* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Cambridge International AS and A Level Physics - Beck-Shop
Accretion disk wikipedia , lookup
Special relativity wikipedia , lookup
Mass versus weight wikipedia , lookup
Electromagnetic mass wikipedia , lookup
Gravitational wave wikipedia , lookup
Old quantum theory wikipedia , lookup
Negative mass wikipedia , lookup
Nuclear physics wikipedia , lookup
Introduction to gauge theory wikipedia , lookup
Weightlessness wikipedia , lookup
Conservation of energy wikipedia , lookup
Aristotelian physics wikipedia , lookup
Speed of sound wikipedia , lookup
Lorentz force wikipedia , lookup
History of physics wikipedia , lookup
Faster-than-light wikipedia , lookup
Woodward effect wikipedia , lookup
Classical mechanics wikipedia , lookup
Photon polarization wikipedia , lookup
First observation of gravitational waves wikipedia , lookup
Anti-gravity wikipedia , lookup
Electromagnetism wikipedia , lookup
Centripetal force wikipedia , lookup
Equations of motion wikipedia , lookup
Work (physics) wikipedia , lookup
Speed of gravity wikipedia , lookup
Matter wave wikipedia , lookup
Newton's laws of motion wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Cambridge University Press 978-1-107-69769-0 – Cambridge International AS and A Level Physics David Sang Graham Jones Gurinder Chadha and Richard Woodside Frontmatter More information David Sang, Graham Jones, Gurinder Chadha and Richard Woodside Cambridge International AS and A Level Physics Coursebook Second Edition © in this web service Cambridge University Press www.cambridge.org University Printing House, Cambridge CB2 8BS, United Kingdom Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org © Cambridge University Press 2010, 2014 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2010 Second edition 2014 Printed in the United Kingdom by Latimer Trend A catalogue record for this publication is available from the British Library ISBN 978-1-107-69769-0 Paperback with CD-ROM for Windows® and MAC® Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Information regarding prices, travel timetables, and other factual information given in this work is correct at the time of first printing but Cambridge University Press does not guarantee the accuracy of such information thereafter. ersity Press www.cambridge.org notice to teachers in the uk It is illegal to reproduce any part of this book in material form (including photocopying and electronic storage) except under the following circumstances: (i) where you are abiding by a licence granted to your school or institution by the Copyright Licensing Agency; (ii) where no such licence exists, or where you wish to exceed the terms of a licence, and you have gained the written permission of Cambridge University Press; (iii) where you are allowed to reproduce without permission under the provisions of Chapter 3 of the Copyright, Designs and Patents Act 1988, which covers, for example, the reproduction of short passages within certain types of educational anthology and reproduction for the purposes of setting examination questions. Example answers and all other end-of-chapter questions were written by the authors. ersity Press Contents Introduction vii Chapter 5: Work, energy and power 69 How to use this book viii Doing work, transferring energy Gravitational potential energy Kinetic energy g.p.e.–k.e. transformations Down, up, down – energy changes Energy transfers Power 71 75 76 76 77 78 80 Chapter 1: Kinematics – describing motion Speed Distance and displacement, scalar and vector Speed and velocity Displacement–time graphs Combining displacements Combining velocities Chapter 2: Accelerated motion 1 2 4 5 6 8 10 14 The meaning of acceleration Calculating acceleration Units of acceleration Deducing acceleration Deducing displacement Measuring velocity and acceleration Determining velocity and acceleration in the laboratory The equations of motion Deriving the equations of motion Uniform and non-uniform acceleration Acceleration caused by gravity Determining g Motion in two dimensions – projectiles Understanding projectiles 18 20 22 24 25 25 28 29 Chapter 3: Dynamics – explaining motion 37 Calculating the acceleration Understanding SI units The pull of gravity Mass and inertia Top speed Moving through fluids Identifying forces Newton’s third law of motion Chapter 4: Forces – vectors and moments Combining forces Components of vectors Centre of gravity The turning effect of a force The torque of a couple 15 15 16 17 17 18 38 39 41 43 44 45 47 49 53 54 56 59 59 63 Chapter 6: Momentum The