Jacaranda 2 HSC 3rd Edition

MICHAEL ANDRIESSEN PETER PENTLAND RICHARD GAUT BRUCE McKAY JILL TACON

JACARANDA HSC SCIENCE

Third edition published 2008 by John Wiley & Sons Australia, Ltd 42 McDougall Street, Milton, Qld 4064 Typeset in 10.5/12pt New Baskerville Michael Andriessen, Peter Pentland, Richard Gaut, Bruce McKay, Jillian Tacon and Upgrade Business Systems (Ric Morante) 2008 First edition published 2001 Michael Andriessen, Peter Pentland, Richard Gaut and Bruce McKay 2001 Second edition published 2003 Michael Andriessen, Peter Pentland, Richard Gaut, Bruce McKay and Jillian Tacon 2003 The moral rights of the authors have been asserted. National Library of Australia Cataloguing-in-Publication data Title: Edition: ISBN: Notes: Target audience: Subjects: Other authors/contributors: Dewey number: Physics 2 HSC course/Michael Andriessen ... [et al.]. 3rd ed. 978 0 7314 0823 8 (pbk.) Includes index. For secondary school age. Physics Textbooks. Andriessen, Michael. 530

Reproduction and communication for educational purposes The Australian Copyright Act 1968 allows a maximum of one chapter or 10% of the pages of this work, whichever is the greater, to be reproduced and/or communicated by any educational institution for its educational purposes provided that the educational institution (or the body that administers it) has given a remuneration notice to Copyright Agency Limited (CAL). Reproduction and communication for other purposes Except as permitted under the Act (for example, a fair dealing for the purposes of study, research, criticism or review), no part of this book may be reproduced, stored in a retrieval system, communicated or transmitted in any form or by any means without prior written permission. All inquiries should be made to the publisher. All activities have been written with the safety of both teacher and student in mind. Some, however, involve physical activity or the use of equipment or tools. All due care should be taken when performing such activities. Neither the publisher nor the authors can accept responsibility for any injury that may be sustained when completing activities described in this textbook. Front and back cover images: Photodisc, Inc. Illustrated by the Wiley Art Studio Printed in Singapore by Craft Print 10 9 8 7 6 5 4 3 2 1

CONTENTSPreface viii About eBookPLUS ix Syllabus grid x Acknowledgements xvi

HSC CORE MODULE Space

Chapter 1: Earths gravitational eld1.1 1.2 1.3 The Earths gravity 3 Weight 6 Gravitational potential energy 7

2

Summary 10 Questions 10 Practical activities

11

Chapter 2: Launching into space2.1 2.2 2.3 Projectile motion 14 Escape velocity 23 Lift-off 24

13


35

Chapter 3: Orbiting and re-entry3.1 3.2 In orbit 39 Re-entry 50

38


58

Chapter 4: Gravity in the solar system 604.1 4.2 4.3 The Law of Universal Gravitation Gravitational elds 65 The slingshot effect 66 61

Summary 70 Questions 70

Chapter 5: Space and time5.1 5.2 5.3

7177

The aether model 72 Special relativity 74 Consequences of special relativity


96

HSC CORE MODULE Motors and generators

Chapter 6: The motor effect and DC electric motors 1006.1 6.2 6.3 6.4 The motor effect 103 Forces between two parallel conductors Torque 107 DC electric motors 109 105


120

Chapter 7: Generating electricity 1227.1 7.2 7.3 7.4 7.5 The discoveries of Michael Faraday 123 Electromagnetic induction 126 Generating a potential difference 127 Lenzs law 128 Eddy currents 131

Summary 134 Questions 134 Practical activities 137

Chapter 8: Generators and power distribution8.1 8.2 8.3 8.4 8.5 Generators 140 Electric power generating stations Transformers 148 Power distribution 151 Electricity and society 156 146

139


Chapter 9: AC electric motors 1639.1 9.2 Main features of an AC motor 164 Energy transformations and transfers 169


HSC CORE MODULE From ideas to implementation

Chapter 10: Cathode rays and the development of television10.1 10.2 10.3 10.4 10.5 10.6

174

The discovery of cathode rays 175 Effect of electric elds on cathode rays 177 Effect of magnetic elds on cathode rays 182 Determining the charge-to-mass ratio of cathode rays Cathode rays waves or particles? 184 Applications of cathode rays 186

183


Chapter 11: The photoelectric effect and black body radiation11.1 11.2 11.3 11.4 11.5

193

Maxwells theory of electromagnetic waves 194 Heinrich Hertz and experiments with radio waves 196 The black body problem and the ultraviolet catastrophe 199 What do we mean by classical physics and quantum theory? The photoelectric effect 202

202


iv

Chapter 12: The development and application of transistors 21212.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 Conductors, insulators and semiconductors Band structures in semiconductors 216 Doping and band structure 219 Thermionic devices 220 Solid state devices 222 Thermionic versus solid state devices 224 Invention of the transistor 225 Integrated circuits 227 213


231

Chapter 13: Superconductivity13.1 13.2 13.3 13.4 13.5 13.6 13.7

232

Interference 233 Diffraction 235 X-ray diffraction 235 Braggs experiment 238 The crystal lattice structure of metals 239 Superconductivity 240 How is superconductivity explained? 243


253

HSC OPTION MODULE Astrophysics

Chapter 14: Looking and seeing14.1 14.2 14.3 14.4 14.5

256

Galileos telescopes 257 Atmospheric absorption of the electromagnetic spectrum 258 Telescopes 261 Seeing 265 Modern methods to improve telescope performance 265


272

Chapter 15: Astronomical measurement15.1 Astrometry 275 15.2 Spectroscopy 279 15.3 Photometry 289

274


302

Chapter 16: Binaries and variables16.1 Binaries 306 16.2 Variables 312

305


318

v

Chapter 17: Star lives17.1 17.2 17.3 17.4

320327

Star birth 321 Main sequence star life 324 Star life after the main sequence Star death 332


HSC OPTION MODULE Medical physics

Chapter 18: The use of ultrasound in medicine 34018.1 18.2 18.3 18.4 18.5 What type of sound is ultrasound? 341 Using ultrasound to detect structure inside the body 343 Producing and detecting ultrasound: the piezoelectric effect 347 Gathering and using information in an ultrasound scan 348 Using ultrasound to examine blood ow 352


Chapter 19: Electromagnetic radiation as a diagnostic tool

361

19.1 X-rays in medical diagnosis 362 19.2 CT scans in medical diagnosis 368 19.3 Endoscopes in medical diagnosis 373


Chapter 20: Radioactivity as a diagnostic tool20.1 Radioactivity and the use of radioisotopes 382 20.2 Positron emission tomography (PET) 392 20.3 Imaging methods working together 394

381


Chapter 21: Magnetic resonance imaging as a diagnostic tool 39821.1 21.2 21.3 21.4 The patient and the image using MRI 399 The MRI machine: effect on atoms in the patient 402 Medical uses of MRI 410 Comparison of the main imaging techniques 412


HSC OPTION MODULE From quanta to quarks

Chapter 22: The atomic models of Rutherford and Bohr22.1 22.2 22.3 22.4 22.5 The Rutherford model of the atom 419 Bohrs model of the atom 423 Bohrs postulates 427 Mathematics of the Rutherford and Bohr models Limitations of the Bohr model of the atom 434

418

429


vi

Chaper 23: Development of quantum mechanics 44023.1 Diffraction 441 23.2 Steps towards a complete quantum theory model of the atom 444


Chapter 24: Probing the nucleus24.1 24.2 24.3 24.4 24.5

453

Discoveries pre-dating the nucleus 454 Discovery of the neutron 458 Discovery of the neutrino 461 The strong nuclear force 466 Mass defect and binding energy of the nucleus

468


Chapter 25: Nuclear ssion and other uses of nuclear physics 47425.1 25.2 25.3 25.4 25.5 25.6 Energy from the nucleus 475 The discovery of nuclear ssion 476 The development of the atom bomb 480 Nuclear ssion reactors 484 Medical and industrial applications of radioisotopes Neutron scattering 492

489


Chapter 26: Quarks and the Standard Model of particle physics 49526.1 Instruments used by particle physicists 496 26.2 The Standard Model of particle physics 503


518

Glossary 521 Appendix 1: Formulae and data sheet 526 Appendix 2: Periodic table 528 Appendix 3: Key words for examination questions Answers to numerical questions 531 Index 536

529

vii

PREFACEThis third edition of Physics 2: HSC Course is revised and updated to meet all the requirements of the amended Stage 6 Physics Syllabus for Year 12 students in New South Wales. Written by a team of experienced Physics teachers, Physics 2 offers a complete resource with coverage of the three core modules as well as three option modules: Quanta to Quarks, Astrophysics and Medical Physics. An additional option topic, The Age of Silicon, is available online. Physics 2 features: full-colour, high-quality, detailed illustrations to enhance students understanding of Physics concepts clearly written explanations and sample problems interest boxes focusing on up-to-date information, current research and new discoveries practical activities at the end of each chapter to support the syllabus investigations key terms highlighted and dened in the context of the chapters and in a complete glossary chapter reviews that provide a summary and a range of problemsolving and descriptive questions.

eBook plus

Next generation teaching and learning

This title features eBookPLUS: an electronic version of the textbook and a complementary set of targeted digital resources. These exible and engaging ICT activities are available online at the JacarandaPLUS website (www.jacplus.com.au). eBookPLUS icons within the text direct students to the online resources, which include: eModelling: Excel spreadsheets that provide examples of numerical and algebraic modelling eLessons: Video and animations that reinforce study by bringing key concepts to life Interactivities: Interactive study activities that enhance student understanding of key concepts through hands-on experience Weblinks: HTML links to other useful support material on the internet.

viii

Next generation teaching and learningAbout eBookPLUSPhysics 2: HSC Course, 3rd edition features eBookPLUS: an electronic version of the entire textbook and supporting multimedia resources. It is available for you online at the JacarandaPLUS website (www.jacplus.com.au).

