HSC PHYSICS. Brian Shadwick

Transcription

1 HSC PHYSICS Brian Shadwick

2 2007 First published 2007 Reprinted 2007, 2008, 2009, 2010 Private Bag 7023 Marrickville NSW 1475 Australia Tel: (02) Fax: (02) All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of. ABN

3 Contents Introduction Verbs to Watch v vi Dot Points Space Motors and Generators From Ideas to Implementation From Quanta to Quarks vii ix xi xiii Questions Space 1 Motors and Generators 39 From Ideas to Implementation 81 From Quanta to Quarks 121 Summaries Space 161 Motors and Generators 181 From Ideas to Implementation 201 From Quanta to Quarks 219 Answers Space 237 Motors and Generators 247 From Ideas to Implementation 259 From Quanta to Quarks 271 Appendix Data Sheet 282 Formula Sheet 283 Periodic Table 284 Dot Point HSC Physics iii Contents

4 Notes Contents iv Dot Point HSC Physics

5 Introduction What the book includes the Board of Studies syllabus for the following topics in the Year 12 Physics course: Also included are typical experimental results for students to analyse if the third column of the syllabus indicates Format of the book The book has been formatted in the following way: 1. Main topic statement (column 1 of syllabus) 1.1etc Syllabus requirement from columns 2 and worth in an examination. As a rough rule, every two lines of answer might be worth one mark. Note that in many involved is worth only one mark. How to use the book You may have done work in addition to this with your teacher as extension work. Obviously this is not covered, but you may need to know this additional work for your school exams. spend more time revising later, and allow you to spend your study time more productively. Dot Point HSC Physics v Introduction

6 Verbs to Watch account/account for State reasons for, report on, give an account of, narrate a series of events or transactions. analyse Identify components and the relationships among them, draw out and relate implications. apply Use, utilise, employ in a particular situation. appreciate Make a judgement about the value of something. assess results or size. calculate clarify Make clear or plain. classify Arrange into classes, groups or categories. compare Show how things are similar and different. construct Make, build, put together items or arguments. contrast Show how things are different or opposite. critically (analyse/evaluate) Add a degree or level of accuracy, depth, knowledge deduce Draw conclusions. demonstrate Show by example. describe Provide characteristics and features. discuss Identify issues and provide points for and against. distinguish Recognise or note/indicate as being distinct or different from, note difference between things. evaluate Make a judgement based on criteria. examine explain Relate cause and effect, make the relationship between things evident, provide why and/or how. extract Choose relevant and/or appropriate details. extrapolate Infer from what is known. identify Recognise and name. interpret Draw meaning from. investigate justify Support an argument or conclusion. outline Sketch in general terms; indicate the main features. predict Suggest what may happen based on available data. propose Put forward (a point of view, idea, argument, suggestion etc) for consideration or action. recall Present remembered ideas, facts or experiences. recommend Provide reasons in favour. recount Retell a series of events. summarise Express concisely the relevant details. synthesise Put together various elements to make a whole. Verbs to Watch vi Dot Point HSC Physics

7 Space Dot Point Page Dot Point Page Use F = mg to determine the weight force of bodies on Earth and other planets Predict the acceleration due to gravity on other planets Perform an experiment to determine the acceleration due to gravity and identify reasons for possible variations from 9.8 m s Explain that a change in gravitational potential energy is related to work done. 6 GPE as the work done to move 2. Rocket launches and gravity Describe the trajectory of a projectile motion Solve projectile motion problems using horizontal and vertical components 2.4 Explain escape velocity in terms of the gravitational constant, and the mass and radius of the planet. 11 velocity. 12 used to explain the forces on an astronaut Perform an experiment to calculate 2.8 Analyse the changing acceleration of a rocket during launch in terms of the Law of Conservation of Momentum and the forces experienced by astronauts. 14 and rotational motion on rocket launches Analyse forces involved in uniform circular motion for a range of objects, including satellites orbiting Earth Solve problems about the centripetal force on a satellite in Earth orbit using: 17 geostationary orbits Outline the contribution to space of one of: Tsiolkovsky, Oberth, Goddard, relationship with G, the mass of the planet and satellite, and the radius of Periods Account for the orbital decay of satellites in LEO Discuss issues associated with safe and landing on the surface Identify that there is an optimum angle achieve this The Solar System and gravity 25 massive object in terms of its effects on other masses. 25 Gravitation Solve problems and analyse information using: Discuss factors affecting the strength of the gravitational force. 27 Law of Universal Gravitation in understanding and calculating the motion of satellites. 28 Dot Point HSC Physics vii Space