idea of momentum Modelling collisions Understanding collisions Explosions and crash-landings Collisions in two dimensions Momentum and Newton’s laws Understanding motion Chapter 7: Matter and materials Density Pressure Compressive and tensile forces Stretching materials Elastic potential energy Chapter 8: Electric fields Attraction and repulsion www.cambridge.org The concept of an electric field Electric field strength Force on a charge Chapter 9: Electric current, potential difference and resistance 85 86 86 89 91 93 95 96 101 102 102 104 105 108 116 117 118 119 122 127 Circuit symbols and diagrams Electric current An equation for current The meaning of voltage Electrical resistance Electrical power 128 129 132 134 135 136 Chapter 10: Kirchhoff’s laws 143 Kirchhoff’s first law Kirchhoff’s second law Applying Kirchhoff’s laws Resistor combinations 144 145 146 148 iii Cambridge International AS and A Level Physics Chapter 11: Resistance and resistivity The I–V characteristic for a metallic conductor Ohm’s law Resistance and temperature Resistivity Chapter 12: Practical circuits Internal resistance Potential dividers Potentiometer circuits Chapter 13: Waves Describing waves Longitudinal and transverse waves Wave energy Wave speed The Doppler effect Electromagnetic waves Electromagnetic radiation Orders of magnitude The nature of electromagnetic waves iv ersity Press 156 157 158 159 162 168 169 172 172 178 179 181 182 183 184 185 186 187 188 Chapter 14: Superposition of waves 192 The principle of superposition of waves Diffraction of waves Interference The Young double-slit experiment Diffraction gratings 193 194 196 200 203 Chapter 15: Stationary waves From moving to stationary Nodes and antinodes Formation of stationary waves Determining the wavelength and speed of sound Chapter 16: Radioactivity Looking inside the atom Alpha-particle scattering and the nucleus A simple model of the atom Nucleons and electrons Forces in the nucleus Fundamental particles? Families of particles Discovering radioactivity Radiation from radioactive substances Discovering neutrinos Fundamental families Fundamental forces Properties of ionising radiation 210 211 212 212 216 222 223 223 225 226 229 229 230 231 231 232 232 232 233 P1: Practical skills at AS level Practical work in physics Using apparatus and following instructions Gathering evidence Precision, accuracy, errors and uncertainties Finding the value of an uncertainty Percentage uncertainty Recording results Analysing results Testing a relationship Identifying limitations in procedures and suggesting improvements Chapter 17: Circular motion 239 240 240 241 241 243 245 246 246 248 250 258 Describing circular motion Angles in radians Steady speed, changing velocity Angular velocity Centripetal forces Calculating acceleration and force The origins of centripetal forces 259 260 261 261 262 264 265 Chapter 18: Gravitational fields 271 Representing a gravitational field Gravitational field strength g Energy in a gravitational field Gravitational potential Orbiting under gravity The orbital period Orbiting the Earth Chapterwww.cambridge.org 19: Oscillations Free and forced oscillations Observing oscillations Describing oscillations Simple harmonic motion Representing s.h.m. graphically Frequency and angular frequency Equations of s.h.m. Energy changes in s.h.m. Damped oscillations Resonance Chapter 20: Communications systems Radio waves Analogue and digital signals Channels of communication Comparison of different channels 272 274 276 276 277 278 279 285 286 287 288 289 291 292 293 296 297 299 309 310 314 317 319 ersity Press Contents Chapter 21: Thermal physics Changes of state Energy changes Internal energy The meaning of temperature Thermometers Calculating energy changes Chapter 22: Ideal gases Particles of a gas Explaining pressure Measuring gases Boyle’s law Changing temperature Ideal gas equation Modelling gases – the kinetic model Temperature and molecular kinetic energy Chapter 23: Coulomb’s law Electric fields Coulomb’s law Electric field strength for a radial field Electric potential Comparing gravitational and electric fields Chapter 24: Capacitance Capacitors in use Energy stored in a capacitor Capacitors in parallel Capacitors in series Comparing capacitors and resistors Capacitor networks Chapter 25: Electronics Components of an electronic sensing system The operational amplifier (op-amp) The inverting amplifier The non-inverting amplifier Output devices Chapter 26: Magnetic fields and electromagnetism Producing and representing magnetic fields Magnetic force Magnetic