Using the JacarandaPLUS websiteTo access your eBookPLUS resources, simply log on to www.jacplus.com.au. There are three easy steps for using the JacarandaPLUS system.

Step 1. Create a user account The rst time you use the JacarandaPLUS system, you will need to create a user account. Go to the JacarandaPLUS home page (www.jacplus.com.au) and follow the instructions on screen. Step 2. Enter your registration code Once you have created a new account and logged in, you will be prompted to enter your unique registration code for this book, which is printed on the inside front cover of your textbook.

LOGIN Once you have created your account, you can use the same email address and password in the future to register any JacarandaPLUS books.

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Troubleshooting Go to the JacarandaPLUS help page at www.jacplus.com.au Contact John Wiley & Sons Australia, Ltd. Email: [email protected] Phone: 1800 JAC PLUS (1800 522 7587)

ix

SYLLABUS GRIDCore module: SPACE (chapters 15, pages 198) 1. The Earth has a gravitational eld that exerts a force on objects both on it and around itStudents learn to: dene weight as the force on an object due to a gravitational eld explain that a change in gravitational potential energy is related to work done dene gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational eld

page 8 7 79

m1 m2 E p = G ------------r

Students: perform an investigation and gather information to determine a value for acceleration due to gravity using pendulum motion or computer- assisted technology and identify reasons for possible variations from the value 2 9.8 m s gather secondary information to predict the value of acceleration due to gravity on other planets analyse information using the expression F = mg to determine the weight force for a body on Earth and for the same body on other planets

page 11

5, 10, 12 6, 10, 12

2. Many factors have to be taken into account to achieve a successful rocket launch, maintain a stable orbit and return to EarthStudents learn to: describe the trajectory of an object undergoing projectile motion within the Earths gravitational eld in terms of horizontal and vertical components describe Galileos analysis of projectile motion explain the concept of escape velocity in terms of the: gravitational constant mass and radius of the planet outline Newtons concept of escape velocity identify why the term g forces is used to explain the forces acting on an astronaut during launch discuss the effect of the Earths orbital motion and its rotational motion on the launch of a rocket analyse the changing acceleration of a rocket during launch in terms of the: Law of Conservation of Momentum forces experienced by astronauts analyse the forces involved in uniform circular motion for a range of objects, including satellites orbiting the Earth compare qualitatively low Earth and geo-stationary orbits dene the term orbital velocity and the quantitative and qualitative relationship between orbital velocity, the gravitational constant, mass of the central body, mass of the satellite and the radius of the orbit using Keplers Law of Periods account for the orbital decay of satellites in low Earth orbit discuss issues associated with safe re-entry into the Earths atmosphere and landing on the Earths surface identify that there is an optimum angle for safe re-entry for a manned spacecraft into the Earths atmosphere and the consequences of failing to achieve this angle

page 1423 14 234 23 2631 312 25, 267 (see also 367) 3941 478 414

Students: solve problems and analyse information to calculate the actual velocity of a projectile from its horizontal and vertical components using:

page 1922, 334

vx = ux v 2 u +2at = vy = uy + 2ay y x = uxt 2 -y = uyt + 1 ayt2

2

2

perform a rst-hand investigation, gather information and analyse data to calculate initial and nal velocity, maximum height reached, range and time of ight of a projectile for a range of situations by using simulations, data loggers and computer analysis identify data sources, gather, analyse and present information on the contribution of one of the following to the development of space exploration: Tsiolkovsky, Oberth, Goddard, Esnault-Pelterie, ONeill or von Braun solve problems and analyse information to calculate the centripetal force acting on a satellite undergoing uniform circular motion about the Earth using

35

32

401, 56, 589

mv F = --------r solve problems and analyse information using: 424, 567

2

4950 505 51

r GM ----- = --------2 2 T 4

3

3. The Solar System is held together by gravityStudents learn to: describe a gravitational eld in the region surrounding a massive object in terms of its effects on other masses in it dene Newtons Law of Universal Gravitation

page 656 612

Students: present information and use available evidence to discuss the factors affecting the strength of the gravitational force solve problems and analyse information using

page 614, 70 612, 70

m1 m2 F = G ------------2 d discuss the importance of Newtons Law of Universal Gravitation in understanding and calculating the motion of satellites identify that a slingshot effect can be provided by planets for space probes 625 669

m1 m2 F = G ------------d

4. Current and emerging understanding about time and space has been dependent upon earlier models of the transmission of lightStudents learn to: outline the features of the aether model for the transmission of light describe and evaluate the Michelson-Morley attempt to measure the relative velocity of the Earth through the aether discuss the role of the Michelson-Morley experiments in making determinations about competing theories outline the nature of inertial frames of reference discuss the principle of relativity describe the signicance of Einsteins assumption of the constancy of the speed of light identify that if c is constant then space and time become relative discuss the concept that length standards are dened in terms of time in contrast to the original metre standard

page 72 724 74 745 745 756 76 77

Students: gather and process information to interpret the results of the MichelsonMorley experiment perform an investigation to help distinguish between non-inertial and inertial frames of reference analyse and interpret some of Einsteins thought experiments involving mirrors and trains and discuss the relationship between thought and reality analyse information to discuss the relationship between theory and the evidence supporting it, using Einsteins predictions based on relativity that were made many years before evidence was available to support it

page 967 978 756, 778 801

(continued)

x

explain qualitatively and quantitatively the consequence of special relativity in relation to: the relativity of simultaneity the equivalence between mass and energy length contraction time dilation mass dilation discuss the implications of mass increase, time dilation and length contraction for space travel

solve problems and analyse information using: 778 889 814 789 858 8992

E = mc

2 2

89, 95 84, 945

v l v = l 0 1 ---2 c t0 t v = -----------------2 v 1 ---2 c m0 m v = -----------------2 v 1 ---2 c

81, 945

88, 95

Core module: MOTORS AND GENERATORS (chapters 69, pages 10172) 1. Motors use the effect of forces on current-carrying conductors in magnetic eldsStudents learn to: discuss the effect on the magnitude of the force on a current-carrying conductor of variations in: the strength of the magnetic eld in which it is located the magnitude of the current in the conductor the length of the conductor in the external magnetic eld the angle between the direction of the external magnetic eld and the direction of the length of the conductor describe qualitatively and quantitatively the force between long parallel

page 1045

Students: solve problems using:

page 107, 11719

I1 I2 F -- = k -------d l perform a rst-hand investigation to demonstrate the motor effect solve problems and analyse information about the force on currentcarrying conductors in magnetic elds using 1057 120 105, 11719

F = BIl sin solve problems and analyse information about simple motors using:

dene torque as the turning moment of a force using: = Fd identify that the motor effect is due to the force acting on a currentcarrying conductor in a magnetic eld describe the forces experienced by a current-carrying loop in a magnetic eld and describe the net result of the forces describe the main features of a DC electric motor and the role of each feature identify that the required magnetic elds in DC motors can be produced either by current-carrying coils or permanent magnets

I1 I2 F current-carrying conductors: -- = k -------d l

= nBIA cos 1078 1045 1023 10911 10911, 112 identify data sources, gather and process information to qualitatively describe the application of the motor effect in: the galvanometer the loudspeaker

114, 11819, 121 11415

2. The relative motion between a conductor and magnetic eld is used to generate an electrical voltageStudents learn to: outline Michael Faradays discovery of the generation of an electric current by a moving magnet dene magnetic eld strength B as magnetic ux density describe the concept of magnetic ux in terms of magnetic ux density and surface area describe generated potential difference as the rate of change of magnetic ux through a circuit account for Lenzs Law in terms of conservation of energy and relate it to the production of back emf in motors explain that, in electric motors, back emf opposes the supply emf explain the production of eddy currents in terms of Lenzs Law

page 1236 126 1267 1278 12830 12930 1312

Students: perform an investigation to model the generation of an electric current by moving a magnet in a coil or a coil near a magnet plan, choose equipment or resources for, and perform a rst-hand investigation to predict and verify the effect on a generated electric current when: the distance between the coil and the magnet is varied the strength of the magnet is varied the relative motion between the coil and the magnet is varied gather, analyse and present information to explain how induction is used in cooktops in electric ranges gather secondary information to identify how eddy currents have been utilised in electromagnetic braking

page 1378 1378

133 132

3. Generators are used to provide large-scale power productionStudents learn to: describe the main components of a generator compare the structure and function of a generator to an electric motor describe the differences between AC and DC generators discuss the energy losses that occur as energy is fed through transmission lines from the generator to the consumer assess the effects of the development of AC generators on society and the environment

page 1401 141, 109, 1645 1425 1514 1478, 156

Students: plan, choose equipment or resources for, and perform a rst-hand investigation to demonstrate the production of an alternating current gather secondary information to discuss advantages and disadvantages of AC and DC generators and relate these to their use analyse secondary information on the competition between Westinghouse and Edison to supply electricity to cities gather and analyse information to identify how transmission lines are: insulated from supporting structures protected from lightning strikes

