[PDF] HSC in 2 Physics Pearson (Stephen Bosi).pdf | Plain Text

Stephen Bosi John O’Byrne Peter Fletcher Joe KhachanJeff Stanger Sandra Woodward PHYSICS @ HSC Sydney, Melbourne, Brisbane, Perth, Adelaide and associated companies around the world

iii Contents Series features vi How to use this book viii Stage 6 Physics syllabus grid x Module 1 Space Module 1 Introduction 2 Chapter 1 Cannonballs, apples, planets and gravity 4 1.1 Projectile motion 4 1.2 Gravity 10 1.3 Gravitational potential energy 16 Practical experiences 20 Chapter summary 22 Review questions 22 Chapter 2 Explaining and exploring the solar system 26 2.1 Launching spacecraft 26 2.2 Orbits and gravity 35 2.3 Beyond Kepler’s orbits 41 2.4 Momentum bandits: the slingshot effect 44 2.5 I’m back! Re-entry 46 Practical experiences 52 Chapter summary 53 Review questions 54 Chapter 3 Seeing in a weird light: relativity 58 3.1 Frames of reference and classical relativity 58 3.2 Light in the Victorian era 61 3.3 Special relativity, light and time 64 3.4 Length, mass and energy 69 Practical experiences 75 Chapter summary 76 Review questions 76 Module 1 Review 80 Module 2 Motors and Generators Module 2 Introduction 82 Chapter 4 Electrodynamics: moving charges and magnetic fields 84 4.1 Review of essential concepts 84 4.2 Forces on charged particles in magnetic fields 89 4.3 The motor effect 90 4.4 Forces between parallel wires 93 Practical experiences 97 Chapter summary 98 Review questions 98Chapter 5 Induction: the influence of changing magnetism 100 5.1 Michael Faraday discovers electromagnetic induction 100 5.2 Lenz’s law 104 5.3 Eddy currents 106 Practical experiences 109 Chapter summary 110 Review questions 110 Chapter 6 Motors: magnetic fields make the world go around 114 6.1 Direct current electric motors 114 6.2 Back emf and DC electric motors 120 6.3 Alternating current electric motors 121 Practical experiences 126 Chapter summary 127 Review questions 127 Chapter 7 Generators and electricity supply: power for the people 130 7.1 AC and DC generators 130 7.2 Transformers 136 7.3 Electricity generation and transmission 141 Practical experiences 148 Chapter summary 149 Review questions 149 Module 2 Review 152 Module 3 From Ideas to Implementation Module 3 Introduction 154 Chapter 8 From cathode rays to television 156 8.1 Cathode ray tubes 156 8.2 Charges in electric fields 160 8.3 Charges moving in a magnetic field 164 8.4 Thomson’s experiment 165 8.5 Applications of cathode rays 167 Practical experiences 170 Chapter summary 171 Review questions 171 Chapter 9 Electromagnetic radiation: particles or waves? 174 9.1 Hertz’s experiments on radio waves 174 9.2 Black body radiation and Planck’s hypothesis 178 9.3 The photoelectric effect 182 9.4 Applications of the photoelectric effect 184 Practical experiences 185 Chapter summary 186 Review questions 187

Contents iv Chapter 10 Semiconductors and the electronic revolution 188 10.1 Conduction and energy bands 189 10.2 Semiconductors 190 10.3 Semiconductor devices 193 10.4 The control of electrical current 197 Practical experiences 201 Chapter summary 202 Review questions 202 Chapter 11 Superconductivity 204 11.1 The crystal structure of matter 204 11.2 Wave interference 205 11.3 X-ray diffraction 207 11.4 Crystal structure 208 11.5 Electrical conductivity and the crystal structure of metals 209 11.6 The discovery of superconductors 211 11.7 The Meissner effect 212 11.8 Type-I and type-II superconductors 212 11.9 Why is a levitated magnet stable? 213 11.10 BCS theory and Cooper pairs 215 11.11 Applications of superconductors 217 Practical experiences 220 Chapter summary 221 Review questions 221 Module 3 Review 224 Module 4 Quanta to Quarks Module 4 Introduction 226 Chapter 12 From Rutherford to Bohr 228 12.1 Atomic timeline 228 12.2 Rutherford’s model of the atom 229 12.3 Planck’s quantised energy 231 12.4 Spectral analysis 232 12.5 Bohr’s model of the atom 235 12.6 Bohr’s explanation of the Balmer series 236 12.7 Limitations of the Rutherford–Bohr model 239 Practical experiences 241 Chapter summary 242 Review questions 243 Chapter 13 Birth of quantum mechanics 247 13.1 The birth 247 13.2 Louis de Broglie’s proposal 248 13.3 Diffraction 250 13.4 Confirming de Broglie’s hypothesis 251 13.5 Electron orbits revisited 252 13.6 Further developments of atomic theory 1924–1930 253 Practical experiences 256 Chapter summary 256 Review questions 257Chapter 14 20th century alchemists 260 14.1 Discovery of the neutron 260 14.2 The need for the strong force 261 14.3 Atoms and isotopes 262 14.4 Transmutation 263 14.5 The neutrino 265 14.6 Was Einstein right? 266 14.7 Binding energy 268 14.8 Nuclear fission 269 14.9 Chain reactions 270 14.10 Neutron scattering 272 Practical experiences 273 Chapter summary 274 Review questions 275 Chapter 15 The particle zoo 279 15.1 The Manhattan Project 279 15.2 Nuclear fission reactors 280 15.3 Radioisotopes 282 15.4 Particle accelerators 286 15.5 The Standard Model 292 Practical experiences 295 Chapter summary 296 Review questions 297 Module 4 Review 300 Module 5 Medical Physics Module 5 Introduction 302 Chapter 16 Imaging with ultrasound 304 16.1 What is ultrasound? 304 16.2 Principles of ultrasound imaging 305 16.3 Piezoelectric transducers 308 16.4 Acoustic impedance 310 16.5 Types of scans 312 16.6 Ultrasound at work 315 Practical experiences 317 Chapter summary 318 Review questions 318 Chapter 17 Imaging with X-rays 320 17.1 Overview and history: types of X-ray images 320 17.2 The X-ray tube 321 17.3 Types of X-rays 322 17.4 Production of X-ray images 324 17.5 X-ray detector technology 326 17.6 Production of CAT X-ray images 326 17.7 Benefits of CAT scans over conventional radiographs and ultrasound 329 Practical experiences 330 Chapter summary 331 Review questions 331

Contents v Chapter 18 Imaging with light 333 18.1 Endoscopy 333 18.2 Medical uses of endoscopes 336 Practical experiences 338 Chapter summary 339 Review questions 339 Chapter 19 Imaging with gamma rays 340 19.1 Isotopes and radioactive decay 340 19.2 Half-life 343 19.3 Radiopharmaceuticals: targeting tissues and organs 344 19.4 The gamma camera 346 19.5 Positron emission tomography 347 Practical experiences 350 Chapter summary 351 Review questions 351 Chapter 20 Imaging with radio waves 354 20.1 Spin and magnetism 354 20.2 Hydrogen in a magnetic field 355 20.3 Tuning in to hydrogen 357 20.4 It depends on how and where you look 359 20.5 The MRI scanner 360 20.6 Applications of MRI 362 Practical experiences 363 Chapter summary 364 Review questions 364 Module 5 Review 366 Module 6 Astrophysics Module 6 Introduction 368 Chapter 21 Eyes on the sky 370 21.1 The first telescopes 370 21.2 Looking up 373 21.3 The telescopic view 374 21.4 Sharpening the image 377 21.5 Interferometry 380 21.6 Future telescopes 382 Practical experiences 383 Chapter summary 384 Review questions 384 Chapter 22 Measuring the stars 388 22.1 How far? 388 22.2 Light is the key 389 22.3 The stellar alphabet 394 22.4 Measuring magnitudes 397 22.5 Colour matters 400 Practical experiences 403 Chapter summary 405 Review questions 405Chapter 23 Stellar companions and variables 407 23.1 Binary stars 407 23.2 Doubly different 411 23.3 Variable stars 413 23.4 Cepheid variables 415 Practical experiences 418 Chapter summary 418 Review questions 419 Chapter 24 Birth, life and death 422 24.1 The ISM 422 24.2 Star birth 423 24.3 Stars in the prime of life 425 24.4 Where to for the Sun? 428 24.5 The fate of massive stars 430 24.6 How do we know? 433 Practical experiences 435 Chapter summary 436 Review questions 436 Module 6 Review 438 Module 7 Skills Module 7 Introduction 440 Chapter 25 Skills stage 2 442 25.1 Metric prefixes 442 25.2 Numerical calculations 443 25.3 Sourcing experimental errors 445 25.4 Presenting research for an exam 446 25.5 Australian scientist 447 25.6 Linearising a formula 447 Chapter 26 Revisiting the BOS key terms 448 26.1 Steps to answering questions 449 Numerical answers 452 Glossary 454 Index 465 Acknowledgements 471 Formulae and data sheets 473 Periodic table 474

vi PHYSICS @ HSC in2 Physics is the most up-to-date physics package written for the NSW Stage 6 Phys\ ics syllabus. The materials comprehensively address the syllabus outcomes and thoroughly p\ repare students for the HSC exam. Physics is presented as an exciting, relevant and fascinating discipline\ . The student materials provide clear and easy access to the content and theory, regular review questions, a full range of exam-style questions and features to develop an interest in the subject. in2 Physics @ HSC student book • The student book closely follows the NSW Stage 6 Physics syllabus and its modular structure. • It clearly addresses both the contexts and the prescribed focus areas (PFAs). • Modules consist of chapters that are broken up into manageable sections. • Checkpoint questions review key content at regular intervals throughout each chapter. • Physics Philes present short, interesting snippets of relevant information about physics or physics applications. • Physics Features highlight important real-life examples of physics. • Physics For Fun—Try This! provide hands-on activities that are easy to do. • Physics Focus brings together physics concepts in the context of one or more PFAs and provides students with a graded set of questions to develop their skills in this vital area. Each student book includes an interactive student CD containing: • an electronic version of the student book. • all of the student materials on the companion website with live links to the website. From cathode rays to television8 168 169 From ideas toimplementation The vertical deflection plates cause the beam to move up or down in synchronisation with an input voltage. For example, a sinusoidal voltage will display a sinusoidal waveform (known as a trace) on the screen. TelevisionCathode ray tube (CRT) television sets used the principles of the cathode ray tube for most of the 20th century. These are now being superseded by plasma and liquid crystal display television sets, which use different operating principles and allow a larger display area with a sharper image. However, the CRT television holds quite a significant historical place in this form of communication. A schematic diagram of a colour CRT television set is shown in Figure 8.5.5. Its basic elements are similar to those of the CRO. The main difference is the method of deflecting the electrons. Magnetic field coils placed outside the tube produce horizontal and vertical magnetic fields inside it. The magnitude and direction of the current determine the degree and direction of electron beam deflection. Recall your right-hand palm rule for the force on charged particles in a magnetic field. The vertical magnetic field will deflect the electrons horizontally; the horizontal field will deflect them vertically. The picture on the screen is formed by scanning the beam from left to right and top to bottom. The electronics in the television switches the beam on and off at the appropriate spots on the screen in order to reproduce the transmitted picture. However, to reproduce colour images, colour television sets need to control the intensity of red, blue and green phosphors on the screen. Three separate electron guns are used, each one aimed at one particular colour. The coloured dots on the screen are clustered in groups of red, blue and green dots that are very close to each other and generally cannot be distinguished by eye without the aid of a magnifying glass. For this reason a method of guiding the different electron beams to their respective coloured dots was devised. A metal sheet, known as a shadow mask (Figure 8.5.6) and consisting of an array of holes, is placed behind the phosphor screen. Each hole guides the three beams to their respective coloured phosphor as the beams move horizontally and vertically. Black and white television sets did not need the shadow mask since they had only one beam. heater cathode (negative)electrons 'boil' off the heated cathode anode (positive) electron beam electrons attracted to the positive anode collimator Figure 8.5.3 The components of an electron gun used in both cathode ray oscilloscopes and CRT televisions V TimeV Time sawtooth voltage for timebase sinusoidal vertical voltage Figure 8.5.4 A sawtooth voltage waveform on the horizontal deflection plates of a CRO sweeps the electron beam across the screen to display the sinusoidal waveform on the vertical deflection plates. electron gunmagnetic coils electron beam fluorescent screen Figure 8.5.5 A television picture tube showing the electron gun, deflection coils and fluorescent screen electron guns deflecting coils focusing coils glass fluorescent screen vacuum mask phosphor dots on screen fluorescent screen mask holes in mask blue beam red beam green beam R G B electron beams Figure 8.5.6 A colour CRT television set has three electron guns that will only strike their respective coloured phosphor dots with the aid of a shadow mask. try this!Do not aDjust your horizontal!If you have access to an old black and white TV set or an old style monochrome computer monitor, try holding a bar magnet near the front of the screen and watch how the image distorts. This occurs because the magnetic field deflects the electrons that strike the screen. DO NOT do this with a colour TV set. This can magnetise the shadow mask and cause permanent distortion of the image and its colour. You can move a bar magnet near the back of a colour TV set to deflect the electrons from the electron gun and therefore distort or shift the image without causing permanent damage to the TV set. Can an osCillosCope be used as a television set? The similarity between the cathode ray oscilloscope (CRO) and CRT television suggests that a CRO can be used as a television set. In fact, there have been some devices that have made use of the CRO as you would a computer monitor. So, in principle, it can be used as a television. One is then forced to ask ‘why did they need to deflect t\ he beam in a television set with magnetic fields rather than with electric \ fields as in the CRO?’ In principle all television sets could be made in the same design as a CRO; however, it is much easier and cheaper to deflect the beam with a magnetic field on the outside of the tube rather than embed electrodes\ in the glass and inside the vacuum—this is a little trickier. So now another question arises: ‘why not deflect the beam of the CRO using magnetic fields, wouldn’t it result in cheaper CROs?’. Cathode ray oscilloscopes are precision instruments. The horizontal sweep rate must be able to be increased to very high frequencies in orde\ r to detect signals that change very quickly. Electric fields can be made to change very quickly without significant extra power requirements. However, a magnetically deflected system requires higher and higher voltages with increasing horizontal and vertical deflection frequencies \ in order to maintain the same current in the coils, and therefore, the same\ angle of beam deflection – thus having a significantly greater power \ requirement. Cathode ray tube television sets, however, only operate at fixed and relatively low scanning horizontal and vertical frequencies. Thus it is simpler and cheaper for the mass market to deflect with a magnetic field. CheCkpoint 8.51 Outline the purpose of a CRO. 2 List the main parts of a CRO. 3 Describe the role of each of these parts in the CRO. 4 State the similarities and differences between th e cathode ray tube CRO and CRT TV. THE COMPLETE PHYSICS PACKAGE FOR NSW STUDENTS