8 Dot Point Page Dot Point Page 3.6 Identify that a slingshot effect can be provided by planets for space probes Understanding time and space Outline the features of the aether model for the transmission of light Describe and evaluate the 4.3 Interpret the results of the 4.4 Discuss the role of the making determinations about competing theories Outline the nature of inertial frames of reference Perform an investigation to distinguish frames of reference Discuss the principle of relativity. 32 of the constancy of the speed of light. 32 thought experiments about mirrors and trains and discuss the relationship between thought and reality Identify that if c is constant, then space and time become relative Discuss the concept that length standards to the original metre standard Discuss the relationship between theory and the evidence supporting on relativity that were made many years before evidence was available to support it. 33 of special relativity in relation to the relativity of simultaneity. 34 of mass and energy Solve problems using: 34 of special relativity in relation to mass Solve problems using the relativistic of special relativity in relation to length contraction Solve problems using the relativistic of special relativity in relation to time dilation Solve problems using the time 4.22 Discuss implications of mass increase, time dilation, length contraction for space travel. 38 Answers to Space 237 Space viii Dot Point HSC Physics

9 Motors and Generators Dot Point Page Dot Point Page 1. Current-carrying conductors Discuss the effect, on the force on a variations in: and conductor Solve problems and analyse information about the force on 40 the force between long, parallel current carrying conductors using: 1.4 Solve problems using: Describe the forces experienced by a the forces Perform an experiment to demonstrate the motor effect. 44 of a force using: Solve problems and analyse information about simple motors using: Identify the motor effect is due to the 1.10 Describe the application of the motor effect in a galvanometer Describe the application of the motor effect in a loudspeaker Describe the main features of a DC electric motor and the role of each feature carrying coils or permanent magnets Generating electricity 51 generation of electricity by a moving magnet Perform an investigation to model the generation of an electric current by moving a magnet in a coil or a coil near a magnet Plan and perform an experiment to predict and verify the effect on a generated current of the distance between the coil and the magnet, the strength of the magnet, and the relative motion between the coil and the magnet. 52 B as 2.6 Describe generated potential difference conservation of energy. 54 of back emf in motors and that this opposes the supply emf Explain production of eddy currents 2.10 Explain how induction is used in cooktops Explain how eddy currents are used in electromagnetic braking Generators Describe the main components of a generator Describe the differences between DC and AC generators. 63 Dot Point HSC Physics ix Motors and Generators

10 Dot Point Page Dot Point Page 3.3 Compare the structure and function of a motor and a generator Discuss advantages and disadvantages of AC and DC generators and relate these to their use Perform an experiment to demonstrate the production of an alternating current Discuss energy losses that occur in transmission lines Assess the effects of the development of AC generators on society Assess the effects of the development of AC generators on the environment Analyse the competition between Edison and Westinghouse to supply electricity to cities Identify how transmission lines are insulated from supporting structures and protected from lightning Transformers Describe the purpose of transformers in electrical circuits. 71 transformers Identify the relationship between the ratio of the number of turns in the primary and secondary coils and the ratio of the primary to secondary voltage Solve problems using: Discuss how the heating effects of eddy currents are minimised in transformers Perform an experiment to model the structure and working of a transformer Discuss the need for transformers in electricity transmission from source to point of use Explain why voltage transformations are related to conservation of energy Discuss why some electrical appliances in the home use transformers Discuss the impact of the development of transformers on society Motors and energy changes Describe the main features of an AC electric motor Perform an investigation to demonstrate the principle of an AC induction motor Identify some of the energy transformations involving the conversion of electrical energy that occur in homes and industry. 79 Answers to Motors and Generators 247 Motors and Generators x Dot Point HSC Physics