page 1601 160 1478 1545

4. Transformers allow generated power to be either increased or decreased before it is usedStudents learn to: describe the purpose of transformers in electrical circuits compare step-up and step-down transformers identify the relationship between the ratio of the number of turns in the primary and secondary coils and the ratio of primary to secondary voltage explain why voltage transformations are related to conservation of energy explain the role of transformers in electricity sub-stations discuss why some electrical appliances in the home that are connected to the mains domestic power supply use a transformer discuss the impact of the development of transformers on society

page 1489 149 14950 14950 154 1489, 153 1523, 156

Students: perform an investigation to model the structure of a transformer to demonstrate how secondary voltage is produced solve problems and analyse information about transformers using:

page 1601 1501

Vp np ----- = ---Vs ns gather, analyse and use available evidence to discuss how difculties of heating caused by eddy currents in transformers may be overcome gather and analyse secondary information to discuss the need for transformers in the transfer of electrical energy from a power station to its point of use 151 1524, 162

xi

5. Motors are used in industries and the home usually to convert electrical energy into more useful forms of energyStudents learn to: describe the main features of an AC electric motor

page 1649

Students: perform an investigation to demonstrate the principle of an AC induction motor gather, process and analyse information to identify some of the energy transfers and transformations involving the conversion of electrical energy into more useful forms in the home and industry

page 172 16970

Core module: FROM IDEAS TO IMPLEMENTATION (chapters 1013, pages 173254) 1. Increased understanding of cathode rays led to the development of televisionStudents learn to: explain why the apparent inconsistent behaviour of cathode rays caused debate as to whether they were charged particles or electromagnetic waves explain that cathode ray tubes allowed the manipulation of a stream of charged particles identify that moving charged particles in a magnetic eld experience a force identify that charged plates produce an electric eld describe quantitatively the force acting on a charge moving through a magnetic eld F = qvB sin discuss qualitatively the electric eld strength due to a point charge, positive and negative charges and oppositely charged parallel plates describe quantitatively the electric eld due to oppositely charged parallel plates outline Thomsons experiment to measure the charge : mass ratio of an electron outline the role of: electrodes in the electron gun the deection plates or coils the uorescent screen in the cathode ray tube of conventional TV displays and oscilloscopes

page 1845 1756 182 1779 182 1779 1779 183 1868

Students: perform an investigation and gather rst-hand information to observe the occurrence of different striation patterns for different pressures in discharge tubes perform an investigation to demonstrate and identify properties of cathode rays using discharge tubes: containing a Maltese cross containing electric plates with a uorescent display screen containing a glass wheel analyse the information gathered to determine the sign of the charge on cathode rays solve problems and analyse information using:

page 191 192

f = qvB sin F = qEand

178, 181, 182, 18990

V E = -d

2. The reconceptualisation of the model of light led to an understanding of the photoelectric effect and black body radiationStudents learn to: describe Hertzs observation of the effect of a radio wave on a receiver and the photoelectric effect he produced but failed to investigate outline qualitatively Hertzs experiments in measuring the speed of radio waves and how they relate to light waves identify Plancks hypothesis that radiation emitted and absorbed by the walls of a black body cavity is quantised identify Einsteins contribution to quantum theory and its relation to black body radiation explain the particle model of light in terms of photons with particular energy and frequency identify the relationships between photon energy, frequency, speed of light and wavelength: E = hf and c = f

page 1968, 2023 1968 199201 205 204 201 5

Students: perform an investigation to demonstrate the production and reception of radio waves identify data sources, gather, process and analyse information and use available evidence to assess Einsteins contribution to quantum theory and its relation to black body radiation identify data sources and gather, process and present information to summarise the use of the photoelectric effect in: solar cells photocells solve problems and analyse information using:

page 211 2056 2078

201, 20910 206

E = hf and c = f process information to discuss Einstein and Plancks differing views about whether science research is removed from social and political forces

3. Limitations of past technologies and increased research into the structure of the atom resulted in the invention of transistorsStudents learn to: identify that some electrons in solids are shared between atoms and move freely describe the difference between conductors, insulators and semiconductors in terms of band structures and relative electrical resistance identify absences of electrons in a nearly full band as holes, and recognise that both electrons and holes help to carry current compare qualitatively the relative number of free electrons that can drift from atom to atom in conductors, semiconductors and insulators identify that the use of germanium in early transistors is related to lack of ability to produce other materials of suitable purity describe how doping a semiconductor can change its electrical properties identify differences in p- and n-type semiconductors in terms of the relative number of negative charge carriers and positive holes describe differences between solid state and thermionic devices and discuss why solid state devices replaced thermionic devices

page 21314 21320 21617, 21920 21315 21819 217, 21920 21920 2205

Students: perform an investigation to model the behaviour of semiconductors, including the creation of a hole or positive charge on the atom that has lost the electron and the movement of electrons and holes in opposite directions when an electric eld is applied across the semiconductor gather, process and present secondary information to discuss how shortcomings in available communication technology led to an increased knowledge of the properties of materials with particular reference to the invention of the transistor identify data sources, gather, process, analyse information and use available evidence to assess the impact of the invention of transistors on society with particular reference to their use in microchips and microprocessors

page 230, 231

2256, 231

2258

4. Investigations into the electrical properties of particular metals at different temperatures led to the identication of superconductivity and the exploration of possible applicationsStudents learn to: outline the methods used by the Braggs to determine crystal structure identify that metals possess a crystal lattice structure describe conduction in metals as a free movement of electrons unimpeded by the lattice identify that resistance in metals is increased by the presence of impurities and scattering of electrons by lattice vibrations describe the occurrence in superconductors below their critical temperature of a population of electron pairs unaffected by electrical resistance discuss the BCS theory discuss the advantages of using superconductors and identify limitations to their use

page 2369 239 240 240 2436 2434 2402, 24650

Students: process information to identify some of the metals, metal alloys and compounds that have been identied as exhibiting the property of superconductivity and their critical temperatures perform an investigation to demonstrate magnetic levitation analyse information to explain why a magnet is able to hover above a superconducting material that has reached the temperature at which it is superconducting gather and process information to describe how superconductors and the effects of magnetic elds have been applied to develop a maglev train process information to discuss possible applications of superconductivity and the effects of those applications on computers, generators and motors and transmission of electricity through power grids

page 2412 2534 2401, 245 2489 2468

xii

Option module: ASTROPHYSICS (chapters 1417, pages 255338) 1. Our understanding of celestial objects depends upon observations made from Earth or space near the EarthStudents learn to: discuss Galileos use of the telescope to identify features of the Moon discuss why some wavebands can be more easily detected from space dene the terms resolution and sensitivity of telescopes discuss the problems associated with ground-based astronomy in terms of resolution and absorption of radiation and atmospheric distortion outline methods by which the resolution and/or sensitivity of groundbased systems can be improved, including: adaptive optics interferometry active optics

page 2578 25860 2624 265 2658

Students: identify data sources, plan, choose equipment or resources for, and perform an investigation to demonstrate why it is desirable for telescopes to have a large diameter objective lens or mirror in terms of both sensitivity and resolution

page 272

2. Careful measurement of a celestial objects position, in the sky, (astrometry) may be used to determine its distanceStudents learn to: dene the terms parallax, parsec, light-year explain how trigonometric parallax can be used to determine the distance to stars discuss the limitations of trigonometric parallax measurements

page 2756 2757 2778

Students: solve problems and analyse information to calculate the distance to a star given its trigonometric parallax using:

page 277, 299300

1 d = -p gather and process information to determine the relative limits to trigonometric parallax distance determinations using recent groundbased and space-based telescopes 3023

3. Spectroscopy is a vital tool for astronomers and provides a wealth of informationStudents learn to: account for the production of emission and absorption spectra and compare these with a continuous black body spectrum describe the technology needed to measure astronomical spectra identify the general types of spectra produced by stars, emission nebulae, galaxies and quasars describe the key features of stellar spectra and describe how these are used to classify stars describe how spectra can provide information on surface temperature, rotational and translational velocity, density and chemical composition of stars

page 2802 27980 285 2867 2889

Students: perform a rst-hand investigation to examine a variety of spectra produced by discharge tubes, reected sunlight, or incandescent laments analyse information to predict the surface temperature of a star from its intensity/wavelength graph

page 303 300, refer 2812

4. Photometric measurements can be used for determining distance and comparing objectsStudents learn to: dene absolute and apparent magnitude explain how the concept of magnitude can be used to determine the distance to a celestial object outline spectroscopic parallax explain how two-colour values (i.e. colour index, B-V) are obtained and why they are useful describe the advantages of photoelectric technologies over photographic methods for photometry

page 291 2912 2935 2937 298

Students: solve problems and analyse information using:

M = m 5 log ----- and

d 10

page 291, 292, 293, 2945, 3001

IA mB mA ---- = 100 ------------------IB 5to calculate the absolute or apparent magnitude of stars using data and a reference star perform an investigation to demonstrate the use of lters for photometric measurements identify data sources, gather, process and present information to assess the impact of improvements in measurement technologies on our understanding of celestial objects 3034 289, 298