vii in2 Physics @ HSC Activity Manual • A write-in workbook that provides a structured approach to the mandatory practical experiences, both first-hand and secondary-source investigations. • Dot point and skills focused. in2 Physics @ HSC Teacher Resource • Editable teaching materials, including teaching programs, so that teachers can tailor lessons to suit their classroom. • Answers to student book and activity manual questions, with fully worked solutions and extended answers and support notes. • Risk assessments for all first-hand investigations. in2 Physics @ HSC companion website Visit the companion website in the student lounge and teacher lounge of Pearson Places • Review questions— auto-correcting multiple-choice questions for each chapter. • Web destinations—a list of reviewed websites that support further investigation. 68 3MODULE from ideas to implementation Chapter 8 f rom cathode rays to television 69 Method1 Set up the equipment as shown in Figure 8.1.1. 2 Observe the patterns and note the pressure in the tube. 3 Replace the tube with the next in the series. 4 Repeat the process of observing the patterns and noting the pressure for each of the tubes in your set. HAZARDHigh voltages are produced by induction coils and may produce unwanted X-rays. The voltages necessary to operate the tubes depend upon the dimensions of the tube and the pressure of the gas in the tube. Generally, the higher the voltage used, the greater the danger of the production of unwanted X-rays. Use the lowest possible voltage and stand a minimum of 1 m away from the equipment. Chapter 8 from Cathode rays to television Changing pressure of discharge tubes Perorm an investigation and gather firs t-hand information to observe the occurr ence of different striation patterns for different pressures in discharge tubes.Physics skillsThe skills outcomes to be practised in th is activity include: 12.1 perform first-hand investigations 12.2 gather first-hand information 14.1 analyse information The complete statement of these skills outcomes can be f ound in the syllabus grid on pages vi–viii. AimTo observe the striation patterns for different pressures in discharge tubes.Hypothesis Theory Ever since Heinrich Geissler and Julius Plücker collaborated to create a tube in which the pressure could be reduced substantially, our understanding of the atom and developing uses for the cathode ray tube have advanced tremendously. Because of this development, it was found that electric current could be passed through air. The different patterns that could be seen depended on the pressure. Normally air is considered to be an insulator, but it can be made to conduct by ionising the air molecules. To do this, the very small fraction of free electrons that are always in air are accelerated (with an electric field). At high pressures these electrons collide frequently with the air, losing their energy and, as a result, do not gain sufficient energy to ionise the air atoms. As pressure is reduced, these electrons travel further before colliding with air molecules, thereby acquiring enough energy to ionise the air molecules. This will produce more free electrons that, in turn, can ionise other atoms. When they are able to travel far enough to gain the energy to be absorbed by atoms, we see a light show (known as a discharge). The lower the pressure, the further the electrons can travel before colliding with gas molecules and producing a discharge. The light that is emitted is a result of the electrons around the gas atom becoming excited (increasing in energy) and re-emitting the photon of light as they return to the ground state (the lowest energy they can have in an atom). Light will also be produced when free electrons recombine with ions and the electrons return to the ground state, emitting photons. As every element has a distinct set of energy levels, the colour of light seen will vary with the element with which the electron collides. EquipmentIf you have the apparatus at school, you can carry out the experiment first hand. The patterns are hard to see unless the room is very dark. • induction coil • discharge tubes at different pressures • connecting wires • DC power supply Alternatively, you can use the simulations in Part B and make observations from them. Risk assessment a Ctivity 8.1first-hand investigation DC power supply Figure 8.1.1 Induction coil and discharge tube For more information on the in2 Physics series, visit www.pearsonplaces.com.au

viii How to use this book in2 Physics @ HSC is structured to enhance student learning and their enjoyment of learning. It contains many outstanding and unique features that will assist students succeed in Stage 6 Physics. These include: • Module opening pages introduce a range of contexts for study, as well as an inquiry activity that provides immediate activities for exploration and discussion. 2 Motors and Generators 83 Figure 4.0.1 A generator produces electricity in each of these wind turbines. 82 The first recorded observations of the relationship between electricity and magnetism date back more than 400 years. Many unimagined discoveries followed, but progress never waits. Before we understood their nature, inventions utilising electricity and magnetism had changed our world forever. Today our lives revolve around these forms of energy. The lights you use to read this book rely on them and the CD inside it would be nothing but a shiny coaster for your cup. We use magnetism to generate the electricity that drives industry, discovery and invention. Electricity and magnetism are a foundation for modern technology, deeply seated in the global economy, and our use impacts heavily on the environment. The greatest challenge that faces future generations is the supply of energy. As fossil fuels dry up, electricity and magnetism will become even more important. New and improved technologies will be needed. Whether it’s a hybrid car, a wind turbine or a nuclear fusion power plant, they all rely on applications of electricity and magnetism. Context InQUIRY ACtIVItY BUIld YoUR own eleCtRIC motoRMany of the devices you use every day have electric motors. They spin your DVDs, wash your clothes and even help cook your food. Could you live without them, and how much do you know about how they work? The essential ingredients for a motor are a power source, a magnetic field and things to connect these together in the right way. It’s not as hard as you think. All you need is a battery, a wood screw, a piece of wire and a cylindrical or spherical magnet. Put these things together as shown in Figure 4.0.2 and see if you can get your motor to spin. Be patient and keep trying. Then try the following activities. 1 Test the effects of changing the voltage you use. You could add another battery in series or try a battery with a higher voltage. 2 Try changing the strength of the magnet by using a different magnet or adding another. What does this affect? 3 Try changing the length of the screw, how sharp its point is or the material it is made from. Does it have to be made of iron? Figure 4.0.2 A simple homopolar motor 1 1 204 Superconductivity 205 from ideaS toimplementation crystal, constructive interference, destructive interference, path length, diffraction grating, Bragg law, phonons, critical temperature, type-I superconductors, type-II superconductors, critical field strength, vortices, flux pinning, BCS theory, Cooper pair, coherence length, energy gap, spin Surprising discoveryJust as an improved understanding of the conducting properties of semiconductors led to the wide variety of electronic devices, research into the conductivity of metals produced quite a surprising discovery called superconductivity. This is the total disappearance of electrical resistance below a certain temperature, which has great potential applications ranging from energy transmission and storage to public transport. An understanding of this phenomenon required a detailed understanding of the crystal structure of conductors and the motion of electrons through them. of interference of electromagnetic radiation, and examine how this was applied to crystals using X-rays. Then we will see how the BCS theory of superconductivity made use of the crystal structure of matter. 1 1 . 1 The crystal structure of matterA crystal is a three-dimensional regular arrangement of atoms. Figure 11.1.1 shows a sodium chloride crystal (ordinary salt also called rock salt when it comes as a large crystal). The crystal is made from simple cubes repeated many times, with sodium and chlorine atoms at the corners of the cubes. Crystals of other materials may have different regular arrangements of their atoms. There are 14 types of crystal arrangements that solids can have. The regular arrangement of atoms in crystals was a hypothesis before Max Von Laue and his colleagues confirmed it by X-ray diffraction experiments. William and Lawrence Bragg took this method one step further by measuring the spacing between the atoms in the crystal. Let us first look at the phenomenon Figure 11.1.1 Crystal structure of sodium chloride. The red spheres represent positive\ sodium ions, and the green spheres represent negative chlorine ions. tr y thiS!Crystals in the kitChenLook at salt grains through a magnifying lens. Each grain is a single crystal that is made from the basic arrangement of sodium and chlorine atoms shown in Figure 11.1.1. Although the grains mostly look irregular due to breaking and chipping during the manufacturing process, occasionally you will see an untouched cubic or rectangular prism that reflects the underlying crystal lattice structure. CheCkpoInT 11.1Explain what is meant by the crystal structure of matter. 1 1 . 2 Wave interferenceThe wave nature of light can be used to measure the size of very small spaces. Recall that two identical waves combine to produce a wave of greater amplitude when their crests overlap, as shown in Figure 11.2.1a (see in2 Physics @ Preliminary sections 6.4 and 7.4). The overlapping waves will cancel to produce a resulting wave of zero amplitude when the crest of one wave coincides with the trough of the other (Figure 11.2.1b). This addition and subtraction is called constructive and destructive interference respectively and is a property of all wave phenomena. As an example, two identical circular water waves in a ripple tank overlap (see Figure 11.2.2). The regions of constructive and destructive interference radiate outwards along the lines as shown. Increasing the spacing between the sources causes the radiating lines to come closer together (Figure 11.2.2b). Figure 11.2.1 Two identical waves (red, green) travelling in opposite directions can \ add (blue) (a) constructively or (b) destructively. Figure 11.2.2 Interference of water waves for two sources that are (a) close together and (b) further apart t = 0 s t = 1 s t = 3 s t = 4 s t = 5 s t = 6 s t = 7 s t = 0 s t = 1 s t = 3 s t = 4 s t = 5 s t = 6 s t = 7 s a b lines of constructive interference lines of destructive interference b a The interference of identical waves from two sources can also be represented by outwardly radiating transverse waves (see Figure 11.2.3). The distance that a wave travels is known as its path length. Constructive interference occurs when the difference in the path length of the two waves is equal to 0, λ, 2 λ, 3 λ, 4 λ or any other integer multiple of the wavelength λ. Destructive interference occurs when the two waves are half a wavelength out of step. This corresponds to a path length difference of λ/2, 3 λ/2, 5 λ/2 etc. constructive interference constructive interference destructive interference waves in phase Figure 11.2.3 Constructive and destructive interference between identical transverse waves from two sources 3 72 Seeing in a weird light: relativity 73 Space PHYSICS FEATURETwISTIng SPACETImE ... And Y oUR mInd There are two more invariants in special relativity. Maxwell’s equations (and hence relativity) requires that electrical charge is invariant in all frames. Another quantity invariant in all inertial frames is called the spacetime interval. You may have heard of spacetime but not know what it is. One of Einstein’s mathematics lecturers Hermann Minkowski (1864–1909) showed that the equations of relativity and Maxwell’s equations become simplified if you assume that the three dimensions of space (x, y , z) and time t taken together form a four‑dimensional coordinate system called spacetime. Each location in spacetime is not a position, but rather an event—a position and a time. Using a 4D version of Pythagoras’ theorem, Minkowski then defined a kind of 4D ‘distance’ between events called the spacetime interval s given by: s 2 = (c × time period) 2 – path length 2 = c 2t 2 – ((∆x)2 + (∆y)2 + (∆z)2) Observers in different frames don’t agree on the 3D path length between events, or the time period between events, but all observers in inertial frames agree on the spacetime interval s between events. In general relativity, Einstein showed that gravity occurs because objects with mass or energy cause this 4D spacetime to become distorted. The paths of objects through this distorted 4D spacetime appear to our 3D eyes to follow the sort of astronomical trajectories you learned about in Chapter 2 ‘Explaining and exploring the solar system’. However, unlike Newton’s gravitation, general relativity is able to handle situations of high gravitational fields, such as Mercury’s precessing orbit around the Sun and black holes. General relativity also predicts another wave that doesn’t require a medium: the ripples in spacetime called ‘gravity waves’. Figure 3.4.6 One of the four ultra-precise superconducting spherical gyroscopes on NASA’s Gravity Probe B, which orbited Earth in 2004/05 to measure two predictions of general relativity: the bending of spacetime by the Earth’s mass and the slight twisting of spacetime by the Earth’s rotation (frame-dragging) 1. The history of physics Mass, energy and the world’s most famous equationThe kinetic energy formula K = 1 2mv 2 doesn’t apply at relativistic speeds, even if you substitute relativistic mass mv into the formula. Classically, if you apply a net force to accelerate an object, the work done equals the increase in kinetic energy. An increase in speed means an increase in kinetic energy. But in relativity it also means an increase in relativistic mass, so relativistic mass and energy seem to be associated. Superficially, if you multiply relativistic mass by c 2 you get mv c 2, which has the same dimensions and units as energy. But let’s look more closely at it. Solve problems and analyse information using: E = mc2l l v cv= −0 2 21t t vcv= −02 21m m vcv= −02 21 How does this formula behave at low speeds (when v 2/c 2 is small)? mc mc vc mc v cv 2 02 2 2 0 2 2 2 1 21 1 = − = −       − Using a well-known approximation formula that you might learn at university, (1 – x )n ≈ 1 – nx for small x:mc v c0 2 2 2 1 21 −      − ≈ mc v c0 2 2 21 1 2 +×       = m0c 2 + 1 2m0v 2 Rearrange: m vc 2 – m0c 2 = ( mv – m0)c 2 ≈ 1 2m0v 2 In other words, at low speeds, the gain in relativistic mass ( m v – m0) multiplied by c 2 equals the kinetic energy—a tantalising hint that at low speed mass and energy are equivalent. It can also be shown to be true at all speeds, using more sophisticated mathematics. In general, mass and energy are equivalent in relativity and c 2 is the conversion factor between the energy unit (joules) and the mass unit (kg). In other words:E = mc 2 where m is any kind of mass. In relativity, mass and energy are regarded as the same thing, apart from the change of units. Sometimes the term mass-energy is used for both. m 0 c 2 is called the rest energy, so even a stationary object contains energy due to its rest mass. Relativistic kinetic energy therefore:mc mc mc vc mcv 2 02 02 2 2 0 2 1 − = − − Whenever energy increases, so does mass. Any release of energy is accompanied by a decrease in mass. A book sitting on the top shelf has a slightly higher mass than one on the bottom shelf because of the difference in gravitational potential energy. An object’s mass increases slightly when it is hot because the kinetic energy of the vibrating atoms is higher. Because c 2 is such a large number, a very tiny mass is equivalent to a large amount of energy. In the early days of nuclear physics, E = mc 2 revealed the enormous energy locked up inside an atom’s nucleus by the strong nuclear force that holds the protons and neutrons together. It was this that alerted nuclear physicists just before World War II to the possibility of a nuclear bomb. The energy released by the nuclear bomb dropped on Hiroshima at the end of that war (smallish by modern standards) resulted from a reduction in relativistic mass of about 0.7 g (slightly less than the mass of a standard wire paperclip). Worked example q UESTIonWhen free protons and neutrons become bound together to form a nucleus, \ the reduction in nuclear potential energy (binding energy) is released, normally in the\ form of gamma rays. Relativity says this loss in energy is reflected in a decrease in mass o\ f the resulting atom. Discuss the implications of mass increase, time dilation and length contraction for space travel. evil tWinSThe most extreme mass–energy conversion involves antimatter. For every kind of matter particle there is an equivalent antimatter particle, an ‘evil twin’, bearing properties (such as charge) of opposite sign. Particles and their antiparticles have the same rest mass. When a particle meets its antiparticle, they mutually annihilate—all their opposing properties cancel, leaving only their mass‑energy, which is usually released in the form of two gamma‑ray photons. Matter– antimatter annihilation has been suggested (speculatively) as a possible propellant for powering future interstellar spacecraft. PRACTICAL EXPERIENCES 350 1 9Imaging with gamma rays 351 Chapter summary mEdICALPhySICS Activity 19.2: HeAl t Hy or diseAsed?Typical images of healthy bone and cancerous bone are shown. The tumours show up as hot-spots. Use the template in the activity manual to research and compare images of healthy and diseased parts of the body. Discussion questions 1 Examine Figure 19.4.2. There is a hot-spot that is not cancerous near the left elbow. Explain. 2 In the normal scan (Figure 19.6.2a), the lower pelvis has a region of high intensity. Why is this? (Hint: It may be soft tissue, not bone. Looking at Figure 19.6.2b might help you with this question.) 3 State the differences that can be observed by comparing an image of a healthy part of the body with that of a diseased part of the body. 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. Review questions ChAPTER 19This is a starting point to get you thinking about the mandatory practical experiences outlined in the syllabus. For detailed instructions and advice, use in2 Physics @ HSC Activity Manual. Activity 19.1: Bone scAnsA bone scan is performed to obtain a functional image of the bones and so can be used to detect abnormal metabolism in the bones, which may be an indicat\ ion of cancer or other abnormality. Because cancer mostly involves a higher than normal Perform an investigation to compare a bone scan with an X-ray image. Figure 19.6.1 Comparison of an X-ray and bone scan of a hand Figure 19.6.2 Bones scans of (a) a healthy person and (b) a patient with a tumour in the skeleton • The number of protons in a nucleus is given by the atomic number, while the total number of nucleons is given by the mass number. • Atoms of the same element with different numbers of neutrons are called isotopes of that element. • Many elements have naturally occurring unstable radioisotopes. • In alpha decay an unstable nucleus decays by emitting an alpha particle ( α-particle). • In beta decay, a neutron changes into a proton and a high-energy electron that is emitted as a beta particle ( β -particle). • In positron decay, a positron—the antiparticle of the electron—is emitted. • When a positron and an electron collide, their total mass is converted into energy in the form of two gamma-ray photons. • In gamma decay a gamma ray ( g) is emitted from a radioactive isotope. • The time it takes for half the mass of a radioactive parent isotope to decay into its daughter nuclei is the half-life of the isotope. • Artificial radioisotopes are produced in two main ways: in a nuclear reactor or in a cyclotron. • A gamma camera detects gamma rays emitted by a radiopharmaceutical in the patient’s body. • PET imaging uses positron-emitting radiopharmaceuticals to obtain images using gamma rays emitted from electron–positron annihilation. PHysicAlly sPeAkingBelow is a list of topics that have been discussed throughout this chapter. Create a visual summary of the concepts in this chapter by constructing a mind map linking the terms. Add diagrams where useful. Radioactive decay Radiation RadioisotopeNucleon Neutron ProtonIsotopeAlpha decay Beta decay Gamma decayAntimatter PET Half-life Bone scanPositron decayScintillator reviewing 1 Recall how the bone scan produced by a radioisotope compares with that from a conventional X-ray. 2 Analyse the relationship between the half-life of a radiopharmaceutical and its potential use in the human body. 3 Explain how it is possible to emit an electron from the nucleus when the electron is not a nucleon. 4 Assess the statement that ‘Positrons are radioactive particles produced when a proton decays’. 5 Discuss the impact that the production and use of radioisotopes has on society. 6 Describe how isotopes such as Tc-99m and F-18 can be used to target specific organs to be imaged. 7 Use the data in Table 19.6.1 to answer the questions: a Which radioactive isotope would most likely be used in a bone scan? Justify your choice. b Propose two reasons why cesium-137 would not be a suitable isotope to use in medical imaging. Table 19.6.1 Properties of some radioisotopesRadioactive sou Rce Radiation emitted Half-lifeC-11 β +, g20.30 minutes Tc-99m g 6.02 hours TI-201 g 3.05 days I-131 β, g8.04 days Cs-137 α 30.17 years U-238 α 4.47 × 10 9 years rate of cell division (thus producing a tumour), chemicals involved in metabolic processes in bone tend to accumulate in higher concentrations in cancerous tissue. This produces areas of concentration of gamma emission, indicating a tumour. Compare the data obtained from the image of a bone scan with that provided by an X-ray image. Discussion questions 1 Identify the best part of the body for each of these diagnostic tools to image. 2 Compare and contrast the two images in terms of the information they provide. a b • Chapter openings list the key words of each chapter and introduce the chapter topic in a concise and engaging way. • Key ideas are clearly highlighted with a and Syllabus flags indicate where domain dot points appear in the student book. The flags are placed as closely as possible to where the relevant content is covered. Flags may be repeated if the dot point has multiple parts, is complex or where students are required to solve problems. • Each chapter concludes with: – a chapter summary – review questions, including literacy-based questions (Physically Speaking), chapter review questions (Reviewing) and physics problems (Solving Problems). Syllabus verbs are clearly highlighted as and where appropriate – Physics Focus—a unique feature that places key chapter concepts in the context of one or more prescribed focus areas. • Chapters are divided into short, accessible sections— the text itself is presented in short, easy-to-understand chunks of information. Each section concludes with a Checkpoint—a set of review questions to check understanding of key content and concepts.

