5 Values for the speed of the object at 1 s intervals can be read from the graph and are given in You can use the data to plot the speed–time graph. Table 1.2.1. The data shows that the speed is Join up the data points on the graph paper with constant over the 5 s time interval. the best straight line to give the line PQ shown in ▼ Table 1.2.1 Figure 1.2.3a. (Details for how to plot a graph are given on pp. 297–8 in the Mathematics for physics Speed/m/s 20 20 20 20 20 20 section.) Time/s 0 1 2 3 4 5 Figure 1.2.3b shows the shape of a speed–time graph for an object accelerating from rest over time interval OA, travelling at a constant speed over time 30 interval AB and then decelerating (when the speed is decreasing) over the time interval BC. The steeper A B speed/m/s 20 gradient in time interval BC than in time interval OA shows that the deceleration is greater than the 10 acceleration. The object remains at rest over the time interval CD when its speed and acceleration are C zero. O 1 2 3 4 5 time/s constant speed speed/m/s ▲ Figure 1.2.2 Constant speed n de tio cel The linear shape (PQ) of the speed–time graph ler a era ce shown in Figure 1.2.3a means that the gradient, and ac tio n hence the acceleration of the body, are constant at rest over the time period OS. O A B C D time/s 40 Q ▲ Figure 1.2.3b Acceleration, constant speed and deceleration 30 Figure 1.2.3c shows a speed–time graph for a speed/m/s P changing acceleration. The curved shape OX means 20 R that the gradient of the graph, and hence the acceleration of the object, change over time period 10 OY – the acceleration is changing. Values for the speed of the object at 1 s intervals S O are given in Table 1.2.3. The data shows that the 1 2 3 4 5 speed is increasing over time interval OY, but by a time/s smaller amount each second so the acceleration is ▲ Figure 1.2.3a Constant acceleration decreasing. 14 9781398310544.indb 14 19/02/21 8:12 PM  Distance–time graphs ▼ Table 1.2.3 LM/OM = 40 m/4 s = 10 m/s, which is the value of the speed. The following statement is true in general: Speed/m/s 0 17.5 23.0 26.0 28.5 30.0 The gradient of a distance–time graph represents Time/s 0 1 2 3 4 5 the speed of the object. Values for the distance moved by the object You can use the data to plot the speed–time graph. recorded at 1 s intervals are given in Table 1.2.4. Join up the data points on the graph paper with a The data shows it moves 10 m in every second so the smooth curve as shown in Figure 1.2.3c. speed of the object is constant at 10 m/s. Note that an object at rest will have zero speed and zero acceleration; its speed–time graph is a ▼ Table 1.2.4 straight line along the horizontal axis. Distance/m 10 20 30 40 Time/s 1 2 3 4 30 X You can use the data to plot the distance–time speed/m/s 20 graph shown in Figure 1.2.4a. 10 L 40 Y O 1 2 3 4 5 30 distance/m time/s ▲ Figure 1.2.3c Changing acceleration 20 10 Using the gradient of M a speed–time graph to O 1 2 3 4 calculate acceleration time/s The gradient of a speed–time graph represents ▲ Figure 1.2.4a Constant speed the acceleration of the object. Figure 1.2.4b shows the shape of a distance–time In Figure 1.2.2, the gradient of AB is zero, as is graph for an object that is at rest over time interval the acceleration. In Figure 1.2.3a, the gradient of OA and then moves at a constant speed in time PQ is QR/PR = 20/5 = 4: the acceleration is constant interval AB. It then stops moving and is at rest over at 4 m/s2. In Figure 1.2.3c, when the gradient along time interval BC before moving at a constant speed OX changes, so does the acceleration. in time interval CD. An object is accelerating if the speed increases with time and decelerating if the speed decreases with time, as shown in Figure constant speed 1.2.3b. In Figure 1.2.3c, the speed is increasing distance/m with time and the acceleration of the object is at rest decreasing. constant speed Distance–time graphs O at rest A B C D An object travelling with constant speed covers equal time/s distances in equal times. Its distance–time graph is a straight line, like OL in Figure 1.2.4a for a constant ▲ Figure 1.2.4b Constant speed speed of 10 m/s. The gradient of the graph is 15 9781398310544.indb 15 19/02/21 8:12 PM  1.2 Motion The speed of the object is higher when the gradient At the start of the timing the speed is 20 m/s, of the graph is steeper. The object is travelling but it increases steadily to 40 m/s after 5 s. faster in time interval AB than it is in time interval If the distance covered equals the area under PQ, CD; it is at rest in time intervals OA and BC when i.e. the shaded area OPQS, then the distance does not change. distance = area of rectangle OPRS + area of triangle PQR When the speed of the object is changing, the 1 gradient of the distance–time graph varies, as in = OP × OS + 2 × PR × QR Figure 1.2.5, where the upward curve of increasing 1 (area of a triangle = 2 base × height) gradient of the solid green line shows the object 1 accelerating. The opposite, upward curve of = 20 m/s × 5 s + 2 × 5 s × 20 m/s decreasing gradient (indicated by the dashed green = 100 m + 50 m = 150 m line) shows an object decelerating above T. Note that when calculating the area from the graph, 40 A the unit of time must be the same on both axes. accelerating The rule for finding distances travelled is true 30 even if the acceleration is not constant. In Figure decelerating 1.2.3c, the distance travelled equals the shaded distance/m 20 area OXY. T 10 accelerating Test yourself C B 5 The speeds of a bus travelling on a straight road are O given below at successive intervals of 1 second. 1 2 3 4 5 time/s Time/s 0 1 2 3 4 ▲ Figure 1.2.5 Non-constant speed Speed/m/s 0 4 8 12 16 a Sketch a speed–time graph using the values. Speed at any point equals the gradient of the b Choose two of the following terms which describe the acceleration of the bus: tangent. For example, the gradient of the tangent constant   changing   positive   negative at T is AB/BC = 40 m/2 s = 20 m/s. The speed at the instant corresponding to T is therefore 20 m/s. c Calculate the acceleration of the bus. d Calculate the area under your graph.