5. The study of binary and variable stars reveals vital information about starsStudents learn to: describe binary stars in terms of the means of their detection: visual, eclipsing, spectroscopic and astrometric explain the importance of binary stars in determining stellar masses classify variable stars as either intrinsic or extrinsic and periodic or nonperiodic explain the importance of the period-luminosity relationship for determining the distance of cepheids

page 30610 3068 312314 315

Students: perform an investigation to model the light curves of eclipsing binaries using computer simulation solve problems and analyse information by applying:

page 31819 308, 318

4 r m1 + m2 = ------------2 G

2 3

6. Stars evolve and eventually dieStudents learn to: describe the processes involved in stellar formation outline the key stages in a stars life in terms of the physical processes involved describe the types of nuclear reactions involved in Main Sequence and post-Main Sequence stars discuss the synthesis of elements in stars by fusion explain how the age of a globular cluster can be determined from its zero-age main sequence plot for an HR diagram explain the concept of star death in relation to: planetary nebula supernovae white dwarfs neutron stars/pulsars black holes

page 3214 32134, 335 3248, 331 332 32930 3323

Students: present information by plotting HertzsprungRussell diagrams for: nearby or brightest stars; stars in a young open cluster; stars in a globular cluster analyse information from an HR diagram and use available evidence to determine the characteristics of a star and its evolutionary stage present information by plotting on an HR diagram the pathways of stars of 1, 5 and 10 solar masses during their life cycle

page 330 335, 338 335

xiii

Option module: MEDICAL PHYSICS (chapters 1821, pages 339416) 1. The properties of ultrasound waves can be used as diagnostic toolsStudents learn to: identify the differences between ultrasound and sound in normal hearing range describe the piezoelectric effect and the effect of using an alternating potential difference with a piezoelectric crystal dene acoustic impedance:

page 3412 347 3445 3446 3456

Z = vand identify that different materials have different acoustic impedances describe how the principles of acoustic impedance and reection and refraction are applied to ultrasound dene the ratio of reected to initial intensity as:

Ir [ Z2 Z1 ] --- = -----------------------2 I0 [ Z2 + Z1 ] identify that the greater the difference in acoustic impedance between two materials, the greater is the reected proportion of the incident pulse describe the situations in which A scans, B scans, and phase and sector scans would be used and the reasons for the use of each describe the Doppler effect in sound waves and how it is used in ultrasonics to obtain ow characteristics of blood moving through the heart outline some cardiac problems that can be detected through the use of the Doppler effect 3456 34851 3525 3545

2

Students: solve problems and analyse information to calculate the acoustic impedance of a range of materials, including bone, muscle, soft tissue, fat, blood and air and explain the types of tissues that ultrasound can be used to examine gather secondary information to observe at least two ultrasound images of body organs identify data sources and gather information to observe the ow of blood through the heart from a Doppler ultrasound video image identify data sources, gather, process and analyse information to describe how ultrasound is used to measure bone density solve problems and analyse information using:

page 345, 358

344, 350, 3556 355, 360 3512 3446, 3589

Z = vand

Ir [ Z2 Z1 ] --- = -----------------------2 I0 [ Z2 + Z1 ]

2

2. The physical properties of electromagnetic radiation can be used as diagnostic toolsStudents learn to: describe how X-rays are currently produced compare the differences between soft and hard X-rays explain how a computed axial tomography (CT) scan is produced describe circumstances where a CT scan would be a superior diagnostic tool compared to either X-rays or ultrasound explain how an endoscope works in relation to total internal reection discuss differences between the role of coherent and incoherent bundles of bres in an endoscope explain how an endoscope is used in: observing internal organs obtaining tissue samples of internal organs for further testing

page 3623 366 36870 3717 3737 375 3767

Students: gather information to observe at least one image of a fracture on an X-ray lm and X-ray images of other body parts gather secondary information to observe a CT scan image and compare the information provided by CT scans to that provided by an X-ray image for the same body part perform a rst-hand investigation to demonstrate the transfer of light by optical bres gather secondary information to observe internal organs from images produced by an endoscope

page 361, 367, 368 3712, 377 380 377, 379

3. Radioactivity can be used as a diagnostic toolStudents learn to: outline properties of radioactive isotopes and their half lives that are used to obtain scans of organs describe how radioactive isotopes may be metabolised by the body to bind or accumulate in the target organ identify that, during decay of specic radioactive nuclei, positrons are given off discuss the interaction of electrons and positrons resulting in the production of gamma rays describe how the positron emission tomography (PET) technique is used for diagnosis

page 3824 384, 385 3923 392 3935

Students: perform an investigation to compare an image of bone scan with an X-ray image gather and process secondary information to compare a scanned image of at least one healthy body part or organ with a scanned image of its diseased counterpart

page 390, 397 388, 390, 391

4. The magnetic eld produced by nuclear particles can be used as a diagnostic toolStudents learn to: identify that the nuclei of certain atoms and molecules behave as small magnets identify that protons and neutrons in the nucleus have properties of spin and describe how net spin is obtained explain that the behaviour of nuclei with a net spin, particularly hydrogen, is related to the magnetic eld they produce describe the changes that occur in the orientation of the magnetic axis of nuclei before and after the application of a strong magnetic eld dene precessing and relate the frequency of the precessing to the composition of the nuclei and the strength of the applied external magnetic eld discuss the effect of subjecting precessing nuclei to pulses of radio waves explain that the amplitude of the signal given out when precessing nuclei relax is related to the number of nuclei present explain that large differences would occur in the relaxation time between tissue containing hydrogen-bound water molecules and tissues containing other molecules

page 399400 4001 4001 4034 4045 4058 4089 40910

Students: perform an investigation to observe images from magnetic resonance image (MRI) scans, including a comparison of healthy and damaged tissue identify data sources, gather, process and present information using available evidence to explain why MRI scans can be used to: detect cancerous tissues identify areas of high blood ow distinguish between grey and white matter in the brain gather and process secondary information to identify the function of the electromagnet, radio frequency oscillator, radio receiver and computer in the MRI equipment identify data sources, gather and process information to compare the advantages and disadvantages of X-rays, CT scans, PET scans and MRI scans gather, analyse information and use available evidence to assess the impact of medical applications of physics on society

page 408, 410, 411, 414 41013

402 41213, 415 415

xiv

Option module: From QUANTA TO QUARKS (chapters 2226, pages 417520) 1. Problems with the Rutherford model of the atom led to the search for a model that would better explain the observed phenomenaStudents learn to: discuss the structure of the Rutherford model of the atom, the existence of the nucleus and electron orbits analyse the signicance of the hydrogen spectrum in the development of Bohrs model of the atom dene Bohrs postulates discuss Plancks contribution to the concept of quantised energy describe how Bohrs postulates led to the development of a mathematical model to account for the existence of the hydrogen spectrum:

page 4213 424 4278 423 42933

Students: perform a rst-hand investigation to observe the visible components of the hydrogen spectrum process and present diagrammatic information to illustrate Bohrs explanation of the Balmer series solve problems and analyse information using:

page 4379 4334 425, 435

1 1 1 -- = R ----- ----- 2 n f n 2 i analyse secondary information to identify the difculties with the RutherfordBohr model, including its inability to completely explain: the spectra of larger atoms the relative intensity of spectral lines the existence of hyperne spectral lines the Zeeman effect 434

1 1 1 -- = R ----- ----- n 2 n 2 f i discuss the limitations of the Bohr model of the hydrogen atom 434

2. The limitations of classical physics gave birth to quantum physicsStudents learn to: describe the impact of de Broglies proposal that any kind of particle has both wave and particle properties dene diffraction and identify that interference occurs between waves that have been diffracted describe the conrmation of de Broglies proposal by Davisson and Germer explain the stability of the electron orbits in the Bohr atom using de Broglies hypothesis

page 4446 4413 446 4467

Students: solve problems and analyse information using:

page 445, 452

h = -----mv gather, process, analyse and present information and use available evidence to assess the contributions made by Heisenberg and Pauli to the development of atomic theory 44851

3. The work of Chadwick and Fermi in producing articial transmutations led to practical applications of nuclear physicsStudents learn to: dene the components of the nucleus (protons and neutrons) as nucleons and contrast their properties discuss the importance of conservation laws to Chadwicks discovery of the neutron dene the term transmutation describe nuclear transmutations due to natural radioactivity describe Fermis initial experimental observation of nuclear ssion discuss Paulis suggestion of the existence of the neutrino and relate it to the need to account for the energy distribution of electrons emitted in -decay evaluate the relative contributions of electrostatic and gravitational forces between nucleons account for the need for the strong nuclear force and describe its properties explain the concept of a mass defect using Einsteins equivalence between mass and energy describe Fermis demonstration of a controlled nuclear chain reaction in 1942 compare requirements for controlled and uncontrolled nuclear chain reactions

page 457 460 456 456 4768 4615 467 4678 46870 4812 4827

Students: perform a rst-hand investigation or gather secondary information to observe radiation emitted from a nucleus using a Wilson cloud chamber or similar detection device solve problems and analyse information to calculate the mass defect and energy released in natural transmutation and ssion reactions

page 51820 4701, 473, 494

4. An understanding of the nucleus has led to large science projects and many applicationsStudents learn to: explain the basic principles of a ssion reactor describe some medical and industrial applications of radioisotopes describe how neutron scattering is used as a probe by referring to the properties of neutrons identify ways by which physicists continue to develop their understanding of matter, using accelerators as a probe to investigate the structure of matter discuss the key features and components of the standard model of matter, including quarks and leptons