ix How to use this book • Module reviews provide a full range of exam-style questions, including multiple-choice, short-response and extended-response questions. 224 225 from ideas toimplementation 3 The review contains questions in a similar style and proportion to the HSC Physics examination. Marks are allocated to each question up to a total of 25 marks. It should take you approximately 45 minutes to complete this review. multiple choice(1 mark each) 1 Predict the direction of the electron in Figure 11.13.1 as it enters the magnetic field. A Straight up B Left C Right D Down 2 The diagrams in Figure 11.13.2 represent semiconductors, conductors and insulators. The diagrams show the conduction and valence bands, and the energy gaps. Which answer correctly labels each of the diagrams? I IIIIIA Conductor InsulatorSemiconductor B Insulator ConductorSemiconductor C Insulator SemiconductorConductor D Semiconductor ConductorInsulator 3 The graph in Figure 11.13.3 shows how the resistance of a material varies with temperature. Identify each of the parts labelled on the graph.I IIIIIA Critical temperature Superconductor materialNormal material B Superconductor material Critical temperatureNormal material C Critical temperature Normal material Superconductor material D Normal material Superconductor materialCritical temperature Figure 11.13.1 An electron in a magnetic field Figure 11.13.2 Energy bands Figure 11.13.3 Resistance varies with temperature – I II III Temperature (K) Resistance (Ω)I II III 4 Experimental data from black body radiation during Planck’s time showed that predicted radiation levels were not achieved in reality. Planck best described this anomaly by saying that: A classical physics was wrong. B radiation that is emitted and absorbed is quantised. C he had no explanation for it. D quantum mechanics needed to be developed. 5 Figure 11.13.4 shows a cathode ray tube that has been evacuated. Which answer correctly names each of the labelled features? I IIIIIA Striations CathodeAnode B Faraday’s dark space Striations Cathode C Crooke’s dark space Anode Faraday’s dark space D Cathode Faraday’s dark spaceStriations extended response 6 Explain, with reference to atomic models, why cathode rays can travel through metals. (2 marks) 7 Outline how the cathode ray tube in a TV works in order to produce the viewing picture. (2 marks) 8 Give reasons why CRT TVs use magnetic coils and CROs use electric plates in order to deflect the beams, given that both methods work. (2 marks). 9 In your studies you were required to gather information to describe how the photoelectric effect is used in photocells. a Explain how you determined which material was relevant and reliable. b Outline how the photoelectric effect is used in photocells. (3 marks) 10 Justify the introduction of semiconductors to replace thermionic devices. (4 marks) 11 Magnetic levitation trains are used in Germany and Japan. The trains in Germany use conventional electromagnets, whereas the one in Japan uses superconductors. Compare and contrast the two systems. (3 marks) 12 a Determine the frequency of red light, which has a wavelength λ = 660 nm. (Speed of light c = 3.00 × 10 8 m s–1) b Calculate the energy of a photon that is emitted with this wavelength. (Planck’s constant h = 6.63 × 10–34 J s) (4 marks) Figure 11.13.4 An evacuated cathode ray tube II III I 48 MODULEmotors andgenerators 2 49 Chapter 6 motors: magnetic fields make the world go around Risk assessment Method 1 Cut a length of cotton-covered wire so that the wire is long enough to wrap around the exterior of a matchbox three times (as shown in Figure 6.2.2). 2 Leave a straight piece (approx. 10 cm long) hanging out and then wind the remainder of the wire around the box 2½ times. Leave another straight piece the same length as at the start, on the opposite side. 3 Wrap the straight pieces around the loops so that they tie both ends. 4 Fan out the loops so that you get equally spaced loops and that it looks like a bird cage (see Figure 6.2.3). 5 Push out the middle of the paper clip as shown and Blu-Tack to the bench. 6 Slip the straight pieces of wire through the paper clip supports. Unwrap the cotton from these parts. 7 Connect an AC power supply to the paper clips. 8 Place two magnets so that a north pole and a south pole face on opposing sides of the cage. 9 Turn on. You may need to give the cage a tap to get it spinning. Results1 Record your observations of the motor. 2 How did adding more magnets affect how the motor ran? 3 When the current is increased, what changes occurred? Motors and torque Solve problems and analyse information about simple motors using: τ = nBIA cos θPhysics skillsThe skills outcomes to be practised in this activity include: 12.4 process information 14.1 analyse information The complete statement of these skills outcomes can be found in the syll\ abus grid on pages vii–viii. Aim Hypothesis Theory The motor effect means that a current-carrying wire experiences a force when placed in a magnetic field. This is the basis for the workings of a motor. For a motor to work as needed, the motion resulting from the motor effect needs to be circular and the force needs to be adjusted so the direction of rotation does not change. QuestionFigure 6.2.1 shows the simplified workings of a motor that you will be making. Label all the parts of the motor. Equipment• insulated wire from which insulation can be removed easily • Blu-Tack • magnets • connecting wires with alligator clips • magnetic field sensor and data logger (if available) • power supply • paperclips matchbox wire loop wire through a b alligator clip wires paper clip cage fanned out power source Figure 6.2.2 Equipment set-up 1 Figure 6.2.3 Equipment set-up 2 First-hand investigationaCt IVI tY 6.2 A: C: D: B:N S Figure 6.2.1 Simplified motor Other features • Physics Philes present short, interesting items to support or extend the text. • Physics for Fun—Try This! activities are short, hands- on activities to be done quickly, designed to provoke discussion. • Physics Features are a key feature as they highlight contextual material, case studies or prescribed focus areas of the syllabus. • A complete glossary of all the key words is included at the end of the student book. • The final two chapters provide essential reference material: ‘Skills stage 2’ and ‘Revisiting the BOS key terms’. • In all questions and activities, except module review questions, the BOS key terms are highlighted. in2 Physics @ HSC Student CD This is included with the student book and contains: • an electronic version of the student book • interactive modules demonstrating key concepts Practical experiences The accompanying activity manual covers all of the mandatory practical experiences outlined in the syllabus. in2 Physics @ HSC Activity Manual is a write-in workbook that outlines a clear, foolproof approach to success in all the required practical experiences. Within the student book, there are clear cross-references to the activity manual: Practical Experiences icons refer to the activity number and page in the activity manual. In each chapter, a summary of possible investigations is provided as a starting point to get students thinking. These include the aim, a list of equipment and discussion questions. Activity 10.2 PRACTICAL EXPERIENCES Activity Manual, Page 94 • the companion website on CD • a link to the live companion website (Internet access required) to provide access to the latest information and web links related to the student book. The complete in2 Physics @ HSC package Remember the other components of the complete package: • in2 Physics @ HSC companion website at Pearson Places • in2 Physics @ HSC Teacher Resource.

x Stage 6 Physics syllabus grid Prescribed focus areas 1. The history of physics H1. evaluates how major advances in scientific understanding and technology have changed the direction or nature of scientific thinking Feature: pp. 12, 29, 72 Focus: pp. 25, 246, 299 2. The nature and practice of physics H2. analyses the ways in which models, theories and laws in physics have been tested and validated Focus: p. 79 3. Applications and uses of physics H3. assesses the impact of particular advances in physics on the development of technologies Feature: pp. 12, 29, 307, 334, 346 Focus: pp. 57, 79, 129, 173, 223, 246, 259, 278 4. Implications for society and the Environment H4. assesses the impacts of applications of physics on society and the environment Feature: pp. 29, 307, 344 Focus: pp. 113, 173, 353 5. Current issues, research and developments in physics H5. identifies possible future directions of physics research Feature: pp. 391, 410 Focus: pp. 79, 113, 173, 223, 353, 386 Module 1 Space 1. The Earth has a gravitational field that exerts a force on objects both \ on it and around it STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE define weight as the force on an object due to a gravitational field 13 perform an investigation and gather information to determine a value for\ acceleration due to gravity using pendulum motion or computer-assisted technology and identify reason(s) for possible variations from the val\ ue 9.8 m s –2 Act. 1.2 explain that a change in gravitational potential energy is related to work done 16 gather secondary information to predict the value of acceleration due to\ gravity on other planets Act. 1.3 define gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational field: mm r = 12 P EG 16 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 Act. 1.3 2. Many factors have to be taken into account to achieve a successful rocke\ t launch, maintain a stable orbit and return to Earth STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE describe the trajectory of an object undergoing projectile motion within the Earth’s gravitational field in terms of horizontal and vertical components 5 solve problems and analyse information to calculate the actual velocity \ of a projectile from its horizontal and vertical components using: v x2 = ux2 v = u + at v y 2 = uy2 + 2ay ∆y ∆x = ux t ∆ y = uyt + 1 2ay t 2 7, 9, 23, 24 describe Galileo’s analysis of projectile motion 5 perform a first-hand investigation, gather information and analyse data \ to calculate initial and final velocity, maximum height reached, range and time of flight of a projectile for a range of situations by using simulations, d\ ata loggers and computer analysis Act. 1.1 explain the concept of escape velocity in terms of the: – gravitational constant – mass and radius of the planet 18 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, O’Neill or von Braun 29 Act. 2.1

xi Stage 6 Physics syllabus grid outline Newton’s concept of escape velocity18 identify why the term ‘g forces’ is used to explain the forces acting on an astronaut during launch 31 discuss the effect of the Earth‘s orbital motion and its rotational motion on the launch of a rocket 34 analyse the changing acceleration of a rocket during launch in terms of the: – Law of Conservation of Momentum – forces experienced by astronauts 30, 33 analyse the forces involved in uniform circular motion for a range of objects, including satellites orbiting the Earth 25, 32, 34, 37, 54, 55solve problems and analyse information to calculate the centripetal forc\ e acting on a satellite undergoing uniform circular motion about the Earth using:\ F mv 2 r = 37, 54, 55 Act. 2.2 compare qualitatively low Earth and geo-stationary orbits 43 define 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 Kepler’s Law of Periods 36, 40, 56 solve problems and analyse information using: r T GM3 2 2 4= π 39, 43, 56 account for the orbital decay of satellites in low Earth orbit 46 discuss issues associated with safe re-entry into the Earth’s atmosphere and landing on the Earth’s surface 47 identify that there is an optimum angle for safe re-entry for a manned spacecraft into the Earth’s atmosphere and the consequences of failing to achieve this angle 47 3. The solar system is held together by gravity STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE describe a gravitational field in the region surrounding a massive object in terms of its effects on other masses in it 13 present information and use available evidence to discuss the factors af\ fecting the strength of the gravitational force Act. 1.3 define Newton’s Law of Universal Gravitation: mm d = 12 2 FG 11 solve problems and analyse information using: mm d = 12 2 FG 23, 24, 25, 37, 54, 55 discuss the importance of Newton’s Law of Universal Gravitation in understanding and calculating the motion of satellites 35, 38 identify that a slingshot effect can be provided by planets for space probes 44

xii Stage 6 Physics syllabus grid 4. Current and emerging understanding about time and space has been depende\ nt upon earlier models of the transmission of light STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE outline the features of the aether model for the transmission of light 61 describe and evaluate the Michelson- Morley attempt to measure the relative velocity of the Earth through the aether 62 gather and process information to interpret the results of the Michelson\ -Morley experiment 62 Act. 3.2 discuss the role of the Michelson- Morley experiments in making determinations about competing theories 62 outline the nature of inertial frames of reference 58 perform an investigation to help distinguish between non-inertial and in\ ertial frames of reference 60 Act. 3.1 discuss the principle of relativity 58analyse and interpret some of Einstein’s thought experiments involving mirrors and trains and discuss the relationship between thought and reality 66 describe the significance of Einstein’s assumption of the constancy of the speed of light 65 analyse information to discuss the relationship between theory and the e\ vidence supporting it, using Einstein’s predictions based on relativity that were made many years before evidence was available to support it 78 identify that if c is constant then space and time become relative 65 discuss the concept that length standards are defined in terms of time in contrast to the original metre standard 79 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 64, 69 solve problems and analyse information using: E = mc 2 ll v cv=−0 2 21 t v cv t0 =− 2 2 1 m v cv m0 =− 2 2 1 66, 69, 72, 77, 78 discuss the implications of mass increase, time dilation and length contraction for space travel 70, 73 Module 2 Motors and Generators 1. Motors use the effect of forces on current-carrying conductors in mag\ netic fields STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE discuss the effect on the magnitude of the force on a current-carrying conductor of variations in: – the strength of the magnetic field in which it is located – the magnitude of the current in the conductor – the length of the conductor in the external magnetic field – the angle between the direction of the external magnetic field and the direction of the length of the conductor 92 perform a first-hand investigation to demonstrate the motor effect Act. 4.1

xiii Stage 6 Physics syllabus grid describe qualitatively and quantitatively the force between long parallel current- carrying conductors: F l kII d= 12 94 solve problems using: F l kII d= 12 94 define torque as the turning moment of a force using: t = Fd 115 solve problems and analyse information about the force on current-carryi\ ng conductors in magnetic fields using: F = BIl sin θ 92 Act. 4.1 identify that the motor effect is due to the force acting on a current-carrying conductor in a magnetic field 90, 116 solve problems and analyse information about simple motors using: t = nBIA cos θ 117 Act. 6.2 describe the forces experienced by a current-carrying loop in a magnetic field and describe the net result of the forces 117 identify data sources, gather and process information to qualitatively d\ escribe the application of the motor effect in: – the galvanometer – the loudspeaker 91, 119 Act. 6.1 describe the main features of a DC electric motor and the role of each feature 115 identify that the required magnetic fields in DC motors can be produced either by current-carrying coils or permanent magnets 115 2. The relative motion between a conductor and magnetic field is used to ge\ nerate an electrical voltage STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE outline Michael Faraday’s discovery of the generation of an electric current by a moving magnet 100 perform an investigation to model the generation of an electric current \ by moving a magnet in a coil or a coil near a magnet 101 Act. 5.1 define magnetic field strength B as magnetic flux density 101 plan, choose equipment or resources for, and perform a first-hand investigation to predict and verify the effect on a generated electric current when: – the distance between the coil and magnet is varied – the strength of the magnet is varied – the relative motion between the coil and the magnet is varied Act. 5.1 describe the concept of magnetic flux in terms of magnetic flux density and surface area 101 gather, analyse and present information to explain how induction is used in cooktops in electric ranges 108 Act. 5.2 describe generated potential difference as the rate of change of magnetic flux through a circuit 103 gather secondary information to identify how eddy currents have been uti\ lised in electromagnetic braking Act. 5.2 113 account for Lenz’s Law in terms of conservation of energy and relate it to the production of back emf in motors 105, 120 explain that, in electric motors, back emf opposes the supply emf 120 explain the production of eddy currents in terms of Lenz’s Law 106 3. Generators are used to provide large scale power production STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE describe the main components of a generator 131 plan, choose equipment or resources for, and perform a first-hand investigation to demonstrate the production of an alternating current Act. 5.1 compare the structure and function of a generator to an electric motor 135 gather secondary information to discuss advantages/disadvantages of AC a\ nd DC generators and relate these to their use 135 Act. 7.1 describe the differences between AC and DC generators 135 analyse secondary information on the competition between Westinghouse and Edison to supply electricity to cities 141 Act. 7.2 discuss the energy losses that occur as energy is fed through transmission lines from the generator to the consumer 144 gather and analyse information to identify how transmission lines are: – insulated from supporting structures – protected from lightning strikes 146 Act. 7.3 assess the effects of the development of AC generators on society and the environment 147