flux density Measuring magnetic flux density Currents crossing fields Forces between currents Relating SI units Comparing forces in magnetic, electric and gravitational fields 327 328 329 331 332 334 336 345 346 348 348 349 350 351 352 354 359 360 360 362 363 366 372 373 375 377 378 379 380 386 387 393 397 398 398 406 407 409 411 411 413 415 416 417 Chapter 27: Charged particles Observing the force Orbiting charges Electric and magnetic fields The Hall effect Discovering the electron 422 423 423 427 428 429 Chapter 28: Electromagnetic induction 435 Observing induction Explaining electromagnetic induction Faraday’s law of electromagnetic induction Lenz’s law Using induction: eddy currents, generators and transformers 436 437 441 443 Chapter 29: Alternating currents Sinusoidal current Alternating voltages Power and a.c. Why use a.c. for electricity supply? Transformers Rectification Chapter 30: Quantum physics Modelling with particles and waves Particulate nature of light The photoelectric effect Line spectra Explaining the origin of line spectra Photon energies Electron energies in solids www.cambridge.org The nature of light – waves or particles? Electron waves Chapter 31: Nuclear physics Balanced equations Mass and energy Energy released in radioactive decay Binding energy and stability Randomness and decay The mathematics of radioactive decay Decay graphs and equations Decay constant and half-life 445 451 452 453 455 457 458 460 466 467 468 471 475 476 477 478 480 480 489 490 491 494 494 496 497 499 501 v Cambridge International AS and A Level Physics Chapter 32: Medical imaging The nature and production of X-rays X-ray attenuation Improving X-ray images Computerised axial tomography Using ultrasound in medicine Echo sounding Ultrasound scanning Magnetic resonance imaging 507 509 511 513 516 518 520 522 P2: Planning, analysis and evaluation 529 Planning Analysis of the data Treatment of uncertainties Conclusions and evaluation of results Appendix 1: Physical quantities and units Prefixes Estimation vi ersity Press 506 530 532 536 538 542 542 542 Appendix 2: Data, formulae and relationships 543 Data Conversion factors Mathematical equations Formulae and relationships 543 543 544 544 Appendix 3: The Periodic Table 545 Glossary 546 Index 555 Acknowledgements 564 Terms and conditions of use for the CD-ROM 566 www.cambridge.org ersity Press Introduction This book covers the entire syllabus of Cambridge International Examinations AS and A Level Physics. It is designed to work with the syllabus that will be examined from 2016. It is in three parts: ■■ ■■ ■■ Chapters 1–16 and P1: the AS level content, covered in the first year of the course, including a chapter (P1) dedicated to the development of your practical skills Chapters 17–32 and P2: the remaining A level content, including a chapter (P2) dedicated to developing your ability to plan, analyse and evaluate practical investigations Appendices of useful formulae, a Glossary and an Index. The main tasks of a textbook like this are to explain the various concepts of physics that you need to understand and to provide you with questions that will help you to test your understanding and prepare for your examinations. You will find a visual guide to the structure of each chapter and the features of this book on the next two pages. When tackling questions, it is a good idea to make a first attempt without referring to the explanations in this Coursebook or to your notes. This will help to reveal any gaps in your understanding. By working out which concepts you find most challenging, and by spending more time to understand these concepts at an early stage, you will progress faster as the course continues. The CD-ROM that accompanies this Coursebook includes answers with workings for all the questions in the book, as well as suggestions for revising and preparing for any examinations you take. There are also lists of recommended further reading, which in many cases will take you beyond the requirements of the syllabus, but which will help you deepen your knowledge and explain more of the background to the physics concepts covered in this Coursebook. In your studies, you will find that certain key concepts come up again and again, and that these concepts form ‘themes’ that link the different areas of physics together. It will help you to progress and gain confidence in tackling problems if you take note of these themes. For this Coursebook, these key concepts include: ■■ ■■ ■■ ■■ ■■ Models of physical systems Testing predictions against evidence Mathematics as a language and