page 4848 48991 492 496502 50313

Students: gather, process and analyse information to assess the signicance of the Manhattan Project to society identify data sources, and gather, process and analyse information to describe the use of: a named isotope in medicine a named isotope in agriculture a named isotope in engineering

page 4804 48991

xv

ACKNOWLEDGEMENTSThe authors would like to thank the following people for their support during the writing of this book: Michael Andriessen gives special thanks to Christine, Sam and Luke for their understanding and patience; Peter Pentland wishes especially to thank his wife Helen Kennedy for her continuing support; Bruce McKay is indebted to close friend and former colleague Barry Mott for his valuable advice; Richard Gaut thanks Stephen and Greta for their helpful suggestions and feedback; Jill Tacon wishes to thank Dr Manjula Sharma and Dr Joe Khachan from the University of Sydney for their valuable advice and Lee Collins from Westmead Hospital for his expert assistance. Yoka McCallums contribution and encouragement is also appreciated, and thanks must go to Dean Bunn for his permission to adapt some practical activities and other material from Physics for a Modern World. The authors and publisher are grateful to the following individuals and organisations for their permission to reproduce photographs and other copyright material. Images Alan Bean/Novaspace Galleries: 2.2 AIP Emilio Segr Visual Achives, W.F. Meggers Collection: 22.8 ANSTO: 20.3, 20.4/Gentech generator courtesy of ANSTO Otto Rogge/ ANTPhoto.com.au: 11.21 Bhathal, R., Astronomy for the HSC, Kangaroo Press 1993, p. 47. Reproduced by permission of Ragbir Bhathal: 17.12(ac) Black & Decker: 9.1 Boeing: 3.9 The Royal Institution, London, UK/ Bridgeman Art Library: 7.1 Courtesy of Brookhaven National Laboratory: 26.8(a, b) Cavendish Laborator y, Cambridge University: 10.1 University of Queensland, Centre for Magnetic Resonance: 21.15(ac) Chicago Historical Society, Birth of the Atomic Age, Painting by Gary Sheahan, 1957: 25.5 Corbis Australia/Australian Picture Library: 13.1; 18.16/ Belt/Corbis/Annie Grifths; 8.17/Corbis; 8.15, 8.16, 11.2, 11.5, 11.12, 23.11, 23.12, 23.13, 23.14, 23.15/Corbis/Bettman; 21.14(d)/Corbis/Howard Sochurek; 7.4/Corbis/Hulton-Deutsch Collection CERN: 26.2 CFHT, 1996 Used with permission: 14.17 Adapted from Physics in Medical Diagnosis, Chapman & Hall 1997, p. 213 g. 5.23. Reproduced with permission of the author Dr Trevor A Delchar: 18.14(a) Digital Stock/Corbis Corporation: page 99; 2.4, 13.18 Digital Vision: 2.1 Dorling Kindersley: 6.1 Image courtesy of Elaine Collin: 19.19 Corbis/Greg Smith: 11.22 Image courtesy of the European Space Agency ESA: 14.13, 15.6 Courtesy of EMI Archives: 19.10 Fermilab National Accelerator Laborator y: 26.1, 26.7, 26.10 Dave Finley, National Radio Astronomy Observatory, courtesy Associated Universities, Inc., and the National Science Foundation: 14.14 Fundamental Photographs, New York: 15.8(a); 15.14, 22.9, 23.6/Wabash Instrument Corp.; 23.2(a)/Ken Kay Getty Images/ Hulton Archive: 14.2, 22.2, 23.8 David Grabham: 19.7, 21.14(c), 21.18(a, b) Medical Physics by J Pope, p. 81, g 4.13 Reprinted by permission of Harcourt Education Ltd: 21.13 Reprinted by permission of HarperCollins Publishers Ltd. Illingworth 1994: 15.21, 16.10 Terry Herter: 16.15, 16.16 Adapted and reproduced from Martin Hollins, Medical Physics, 2nd edition, Nelson Thornes 2001, pp. 114, 122, 127, 100, 101, 186, 197: 18.6, 18.17, 19.6, 19.16, 19.17, 20.7(b), 21.6 The Fermion Particles and The Boson Force Carriers, From Quarks to the Cosmos: Tools of Discovery by Leon M Lederman and David N Schramm. 1989, 1995 Scientic American Library. Reprinted by permission of Henry Holt and Company, LLC: table 26.4 Courtesy of Hologic: 18.11 www.imageaddict.com.au: 14.8, 14.10 ImageState: 10.5 Kamioka Observatory, ICRR (Institute for Cosmic Ray Research), The University of Tokyo: 24.1 IEE Review March 2001, Vol 47, 102, p 42. Reproduced with permission of IET. www.theiet.org: 13.25 Jared Schneidman Design: 12.24 JAS Photography/John Sowden: 2.3 Kenneth Krane, Modern Physics 2nd edition, 1996, p. 24. Used by permission of John Wiley & Sons, Inc.: 5.4 Resnick, R, Introduction to Special Relativity, gures 1.4 and 1.6, John Wiley & Sons Inc., 1968: 5.5 Halliday et al., Fundamentals of Physics Extended, 5th edition, John Wiley & Sons, Inc. 1997, gures 37.27 (b, c and d), 43.3, 37.22, 43.6. Used by permission of John Wiley & Sons, Inc.: 13.9, 13.12, 22.5, 22.12, 24.15 Webster, J G (ed), Medical Instrumentation, 3rd edition, 1998, p. 559, adapted and used by permission of John Wiley & Sons, Inc.: 20.7(a) Adapted from The Particle Adventure, produced by the Particle Data Group, Lawrence Berkeley National Laborator y: 26.3, 26.4 Bruce McKay: 13.4, 22.1, 23.2(b, c), 26.11 David Malin Images: 15.1 Mary Evans Picture Library: 14.3 Cambridge Encyclopedia of Astronomy, ed. by Dr Simon Mitton, Jonathon Cape, 1977, Cambridge University. Reproduced with pemission of Simon Mitton: 15.8(b), 17.13 Barbara Mochejska (Copernicus Astronomical Center), Andrew Szentgyorgyi (HarvardSmithsonian Center for Astrophysics), F. L. Whipple Observatory: 17.11(b) NASA: 2.28, 3.1/MSFC, 3.6, 3.8, 4.8/NSSDC, 14.1/ STSCI, 14.7, 17.3/NOAO, 17.16/The Hubble Heritage Team, 17.18(a)/ESA/ASU/J Hester and A Loll, 17.18(b)/CXC/ASU/ J Hester et al. Newspix: 20.13/Jody DArcy, 25.2 Moriel NessAiver: 21.2 Department of Nuclear Medicine, The Queen Elizabeth Hospital, South Australia: 20.7(d) De Jong et al., Heinmann Physics Two, p. 237. Reproduced with permission from Pearson Education Australia: 13.2 Adapted from David Heffernan, Physics Contexts 2, Pearson Education Australia 2002, p. 315. Reproduced with permission of Pearson Education Australia: 18.8 Peter Pentland: 9.9 Philips Medical Systems: 18.3(b), 19.11 Photodisc, Inc.: pages 1, 173, 255, 339, 417; 1.1, 4.1, 8.1, 8.24(a, b), 10.22, 11.19, 17.1, 18.1, 18.3(c), 19.9(a), 20.15(a), 21.17, 25.1 photolibrary.com: 9.4/Tom Marexchal, 13.26(b)/Photo Researchers Inc., 17.11(a)/John Chumack; 18.15(a, b), 19.14, 20.9, 21.1, 21.3, 21.14(a, b), 23.1/ Phototake; 19.8/Phototake Science; 19.9(b), 20.14/Phototake Science/Science Ltd; 20.1/Phototake Science/ISM photolibrary.com/Science Photo Librar y: 4.2, 5.1, 7.2, 14.5, 15.22, 19.1, 22.7; 3.11/NASA; 10.26(b)/Peter Apraham; 11.1, 14.6/David Nunuk; 12.1/John Walsh; 12.23/Martin Dohrn; 12.25(b)/Andrew Syred; 18.7/P Saada/Eurelios; 20.5/Philippe Plailly; 20.6(a)/Dr P Marazzi; 20.6(b, c)/CNRI; 20.11/Zephyr; 20.15(b)/Hank Morgan; 21.16/Dept of Cognitive Neurology; The Picture Source/Terry Oakley: 6.24, 12.12(b), 12.22, 12.25(a) Greg Pitt: 20.7(c) Science Museum/Science & Society Picture Library: 24.8 Reprinted from Medical Physics, 1978, John Wiley & Sons Inc. with permission from the authors, John R Cameron and James G Skofronick 1992: 19.5(a, b) Peter Storer: 8.22 Sudbury Neutrino Observatory/R Chambers: 24.13 SP-AusNet: 8.21 Courtesy of Transrapid International-USA, Inc.: 13.26(a) Reproduced with kind permission of TransGrid: 8.20 Photo UC Regents/Lick Observatory: 16.1 Richard Wainscoat: 14.19 Jack Washburn: 13.11(b) Westmead Hospital Medical Physics Department: 18.14(b), 20.10(a, b), 20.12(a, b), 20.16 Justine Wong: 19.13(a-d) Courtesy of Xerox Corporation: 10.9

Text Extracts from Physics Stage 6 Syllabus Board of Studies NSW, 2002 (pages xxv) Data and formulae sheets from Physics Higher School Certicate Examination Board of Studies NSW (pages 5267) Higher School Certicate Assessment Support Document Board of Studies NSW, 1999 (key words, pages 52930)

Every effort has been made to trace the ownership of copyright material. Information that will enable the publisher to rectify any error or omission in subsequent editions will be welcome. In such cases, please contact the Permissions Section of John Wiley & Sons Australia, Ltd, who will arrange for the payment of the usual fee.

xvi

HSC CORE MODULE

Chapter 1Earths gravitational eld

Chapter 2Launching into space

Chapter 3Orbiting and re-entry

Chapter 4Gravity in the solar system

Chapter 5Space and time

SPACE

CHAPTER

1

EARTHS GRAVITATIONAL FIELDRememberBefore beginning this chapter, you should be able to: recall and apply Newtons Second Law of Motion: F = ma.