xiv Stage 6 Physics syllabus grid 4. Transformers allow generated voltage to be either increased or decreased \ before it is used STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE describe the purpose of transformers in electrical circuits 136 perform an investigation to model the structure of a transformer to demo\ nstrate how secondary voltage is produced Act. 7.3 compare step-up and step-down transformers 137 solve problems and analyse information about transformers using: V Vn np s p s= 137 Act. 7.3 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 137 gather, analyse and use available evidence to discuss how difficulties of heat\ ing caused by eddy currents in transformers may be overcome 139 Act. 7.3 explain why voltage transformations are related to conservation of energy 139 gather and analyse secondary information to discuss the need for transfo\ rmers in the transfer of electrical energy from a power station to its point of u\ se 145 Act. 7.3 explain the role of transformers in electricity substations 142 discuss why some electrical appliances in the home that are connected to the mains domestic power supply use a transformer 136, 144 discuss the impact of the development of transformers on society 147 5. Motors are used in industries and the home usually to convert electrical\ energy into more useful forms of energy STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE describe the main features of an AC electric motor 124 perform an investigation to demonstrate the principle of an AC induction\ motor Act. 6.3 gather, process and analyse information to identify some of the energy transfe\ rs and transformations involving the conversion of electrical energy into m\ ore useful forms in the home and industry 124, 153 Act. 7.3 Module 3 From Ideas to Implementation 1. Increased understandings of cathode rays led to the development of telev\ ision STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE explain why the apparent inconsistent behaviour of cathode rays caused debate as to whether they were charged particles or electromagnetic waves 157 perform an investigation and gather first-hand information to observe th\ e occurrence of different striation patterns for different pressures in di\ scharge tubes Act. 8.1 explain that cathode ray tubes allowed the manipulation of a stream of charged particles 157 perform an investigation to demonstrate and identify properties of catho\ de rays using discharge tubes: – containing a Maltese cross – containing electric plates – with a fluorescent display screen – containing a glass wheel analyse the information gathered to determine the sign of the charge on \ cathode rays Act. 8.2 Act. 8.2 identify that moving charged particles in a magnetic field experience a force 164 solve problem and analyse information using: F = qvB sin θ F = qE and E V d = 162, 164 identify that charged plates produce an electric field 161

xv Stage 6 Physics syllabus grid describe quantitatively the force acting on a charge moving through a magnetic field: F = qvB sin θ 164 discuss qualitatively the electric field strength due to a point charge, positive and negative charges and oppositely charged parallel plates 160 describe quantitatively the electric field due to oppositely charged parallel plates 161 outline Thomson’s experiment to measure the charge/mass ratio of an electron 165 outline the role of: – electrodes in the electron gun – the deflection plates or coils – the fluorescent screen – in the cathode ray tube of conventional TV displays and oscilloscopes 167 2. The reconceptualisation of the model of light led to an understanding of\ the photoelectric effect and black body radiation STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE describe Hertz’s observation of the effect of a radio wave on a receiver and the photoelectric effect he produced but failed to investigate 182 perform an investigation to demonstrate the production and reception of \ radio waves Act. 9.1 outline qualitatively Hertz’s experiments in measuring the speed of radio waves and how they relate to light waves 175 identify data sources, gather, process and analyse information and use available evidence to assess Einstein’s contribution to quantum theory and its relation to black body radiation Act. 9.2 identify Planck’s hypothesis that radiation emitted and absorbed by the walls of a black body cavity is quantised 179 identify data sources, gather, process and present information to summarise the use of the photoelectric effect in photocells 184 Act. 9.3 identify Einstein’s contribution to quantum theory and its relation to black body radiation 179 solve problems and analyse information using: E = hf and c = f λ 181 Act. 9.3 explain the particle model of light in terms of photons with particular energy and frequency 179 process information to discuss Einstein and Planck’s differing views about whether science research is removed from social and political forces Act. 9.4 identify the relationships between photon energy, frequency, speed of light and wavelength: E = hf and c = f λ 179

xvi Stage 6 Physics syllabus grid 3. limitations of past technologies and increased research into the structur\ e of the atom resulted in the invention of transistors STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE identify that some electrons in solids are shared between atoms and move freely 189 perform an investigation to model the behaviour of semiconductors, inclu\ ding 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 field is applied across the semiconductor Act. 10.1 describe the difference between conductors, insulators and semiconductors in terms of band structures and relative electrical resistance 189 gather, process and present secondary information to discuss how shortcomings \ in available communication technology lead to an increased knowledge of \ the properties of materials with particular reference to the invention of th\ e transistor Act. 10.2 identify absences of electrons in a nearly full band as holes, and recognise that both electrons and holes help to carry current 191 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 Act. 10.2 compare qualitatively the relative number of free electrons that can drift from atom to atom in conductors, semiconductors and insulators 190 identify data sources, gather, process and present information to summarise the effect of light on semiconductors in solar cells Act. 10.3 identify that the use of germanium in early transistors is related to lack of ability to produce other materials of suitable purity 199 describe how ‘doping’ a semiconductor can change its electrical properties 193 identify differences in p and n-type semiconductors in terms of the relative number of negative charge carriers and positive holes 193 describe differences between solid state and thermionic devices and discuss why solid state devices replaced thermionic devices 199 4. Investigations into the electrical properties of particular metals at di\ fferent temperatures led to the identification of superconductivity and the exploration of possible appl\ ications STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE outline the methods used by the Braggs to determine crystal structure 208 process information to identify some of the metals, metal alloys and com\ pounds that have been identified as exhibiting the property of superconductivity and their critical temperatures 211 identify that metals possess a crystal lattice structure 209 perform an investigation to demonstrate magnetic levitation Act. 11.1 describe conduction in metals as a free movement of electrons unimpeded by the lattice 209 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 Act. 11.1 identify that resistance in metals is increased by the presence of impurities and scattering of electrons by lattice vibrations 209 gather and process information to describe how superconductors and the e\ ffects of magnetic fields have been applied to develop a maglev train Act. 11.1 describe the occurrence in superconductors below their critical temperature of a population of electron pairs unaffected by electrical resistance 215 process information to discuss possible applications of superconductivit\ y and the effects of those applications on computers, generators and motors and transmission of electricity through power grids 219 Act. 11.1 discuss the BCS theory 215 discuss the advantages of using superconductors and identify limitations to their use 217

xvii Stage 6 Physics syllabus grid Module 4 From Quanta to Quarks 1. Problems with the Rutherford model of the atom led to the search for a m\ odel that would better explain the observed phenomena STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE discuss the structure of the Rutherford model of the atom, the existence of the nucleus and electron orbits 230, 244 perform a first-hand investigation to observe the visible components of \ the hydrogen spectrum Act. 12.1 analyse the significance of the hydrogen spectrum in the development of Bohr’s model of the atom 236 process and present diagrammatic information to illustrate Bohr’s explanation of the Balmer series 236 Act. 12.1 define Bohr’s postulates 236solve problems and analyse information using: 1 1 1 2 λ       R nf 2 ni =− 233, 245 Act. 12.1 discuss Planck’s contribution to the concept of quantised energy 231 analyse secondary information to identify the difficulties with the Ruth\ erford- Bohr model, including its inability to completely explain: – the spectra of larger atoms – the relative intensity of spectral lines – the existence of hyperfine spectral lines – the Zeeman effect Act. 12.2 describe how Bohr’s postulates led to the development of a mathematical model to account for the existence of the hydrogen spectrum: 1 1 1 2 λ       R nf 2 ni =− 237, 244 discuss the limitations of the Bohr model of the hydrogen atom 239 2. The limitations of classical physics gave birth to quantum physics STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE describe the impact of de Broglie’s proposal that any kind of particle has both wave and particle properties 250, 259 solve problems and analyse information using: λ h mv = 249, 258 define diffraction and identify that interference occurs between waves that have been diffracted 250, 257 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 255 Act. 13.1 describe the confirmation of de Broglie’s proposal by Davisson and Germer 251, 257 explain the stability of the electron orbits in the Bohr atom using de Broglie’s hypothesis 253, 257

xviii Stage 6 Physics syllabus grid 3. The work of Chadwick and Fermi in producing artificial transmutations le\ d to practical applications of nuclear physics STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE define the components of the nucleus (protons and neutrons) as nucleons and contrast their properties 261, 278 perform a first-hand investigation or gather secondary information to ob\ serve radiation emitted from a nucleus using Wilson Cloud Chamber or similar detection device Act. 14.1 discuss the importance of conservation laws to Chadwick’s discovery of the neutron 261, 275 solve problems and analyse information to calculate the mass defect and \ energy released in natural transmutation and fission reactions 267, 277 define the term ‘transmutation’ 263 describe nuclear transmutations due to natural radioactivity 263 describe Fermi’s initial experimental observation of nuclear fission 269 discuss Pauli’s suggestion of the existence of neutrino and relate it to the need to account for the energy distribution of electrons emitted in β-decay 266, 276 evaluate the relative contributions of electrostatic and gravitational forces between nucleons 261 account for the need for the strong nuclear force and describe its properties 262 explain the concept of a mass defect using Einstein’s equivalence between mass and energy 267 describe Fermi’s demonstration of a controlled nuclear chain reaction in 1942 270, 275 compare requirements for controlled and uncontrolled nuclear chain reactions 271, 275 4. An understanding of the nucleus has led to large science projects and many applications STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE explain the basic principles of a fission reactor 280, 298gather, process and analyse information to assess the significance of the Manhattan Project to society 280 Act. 15.1 describe some medical and industrial applications of radioisotopes 283, 298identify 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 284, Act. 15.2 describe how neutron scattering is used as a probe by referring to the properties of neutrons 272, 298 identify ways by which physicists continue to develop their understanding of matter, using accelerators as a probe to investigate the structure of matter 286, 299 discuss the key features and components of the standard model of matter, including quarks and leptons 292, 298

xix Stage 6 Physics syllabus grid Module 5 Medical Physics 1. The properties of ultrasound waves can be used as diagnostic tools STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE identify the differences between ultrasound and sound in normal hearing range 305 solve problems and analyse information to calculate the acoustic impedan\ ce of a range of materials, including bone, muscle, soft tissue, fat, blood an\ d air and explain the types of tissues that ultrasound can be used to examine 312 describe the piezoelectric effect and the effect of using an alternating potential difference with a piezoelectric crystal 308 gather secondary information to observe at least two ultrasound images o\ f body organs Act. 16.1 define acoustic impedance: Z = ρυ and identify that different materials have different acoustic impedances 310, 311 identify data sources and gather information to observe the flow of bloo\ d through the heart from a Doppler ultrasound video image Act. 16.2 describe how the principles of acoustic impedance and reflection and refraction are applied to ultrasound 311 identify data sources, gather, process and analyse information to describe how ultrasound is used to measure bone density 315 Act. 16.3 define the ratio of reflected to initial intensity as: I I ZZ ZZr o= −     +     21 21 2 2 310 solve problems and analyse information using: Z = ρυ and I I ZZ ZZr o= −     +     21 21 2 2 310, 311 identify that the greater the difference in acoustic impedance between two materials, the greater is the reflected proportion of the incident pulse 310 describe situations in which A scans, B scans and sector scans would be used and the reasons for the use of each 312 describe the Doppler effect in sound waves and how it is used in ultrasonics to obtain flow characteristics of blood moving through the heart 315 outline some cardiac problems that can be detected through the use of the Doppler effect 316 2. The physical properties of electromagnetic radiation can be used as diag\ nostic tools STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE describe how X-rays are currently produced 321 gather information to observe at least one image of a fracture on an X-r\ ay film and X-ray images of other body parts Act. 17.1 compare the differences between ‘soft’ and ‘hard’ X-rays 322 gather secondary information to observe a CAT scan image and compare the information provided by CAT scans to that provided by an X-ray image for the same body part Act. 17.1 explain how a computed axial tomography (CAT) scan is produced 326 perform a first-hand investigation to demonstrate the transfer of light \ by optical fibres Act. 18.1 describe circumstances where a CAT scan would be a superior diagnostic tool compared to either X-rays or ultrasound 329 gather secondary information to observe internal organs from images prod\ uced by an endoscope Act. 18.1 explain how an endoscope works in relation to total internal reflection 334 discuss differences between the role of coherent and incoherent bundles of fibres in an endoscope 336 explain how an endoscope is used in: – observing internal organs – obtaining tissue samples of internal organs for further testing 337

xx Stage 6 Physics syllabus grid 3. Radioactivity can be used as a diagnostic tool STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE outline properties of radioactive isotopes and their half-lives that are used to obtain scans of organs 340, 343, 344perform an investigation to compare an image of bone scan with an X-ray \ image Act. 19.1 describe how radioactive isotopes may be metabolised by the body to bind or accumulate in the target organ 344 gather and process secondary information to compare a scanned image of a\ t least one healthy body part or organ with a scanned image of its diseased coun\ terpart Act. 19.2 identify that during decay of specific radioactive nuclei positrons are given off 342 discuss the interaction of electrons and positrons resulting in the production of gamma rays 342 describe how the positron emission tomography (PET) technique is used for diagnosis 349 4. The magnetic field produced by nuclear particles can be used as a diagno\ stic tool STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE identify that the nuclei of certain atoms and molecules behave as small magnets 355 perform an investigation to observe images from magnetic resonance image\ (MRI) scans, including a comparison of healthy and damaged tissue Act. 20.1 identify that protons and neutrons in the nucleus have properties of spin and describe how net spin is obtained 354 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 flow – distinguish between grey and white matter in the brain Act. 20.1 explain that the behaviour of nuclei with a net spin, particularly hydrogen, is related to the magnetic field they produce 355 gather and process secondary information to identify the function of the\ electromagnet, radio frequency oscillator, radio receiver and computer in the MRI equipment Act. 20.1 describe the changes that occur in the orientation of the magnetic axis of nuclei before and after the application of a strong magnetic field 355 identify data sources, gather and process information to compare the adv\ antages and disadvantages of X-rays, CAT scans, PET scans and MRI scans Act. 20.2 define precessing and relate the frequency of the precessing to the composition of the nuclei and the strength of the applied external magnetic field 356 gather, analyse information and use available evidence to assess the impact of\ medical applications of physics on society Act. 20.3 discuss the effect of subjecting precessing nuclei to pulses of radio waves 357 explain that the amplitude of the signal given out when precessing nuclei relax is related to the number of nuclei present 359 explain that large differences would occur in the relaxation time between tissue containing hydrogen bound water molecules and tissues containing other molecules 360