problem-solving tool Matter, energy and waves Forces and fields In this Coursebook, the mathematics has been kept to the minimum required by the Cambridge International Examinations AS and A Level Physics syllabus. If you are also studying mathematics, you may find that more advanced techniques such as calculus will help you with many aspects of physics. Studying physics can be a stimulating and worthwhile experience. It is an international subject; no single country has a monopoly on the development of the ideas. It can be a rewarding exercise to discover how men and women from many countries have contributed to our knowledge and well-being, through their research into and application of the concepts of physics. We hope not only that this book will help you to succeed in your future studies and career, but also that it will stimulate your www.cambridge.org curiosity and fire your imagination. Today’s students become the next generation of physicists and engineers, and we hope that you will learn from the past to take physics to ever-greater heights. vii Cambridge International AS and A Level Physics How to use this book Each chapter begins with a short list of the facts and concepts that are explained in it. AS Level Physics Describing movement 1 Our eyes are good at detecting movement. We notice even quite small movements out of the corners of our eyes. It’s important for us to be able to judge movement – think about crossing the road, cycling or driving, or catching a ball. Figure 1.1 shows a way in which movement can be recorded on a photograph. This is a stroboscopic photograph of a boy juggling three balls. As he juggles, a bright lamp flashes several times a second so that the camera records the positions of the balls at equal intervals of time. If we knew the time between flashes, we could measure the photograph and calculate the speed of a ball as it moves through the air. Learning outcomes You should be able to: ■■ ■■ ■■ ■■ define displacement, speed and velocity draw and interpret displacement–time graphs describe laboratory methods for determining speed use vector addition to add two or more vectors AS Level Physics The text and illustrations describe and explain all of the facts and concepts Speed that We you need to know. The chapters, and often the content within them as can calculate the average speed of something moving if If you look at the speedometer in a car, it doesn’t well,weare arranged a similar sequence to your but with AS and know the distance itin moves and the time it takes: tell yousyllabus, the car’s average speed; rather, it tells you its speed at the instant when book. you look at it. This is the car’s A Levelaverage content clearly halves of the distance separated into the two speed = 2 Figure 13.3 or a similar graph of displacement against time illustrates the following important definitions about waves and wave motion: ■■ viii ■■ ■■ ■■ ersity Press ■■ 180 The distance of a point on the wave from its undisturbed position or equilibrium position is called the displacement x. The maximum displacement of any point on the wave from its undisturbed position is called the amplitude A. The amplitude of a wave on the sea is measured in units of distance, e.g. metres. The greater the amplitude of the wave, the louder the sound or the rougher the sea! The distance from any point on a wave to the next exactly similar point (e.g. crest to crest) is called the wavelength λ (the Greek letter lambda). The wavelength of a wave on the sea is measured in units of distance, e.g. metres. The time taken for one complete oscillation of a point in a wave is called the period T. It is the time taken for a point to move from one particular position and return to that same position, moving in the same direction. It is measured in units of time, e.g. seconds.. The number of oscillations per unit time of a point in a wave is called its frequency f. For sound waves, the higher the frequency of a musical note, the higher is its pitch. Frequency is measured in hertz (Hz), where 1 Hz = one oscillation per second (1 kHz = 103 Hz and 1 MHz = 106 Hz). The frequency f of a wave is the reciprocal of the period T: 1 f= T Waves are called mechanical waves if they need a substance (medium) through which to travel. Sound is one example of such a wave. Other cases are waves on strings, seismic waves and water waves (Figure 13.4). Some properties of typical waves are given on page 183 in Table 13.1. Figure 1.1 This boy is juggling three balls. A stroboscopic lamp flashes at regular intervals; the camera is moved to one side