11 From Ideas to Implementation Dot Point Page Dot Point Page 1. Cathode rays Explain that cathode ray tubes allowed the manipulation of charged particles Explain why the apparent behaviour of cathode rays caused debate as to whether they were charged particles or electromagnetic waves Perform an investigation to identify properties of cathode rays using discharge tubes containing: and analyse the information to determine the sign of the charge on cathode rays Perform an investigation to observe the different patterns of striations in cathode ray tubes at different pressures Identify that moving charged particles strength due to point, positive and negative charges Identify that charged plates produce strength due to oppositely charged parallel plates. 87 a moving charged particle in a using: F = qe F = qvbsin Outline the experiment by Thomson to measure the charge/mass ratio of an electron For cathode ray tubes, outline the role of: 2. The photoelectric effect and black body radiation 93 measuring the speed of radio waves and how they relate to light waves. 93 effect of a radio wave on a receiver and the photoelectric effect he produced but failed to investigate Perform an experiment to show the production and reception of radio waves. 94 radiation emitted and absorbed by the black body radiation. 96 black body radiation Explain the particle model of light in terms of photons with particular energy 2.8 Identify the relationships between light and wavelength using: and Solve problems using: and Summarise the use of the photoelectric effect in solar cells and photocells. 101 research is removed from social and political forces. 102 Dot Point HSC Physics xi From Ideas to Implementation

12 Dot Point Page Dot Point Page 3. Transistors Identify that some electrons in solids are shared between atoms and move freely Describe, in terms of band structures and relative electrical resistance, the differences in conductors, insulators, semiconductors Identify absences of electrons in nearly full bands as positive holes, and recognise that electrons and holes help to carry current. 105 number of free electrons in conductors, semiconductors and insulators Perform an experiment to model the behaviour of semiconductors Identify that the use of germanium in early transistors was related to the inability to produce other materials of suitable purity Describe how doping a semiconductor can change its electrical properties. 108 semiconductors in terms of their relative numbers of negative charge carriers and positive holes Describe differences between solid state and thermionic devices and why solid state replaced thermionic devices Discuss how shortcomings in communications technology led to an increased knowledge of the properties of materials with reference to the invention of transistors Assess the impact of transistors on society with particular reference to their use in microchips and microprocessors Identify data sources, gather, process and present information to summarise the effect of light on semiconductors in solar cells Superconductors Outline the methods used by the Braggs to determine crystal structure Identify that metals possess a crystal lattice structure Describe conduction in metals as a movement of free electrons unimpeded by the lattice Identify that resistance in metals is increased by the presence of impurities and scattering of electrons by lattice vibrations Describe the occurrence in superconductors below their critical temperature of a population of electron pairs unaffected by electrical resistance Identify some of the metals, alloys superconductivity and their critical temperatures Discuss the BCS theory Discuss the advantages of using superconductors and identify limitations to their use Explain why a magnet is able to hover above a superconducting material below its critical temperature Perform an investigation to demonstrate magnetic levitation Describe how superconductors and been applied to develop a maglev train Discuss possible applications of superconductivity and the effects of those applications on computers, generators, motors and the transmission of electricity through transmission grids. 120 Answers to From Ideas to Implementation 259 From Ideas to Implementation xii Dot Point HSC Physics