xxi Stage 6 Physics syllabus grid Module 6 Astrophysics 1. Our understanding of celestial objects depends upon observations made fr\ om Earth or from space near the Earth STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE discuss Galileo’s use of the telescope to identify features of the Moon 371 Act. 21.1identify 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 resol\ ution 377 Act. 21.2 discuss why some wavebands can be more easily detected from space 373 define the terms ‘resolution’ and ‘sensitivity’ of telescopes 375 discuss the problems associated with ground-based astronomy in terms of resolution and absorption of radiation and atmospheric distortion 373, 378 outline methods by which the resolution and/or sensitivity of ground-based systems can be improved, including: – adaptive optics – interferometry – active optics 378, 380 2. Careful measurement of a celestial object’s position in the sky (astrometry) may be used to determine its distance STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE define the terms parallax, parsec, light-year 388 solve problems and analyse information to calculate the distance to a st\ ar given its trigonometric parallax using: d1 p = Act. 22.1 explain how trigonometric parallax can be used to determine the distance to stars 388 gather and process information to determine the relative limits to trigo\ nometric parallax distance determinations using recent ground-based and space-bas\ ed telescopes Act. 22.2 discuss the limitations of trigonometric parallax measurements 389 3. Spectroscopy is a vital tool for astronomers and provides a wealth of in\ formation STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE account for the production of emission and absorption spectra and compare these with a continuous black body spectrum 390 perform a first-hand investigation to examine a variety of spectra produ\ ced by discharge tubes, reflected sunlight, or incandescent filaments Act. 22.3 describe the technology needed to measure astronomical spectra 390 analyse information to predict the surface temperature of a star from it\ s intensity/ wavelength graph Act. 22.4 identify the general types of spectra produced by stars, emission nebulae, galaxies and quasars 393 describe the key features of stellar spectra and describe how these are used to classify stars 395 describe how spectra can provide information on surface temperature, rotational and translational velocity, density and chemical composition of stars 393

xxii Stage 6 Physics syllabus grid 4. Photometric measurements can be used for determining distance and compar\ ing objects STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE define absolute and apparent magnitude 398 solve problems and analyse information using: Mm d 10 =−       5 log and I I 100A B= (mB – mA)/5 to calculate the absolute or apparent magnitude of stars using data and \ a reference star 400 explain how the concept of magnitude can be used to determine the distance to a celestial object 399 perform an investigation to demonstrate the use of filters for photometr\ ic measurements Act. 22.5 outline spectroscopic parallax 401identify data sources, gather, process and present information to assess the impact of improvements in measurement technologies on our understanding \ of celestial objects Act. 22.6 explain how two-colour values (i.e. colour index, B – V) are obtained and why they are useful 401 describe the advantages of photoelectric technologies over photographic methods for photometry 397 5. The study of binary and variable stars reveals vital information about s\ tars STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE describe binary stars in terms of the means of their detection: visual, eclipsing, spectroscopic and astrometric 411 perform an investigation to model the light curves of eclipsing binaries\ using computer simulation Act. 23.1 explain the importance of binary stars in determining stellar masses 408 solve problems and analyse information by applying: m + m GT12 2 r3 2 4 = π 420 classify variable stars as either intrinsic or extrinsic and periodic or non-periodic 413 explain the importance of the period– luminosity relationship for determining the distance of cepheids 416

xxiii Stage 6 Physics syllabus grid 6. Stars evolve and eventually ‘die’ STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE describe the processes involved in stellar formation 423 present information by plotting Hertzsprung–Russell diagrams for: – nearby or brightest stars – stars in a young open cluster – stars in a globular cluster Act. 24.1 outline the key stages in a star’s life in terms of the physical processes involved 428 analyse information from an HR diagram and use available evidence to det\ ermine the characteristics of a star and its evolutionary stage 437 describe the types of nuclear reactions involved in Main-Sequence and post- Main Sequence stars 425, 430 present information by plotting on a HR diagram the pathways of stars of\ 1, 5 and 10 solar masses during their life cycle 437 discuss the synthesis of elements in stars by fusion 425, 430 explain how the age of a globular cluster can be determined from its zero-age main sequence plot for a HR diagram 433 explain the concept of star death in relation to: – planetary nebula – supernovae – white dwarfs – neutron stars/pulsars – black holes 429, 431

Space Context 2 Figure 1.0.1 The knowledge of how things move through space, influenced by gravity, has transformed the way we work, play and think. 1 Modern physics was born twice. The first time (arguably) was in the 17\ th century when Newton used his three laws of motion and his law of universal gravi\ tation to connect Galileo’s equations of motion with Kepler’s laws of planetary motion. Then early in the 20th century, when many thought physics had almost finished the job of explaining the universe, it was unexpectedly born again. Einstein, in tr\ ying to understand the nature of light, proposed the special and general theorie\ s of relativity (and simultaneously helped launch quantum mechanics).Space was the common thread—Kepler, Galileo, Newton and Einstein were all trying to understand the motion of objects (or light) through space. Newton’s laws of mechanics and his theory of gravitation led to space exploration and artificial satellites for communication, navigation and \ monitoring of the Earth’s land, oceans and atmosphere. Einstein’s theory of relativity showed that mass and energy are connected, and that length, mass and even space and time are rubbery. Relativity has come to underlie most new areas of physics developed since then, including cosmology, astrophysics, radioactivity, particle physics, quantum electrodynamics, anything involving very precise measurements of\ time and the brain-bending ‘string theory’. So, whenever you use the global positioning system (GPS), consult Goog\ le maps, check the weather report or make an international call on your mobile phone, remember that the technology involved can be traced directly back to phy\ sics that started 400 years ago.

3 Figure 1.0.2 The revolution in our understanding of the universe started with the humble question of how projectiles move. InquIry aCtIvIty Go ballIstIC! The path through the air of an object subject only to gravity and air re\ sistance, is called a ballistic trajectory. If the object is compact and its speed is low, then air resistance is negligible and its trajectory is a parabola. Investigate parabolic trajectories using a tennis ball, an A4 piece of p\ aper, a whiteboard or a blackboard and a digital camera. 1 On a board about 2 m wide, draw an accurate grid of horizontal and vertical lines 10 cm apart. 2 With a firmly mounted camera, take a movie of a tennis ball thrown slowly\ in front of the board. Try different angles and speeds to get eight or more frames with the ball on screen, and get as much of a clear parabolic shape (including the point of maximum height) as you can. 3 Using video-editing software, view the best movie, frame by frame, on a computer. If your software allows it, create a single composite image with all the ball’s positions shown on one image, to show the parabolic trajectory. 4 If you can’t do that, then for each frame, on the board, and using th\ e grid, estimate the x - and y-coordinates of the ball’s centre to the nearest 5 cm or better. Some video software allows you to read the x- and y -coordinates (in pixels) by clicking on the image. 5 Plot a graph of x versus y to produce a graph of the parabolic trajectory. The graph might be a bit irregular because of random error in reading the blackboa\ rd scale. 6 Video the trajectory of a loosely crumpled-up piece of A4 paper. Now air resistance is NOT negligible. Does the trajectory still look like an ide\ al parabola?

1 cannonballs, apples, planets and gravity 4 projectile, trajectory, parabola, ballistics, vertical and horizontal components, Galilean transformation, range, launch angle, time of flight, inverse square law, law of universal gravitation, universal gravitation constant G, gravitational field g, test mass, central body, density, gravimeter, low earth orbit, gravitational potential energy, escape velocity, gravitationally bound 1. 1 Projectile motion Up and down, round and round Before Galileo Galilei (1564–1642), it was a common belief that an object such as a cannonball projected through open space (a projectile) would follow a path ( trajectory) through the air in a nearly straight line until it ran out of ‘impetus’ and then drop nearly straight down in agreement with the ideas of Aristotle. However, through experiments (Figure 1.1.1) in which he rolled balls off the edge of a table at different speeds and then marked the position of collisions with the ground, Galileo demonstrated that the trajectory of a falling ball is actually part of a parabola (see Figure 1.1.2). Remember that a parabola is the shape of the graph of a quadratic equation. The immediate result of Galileo’s discovery was that the art of firing cannonballs at your enemies became a science (ballistics). However, there were also more far-reaching, constructive consequences. What goes up must come down One of the powers of physics is that it enables us to find connections between seemingly unconnected things and then use those connections to predict new and unexpected phenomena. What started as separate questions about the shape of the path of cannonballs through the air and the speed of the Moon’s orbit around the Earth eventually led to the law of gravitation. This explained how the solar system works, but also led to the development of artificial satellites and spacecraft for the exploration of the solar system. Figure 1.1.1 Galileo’s laboratory notes on his experiments showing that projectiles follow parabolic paths

5 Space Opponents of Copernicus’ heliocentric universe claimed that if the Earth was rotating and orbiting the Sun, then a person jumping vertically into the air would have the ground move under their feet, so that they would land very far away from where they started. Galileo argued that a person jumping from a moving Earth is like a projectile dropped by a rider on a horse (representing the Earth) moving with a constant velocity (Figure 1.1.3). From the rider’s point of view, the projectile would appear to drop vertically, straight to the ground, accelerating downwards the whole time. A bystander who is stationary relative to the ground would see the rider, horse and projectile whoosh past and, like any other projectile, the dropped object would appear to follow a parabolic trajectory. Galileo argued that the parabolic motion of the projectile was made up of two separable parts: its accelerating vertical motion as seen by the rider, and its constant horizontal velocity (which is the same as that of the horse). Recall from your Preliminary physics course that these two contributions to velocity are called vertical and horizontal components (see in2 Physics @ Preliminary section 2.2, p 26). Galileo then argued that the Earth doesn’t zoom away under your feet because at the moment you jump upwards you already have the same horizontal component of velocity as the Earth’s surface. Relative to the Earth’s surface, your horizontal velocity is zero and so you land on the same spot. In connecting the two problems of projectile motion and a moving Earth, Galileo developed two important new concepts. The first is the idea that the parabolic trajectory of a projectile can be divided into vertical and horizontal components. The second is the idea of measuring motion relative to another moving observer (or ‘frame of reference’). The formula v B (relative to A) = v B – v A (see in2 Physics @ Preliminary, p 8) is used to transform velocities relative to different frames of reference. This formula is sometimes called the Galilean transformation. Components of a trajectory The ideal parabolic trajectory is an approximation that works under two conditions: 1 Air resistance is negligible (gravity is the only external force). 2 The height and range (horizontal displacement) of the motion are both small enough that we can ignore the curvature of the Earth. Describe Galileo’s analysis of projectile motion. Describe the trajectory of an object undergoing projectile motion within the Earth’s gravitational field in terms of horizontal and vertical components. a b Figure 1.1.3 Trajectory of the rider’s projectile as seen by (a) the rider and (b) an observer on the gro\ und Horizontal displacement Vertical displacement Figure 1.1.2 This graph of a parabolic trajectory shows the vertical and horizontal components of displacement separately. The projectile positions are plotted at equal time intervals.

cannonballs, apples, planets and gravity 1 6 75°90° 60° 45° 30° 15° Figure 1.1.4 For a fixed initial speed, maximum range occurs for a 45° angle of launch and maximum height occurs for a 90° angle of launch. The first condition is true for compact and low-speed projectiles. The second is true in almost all human-scale situations, typically at or near the Earth’s surface. Let’s analyse an example of ideal projectile motion. Recall that the acceleration due to gravity is g = 9.8 m s –2 (see in2 Physics @ Preliminary section 1.3). Here we are going to write it as a vector g. Clearly its direction is downwards. Consider the trajectory of a ball. We start by separating the horizontal and vertical components of its motion. While the ball is in the air, the only external force on it is gravity acting downwards, so there is a constant vertical acceleration a y = g , illustrated by the changing vertical spacing of projectile positions plotted at equal time intervals in Figure 1.1.2. The net horizontal force is zero, so, consistent with Newton’s first law, horizontal velocity is constant (a x = 0), which is clear from the equal horizontal spacing of the projectile positions plotted at equal time intervals in Figure 1.1.2. We can recycle the kinematics (SUVAT) equations from the Preliminary course. (See in2 Physics @ Preliminary section 1.3.) s = v t (1) s = u t + 1 2 a t 2 (4) s v = + u 2 t (2) v 2 = u 2 + 2as (5) v = u + at (3) Here we need to apply them separately to the vertical (y ) and horizontal (x) components of motion. Instead of displacement s , we’ll use ∆x = x f – x i for horizontal displacement and ∆ y = y f – y i for vertical displacement. We’ll put subscripts on the initial and final vertical velocities (u y and v y for example). We only need to use SUVAT equations 3, 4 and 5. θ i is the launch angle (between the initial velocity u and the horizontal axis). Remember to adjust the sign of g to be consistent with your sign convention. In problems involving gravity, up is normally taken as positive, making the vector g negative (i.e. g = –9.8 m s –2). In the syllabus, v x 2 = u x2 is included for completeness; but is unnecessary, as it can be derived from v x = u x. Some properties of ideal parabolic trajectories are: • At the maximum height of the parabola, vertical velocity v y = 0. • The trajectory is horizontally symmetrical about the maximum height position. • The projectile takes the same time to rise to the maximum height as it takes to fall back down to its original height. • For horizontal ground, initial speed = final speed. • Maximum possible height occurs for a 90° launch angle. The maximum possible range (for horizontal ground) occurs for a 45° launch angle (Figure 1.1.4). • Independent of their initial velocity, all objects projected horizontally from the same height have the same time of flight as one dropped from rest from the same height, because they all have a zero initial vertical velocity (Figure 1.1.5). activity 1.1 pRacTIcaL eXpeRIeNceSActivity Manual, Page 1 Table 1.1.1 Equations of projectile motion Horizontal components Vertical components ux = u cos θi uy = u sin θi vx = u x vy = u y + gt ∆x = u xt ∆y = u yt + 1 — 2gt 2 vx 2 = u x 2 vy 2 = u y 2 + 2g∆y

7 Space BaLLISTIcS IS a dRag A ir resistance or ‘drag’ introduces deceleration in both the vertical and horizontal directions, distorting the ballistic trajectory from an ideal parabola. As a projectile becomes less compact, air resistance increases relative to weight. The range decreases, the trajectory becomes less symmetrical, and the final angle becomes steeper. The launch angle for maximum range decreases. In extreme cases (for example, a loosely crushed piece of paper), the trajectory seems to approach Aristotle’s prediction: it moves briefly in a nearly straight line and then drops nearly vertically. no air resistance increasing air resistance Figure 1.1.6 The effect of increasing air resistance Figure 1.1.5 Multiflash photo of two falling objects. All horizontally projected objects have the same time of flight as an object dropped from rest from the same height. 100 mm Target practice You now have all the equations you need to ‘do some damage’, so let’s launch some projectiles. Safety warning! The following worked example may seem dangerously long because it illustrates several alternative methods of solving projectile problems rolled into one. Worked example q uestIon You throw a ball into the air (Figure 1.1.7). You release the ball 1.50 m above the ground, with a speed of 15.0 m s –1, 30.0° above horizontal. The ball eventually hits the ground. Answer the following questions, assuming air resistance is negligible. a For how long is the ball in the air before it hits the ground (time of \ flight)? b What is the ball’s maximum height? c What is the ball’s horizontal range? d With what velocity does the ball hit the ground? Solve problems and analyse information to calculate the actual velocity of a projectile from its horizontal and vertical components using: v x2 = u x2 v = u + at v y 2 = u y2 + 2a y ∆ y ∆ x = u xt ∆ y = u yt + 1 2ayt2 1.50 m Figure 1.1.7 Throwing a ball into the air

cannonballs, apples, planets and gravity 1 8 solutIon Always draw a diagram! Divide the motion into vertical (y) and horizontal (x) components. Choose the origin to be the point of release, so x i = y i = 0. This is not always the most convenient choice of origin . Use the sign convention + → & +↑ . Components of initial velocity u (Figure 1.1.8): u x = +u cos θ i = +15.0 cos 30.0° = +13.0 m s –1 uy = +u sin θi = +15.0 sin 30.0° = +7.50 m s –1 The only external force is gravity so vertical acceleration is g = –9.80 m s –2. There is no horizontal force, therefore a x = 0 m s –2 (constant horizontal velocity). initial velocity u ux uy θi = 30.0° final velocity v vx vy θf Figure 1.1.8 Components of initial and final velocities a The ball hits the ground when vertical displacement ∆y = –1.50 m. Find final vertical velocity: v y 2 = u y 2 + 2g ∆y = 7.50 2 + 2 × –9.80 × –1.50 = 85.65 v y = 85.65 = 9.255 m s –1 (must be downwards), so v y = –9.255 m s –1 Find t : v y = u y + gt = –9.255 = +7.50 + (–9.80) × t Rearrange, solve: t = −− − 9 255 750 9 80 .. . = 1.71 s The ball hits the ground 1.71 s after being thrown. Alternative method using the quadratic formula ∆y = u yt + 1 2 gt 2 = –1.50 m Substitute, rearrange: 1.50 + 7.50 × t + 1 2 × –9.80 × t 2 = 0 Quadratic, solve for t : t = −± +×× −× 75 7504 4901 50 24 90 2 .. .. . = –0.179 s or +1.71 s Two solutions: Reject the physically irrelevant negative solution, so t = 1.71 s. b At maximum height, vertical velocity v y = 0, so use v y 2 = u y 2 + 2g ∆y. 0 = u y2 + 2g∆y max = 7.50 2 + 2 × (–9.80) × ∆y max Rearrange, solve: ∆y max = 750 29 80 2 . . × = +2.87 m above the point of release, so height above ground = 2.87 m + 1.50 m = 4.37 m above the ground. Alternative method Use v y = u y + gt to find the time t when v y = 0, then use ∆y = u yt + 1 2gt 2 to find vertical displacement. c From part a, we know the time of flight t = 1.71 s. Horizontal displacement in this time is: ∆x = u xt = +13.0 m s –1 × 1.71 s = +22.2 m = 22.2 m (to the right)