at a steady rate to show separate images of the boy. instantaneous speed. time In symbols, this is written as: Questions throughout the text QUESTION give you a chance to check that 1 Look at Figure 1.2. The runner ran 10 000 m, and youthehave understood the Calculate topic his clock shows the total time taken. during the race. youaverage havespeed just read about. You can find the answers to these questions on the CD-ROM. Units d QUESTION v= t 1where Determine wavelength of eachtravelled v is thethe average speed and amplitude d is the distance thet.two shown in Figure1.2) 13.5. in of time Thewaves photograph (Figure shows Ethiopia’s Kenenisa 6 Bekele posing next to the scoreboard after breaking 4 the world record in a a men’s 10 000 metres race. 2 on the clock in the photograph b The time enables us to 0 work out his average 5 10 speed. 15 20 25 30 35 –2 If the object is moving at a constant speed, this –4 Distance / cm equation will give us its speed during the time taken. If its –6 speed is changing, then the equation gives us its average Figure 13.5 Two waves – for Question 1. speed. Average speed is calculated over a period of time. Displacement / cm Chapter 1: Kinematics – describing motion There is a short context at the beginning of each chapter, containing an example of how the material covered in the chapter relates to the ‘real world’. In the Système Internationale d’Unités (the SI system), distance is measured in metres (m) and time in seconds (s). Therefore, speed is in metres per second. This is written as m s−1 (or as m/s). Here, s−1 is the same as 1/s, or ‘per second’. There are many other units used for speed. The choice of unit depends on the situation. You would probably give the speed of abook snail in different the speed of a racing This does units notfrom contain BOX 13.1: Measuring frequency car. Table 1.1 includes some alternative units of speed. AS Level Physics detailed instructions for doing Note that in many calculations it is necessary to work You can measure the frequency of soundwww.cambridge.org waves −1). experiments, but you particular in SI units (m s using a cathode-ray oscilloscope (c.r.o.). Figure 13.6 will find background metresinformation per second QUESTIONS about the practical workper you centimetres second km s−1 per second need do inhow these Boxes. There 7 to Calculate muchkilometres gravitational potential km h−1 or km/h kilometres hour energy is gained if you climbP1 aper flight of stairs. are also two chapters, and Assume that you have a mass of 52 kg and that the mph miles per hour P2, which detailed height provide you lift yourself is 2.5 m. Table 1.1 Units of speed. information about practical 8 A climber of mass 100the kg (including the equipment she is carrying) ascends from sea level to the top skills you need to develop during of a mountain 5500 m high. Calculate the change your course. in her gravitational potential energy. shows how. A microphone is connected to the input of the c.r.o. Sound waves are captured by the microphone and converted into a varying voltage which has the same frequency as the sound waves. This voltage is displayed on the c.r.o. screen. Figure 1.2 Ethiopia’s Kenenisa Bekele set a new world record is best tometres think ofrace a c.r.o. as a voltmeter which forItthe 10 000 in 2005. is capable of displaying a rapidly varying voltage. To do this, its spot moves across the screen at a steady speed, set by the time-base control. At the same time, the spot moves up and down according to the voltage of the input. Hence the display on the screen is a graph of the varying voltage, with time on the (horizontal) x-axis. If we know the horizontal scale, we can determine the period and hence the frequency of the sound wave. Worked example 1 shows how to do this. (In Chapter 15 we will look at one method of measuring the wavelength of sound waves.) m s−1 cm s−1 a A toy car works by means of a stretched rubber band. What form of potential energy does the car store when the band is stretched? b A bar magnet is lying with its north pole next to the south pole of another bar magnet. A student pulls them apart. Why do we say that the magnets’ potential energy has increased? Where has this energy come from? 9 Kinetic energy As well as lifting an object, a force can make it accelerate. 