Key contentAt the end of this chapter you should be able to: make a comparison between the acceleration due to gravity at various places over the Earths surface as well as at other locations throughout the solar system dene weight as the force on an object due to a gravitational eld explain that work done to raise or lower a mass in a gravitational eld is directly related to a change in the gravitational potential energy of the mass calculate the weight of a body on Earth, above the Earth or on other planets dene gravitational potential energy as the work done in moving an object from a very large distance away to a point in a gravitational eld.

Figure 1.1 The Earth rising as seen from the Moon

Gravity is a force of attraction that exists between any two masses. Usually this is a very small, if not negligible, force. However, when one or both of the masses is as large as a planet, then the force becomes very signicant indeed. The force of attraction between the Earth and our own bodies is the force we call our weight. This force exists wherever we are on or near the Earths surface (although, as we shall see, with some variation). We can say that a gravitational eld exists around the Earth and we live within that eld.

1.1 THE EARTHS GRAVITYThe Earth is surrounded by a gravitational eld. This type of eld, discussed in more general terms in chapter 4, is a vector eld within which a mass will experience a force. (Other vector elds include electric and magnetic elds.) The gravitational eld around the Earth can be drawn as shown in gure 1.2. Note that the direction of a eld line at any point is the direction of the force experienced by a mass placed at that point.Figure 1.2 The gravitational eld around the Earth

The eld vector: gA eld vector is a single vector that describes the strength and direction of a uniform vector eld. For a gravitational eld, the eld vector is g.

A eld vector is a single vector that describes the strength and direction of a uniform vector eld. For a gravitational eld the eld vector is g, which is dened in this way: F g = --m where F = force exerted (N) on mass m m = mass (kg) in the eld 1 g = the eld vector (N kg ). Vector symbols are indicated here in bold italics. The direction of the vector g is the same as the direction of the associated force. Note that a net force applied to a mass will cause it to accelerate. Newtons Second Law describes this relationship:

1.1Using a pendulum to determine g

F a = --m where a = acceleration (m s ). Hence, we can say that the eld vector g also represents the acceleration due to gravity and we can calculate its value at the Earths surface as described below. The Law of Universal Gravitation (discussed in more detail in chapter 4) says that the magnitude of the force of attraction between the Earth and an object on the Earths surface is given by: mE mO F = G -------------rE 22

CHAPTER 1 EARTHS GRAVITATIONAL FIELD

3

where mE = the mass of the Earth 24 = 5.97 10 kg mO = mass of the object (kg) rE = radius of the Earth 6 = 6.38 10 m. From the dening equation for g, on the previous page, we can see that the force experienced by the mass can also be described by: F = mOg. mE mO Equating these two we get: mOg = G -------------- . rE 2 mE This simplies to give: g = G -----rE 2 ( 6.672 10 ) ( 5.974 10 ) = ------------------------------------------------------------------------ . 6 2 ( 6.378 10 ) Hence, g 9.80 m s . The value of the Earths radius used here, 6378 km (at the Equator), is 2 an average value so the value of g calculated, 9.80 m s , also represents an average value.2

11

24

Variations in the value of gVariation with geographical locationThe actual value of the acceleration due to gravity, g, that will apply in a given situation will depend upon geographical location. Minor variations in the value of g around the Earths surface occur because: the Earths crust or lithosphere shows variations in thickness and structure due to factors such as tectonic plate boundaries and dense mineral deposits. These variations can alter local values of g. the Earth is not a perfect sphere, but is attened at the poles. This means that the value of g will be greater at the poles, since they are closer to the centre of the Earth. the spin of the Earth creates a centrifuge effect that reduces the effective value of g. The effect is greatest at the Equator and there is no effect at the poles. As a result of these factors, the rate of acceleration due to gravity at the surface of the Earth varies from a minimum value at the Equator of 2 2 9.782 m s to a maximum value of 9.832 m s at the poles. The usual 2 value used in equations requiring g is 9.8 m s .

Variation with altitudeThe formula for g shows that the value of g will also vary with altitude above the Earths surface. By using a value of r equal to the radius of the Earth plus altitude, the following values can easily be calculated. It is clear from table 1.1 that the effect of the Earths gravitational eld is felt quite some distance out into space. mE The formula used is: g = G ------------------------------------- . 2 ( r E + altitude ) Note that as altitude increases the value of g decreases, dropping to zero only when the altitude has an innite value.

4

SPACE

Table 1.1 The variation of g with altitude above Earths surfaceALTITUDE (km) g (m s )2

COMMENT

0 8.8 80 200 250 400 1 000 40 000

9.80 9.77 9.54 9.21 9.07 8.68 7.32 0.19

Earths surface Mt Everest Summit Arbitrary beginning of space Mercury capsule orbit altitude Space shuttle minimum orbit altitude Space shuttle maximum orbit altitude Upper limit for low Earth orbit Communications satellite orbit altitude

Variation with planetary bodyThe formula for g also shows that the value of g depends upon the mass and radius of the central body which, in examples so far, has been the Earth. Other planets and natural satellites (moons) have a variety of masses and radii, so that the value of g elsewhere in our solar system can be quite different from that on Earth. The following table presents a few examples. m planet The formula used here is: g = G -------------2 . r planet Table 1.2 A comparison of g on the surface of other planetary bodiesBODY MASS (kg) RADIUS (km) g (m s )2

1.2Weight values in the solar system and g

Moon Mars Jupiter Pluto

7.35 10 6.42 10 1.90 10 1.31 10

22

1 738 3 397 71 492 1 151

1.6 3.7 24.8 0.66

23

27

22

SAMPLE PROBLEM

1.1

Determining acceleration due to gravity above the MoonFor each of the Apollo lunar landings, the command module continued orbiting the Moon at an altitude of about 110 km, awaiting the return of the Moon walkers. Determine the value of acceleration due to gravity at that altitude above the surface of the Moon (the radius of the Moon is 1738 km). mM g = G -------------------------------------2 ( r M + altitude ) ( 6.67 10 ) ( 7.35 10 ) = -----------------------------------------------------------------6 5 2 ( 1.738 10 + 1.1 10 ) = 1.4 m s2

SOLUTION

11

22

That is, the acceleration due to gravity operating on the orbiting command 2 module was approximately 1.4 m s .

CHAPTER 1 EARTHS GRAVITATIONAL FIELD

5

1.2 WEIGHTWeight is dened as the force on a mass due to the gravitational eld of a large celestial body, such as the Earth.

Weight is dened as the force on a mass due to the gravitational eld of a large celestial body, such as the Earth. Since it is a force, it is measured in newtons. We can use Newtons Second Law to dene a simple formula for weight: Newtons Second Law states: F = ma and hence: W = mg where W = weight (N) m = mass (kg) 2 g = acceleration due to gravity at that place (m s ).

F

F

F

W W F

Figure 1.3 There is always a gravitational force between any two masses. When one of the masses is as large as a planet, the force on a small mass is called weight.

SAMPLE PROBLEM

1.2SOLUTION

Determining the weight of an astronautWhat would be the weight of a 100 kg astronaut (a) on the Earth, (b) on the Moon and (c) in an orbiting space shuttle? Use the values of g shown in tables 1.1 and 1.2. Note that the astronauts mass does not change with position but weight does. (a) On the Earth WE = mgE = 100 9.8 = 980 N (b) On the Moon WM = mgM = 100 1.6 = 160 N (c) In orbit WO = mgO = 100 8.68 (at maximum altitude) = 868 N There is an apparent contradiction in this last answer. The astronaut in orbit still has a considerable weight, rather than being weightless. However, the answer is correct because, as we have already seen, the Earths gravitational eld extends quite some distance out into space. Why then do space shuttle astronauts experience weightlessness? As we shall see later, the weightlessness they feel is not real but only apparent, and is a consequence of their orbital motion around the Earth.

Many numerical HSC questions allocate marks for working. These marks are earned at the substitution line; that is, the line following the formula into which data values are correctly substituted. Usually no marks are awarded for a formula on its own. You should develop the habit of showing all your workings, especially the substitution line.

6

SPACE

1.3 GRAVITATIONAL POTENTIAL ENERGYGravitational potential energy, Ep, is the energy of a mass due to its position within a gravitational eld. On a large scale, gravitational potential energy is dened as the work done to move an object from innity (or some point very far away) to a point within a gravitational eld.