9 Space d x-component of final velocity: v x = +13.0 m s –1 y-component of final velocity: v y = –9.255 m s –1 (down) (from part a) To find magnitude, use Pythagoras’ theorem (see Figure 1.1.8): v = vvxy22+ = 13 925522+ . = 15.96 ≈ 16.0 m s –1 Direction: tan θf = v vy x= 92 5 13 0 . . , so θ f = 35.4° down from horizontal Alternative magnitude calculation Negligible air resistance, ∴ mechanical energy = kinetic energy + gravitational potential energy and is conserved (see in2 Physics @ Preliminary section 4.2). Near the Earth’s surface, gravitational potential energy U = mgh. Using the ground as h = 0: K i + U i = K f + U f Cancel m: 1 2mvi2 + m ghi = 1 2mvf 2 + m ghf Substitute: 1 215.0 2 + 9.80 × 1.50 = 1 2vf2 + 0 Rearrange, solve: vf=+ ×× 15 02 9801 50 2.. . = 15.94 ≈ 15.9 m s –1 This is the same as for the previous method within the three-figure prec\ ision of the calculation, but doesn’t tell us the direction. In the previous example, time of flight was determined by the vertical component—the flight ended when the ball hit the ground. However, if the projectile hits a vertical barrier such as a wall, then the time of flight is determined by the horizontal component. Worked example q uestIon Suppose you kick a ball at 22.0 m s –1, 20.0° above the horizontal, towards a wall 21.0 m away (Figure 1.1.9). Ignore air resistance and the ball’s radius. a What is the ball’s time of flight (before hitting the wall)? b At what height does the ball hit the wall? c Is that the greatest height reached by the ball? solutIon Solve problems and analyse information to calculate the actual velocity of a projectile from its horizontal and vertical components using: v x2 = u x2 v = u + at v y 2 = u y2 + 2a y ∆ y ∆ x = u xt ∆ y = u yt + 1 2ayt2 Figure 1.1.9 The ball hits the wall. Choose the origin to be the initial position, so x i = y i = 0. Use the sign convention +↑ and + →. u x = 22.0 cos 20.0° (right) = +20.7 m s –1 uy = 22.0 sin 20.0° (up) = +7.52 m s –1

cannonballs, apples, planets and gravity 1 10 1. 2 Gravity In Ptolemy’s universe, the Sun, Moon and planets each had a separate clockwork- like mechanism to keep it in motion. Copernicus and Kepler greatly improved the picture, but Isaac Newton finally showed there was a single mechanism for them all—the force of gravity. The calculations of parabolic trajectories in section 1.1 work well close to the Earth’s surface where g is constant. However, if we’re going to venture out into space, we can’t use these simple equations. We need to look at the force of gravity on a larger scale. Newton’s law of universal gravitation Newton assumed several properties of gravity (see in2 Physics @ Preliminary section 13.5): • All ‘massive’ objects (that is, objects with mass) attract each other. The larger the masses, the larger the force. a The ball hits the wall when the horizontal displacement ∆x = +21.0 m. Substitute: ∆x = u xt = +21.0 m = +20.7 m s –1 × t Rearrange, solve: t= + + − 21 0 20 7 1 . . m ms = 1.014 s ≈ 1.01 s b The ball hits the wall at a height (vertical displacement) of ∆y = u yt + 1 2gt 2. Substitute, solve: ∆y = +7.52 × 1.014 + 0.5 × –9.80 × 1.014 2 = +2.587   The ball hits the wall ≈ 2.59 m above ground. c Check if the ball reaches maximum height of the parabola before hitting \ the wall. Time of flight = 1.01 s. v y = 0 at maximum height of parabola. Find the time taken to reach maximum height. Substitute: v y = 0 = u y + gt = +7.52 + –9.80 × t Rearrange, solve: t= 75 2 98 0 . . = 0.767 s which is less than time of flight The ball would reach the maximum height of the parabola before hitting t\ he wall, therefore the final height is NOT the maximum height for the trajectory. CheCkPoInt 1.1 1 Determine the horizontal acceleration of a projectile in flight. Determi\ ne its vertical acceleration. (Assume negligible air resistance.) 2 What angle of launch gives maximum horizontal range? What angle of launc\ h gives the maximum possible height? (Assume negligible air resistance.) 3 What is another name for air resistance? 4 If you throw a ball horizontally from the roof, and drop another at the \ same time, which one will hit the ground first? 5 Describe the two conditions that must apply so that a trajectory is a parabola. 6 List the 8 equations used in calculations of projectile motion. Explain why at least one of them is unnecessary.

11 Space • Like light intensity, the magnitude of the force decreases with distance according to the inverse square law (see in2 Physics @ Preliminary sections 6.1 and 15.1). However, astronomer Ismael Boulliau had suggested this before him. • The law of gravitation is universal—it applies throughout the universe and is responsible for the orbits of all the planets and moons. All this is expressed mathematically as the law of universal gravitation: FG mm dG= 12 2 where F G is the magnitude of the force of gravitational attraction between two masses m 1 and m 2 and d is the distance between their centres of mass (see in2 Physics @ Preliminary section 3.6). The universal gravitational constant G (‘big G ’) is 6.67 × 10 –11 N m 2 kg –2 in SI units. It should not be confused with ‘little g ’, 9.8 m s –2. More properties of gravitation: • The direction of the force acts along the line joining the centres of the two masses and is always attractive. • The formula is strictly correct for point masses and spheres, but works well for non-spheres. • The formula must be modified if one mass penetrates the surface of the other—gravity would not approach infinity if you were to burrow towards the centre of the Earth. • The resultant force on a mass due to the presence of other masses is the vector sum of the individual forces on the first mass due to each of the other individual masses. Worked example q uestIon Calculate the gravitational force between the Earth and the Moon. Data: Earth’s mass m E = 5.97 × 10 24 kg Moon’s mass m M = 7.35 × 10 22 kg Average Earth–Moon distance d EM = 3.84 × 10 8 m Universal gravitational constant G = 6.67 × 10 –11 N m 2 kg –2 solutIon FGmm dG EM EM= = ×× ××× 2 11 24 22 6671 05 9710 7351 0 3 .. . ( – . . ) 84 10 82 × = 1.98 × 10 20 N Define Newton’s Law of Universal Gravitation: FG mm d= 12 2 TR y ThIS! sligHtly attractiVe You can see the feeble force of gravity acting between objects in your garage. John Walker’s Fourmilab website describes step by step how you can perform a crude version of the Cavendish experiment in your own garage (see Physics Focus ‘How to weigh the Earth’ at the end of this chapter), using commonly found household items and a video camera. If you’re feeling too lazy to do it yourself, you can just download sped-up videos of the experiment in progress. Figure 1.2.1 Cavendish apparatus at home

cannonballs, apples, planets and gravity 1 12 PhysICs Feature Don’t unDerestImate the PoWer oF boreDom boreDom Part 1 B ored? Don’t just write graffiti—try revolutionising physics! In 16\ 65, an outbreak of bubonic plague around London closed Cambridge University, so Isaac Newton (aged 23) escaped for 2 years to his mother’s farm. He was not a very good farmer, so he fended off his city-boy boredom by inventing calculus and using prisms to show that white light is actually a mixture\ of colours (the spectrum). To top this off, when he saw an apple fall off his mother’s tree, he wondered if the force accelerating the apple downwards was also responsible for keeping the Moon orbiting the Earth. So he began formulating his theory of gravitation. His mathematics profe\ ssor was so impressed that a couple of years after Newton returned to Cambrid\ ge, he resigned and handed his professorship to Newton. After this initial investigation, it took Newton another 20 years to ful\ ly develop and finally publish his law of universal gravitation. Now let’s try an example with more than two masses. Worked example q uestIon A 1000 kg spacecraft is in the vicinity of the Earth–Moon system. The spacec\ raft is at the origin, the Moon is on the positive y-axis and the Earth is on the positive x-axis (Figure 1.2.2). Given that the Earth–spacecraft and Moon–spacecraft dista\ nces are 3.82 × 10 8 m and 3.91 × 10 7 m respectively, calculate the resultant gravitational force on the spacecraft. Data: Earth’s mass m E = 5.97 × 10 24 kg Moon’s mass m M = 7.35 × 10 22 kg Universal gravitational constant G = 6.67 × 10 –11 N m 2 kg –2 solutIon Force due to Moon: F SM = Gmm d SM SM 2 = 6671 0 1000 7351 0 39 11 0 11 22 72 .. (. ) – ×× ×× × = 3.207 N (+y direction) Force due to Earth: F SE = Gmm d SE SE 2 = 6671 0 1000 5971 0 38 21 0 11 24 82 .. (. ) – ×× ×× × = 2.729 N (+x direction) Magnitude of resultant: Fre s N =+ = 3 207 2729 421 22 .. . Direction: tan. . θ= 3 207 2 729 , so θ = +49.6° from the x-axis Moon Earth spacecraft Figure 1.2.2 A spacecraft in the Earth–Moon system FSE FSM Fres θ θ spacecraft Figure 1.2.3 Gravitational force vector diagram. Note; This does not resemble the position vector diagram in Figure 1.2.2. 1. The history of physics 3. Applications and uses of physics Figure 1.2.4 Graffiti carved on a stone at the King’s School in Grantham, England, by Isaac Newton, then about 10 years old

13 Space boreDom Part 2 I t is said that, at age 17, Galileo was attending church and, bored, was watching a lantern swing from the ceiling. Using his pulse as a stopwatch, he observed that the oscillation period of a pendulum barely \ changed as its amplitude gradually decreased. Back at home he started experiments confirming that the oscillation period depends on pendulum length L, but not at all on mass and only slightly on amplitude. He proposed (correctly) that pendulums could be used to create the first \ accurate mechanical clocks. We now know that, consistent with Galileo’s observations, for a simple mass-on-string pendulum the formula for oscillation period T is: T = 2π Lg The formula is an approximation, but if the maximum swing angle is less than 15° from vertical, the formula is correct within 0.5%. With this formula and a pendulum, you can measure the value of ‘little g’, which varies slightly between locations around the world. Figure 1.2.5 Young Galileo watches a swinging lantern in Pisa cathedral. Weight and gravitational fields As far as we know, the universal gravitational constant G is a fundamental constant, unchanging with position or time. But the acceleration due to gravity g is different on other astronomical bodies, at different heights and even at different positions on the Earth’s surface. Recall that weight w = mg is defined as the force on an object due to gravity (see in2 Physics @ Preliminary section 3.2); in other words, F G = w = mg. ‘Little g’, the acceleration due to gravity, can also be thought of as the strength of the gravitational field. However, the word weight is usually reserved for the case in which the gravitational field is due to a body of astronomical size, such as a planet. Any massive object can be described as being surrounded by a gravitational field, a region within which other objects experience an attractive force. Just as for electrical and magnetic fields (see in2 Physics @ Preliminary sections 10.6, 12.3 and 12.4), we can draw diagrams of gravitational field lines (Figure 1.2.6). The arrows on the field lines around a mass, point in the direction of the force acting on another (normally much smaller) test mass. Gravitational field is a vector (g ). The density of the field lines at any particular point in space represents g , the magnitude of the field at that point, and the direction of the field lines represents the direction of this vector. Field lines run in radial directions from point masses or spherical masses. Using a small test mass m , let’s derive g, the magnitude of the gravitational field due to a planet of mass M . The weight w of the test mass is defined as the force on m due to the planet’s gravity; that is: w = mg = F G = G mM d 2 activity 1.2pRacTIcaL eXpeRIeNceSActivity Manual, Page 5 Describe a gravitational field in the region surrounding a massive object in terms of its effects on other masses in it. Define weight as the force on an object due to a gravitational field.

cannonballs, apples, planets and gravity 1 14 a Divide both sides by test mass m: gF m G M d == G 2 Newton’s equation for gravitational force is symmetrical—you can choose either mass as the test mass and calculate the field around the other and still get the same magnitude of force when you multiply them together because of Newton’s third law (see in2 Physics @ Preliminary section 3.5)—the two masses are an action–reaction pair. However, if one of the masses is much larger (such as a planet), it is more convenient to calculate the field around it and use the smaller mass as the test mass. In astronomical situations where one of the bodies (such as a planet or star) is very much larger, the larger body is sometimes called the central body. Because of its large mass, the central body experiences negligible gravitational\ accelerations compared with a small test mass. Strictly speaking, the acceleration g is the acceleration of the test mass towards the common centre of mass of the whole system of two masses. However, if the central body is much larger than the test mass, we can ignore its acceleration, so g effectively becomes the acceleration of the test mass towards the central body. Gravitational field is a vector, so when calculating the resultant field due to several bodies, the approach is identical to calculating the resultant gravitational force due to several bodies—calculate the field due to each individual mass and then find the vector sum of the fields. Worked example q uestIon Calculate g E the magnitude of the gravitational field at the Earth’s surface. Data: Earth’s mass m E = 5.97 × 10 24 kg Earth’s radius r E = 6.37 × 10 6 m Universal gravitational constant G = 6.67 × 10 –11 N m 2 kg –2 solutIon gGM dE E= 2 The test mass is at the Earth’s surface, ∴ d = r E Substitute: g E = 6671 05 9710 63 7 10 11 24 2 6 .. (. ) – ×× × × = 9.81 m s –2 This should be a very familiar result. Variations in gravitational field Newton’s gravitation equation says that the magnitude of a planet’s gravitational field depends on the mass of the planet and decreases with distance from the planet’s centre. For example, on Earth, the value of g is 0.28% lower at the top of Mt Everest than at sea level. Also, because the Earth has a slightly larger radius near the equator than at the poles (the ‘equatorial bulge’), g is slightly lower at the equator. Except at the poles, there is an additional (fictitious) decrease in g activity 1.3 pRacTIcaL eXpeRIeNceSActivity Manual, Page 11 Figure 1.2.6 Gravitational field lines around the Earth (a) on an astronomical scale and (b) near the surface b