76 Important other Again, work isequations done by the forceand and energy is transferred to theare object. In this case, say that it hasboxes. gained kinetic facts shown inwe highlight energy, Ek. The faster an object is moving, the greater its kinetic energy (k.e.). Figure 13.4 The impact of a droplet on the surface of a liquid creates a vibration, which in turn gives rise to waves on the surface. Figure 13.6 Measuring the frequency of sound waves from a tuning fork. For an object of mass m travelling at a speed v, we have: kinetic energy = 12 × mass × speed2 WORKED EXA 3 Calculate th mass 800 kg 30 m s−1. Step 1 Cal Ek = 12 mv2 = = 160 kJ Step 2 Cal Ek = 12 mv2 = = 360 kJ Step 3 Cal change in k Hint: Take c by squaring change in s incorrect va QUESTIONS 10 Which has travelling 250 kg tra 11 Calculate mass 200 the groun it at 12.2 m Ek = 12 mv2 Deriving the formula for kinetic energy The equation for k.e., Ek = 12mv2, is related to one of the equations of motion. We imagine a car being accelerated from rest (u = 0) to velocity v. To give it acceleration a, it is pushed by a force F for a distance s. Since u = 0, we can write the equation v2 = u2 + 2as as: 2 g.p.e.–k.e A motor drags th hill. The car runs as it goes (see Fig to reach the top o first. It accelerate The motor pro car to the top of t ersity Press In the earlier examples, we described how the ‘motion’ of one trolley appeared to be transferred to a second trolley, or shared with it. It is more correct to say that it is the trolley’s momentum that is transferred or shared. (Strictly speaking, we should refer to linear momentum, because there is another quantity called angular momentum which is possessed by spinning objects.) As with energy, we find that momentum is also conserved. We have to consider objects which form a closed system – that is, no external force acts on them. The principle of conservation of momentum states that: Within a closed system, the total momentum in any direction is constant. The principle of conservation of momentum can also be expressed as follows: A group of colliding objects always has as much momentum after the collision as it had before the collision. This principle is illustrated in Worked example 1. QUESTIONS 2 Calculate the momentum of each of the following objects: a a 0.50 kg stone travelling at a velocity of 20 m s−1 b a 25 000 kg bus travelling at 20 m s−1 on a road c an electron travelling at 2.0 × 107 m s−1. (The mass of the electron is 9.1 × 10−31 kg.) 3 Two balls, each of mass 0.50 kg, collide as shown in Figure 6.6. Show that their total momentum before the collision is equal to their total momentum after the collision. before 2.0 m s–1 3.0 m s–1 For a closed system, in any direction: after 2.0 m s–1 B A How to use this book 1.0 m s–1 B A Wherever you needof to know how to use a formula to carry out a calculation, total momentum objects before collision total momentum of objectsto aftershow collision you howFigure 6.6 this. For Question 3. there are worked= example boxes to do 88 WORKED EXAMPLE 1 Step 1 Make a sketch using the information given in the question. Notice that we need two diagrams to show the situations, one before and one after the collision. Similarly, we need two calculations – one for the momentum of the trolleys before the collision and one for their momentum after the collision. In Figure 6.5, trolley A of mass 0.80 kg travelling at a velocity of 3.0 m s−1 collides head-on with a stationary trolley B. Trolley B has twice the mass of trolley A. The trolleys stick together and have a common velocity of 1.0 m s−1 after the collision. Show that momentum is conserved in this collision. Step 2 Calculate the momentum before the collision: before uA = 3.0 m s–1 A positive direction uB = 0 B 0.80 kg 0.80kg 0.80 kg momentum of trolleys before collision after = mA × uA + mB × uB = (0.80 × 3.0) + 0 = 2.4 kg m s−1 vA+B = 1.0 m s–1 A 0.80 kg A Level Physics Trolley B has no momentum before the collision, because it is not moving. B 0.80 kg 0.80kg Step 3 Calculate the momentum after the collision: Glossary momentum of trolleys after collision AS Level Physics Key words are highlighted in the text when they are first introduced. = (mA + mB) × vA+B = (0.80 + 1.60) × 1.0 Base units, derived units The metre, kilogram and second are three of the seven SI base units.constant These areThe defined withofgreat precision so that Avogadro number particles in one every standards laboratory can reproduce mol−1), mole of any substance approximately (6.02them × 1023correctly. OtherNunits, such as units of speed (m s−1) and denoted A. ) are that known as derived unitsor because acceleration s−2idea band theory(m The electrons in a solid liquid absorption line spectrum A dark line of a unique are combinations of certain base units. units, You willthey also find definitions ofSome can have