Point x

Work done = Fr = mgh

Ground

Figure 1.4 Gravitational potential energy, Ep = work done to move up to the point from the ground (the zero level)

Gravitational potential energy, Ep, is the energy of a mass due to its position within a gravitational eld. Here on Earth, the Ep of an object at some point, x, above the ground is easily found as it is equal to the work done to move the object from the ground up to the point, x, as shown in gure 1.4. Gravitational potential energy Ep = work done to move to the point = force required distance moved (since work W = Fr) = (mg) h = mgh Hence, in this case Ep = mgh. We chose the ground as our starting point because this is our dened zero level; that is, the place where Ep = 0. Note that since work must be done on the object to lift it, it acquires energy. Hence, at point x, Ep is greater than zero. On a larger, planetary scale we need to rethink our approach. Due to the inverse square relationship in the Law of Universal Gravitation, the force of attraction between a planet and an object will drop to zero only at an innite distance from the planet. For this reason we will now choose innity (or some point a very large distance away) as our level of zero potential energy. There is a strange side effect of our choice of zero level. Because gravitation is a force of attraction, work must be done on the object to move it from a point, x, to innity; that is, against the eld so that it gains energy, Ep. Therefore, Ep at innity > Ep at point x but Ep at innity = 0 so that Ep at point x < 0 that is, Ep at point x has a negative value! (see gure 1.5)

Planet

Work must be done to move a mass against a gravitational field. Point x Ep at surface

W ... g force > 1 W Accelerating down W

F F 1

Figure 2.20 Riders on a rollercoaster experience changing g forces.

Typical altitude (km)

9 8 7 6

r ze Neaorc ro gf e

2.25 g

2.25 g

Variations in acceleration and g forces during a typical launchAs shown in gure 2.17, prior to lift-off a rocket has zero acceleration because of the balance that exists between the weight force and the reaction force plus thrust. The astronaut within is experiencing a one g load. This initial condition will not change until the building thrust exceeds the weight of the rocket, at which point the rocket will lift off. Since the thrust now exceeds the weight, there is a net force upwards on the rocket, which begins to accelerate upwards. The g force experienced by the rocket will have a value slightly greater than one. From this point onwards, the mass of the rocket begins to decrease as fuel is consumed and, hence, the rate of acceleration and subsequent g force steadily climbs, reaching maximum values just before the rocket has exhausted its fuel. At this point a single-stage rocket becomes a projectile, eventually falling to Earth. A multi-stage rocket, however, drops the spent stage away, momentarily experiencing zero g conditions as it coasts. The second-stage rocket res and quickly develops the necessary thrust to exceed the effective weight at its altitude, and then starts to accelerate again. The g force experienced by the rocket and astronaut begins again at a value marginally greater than one and gradually builds to its maximum value just as the second-stage fuel supply is exhausted. If there is a third stage, the process is repeated. The variation in g forces varied during the launch of Saturn V, a large three-stage rocket used to launch the Apollo spacecraft, is shown in gure 2.22. Note that the jagged peaks on the graph are due to the sequential shutdown of the multiple rocket engines of each stage a technique designed specically to avoid extreme g forces.

Figure 2.21 Aircraft trajectory to simulate near-weightlessness

2.2Acceleration and load during the Apollo 10 launch

30

SPACE

4

3

Sequential shutdown of multiple engines avoids excessive peaks.

2

1 1st stage 0 2nd stage 3rd stage 800

This gure shows that Apollo astronauts experienced a peak load of four g during lift-off. This is a signicant force at four g a person begins to lose their colour vision and peripheral vision. Soon after this the person will black out; although each individual has their own threshold level. In the rst manned US space ight, astronaut Alan Shepard had to tolerate a peak g force of 6.3 g during launch. Rocket design has improved since then space shuttle astronauts never experience loads greater than three g due to the shuttles ability to throttle back its liquid fuel engines. This is discussed in more detail in chapter 3.

g force

0

100 200 300 400 500 600 700 Seconds since lift-off

The effect of the Earths motion on a launchWhy do cricket fast bowlers run up to the wicket before bowling the ball? The answer is that the velocity at which the ball is bowled is greater than it would have been if the bowler had not run up. This is because the velocity of the ball relative to the ground is equal to the velocity of the ball relative to the bowler, plus the velocity of the bowler relative to the ground. Algebraically, this is expressed as:ball ground

Figure 2.22 Variations in g forces during an ApolloSaturn V launch

Ro

tati o

n of

Ea r t

v

= ballvbowler + bowler vground.

h

Figure 2.23 A rocket heading into orbit is launched to the east to receive a velocity boost from the Earths rotational motion.

Sun

Earth's motion

Figure 2.24 The ight of a rocket heading into space is timed so that it can head out in the direction of the Earths motion and thereby receive an extra boost.

In other words, a moving platform (the bowler) offers a boost to the velocity of a projectile (the ball) launched from it, if launched in the direction of motion of the platform. The same principle applies to a rocket launched from the Earth. Consider that the Earth is revolving around the Sun at approximately 1 107 000 km h relative to the Sun. In addition, the Earth rotates once on its axis per day so that a point on the Equator has a rotational velocity of 1 approximately 1700 km h relative to the Sun. Hence, the Earth is itself a moving platform with two different motions which can be exploited in a rocket launch to gain a boost in velocity. Engineers planning to launch a rocket into orbit can exploit the Earths rotation in order to achieve the velocity needed for a stable orbit. This is done by launching in the direction of the Earths rotation; that is, by launching toward the east, as shown in gure 2.23. In this way, the rotational velocity of the launch site relative to the Sun will add to the orbital velocity of the rocket relative to the Earth, to produce a higher orbital velocity achieved by the rocket relative to the Sun. In a similar way, engineers planning a rocket mission heading further into space can exploit the Earths revolution around the Sun by planning the launch for a time of year when the direction of the Earths orbital velocity corresponds to the desired heading. Only then is the rocket launched up into orbit. The rocket is allowed to proceed around its orbit until the direction of its orbital velocity corresponds with the Earths, and then its engines are red to push it out of orbit and further into space, as shown in gure 2.24. In this way the Earths orbital velocity relative to the Sun adds to the rockets orbital velocity relative to the Earth, to produce a higher velocity achieved by the rocket relative to the Sun.

CHAPTER 2 LAUNCHING INTO SPACE

31

Planning of this sort clearly favours certain times of the year over others, or even certain times of day depending upon the ight mission. These favourable periods are referred to as launch windows.

PHYSICS IN FOCUS Space exploration and rocket science pioneershe Chinese discovered gunpowder and used it to create reworks. By the eleventh century, the Chinese were using simple rockets called re arrows as weapons. In the late 1700s a British artillery ofcer, William Congreve, developed simple rockets for use by the British army. The Hale rockets followed 50 years later. Despite all of this, modern rocket science didnt begin in earnest until the late 1800s and early 1900s. Listed here are some of the most notable pioneers. Konstantin Tsiolkovsky (18571935) was a Russian mathematics teacher who took an interest in rocketry, being inspired by Jules Vernes book From the Earth to the Moon. Working entirely on his own, he developed precise calculations for space ight and the details of many aspects of rocket design and space exploration. His work was purely theoretical as he performed no experiments, but his published work inuenced rocket development around the world, especially in Russia. His ideas were wide ranging from the very pragmatic, such as the design of a liquid-fuel rocket engine featuring throttling capability and multi-staging, to the (then) fanciful, such as space stations and articial gravity, terraforming of other planets and extraterrestrial life. He was the inspiration for men such as Sergei Korolev (1906 1966) who was the Russian Chief Constructor responsible for Sputnik I and the Vostok rocket. Sputnik I was the worlds rst articial satellite, while the Vostok rocket was used to send Yuri Gagarin into a single orbit of the Earth on 12 April 1961. This was the rst time that a person had entered space. Robert H. Goddard (18821945) was an American college professor of physics with a passion for rocketry. Also inspired by Jules Verne as a boy, Goddard decided early to dedicate his life to rocketry. Unlike Tsiolkovsky, Goddard was an engineer and an experimentalist. He conceived ideas then tested them, patenting those that were successful. He built and tested the worlds rst liquid-fuel rocket, which solved many technical problems such as fuel valving for throttle, start and stop, fuel injection, engine cooling and ignition. He was the rst to use

T

gyroscopes and vanes for guidance, and to separate the payload from the rocket in ight and return it to Earth. Herman Oberth (18941992) was born in Romania but lived in Germany. Purely a theorist, he was yet another inspired by Jules Verne. He wrote a doctoral thesis titled By Rocketry to Space. Although the University of Heidelberg rejected the thesis, he had the work published privately as a book. It promptly sold out. The subject of rocketry captured the publics imagination and Oberth was himself inspiring a new generation of rocket scientists. He was an early member of the VfR, or Society for Space Travel, and published another book titled The Road to Space Travel. This work won an award and Oberth used the prize money to purchase rocket motors for the VfR, assisting its development efforts. One of those inspired by Oberth was Wernher von Braun (19121977) who became the rocket engineer responsible for the development of the V2 rocket, which was used to bomb London during World War II, and later the Mercury-Redstone rocket which put the rst Americans into space. Roberts Esnault-Pelterie (18811957) was a French rocket pioneer. He published two important books Astronautics in 1930 and Astronautics Complement in 1934. He suggested the idea that rockets be used as long-range ballistic missiles, and the French Army employed him to develop these rockets. He experimented with various liquid fuels in rocket motors of his design, starting with liquid oxygen and gasoline, then nitrogen peroxide and benzene, before attempting liquid oxygen and tetranitromethane. This last combination caused him a major hand injury. Theodore von Karman (18811963) was born in Hungary but later settled in America. In the 1930s he became a professor of aeronautics at Caltech. There he established the Jet Propulsion Laboratory dedicated to rocket work. The JPL still exists today, working closely with NASA and specialising in exploration of the solar system by space probe.