15 Space measurements that gets more severe as one approaches the equator. Because of the Earth’s rotation, the (downward) centripetal acceleration (see in2 Physics @ Preliminary section 2.3) of the ground appears to be subtracted from the true value of g . In fact this centripetal effect is responsible for the formation of the equatorial bulge, which was predicted by Newton before it was measured. The Sun and Moon also exert a weak gravitational force on objects at the Earth’s surface, so the magnitude and direction of g vary slightly, depending on the positions of the Sun and Moon. Variation in g caused by the positions of the Sun and Moon relative to the oceans is responsible for the pattern of tides. Strictly speaking, Newton’s gravitation equation written in the form above assumes that the planet is a perfectly uniform sphere. Close to the surface of a planet, local deviations from uniform density can result in small local changes in the magnitude and direction of g . The magnitude will be slightly larger than average when measured on the ground above rock (such as iron ore) of high density ρ (mass per unit volume) and lower above rock containing low-density minerals (such as salt or oil), an effect exploited by geologists in mineral exploration. The Earth’s crust is less dense than the mantle, so variations in thickness of the crust also affect g . Variation in g is measured using a gravimeter, the simplest kind being an accurately known mass suspended from a sensitive spring balance. Variations in g on larger distance scales around the Earth can be measured using satellites orbiting in low Earth orbit. Deviations in the orbital speed of satellites indicate that, in addition to the equatorial bulge, Earth is also slightly pear-shaped—pointier at the North Pole than the South Pole. hooke’S La W I saac Newton had enemies, and Robert Hooke (1635–1703) was probably his greatest. They argued bitterly over (among other things) who first suggested the inverse square law for gravity. Hooke was an accomplished experimental physicist, astronomer, microscopist, biologist, linguist, architect and inventor. He is best remembered for the discovery of (biological) cells and the invention of the spring balance (see in2 Physics @ Preliminary section 3.2), which exploits Hooke’s law F = ‑k x. The force F exerted by a spring is proportional to x, the change in spring length. The ‘spring constant’ k is a measure of the spring’s stiffness. A calibrated spring balance can measure weight, and, if used with an accurately calibrated mass, it can be used as a gravimeter to measure g. Figure 1.2.7 Hooke’s notes on the behaviour of springs Interactive Module

cannonballs, apples, planets and gravity 1 16 1. 3 Gravitational potential energy We’ve already mentioned gravitational potential energy (GPE) U = mgh (see in2 Physics @ Preliminary section 4.1) in part d of the worked example accompanying Figure 1.1.7. This formula for GPE is an approximation that only works close to the Earth’s surface, where g is very nearly constant. It’s good enough for projectile motion but, as you now know, g decreases with distance, so we need a more accurate formula to understand energy on an astronomical scale. Work and GPE For clarity we’ll use the symbol E P instead of U to denote gravitational potential energy calculated using the more accurate formula, even though the two symbols are really interchangeable. Potential energy is energy stored by doing work against any force (such as gravity) that depends only on position; therefore, gravitational potential energy E P is energy stored by doing work against the force of gravity. It can be shown (using calculus to derive the work done against gravity by changing the separation of two masses) that: EG mm rP=− 12 where m 1 and m 2 are two masses separated by a displacement (or separation) r and G is the universal gravitational constant. Note that E P is always negative and approaches zero as displacement r approaches infinity (Figure 1.3.1). EP for a separation r is the work that would need to be done by a force opposed to gravity in moving the masses together, starting at ‘infinite’ separation where E P = 0 and bringing them to a separation of r (with no net change in speed). Equivalently, E P is the work done by gravity while the masses are moved apart, starting at a separation of r to a position of ‘infinite’ separation (with no net change in speed). The gravitational potential energy does not depend on the path taken by the masses to get to their final positions; it depends only on the final separation r . The formula isn’t affected by the choice of which mass to move, although normally we treat a large mass such as the Sun or a planet as an immoveable central body and the smaller mass as a moveable test mass. The formula seems to imply that E P approaches negative infinity as the test mass approaches the centre of a planet. However, this formula no longer applies in this form once one mass penetrates the surface of the other. Explain that a change in gravitational potential energy is related to work done. Define gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational field: EG mm rP=− 12 CheCkPoInt 1.2 1 Write down Newton’s law of universal gravitation. 2 Define weight. 3 What part of Newton’s formula for gravitational force is responsible for the inverse square \ law behaviour? 4 What are two names for the quantity g? 5 List three factors responsible for (real) variations in g around the Earth. 6 Outline the differences between G and g.

17 Space Worked example questIon A piece of space junk of mass m J drops from rest from a position of 30 000 km from the Earth’s centre. Calculate the final speed v f it attains when it reaches a height of 1000 km above the Earth’s surface. Assume that above 1000 km, air resistance is negligible. Data: Earth’s mass m E = 5.97 × 10 24 kg Earth’s radius r E = 6.37 × 10 6 m Universal gravitational constant G = 6.67 × 10 –11 N m 2 kg –2 solutIon Air resistance is negligible, so total mechanical energy (kinetic + pot\ ential energy) is conserved. Assume that because of the enormous mass of the Earth, its ch\ ange in velocity is negligible. Use the Earth as the frame of reference. Don’t forget \ to convert to SI units. K i + EPi = K f + E P Cancel m J: 1 2 mJvi2 – G mm r JE i = 1 2 mJvf2 – G mm r JE f Substitute: 0– 6.67 10 6.67 10 –11 f– ×× × × =− × 59 71 0 30 01 0 1 2 24 6 2 . . v 1 11× × +× 59 71 0 63 71 00 10 24 6 . (. .) Rearrange, solve: vf –1 1 6.67 10 =× ×× ×× −     −− 25 9710 10 73 7 10 30 0 24 66 . ..    == −− 9030 903 11 ms kms . Note that this result doesn’t depend on m J. Figure 1.3.1 Plots of gravitational force (F G) and gravitational potential energy (E P) versus separation between a test mass m t and the Earth m E, starting at one Earth radius r E. The vertical F G and E P axes are not drawn to the same scale. FG EP –Gm tmE rE +Gm tmE rE 2rE 0 3r E 4rE 5rE separation r E2

cannonballs, apples, planets and gravity 1 18 Escape velocity: what goes up …? Isaac Newton showed that what goes up doesn’t necessarily come down. Normally, if one fires a projectile straight up, the object will decelerate until its velocity changes sign and it falls back down. However, if a projectile’s initial velocity is high enough, the 1/d 2 term in the gravity equation will cause the acceleration g to decrease with height too rapidly to bring the projectile to a stop so it will never turn back—it can ‘escape’ the planet’s gravitational field. The minimum velocity that allows this is called the escape velocity. Strictly speaking, it’s really a speed, because the initial direction of the projectile isn’t critical. Newton treated the projectile as a cannonball (with no thrust) so that, other than the initial impulse from the cannon, the only force acting on it is gravity. He conceived escape velocity using his force equation, and the escape velocity formula can be derived from it. However, a more modern derivation using energy is easier and similar to the previous worked example. Let m be the mass of a projectile, M the mass of a planet, v e the initial speed and r the initial position (the planet’s radius if you are on the surface). Assume air resistance is negligible, so total mechanical energy (KE + GPE) is conserved (see in2 Physics @ Preliminary section 4.2). K i + E Pi = K f + E Pf The escape velocity represents the minimum limiting case where the projectile ‘just reaches infinite displacement’ with zero speed; in other words, K f = E Pf = 0. 1 2 00 2 mv Gm M re −= + Rearrange, cancel m: vGM re= 2 If the initial speed is greater than this, the projectile will maintain a non-zero speed even as it approaches infinite displacement. Note that the escape velocity depends only on the planet’s mass and the projectile’s starting position r but not on the projectile’s mass. You may be puzzled that in the above derivation, the total mechanical energy (sum of KE and GPE) was exactly zero. This means that the escaping projectile has just enough (positive) KE to overcome its negative potential energy. When the mechanical energy is less than zero, there is not enough KE to overcome the GPE and the two masses are said to be gravitationally bound. When the total mechanical energy ME > 0, the KE can overcome the GPE and the two bodies are no longer bound together. This concept of binding also applies to the other three fundamental forces (including electromagnetism, which binds electrons to the nucleus of an atom). The escape velocity from the Earth’s surface is: 26 .671 0 ms –11 ×××× × == − 59 71 0 63 71 0 11 200 112 24 6 1 . . .k ms −1 Outline Newton’s concept of escape velocity. Explain the concept of escape velocity in terms of the: – gravitational constant – mass and radius of the planet.

19 Space This idealised escape velocity needs to be modified when applied to real spacecraft. First, the derivation ignores air resistance in the atmosphere (hundreds of kilometres thick), which would increase the escape velocity. Second, in a real rocket, engines produce an extra force—thrust—that can accelerate a craft to a higher altitude where the escape velocity is lower. It also ignores other sources of gravitational fields such as the Sun, Moon and planets. The escape velocity for a projectile under the gravitational influence of more than one body is given by: v e total = ve12 +ve 22 +  where v e total is the escape velocity for the total system and v e1, ve2 … are the escape velocities from the individual bodies within the system, calculated for the projectile using the same starting position in space. ULTIma Te fRISBee W as the first artificial object to leave the solar system a giant steel frisbee? In the 1950s, the US started testing nuclear bombs underground, to minimise atmospheric nuclear fallout. In 1957, during Operation Plumbbob in the Pascal-B test, a nuclear bomb was detonated at\ the bottom of a 150 m shaft sealed with concrete and a 900 kg, 10 cm thick steel cap. The steel cap fired upwards at enormous speed and was never seen again. Before the test, it was estimated that an extreme upper limi\ t for the speed of the steel cap would be 67 km s –1. This is well above the escape velocity for the whole solar system (43.6 km s –1 from Earth), starting an urban myth that it beat the Voyager probes (launched in 1977) out of the solar system. A later, more realistic, estimate suggested that, at most, the cap had a speed of 1.4 km s –1, reaching an altitude of less than 95 km. CheCkPoInt 1.3 1 Define under what circumstances it is suitable to use the simplified formula U = mgh for gravitational potential energy (GPE). 2 Write down the more accurate formula for GPE. 3 What limit does GPE approach as the separation of the two masses approac\ hes infinity? 4 On what factors does Newton’s idealised escape velocity depend? 5 What other factors affect escape velocity in realistic situations?

pRacTIcaL eXpeRIeNceS 20 1 cannonballs, apples, planets and gravity chapTeR 1 This is a starting point to get you thinking about the mandatory practical experiences outlined in the syllabus. For detailed instructions and advice, use in2 Physics @ HSC Activity Manual. aCtIvIty 1.1: ProjeCtIles A ball is rolled down a ramp, whose dimensions will be known to you. Predict where the ball will land. Equipment: aluminium track, ball bearing, metre ruler, measuring tape, shoe. Perform a first-hand investigation, gather information and analyse data to calculate initial and final velocity, maximum height reached, range and time of flight of a projectile for a range of situations by using simulations, data loggers and computer analysis. Discussion questions 1 List assumptions you have made in order to make an estimate of the range. 2 Assess how reliable is your method. 3 Explain how changing the original angle of the ramp will affect the range of the ball. aCtIvIty 1.2: DetermInInG the value oF a CCeleratIon Due to GravIty Use the motion of a pendulum to gather data to determine the acceleration due to gravity. Equipment: pendulum (string and mass), retort stand and clamp, stopwatch, metre ruler, data logger. Figure 1.4.1 Equipment set-up for this activity ruler ball bearing track retort stand string mass Perform an investigation and gather information to determine a value for acceleration due to gravity using pendulum motion or computer-assisted technology and identify reason(s) for possible variations from the value 9.8 m s –2. Figure 1.4.2 Pendulum apparatus set-up

21 Space Process the information you have gathered using the spreadsheet template. Complete the template to calculate the values of acceleration due to gravity on other planets. Discussion questions1 Determine which planet has the largest value for acceleration due to gravity at its surface. (Note that the gas giants Jupiter, Saturn, Uranus and Neptune don’t have a well-defined boundary between the atmosphere and a solid planet surface. The visible ‘surface’ is fluid, i.e. gas and/or liquid.) 2 Identify the factors that affect the acceleration due to gravity. Gather secondary information to predict the value of acceleration due to gravity on other planets. Present information and use available evidence to discuss the factors affecting the strength of the gravitational force. 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. Discussion questions 1 Explain what you did in order to make the experiment reliable. 2 Galileo originally thought that the period of the pendulum did not depend\ at all on the amplitude of the swing. Is this true? Explain how you can take this into account in your experiment. 3 How does your value compare with the accepted value? 4 Outline another method that would allow you to achieve the same aim. aCtIvIty 1.3: GravIty— out oF thIs WorlD Use the spreadsheet template to gather appropriate information to help you predict the acceleration due to gravity at the surface of other planets. Figure 1.4.3 Spreadsheet template

22 1 cannonballs, apples, planets and gravity Review questions chapter summary PhysICally sPeakInG Complete each definition by using a keyword taken from the list at the b\ eginning of the chapter.To approach infinite distance from a massive central body, a projectile must start with _________________ . The path of a projectile is known as a _________________ . The formula for converting velocities between frames of reference is the\ _________________ . A projectile’s maximum horizontal displacement is its _________________ . Universal gravitation and the intensity of light both follow the _________________ . Close to the Earth’s surface and subject only to gravity, a projectile’s path is a _________________ . The acceleration of a _________________ near the central body equals the gravitational field. Close to the Earth’s surface, all objects projected horizontally from the same height have \ the same _________________ . A _________________ is apparatus used to assist in mineral exploration. If drag is negligible, then a projectile’s range is determined only by initial velocity and _________________ . • If air resistance (drag) is negligible and g is very nearly constant (for example near a planet’s surface), then the trajectory of a projectile is a parabola. • The formula for transforming velocity within one frame of reference into one relative to another frame of reference is called the Galilean transformation: v B (relative to A) = v B – v A • Parabolic projectile motion can divided into vertical and horizontal components. The vertical component has a downward acceleration of g and the horizontal component has a constant velocity. • In parabolic projectile motion, the equations of motion are: Horizontal components: u x = u cos θ i, vx = u x, ∆x = u xt, v x 2 = u x2 Vertical components: u y = u sin θ i, vy = u y + gt, ∆y = u yt + 1 2g t2, v y 2 = u y2 + 2g ∆y • For horizontal ground, the maximum possible range occurs for a 45° launch angle. The maximum possible height occurs for a 90° launch angle. • All objects projected horizontally from a particular height have the same time of flight as one dropped from rest from the same height. • If a trajectory ends when the projectile hits the ground, time of flight is determined by the vertical component. If the projectile hits a vertical barrier, then time of flight is determined by the horizontal component. • Newton’s law of universal gravitation: FG mm dG= 12 2 • Gravitational acceleration (g ) towards a central body such as a planet is also called its gravitational field. It depends on the central body mass M and the distance d from its centre: gGM d = 2 The force of gravity on an object in that field is called its weight: w = mg. • Gravitational field g measured near the Earth’s surface varies slightly with distance from the Earth’s centre and density of the surrounding material. The centripetal acceleration of the Earth’s surface also decreases measured values of g (only an apparent effect). • Gravitational potential energy (GPE) is the work done by a force opposing gravity in moving masses together starting at ‘infinite’ separation and bringing them to a separation of r (with no net change in speed). • The simple formula for GPE (U = mgh) is an approximation that only works at or near the surface of a planet. The more accurate expression is: EG mm rP=− 12 • E P approaches zero as separation of the two masses approaches infinity. • The minimum initial velocity that a projectile needs to have in order to escape a planet’s gravitational field is called escape velocity: v GM re= 2

23 Space revIeWInG 1 Given that the Earth rotates, account for why when you jump straight up, you land on the same spot. 2 The high jump and the long jump both involve a run-up and then a jump. Using ideas from projectile motion, briefly compare and contrast the ideal characteristics of the run-up and jump for the two sports. 3 A projectile takes 1.25 s to reach its maximum height. What is its time of flight, assuming the ground is horizontal and drag is negligible? 4 Explain why (assuming negligible air resistance) all objects projected horizontally from the same height have the same time of flight as an object dropped from that height, regardless of their initial speed. 5 Predict what would happen to the magnitude of the gravitational force between two masses: a if one of the masses were doubled b if both masses were doubled c if the distance between the masses were doubled. 6 Describe how (and explain why) g would differ slightly from average at a point on the Earth’s surface above an oil deposit. 7 You’ve seen diagrams of electrical field lines around positive charges in which the arrows point outwards (see in2 Physics @ Preliminary section 10.6). Briefly discuss the possibility of a planet with gravitational field lines that point outwards. Propose how you would expect a test mass to behave there. 8 Without doing a calculation, deduce the speed at which a meteorite would hit the Earth’s surface if it started from rest at a very large distance from the Earth. Justify your answer. Ignore air resistance and gravity of other astronomical bodies. (Hint: The value is one already calculated elsewhe\ re in this chapter.) 9 Read the definition of gravitational potential energy E P in section 1.3 page 16. Explain why it is necessary to specify in the definition that the work is done with no net change in speed. (Hint: What other form of energy is involv\ ed?) solvInG Problems 10 Repeat the calculation in the worked example accompanying Figure 1.1.7, \ assuming that the ball lands on the flat roof of a 2.5 m high garage, instead of the ground. 11 Consider the worked example accompanying Figure 1.1.9. Keeping everything unchanged except initial speed: a What would the initial speed of the ball need to be if the ball hit the \ wall when it was just at its maximum possible height? What would be its time \ of flight? b What would the initial speed of the ball need to be if the ball hit the \ ground just in front of the wall? What be would its time of flight? 12 By considering the vertical component of velocity and ignoring air resis\ tance, derive an expression (containing initial speed u and launch angle θ) for the time taken for a projectile near the Earth’s surface to reach its maximum height. Then show that the time of flight for a projectile fired over ho\ rizontal ground is given by: t u g = 2 sin θ Solve problems and analyse information to calculate the actual velocity of a projectile from its horizontal and vertical components using: v x 2 = u x 2 v = u + at v y 2 = u y 2 + 2a y∆ y ∆ x = u xt; ∆ y = u yt + 1 2ayt 2 Solve problems and analyse information using: FG mm d = 12 2 Solve problems and analyse information to calculate the actual velocity of a projectile from its horizontal and vertical components using: v x 2 = u x 2 v = u + at v y 2 = u y 2 + 2a y∆ y ∆ x = u xt; ∆ y = u yt + 1 2ayt 2