energies within ranges or derived bands, between wavelength seen in a continuous spectrum. such as the newton and the joule, have special names which are forbidden values. these words in the Glossary. acceleration The rate of change of an object’s velocity: which are more convenient to use than giving them in bandwidth (communications) A measure of the width of Δv terms of base units. The definition of the newton will show a= a range of frequencies being transmitted. Δt you how this works. base units Defined units of the SI system from which all Unit: m s−2 . other units are derived. Defining the newton accuracy An accurate value of a measured quantity is one Cambridge International AS Level Physics Isaac Newton significant best fit line A(1642–1727) straight lineplayed drawnaas closely aspart possible to which is close to the true value of the quantity. in scientific of force. Building on lie thedeveloping points of athe graph so thatidea similar numbers of points acoustic impedance Acoustic impedance Z is the product Galileo’s above andearlier belowthinking, the line. he explained the relationship of the density ρ of a substance and the speed c of sound in between force, mass acceleration, which we now write binding energy Theand minimum external energy required that substance (Z = ρc). Unit: kg m−2 s−1. as F = ma. For thisneutrons reason, the unit of of force is named to separate all the andSIprotons a nucleus. There is a summary of activity The rate of decay or disintegration of nuclei in a after him. bit A basic unit of information storage, the amount of radioactive sample. key points at the end We can use the equation F = ma to define the newton (N). ■ Forces are vector quantities that can be added by ■ The principle of moments states that, for information any object stored by a device that exists in only two ampere The SI unit of electric current (abbreviated A). of each chapter. You distinct states, usually given as the binary digits 0 and 1. means of a vector triangle. Their resultant can be that is in equilibrium, the sum of the clockwise amplitude displacement of point a particle from by the determined using trigonometry or by scale drawing.The maximum moments about any provided One newton is the force that will give aconstant 1 kg massgiven an by might find this helpful Boltzmann constant A fundamental 546 its equilibrium position.forces acting on the object equals the sum ofacceleration the of 1 m s−2 in the direction of the force. R ■ Vectors such as forces can be resolved into and NA is the = , where R is−2the ideal gas constant when you are revising. 40 same kpoint. −2 amplitude modulation A form of modulation in which anticlockwise moments about that N or 1 N = 1 kg m s 1 N = 1 kg × 1 m s A components. Components at right angles to one Avogadro constant. the signal causes variations in the amplitude of a carrier another can be treated independently of one another. ■ A couple is a pair of equal, parallel but opposite forces wave.the law The pressure exerted by a fixed mass of gas For a force F at an angle θ to the x-direction, whose effect is to produce a turning effectBoyle’s on a body The seven base units is inversely proportional to its volume, provided the analogue signal A signal that isgiving continuously variable, components are: without it linear acceleration. temperature thestudy gas remains constant. having a continuum of torque possibleofvalues. In mechanicsof(the of forces and motion), the units x-direction: F cos θ a couple = one of the forces × perpendicular we use are based on X-rays three base units: when the metre, kilogram braking radiation produced electrons are analogue-to-digital conversion (ADC) the Conversion distance between forces of a y-direction: F sin θ and second.(also As wecalled moveBremsstrahlung into studying electricity, decelerated radiation).we will continuous analogue■ signal toobject discrete numbers. the resultant For an to digital be in equilibrium, force ■ The moment of a force = force × perpendicular need to add another base unit, the ampere. requires www.cambridge.org The ratio of charge stored by aHeat capacitor to angular The angle through anzero object on the object which must be and thecapacitance resultant distance of the pivot from the line of action of displacement acting another base difference unit, the kelvin the potential across(the it. unit of temperature). moves in a circle. moment must be zero. the force. Table 3.2 shows the seven base units of the SI system. carrier wave A waveform (usually sinusoidal) which is angular frequency The frequency