32

SPACE

CHAPTER REVIEW

SUMMARY A projectile is any object that is launched into the air. The path of a projectile, called its trajectory, has a parabolic shape if air resistance is ignored. The trajectory can be analysed mathematically by regarding the vertical and horizontal components of the motion separately. The vertical motion of a projectile is uniformly accelerated motion and can be analysed using these equations: vy = uy + ayt 2 -y = uyt + 1 ayt 2 2 2 vy = uy + 2ay y. The horizontal motion of a projectile is constant velocity and can be analysed using these equations: vx = ux 2 2 vx = ux x = uxt. Escape velocity is the vertical velocity that a projectile would need to just escape the gravitational eld of a planet. It is given by the equation: Escape velocity = 2Gm planet ---------------------- . r planet

QUESTIONS1. Explain why it is that the vertical and horizontal components of a projectiles motion are independent of each other. Identify any common variables. 2. Describe the trajectory of a projectile. 3. List any assumptions we are making in our treatment of projectile motion. 4. Describe Galileos contribution to our knowledge of projectile motion. 5. What is the mathematical signicance of vertical and horizontal motions being perpendicular? 6. Describe the strategy you can employ to determine a projectiles: (a) velocity (c) trip time (b) maximum height (d) range. 7. Describe the effect of air resistance on the trajectory of a projectile. 8. A volleyball player sets the ball for a team mate. In doing so she taps the ball up at 1 5.0 m s at an angle of 80.0 above the horizontal. If her ngers tapped the ball at a height of 1.9 m above the oor, calculate the maximum height to which the ball rises? 9. An extreme cyclist wants to perform a stunt in which he rides up a ramp, launching himself into the air, then ies through a hoop and lands on another ramp. The angle of each ramp is 30.0 and the cyclist is able to reach the launch height of 1.50 m with a launching 1 speed of 30.0 km h . Calculate: (a) the maximum height above the ground that the lower edge of the hoop could be placed (b) how far away the landing ramp should be placed. 1 10. A football is kicked with a velocity of 35.0 m s at an angle of 60.0. Calculate: (a) the hang time of the ball (time in the air) (b) the length of the kick. 11. A basketball player stands 2.50 m from the ring. He faces the backboard, jumps up so that his hands are level with the ring and launches 1 the ball at 5.00 m s at an angle of 50.0 above the horizontal. Calculate whether he will score. 12. A cannons maximum range is achieved with a ring angle of 45.0 above the horizontal. If its 1 muzzle velocity is 750.0 m s , calculate the range achieved with a ring angle of: (a) 40.0 (b) 45.0 (c) 50.0.

A rocket is different from a projectile because it continues to be propelled after it is launched, accelerating throughout most of its upward journey. Rockets differ from other engines such as jets because they carry with them the oxygen required to burn their fuel. The forward progress of a rocket can be explained using Newtons Third Law (equal and opposite forces) as well as by the conservation of momentum (total change in momentum equals zero). The acceleration of a rocket can be determined using Newtons Second Law: F = ma. The term g force is used to describe apparent weight as a multiple of normal weight, and is closely related to acceleration. During a rocket launch the g force experienced by an astronaut increases because the mass of fuel is reducing, even though the thrust remains essentially the same. The revolution and rotation of the Earth can be used to provide a launched rocket with an additional boost, allowing it to save fuel in achieving its target velocity.


33

13. A coastal defence cannon res a shell horizontally from the top of a 50.0 m high cliff, directed out to sea as shown in gure 2.25, 1 with a velocity of 1060.0 m s . Calculate the range of the shells trajectory.1060.0 m s1

BODY

MASS (kg)

RADIUS (km)

ESCAPE VELOCITY 1 (m s )

Mercury Venus Io Callisto

3.3 10 4.9 10 8.9 10 1.1 10

23

2410 6052 1821 2400

24

22

23

50.0 m

Figure 2.25

14. To increase the range of the shell in question 13, the cannon is lifted, so that it now points up at an angle of 45.0 as shown in gure 2.26. Calculate the new range.

18. A certain model rocket has a pre-launch mass of 87.3 g, of which 10.5 g is propellant. It is able to deliver a thrust of 6.10 N. Assuming that the rocket is red directly up, calculate: (a) the initial rate of acceleration and g force (b) the nal rate of acceleration and g force just prior to exhaustion of the fuel. 19. If a rocket had a mass of 32 000 kg, of which 85% was fuel, and a thrust of 400 000 N, calculate: (a) the rate of acceleration and g force at lift-off (b) the rate of acceleration and g force just prior to exhaustion of the fuel. Assume it is travelling horizontally and accelerating up to orbital velocity. 20. Identify the stage of a space mission during which an astronaut experiences the greatest g forces. Describe strategies that spacecraft designers can employ to ensure the survival of living occupants as well as delicate payloads. 21. Discuss the manner in which the rotation of the Earth and the revolution of the Earth around the Sun can be utilised by rocket designers. 22. (a) Explain rocket propulsion in terms of the Law of Conservation of Momentum. (b) Construct a diagram of a rocket to show the force pair that must exist due to Newtons Third Law.

1060.0 m s1 45

50.0 m

Figure 2.26

15. Identify the variables upon which the escape velocity of the Earth depends. If the mass of the Earth were somehow changed to four times its real value, state how the value of the escape velocity would change. 16. Outline Newtons concept of escape velocity. 17. Calculate the escape velocity of the following planets, using the data shown in the following table.

CHAPTER REVIEW

34

SPACE

PRACTICAL ACTIVITIES

2.1 MODELLING PROJECTILE MOTIONAimTo model projectile motion by studying the motion of a ball bearing projected onto an inclined plane.

Method1. Set up the apparatus as shown in gure 2.27. 2. Set up the inclined plane at an angle of approximately 20 and place the graph paper on it so that the ball will enter onto the inclined plane at a major division on the paper. 3. Clamp the ruler so that the ball bearing rolling from it onto the inclined plane will be projected horizontally. Adjust the angle of the ruler so the path of the ball bearing will t on the graph paper. 4. Having adjusted the apparatus, place a piece of carbon paper on the graph paper and record the motion of the ball bearing projected onto the inclined plane. 5. Remove the carbon paper and highlight the path for easier analysis. 6. We will assume that the horizontal velocity of the ball bearings motion remained constant. Therefore, the ball bearing took equal times to travel horizontally between the major divisions on the graph paper. Thus we can arbitrarily call one of these major divisions a unit of time. Beginning at the point where the ball entered the graph paper, label these major divisions 0, 1, 2, 3 . . . time intervals.

Apparatus30 cm 30 cm board retort stand and clamp carbon paper ball bearing graph paper 30 cm ruler (the ramp)

TheoryGalileo found that he could slow down the action of acceleration due to gravity by rolling a ball down a slope. In this way things happened slow enough for him to observe them. We are going to use that same strategy to slow down a projectile motion by projecting a ball bearing across an inclined plane. Recall that projectile motion can be considered as the addition of two linear motions at right angles to each other the horizontal, constant velocity motion and the vertical, constant acceleration motion. In the horizontal motion: x = uxt In the vertical motion: but we will let Thus-y = uyt + 1 ayt , 22

Analysis1. Record and tabulate the distance down the slope that the ball bearing travelled during each time interval. 2. Determine the average speed of the ball bearing down the slope during each time interval. Your answers should be in cm per time unit. 3. Plot a graph of average speed down the slope versus time and determine a value for the acceleration of the ball down the slope. Your answer 2 will be in cm per (time unit) .

uy = 0-y = 1 ayt 22

We will assume that frictional forces can be neglected.Clamp

QuestionsBall bearing Ruler Carbon paper

Retort stand

Books for support 30 cm 30 cm board Graph paper

Figure 2.27 The path of the projectile (ball bearing) is marked as it rolls down the ramp on the carbon paper.

1. What do these graphs indicate about the motion of the ball down the plane? 2. What assumptions have been made in order to obtain these results? 3. How would the path of the ball bearing differ if: (a) the inclined plane was raised to a steeper angle while keeping the ramp as it was? (b) the angle of the ramp was raised and the inclined plane was kept as it was? 4. The ball moves faster across the bottom of the paper than across the top, which represents an increase in kinetic energy. What is the source of this extra energy? Try to nd out why the rolling mass of the ball introduces a problem into this energy conversion.


35

2.2 ACCELERATION AND LOAD DURING THE APOLLO 10 LAUNCHAimTo determine acceleration and load conditions applicable during the launch of Apollo 10.

TheoryApollo 10 was launched on 18 May 1969, carrying a crew of three Stafford, Young and Cernan. The rocket used for the Apollo missions was the Saturn V, the largest rocket ever built. Figure 2.28 is a press release diagram from 1969 and we will use it to extract some performance gures.

Note : The diagram distinguishes between the launch vehicle and the spacecraft. The spacecraft differed between missions, but on Apollo 10 it consisted of the Lunar Module (LM) with a mass of 13 941 kg, and the Service Module (SM) and Command Module (CM) with a combined mass of 28 834 kg. The CM was the only part of the entire rocket to return to Earth. The launch vehicle, the Saturn V rocket itself, was made up of three stages. The rst stage consisted of ve Rocketdyne F-1 engines, which burned liquid oxygen and kerosene. Upon launch it would burn for approximately 150 s before it was exhausted at an altitude of about 70 km. It then separated from the rocket an

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