24 1 cannonballs, apples, planets and gravity 13 A marble rolls horizontally off the edge of a 1.00 m high table with a speed of 3.00 m s –1. Calculate the speed with which it hits the ground, by: a using the equations of projectile motion b assuming the conservation of mechanical energy (using the simple version of the equation for GPE). 14 Repeat the calculation in the worked example accompanying Figure 1.2.2, \ with the positions of the Moon and Earth swapped. 15 Using your own mass, calculate the maximum force of gravity exerted by the planet Mars (m = 6.42 × 10 23 kg) on you, given that the closest approach of Mars to Earth is approximately 5.6 × 10 10 m. How close would you need to stand to the centre of mass of a 10 tonne truck for the magnitude of the gravitational force it exerts on you to be the same? (1 tonne = 1000 kg) 16 Show that g is 0.28% lower on top of Mt Everest (8848 m) than at sea level. Data: Mean Earth radius r E = 6.367 × 10 6 m. 17 Calculate the change in GPE in moving a 10 kg object from an initial position 1000 km above the surface of the Earth to a final position at a distance from the Earth equivalent to the mean orbital radius of the Moo\ n (r = 3.84 × 10 8 m). Assume the Moon is on the opposite side of its orbit at the time and you can ignore its gravitational effect. 18 Using the data and answer from Question 17, calculate the speed at which you would need to project the 10 kg object radially outwards from the initial position so that it would just reach the final position, stop an\ d fall back to Earth. (You can ignore air resistance above an altitude of ~1000 km.) 19 a Calculate the velocity required for a projectile to escape the Sun’s gravitational field (m Sun = 1.99 × 10 30 kg) if launched from the orbital radius of the Earth (1.50 × 10 11 m), if the Earth and other planets weren’t there. b Using part a and Earth’s escape velocity (11.2 km s –1), show that the total escape velocity from the solar system for a projectile launched from Earth is 43.6 km s –1. Assume the projectile doesn’t pass near other planets. extensIon 20 By considering the horizontal component of displacement for a projectile\ and your answer for Question 12, derive an expression (containing initial speed u and launch angle θ) for the horizontal range. Either by using calculus or by considering the properties of trigonometric functions, sh\ ow that the maximum range is attained for a launch angle of 45°. 21 A wildlife reserve ranger needs to hit a monkey in a tree with a tranqui\ liser dart in order to capture and examine it. The barrel of the dart gun is pointing exactly at the monkey. The angle between the barrel of the dart gun and the horizontal is not 90°. At the instant the ranger fires, t\ he monkey is startled and drops from rest to the ground below. Show that the dart will hit the monkey. (Hint: Show that by the time the dart reaches the horizontal position of the monkey, both the dart and the monkey have the same vertical position. Assume that air resistance is negligible.) Solve problems and analyse information using: FG mm d= 12 2 Solve problems and analyse information to calculate the actual velocity of a projectile from its horizontal and vertical components using: v x2 = u x2 v = u + at v y 2 = u y2 + 2a y∆ y ∆ x = u xt; ∆ y = u yt + 1 2ayt2 Review Questions

25 Space PhysICs FoCus hoW to WeIGh the earth Solve problems and analyse information using: FG mm d= 12 2 Analyse the forces involved in uniform circular motion for a range of objects, including satellites orbiting the Earth. Newton first tested his law of universal gravitation by showing that gravity was responsible for both the acceleration of a falling apple (9.8 m s –2) and the centripetal acceleration (see in2 Physics @ Preliminary section 2.3) of the orbiting Moon. However, he didn’t know the Earth’s mass M E or the value of G, but by using ratios of acceleration and distance squared, he showed that GM E = ad 2 is the same for an apple and the Moon, confirming that the same law of gravity applied to both. In 1798, the Earth’s mass was finally measured. Henry Cavendish (1731–1810) (who discovered hydrogen) measured the average density of the Earth ρ E to be 5.448 times denser than water (1000 kg m –3). The experiment was designed by John Michell (1724 –1793) (who first predicted the existence of black holes). Since the Earth’s radius was accurately known, this was equivalent to both ‘weighing the Earth’ and measuring the value of G. Cavendish used an extremely sensitive ‘torsional balance’ (Figure 1.4.4) to measure the tiny gravitational attraction between two small lead spheres m (attached to a thin 1.86 m rod) and two nearby large lead spheres M. From the angle of twist θ in the calibrated torsion wire, he determined the gravitational force between the spheres. From this, and using Newton’s equation for gravitational force, he calculated the Earth’s average density. Vibrations, temperature variations and slight air movements would disturb the apparatus, so it was built into a small sealed building, with Cavendish outside, operating the apparatus via cords and pulleys, and making observations through telescopes in the walls. The shift in position of the smaller masses was about 4 mm. 1 Because of Earth’s gravitational field, the Moon must accelerate towards Earth. Why doesn’t the Moon crash into Earth? 2 Using Cavendish’s value for Earth’s density ρ, the definition   ρ = mass volume and the mean radius r E = 6.37 × 10 6 m, calculate the Earth’s mass and compare it with the modern value. 3 Using Newton’s universal gravitation equation, Cavendish’s value for m E, the modern values for r E and g = 9.8 m s –2, calculate G and compare it with the modern value. 4 Using the modern value for G, calculate the total gravitational force between the spheres measured by Cavendish. (Hint: Calculate the force between a small and a large sphere in a single pair and double it. Ignore the thin rod etc.) Distance between sphere centres r = 0.225 m, large sphere mass M = 158 kg, small sphere mass m = 0.73 kg 5 Typical laser printer paper weighs 0.080 kg m –2. Calculate the size (in mm) of a square piece of printer paper that would have a weight on Earth equivalent to the force in Question 4 . 1. The history of physics torsion wire M M F r F m m θ Figure 1.4.4 (a) Schematic and (b) cutaway view of the apparatus used by Cavendish to ‘weigh the Earth’ a b

2 26 Explaining and exploring the solar system 2.1 Launching spacecraft In his book Philosophiae Naturalis Principia Mathematica (Principia for short), Newton used his law of gravity and laws of motion to explain Kepler’s laws of planetary motion, but also predicted the launching of artificial satellites and projectiles capable of escaping Earth’s gravity. Once you understand the physics behind something, it becomes possible to create new technology. In the case of space flight, it took 300 years to release the potential buried within Newton’s equations, via the 2000-year-old Chinese technology of fireworks. A bite-size history of rocketry For most of the history of rocketry, starting with the invention by the Chinese of gunpowder (the first rocket fuel or propellant) sometime between 300 b c e and 850 c e, the technology was driven mainly by military applications. The Chinese invented the first rockets or ‘fire arrows’ (fireworks tied to arrows). Some of the early milestones of this history are summarised in Table 2.1.1 in the Physics Feature ‘Fire Arrows’ on page 29. Only in the 20th century were civilian and scientific applications of rocketry (space exploration, Earth monitoring and communications) finally considered to be potentially as important as the military ones. Getting up there How many times have you been told to ‘stop dreaming and be practical’? For scientists and engineers, both dreams and practical know-how were potent tools to turn the understanding of the physics of gravity and motion into the technology of space travel. Most of the important pioneers of rocketry were inspired to pursue dreams of space travel by reading Jules Verne’s (1828–1905) story From the Earth to the Moon, or the stories of HG Wells (1866–1946). But they also had a solid grounding in physics and engineering. propellant, impulse, exhaust velocity, reaction device, thrust, payload, g-force, effectively weightless, lift-off, Kepler’s laws, satellite, ellipse, orbital velocity, eccentric, semimajor axis, periapsis, apoapsis, perihelion, aphelion, perigee, apogee, hyperbola, closed or stable orbit, geosynchronous, geostationary, medium Earth orbit, semi-synchronous, gravity assist, slingshot effect, re-entry, orbital decay, drag, lift, supersonic, hypersonic, shock wave, heat shield, ablation Figure 2.1.1 The Apollo 11 mission: the launch of a Saturn 5 booster—the largest rocket in history—on its way to deliver the first humans to the Moon

27 spacE Here we’ll concentrate on the important rocket researchers of the 20th century, the period in which the most rapid scientific advances took place. Below is a list their most important contributions. Konstantin Tsiolkovsky (1857–1935) Tsiolkovsky (also Tsiolkovskii), a Russian mathematics teacher, derived the basic rocketry equations including the ‘Tsiolkovsky rocket equation’ (see Physics Phile ‘This is rocket science’, p 30), used Newton’s definition of escape velocity to calculate it for Earth, and proposed multi-stage rockets and steerable thrusters. He advocated the use of liquid propellants (including liquid hydrogen) because they could be controlled using valves and would give a larger impulse than solids (see in2 Physics @ Preliminary section 4.5). He also wrote science fiction, predicting space stations, and space colonies using biological recycling of food and oxygen and airlocks for moving between a spacecraft and vacuum. Robert Goddard (1882–1945) Goddard, a US physicist, invented and tested many practical aspects of rockets, launching the first liquid-propellant rockets (liquid oxygen–gasoline) in 1926. He confirmed experimentally that rockets work in vacuum and showed that an hourglass-shaped de Laval steam nozzle greatly increased rocket efficiency. He launched the first scientific payload (camera, thermometer and barometer) that parachuted back to Earth, and steered rockets using vanes to direct exhaust gas and a gimballed (pivoted) nozzle under the automatic control of a gyroscope. He even experimented with very futuristic ion thrusters. Goddard attracted public ridicule by predicting travel to the Moon (see in2 Physics @ Preliminary Physics Phile p 43). He was mostly ignored by the US government, but he strongly influenced Oberth, von Braun and Korolyov (see below). Robert Esnault-Pelterie or REP (1881–1957) REP, a French aircraft designer, wrote on interplanetary travel, calculated the energies and flight times for trips to the Moon, Venus and Mars and proposed atomic energy to power interplanetary craft. With André Hirsch, he established the REP–Hirsch Prize for aeronautics, the first winner being Oberth (below). In 1931, Esnault-Pelterie conducted early experiments with liquid propellants (petrol–liquid oxygen, benzene–nitrogen peroxide and tetranitromethane) and developed a gimballed nozzle. Herman Oberth (1894–1989) The German physicist Oberth’s PhD thesis describing space travel was initially rejected as ‘utopian’ (though it was later accepted), so he published it as an influential book By Rocket into Planetary Space. In it he developed equations for space flight, proposed a design for a two-stage rocket using hydrogen–oxygen propellant and described craft for human space exploration. A follow-up book won him the REP–Hirsch Prize, which he used to purchase rocket engines for research assisted by his student Wernher von Braun. He worked (with von Braun) on both the Nazi V -2 rocket program and later the American rocket program. In 1953 he published Man in Space, proposing space stations, space-based telescopes and space suits. Figure 2.1.2 Konstantin Tsiolkovsky Figure 2.1.3 Robert Goddard Figure 2.1.4 Robert Esnault-Pelterie Figure 2.1.5 Herman Oberth activity 2.1 pRacTIcaL EXpERIENcEsActivity Manual, Page 14

Explaining and exploring the solar system 2 28 Wernher von Braun (1912–1977) As a student, von Braun (German physicist and aeronautical engineer) tested Oberth’s rocket engines. He was an early amateur researcher in the Spaceflight Society, which was taken over by the Nazis. Under the Nazis von Braun led the team that developed the alcohol–oxygen-fuelled A4 (or V-2) rocket used on Allied cities including London, killing and wounding thousands. After th\ e war, he joined the US army’s nuclear missile program. He dreamed of a civilian space program. In magazines and television, he publicly promoted exploration to the Moon and Mars with permanent colonies and orbiting space stations serviced by re-usable shuttle-type craft. In 1957 the USSR launched Sputnik, the first artificial satellite, shocking the US and leading to the ‘space race’ of the 60s between the USSR and the US. In response, a civilian space agency, the National Aeronautics and Space Administration (NASA), was formed, and in 1960 von Braun became director of its Marshall Space Flight Center. He became a major figure in the race to the Moon (the Apollo missions) announced in 1961 by President Kennedy. He led the project to construct the largest rocket ever built—the Saturn 5 (Figure 2.1.1). As is well known, the US won the race to the Moon in 1969, although they spent much of the 60s catching up to many USSR space ‘firsts’. The race also led to rapid development of civilian satellites for communications, Earth surface–atmospheric monitoring and scientific space exploration. Sergey Korolyov (also Sergei Korolev) (1907–1966) Korolyov, a Ukrainian-born Russian aircraft designer, was known only as the ‘Chief Designer’ of the USSR space program—his name was kept secret until his death. He helped set up the Jet Propulsion Research Group, which launched liquid-fuelled rockets in 1933, and led to the USSR government forming the Jet Propulsion Research Institute, with Korolyov as Deputy Chief. During Stalin’s Great Purge of 1938, Korolyov was imprisoned for 6 years, then released to become a rocket designer in the nuclear missile program, where he quickly improved on the design of captured Nazi V -2 missiles. Like his US rival von Braun, he dreamed of space travel and tried to convince his government to allow civilian projects. In 1957, he was allowed to launch the first artificial satellite Sputnik into orbit, starting the space race. He oversaw a string of space firsts (and failures): first animal (dog) in orbit, first unmanned Moon landing, first image of the unseen side of the Moon, first man and first woman in orbit, first extra-vehicular activity (space walk), first fly-pasts of Venus and Mars and more. Launch failures of four N1 boosters (rival to von Braun’s Saturn 5) and Korolyov’s death in 1966 helped to lose the race to the Moon for the USSR. Gerard O’Neill (1927–1992) O’Neill, a US physicist, invented the particle storage ring used in particle accelerators, and an early wireless computer network. He led development of a satellite positioning system—a precursor to the US global positioning system (GPS). Through conferences, papers and books, he was an energetic advocate of space travel. He proposed colonies in cylindrical spacecraft positioned at Figure 2.1.7 Sergey Korolyov Figure 2.1.6 Wernher von Braun Figure 2.1.8 Gerard O’Neill

29 spacE PHYSICS FEATURE ‘Lagrange points’. (These are five stable locations around pairs of orbiting bodies such as Earth and Moon at which a test mass can remain indefinitely, requiring little or no thrust.) He suggested that colonists would live on the inner surface of these cylinders 3 km in radius and 20 km long. The cylinders would spin, using centripetal force, to simulate gravity, and the inside would be covered with Earth-like geography. FIRE ARRowS T he following table is a very incomplete summary of some of the highlights of the 24-century long history of rocketry. 1. The history of physics 4. Implications for society and the environment 3. Applications and uses of physics Table 2.1.1 Some milestones in the pre-20th century history of rocketry 300 BCE to 850 At some time between these dates, the Chinese invent gunpowder and firew\ orks. 1150–1200 The Chinese develop the first rockets, ‘fire arrows’ (fireworks t\ ied to arrows), and projectile weapons including grenades and cannons are used against invad\ ing Mongols. 1200–1300 Invading Mongols bring Chinese rocket technology to Europe and the Arabi\ an Peninsula. 1529–1556 Conrad Haas (Austria) proposes the first designs for multi-staged rock\ ets. 1687 Isaac Newton publishes Philosophiae Naturalis Principia Mathematica containing his three laws of motion and the law of universal gravitation. He define\ s escape velocity and predicts artificial satellites. ~1730 German Colonel von Geissler manufactures rockets (up to 54 kg) for war\ fare. 1792, 1799 Sultan Tipu (India) uses iron-cased 1 km range rockets against British troops. 1803–1806 Impressed by Tipu, Sir William Congreve (Britain) develops more accurate 3 km range rockets up to 136 kg, which were used successfully against Napoleo\ n’s ships and against the Americans in the war of 1812. 19th century Engineers, scientists, inventors and crackpots experiment with non-milit\ ary applications of rockets. 1821 Rocket-propelled harpoons are used to hunt whales. 1861–1865 Rockets are used in the American Civil War. 1865 Science fiction writer Jules Verne (France) publishes From the Earth to the Moon. 1903 Konstantin Tsiolkovsky (Russia) publishes reports in which he applies rigorous physics to rocketry and discusses the possibility of space travel. Figure 2.1.9 The Chinese character for ‘rocket’ translates literally as ‘fire-arrow’. 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, O’Neill or von Braun.

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