of a sinusoidal Remember that all other units can be derived from these modulated by an input signal to carry information. oscillation expressed in radians per second: seven. The equations that relate them are the equations 2π Chapter 15: Stationary waves centre gravity point the entire of an angular frequency ω = that youofwill learnThe as you go where along (just as F =weight ma relates T object appears to act. the newton to the kilogram, metre and second). The unit angular velocity The rate of change of the angular centripetal Theisresultant an object of luminousforce intensity not partforce of theacting A/ASon course. position of an object as it moves along a curved path. moving in a circle; it is always directed towards the centre Questions at the end of each chapter begin with shorter answer then move on to more antinode Aquestions, point on a stationary wave with maximum Base unit Symbol Base unit of the circle. 64 amplitude. demanding exam-style questions, some of which may require use of knowledge from previous characteristic length x, l, s etc. m (metre) radiation Very intense X-rays produced in atomic mass unit A unit of mass (symbol u) mass m kg (kilogram) chapters. Answers to these questions can be found on theapproximately CD–ROM. an X-ray tube, having specific wavelengths that depend on −27 kg. The mass of an equal to 1.661 × 10 1 A ship is pulled at a constant speed by two small boats, A and B, as shown in Figure 4.27. The engine of the the time t s (second) target metal. atom of 126 C = 12.000 u exactly. ship does not produce any force. electriccarrier current Any charged particle, I (ampere) charge such asAan electron, 1 Figure 15.19 shows a stationary wave on a string. attenuation The gradual loss in strength or intensity of a thermodynamic T K (kelvin) responsible for atemperature current. signal. A amount oflaw substance n (mole) Charles’s The volume occupied by a gas mol at constant average speed The total distance travelled by an object pressure directly proportional 40° luminousisintensity I to its thermodynamic cd (candela) divided by the total time taken. (absolute) temperature. Figure 6.5 The state of trolleys A and B, before and after the collision. = 2.4 kg m s−1 see thermodynamic scale. absolute scale of temperature; So, both before and after the collision, the trolleys have absolute zero The temperature at which a system has a combined momentum of 2.4 kg m s−1energy; . Momentum has to −273.15 °C. minimum internal equivalent been conserved. Summary End-of-chapter questions End-of-chapter questions 40° vibrator Figure 15.19 For End-of-chapter Question 1. Figure 4.27 For End-of-chapter Question 1. Table 3.2 SI base quantities and units. In this course, you will learn about all of these except the candela. B a On a copy of Figure 15.19, label one node (N) and one antinode (A). b Mark on your the wavelength ofship the standing The tension in each cablediagram between A and B and the is 4000 N.wave and label it λ. c a The frequency of the vibratorthe is doubled. Describe the changes inthe theship. standing wave pattern. a Draw free-body diagram showing three horizontal forces acting on b Draw a vector diagram scale showing forces and usea your to find filled the value 2 A tuning fork whichto produces a note these of 256three Hz is placed above tubediagram which is nearly with water. of the drag force onisthe ship. until resonance is first heard. The water level lowered a Explain what is meant by the term resonance. b The length of the column of air above the water when resonance is first heard is 31.2 cm. Calculate the speed of the sound wave. 3 a State two similarities and two differences between progressive waves and stationary waves. b Figure 15.20 shows an experiment to measure the speed of a sound in a string. The frequency of the vibrator is adjusted until the standing wave shown in Figure 15.20 is formed. vibrator 75 cm [2] [1] [1] [1] [2] [1] [2] [4] pulley slotted masses Figure 15.20 For End-of-chapter Question 3. i On a copy of the diagram, mark a node (label it N) and an antinode (label it A). [2] 219 QUESTION 4 The pull weight) i internati of force a reasons useful de Other SI un Using only seve of quantities ha would be confu units were also were defined as of water would unlikely that th exactly the mas kilogram, whic which ix all mass All other un is done using th speed is define speed in the SI Since the de units for force Equations t same base unit not happen the When each te the equation QUESTIONS 5 Determi a press b energ c densi 6 Use base equation a press =d b dista = in