13 From Quanta to Quarks Dot Point Page Dot Point Page 1. Models of the atom Discuss the Rutherford model of the atom. 122 hydrogen spectrum in the development of the Bohr model Perform an experiment to observe the visible components of the hydrogen spectrum. 123 to a mathematical model to account for the hydrogen spectrum Solve problems and analyse information using: Process and present diagrams to show 1.9 Discuss the limitations of the Bohr model of the hydrogen atom. 130 model, including its inability to explain spectra of larger atoms, lines and the Zeeman effect Development of quantum physics 131 proposal that any kind of particle has both wave and particle properties Solve problems and analyse information using: 131 interference occurs between waves that have been diffracted. 132 proposal by Davisson and Germer Explain the stability of the electron orbits in the Bohr atom using 2.6 Assess the contribution made by Heisenberg and Pauli to atomic theory Development of nuclear physics 135 and contrast their properties Discuss the importance of the discovery of the neutron Describe nuclear transmutations due to natural radioactivity Perform an experiment to observe radiation emitted from a nucleus using a Wilson cloud chamber or similar device. 139 neutrino and the need to account for 3.8 Evaluate the relative contribution of electrostatic and gravitational forces between nucleons Account for the need for the strong nuclear force and describe its properties Explain the concept of mass defect mass and energy Solve problems to calculate the mass defect and energy released in natural a nuclear chain reaction in and uncontrolled chain reactions. 147 Dot Point HSC Physics xiii From Quanta to Quarks

14 Dot Point Page Dot Point Page 4. Applications of nuclear physics Explain the basic principles of a Manhattan Project to society Describe some medical and industrial applications of radioisotopes Describe the use of a named isotope in medicine, agriculture, and engineering Describe how neutron scattering is used as a probe by referring to the properties of neutrons Identify ways by which physicists continue to develop their understanding of matter using accelerators as a probe to investigate the structure of matter Discuss the key features and components of the standard model Answers to From Quanta to Quarks 271 From Quanta to Quarks xiv Dot Point HSC Physics

15 DOT POINT Space Dot Point HSC Physics 1 Space

16 1. The Earth has a gravitational field that exerts a force on objects both on it and around it Predict the weight of a 5 kg object on Earth compared to its weight on Jupiter, and explain the reasoning behind your prediction. The gravitational acceleration on Jupiter is about 24.8 m s Complete the table to compare mass and weight. Mass Weight 1.2 Use F = mg to determine the weight force of bodies on Earth and other planets Determine the weight of an object of mass 3.0 kg on Earth and on Mars which has a An object has a mass of 12 kg on Earth and a weight of N on Saturn. Calculate the Space 2 Dot Point HSC Physics

17 1.2.3 A mass is placed on a set of bathroom scales on Earth and the scales read 10 kg. The same scales and the mass are taken to the Moon to show that the mass of an object is constant regardless of where it is in the Universe. When placed on the scales on the Moon however, the scales read 1.67 kg. Account for this reading. 1.3 Predict the acceleration due to gravity on other planets The table shows masses and diameters of the Sun, our Moon and the planets in the Solar System. (a) Complete the fourth column of the table by ranking the gravitational force on each object from smallest (1) to largest (11) given the values for the Sun, the Earth and Pluto. on each object given the three values for the Moon, Earth and the Sun. Object Mass of object (kg) Diameter of object (km) Gravitational force (smallest (1) to largest (12)) Gravitational acceleration (m s 2 ) The Sun Mercury Venus Earth The Moon Mars Jupiter Saturn Uranus Neptune Pluto An object has a mass of 60 kg on Mars where the gravitational acceleration is 0.38 that of Earth. (a) What will be the mass of the object on Mars? (b) What will be the weight of the object on Earth? Dot Point HSC Physics 3 Space

18 (c) What will be the weight of the object on Mars? (d) What will be the mass of the object on a planet where the acceleration due to gravity is 2.5 times larger than that on Earth? (e) What will be the weight of the object on this planet? 1.4 Perform an experiment to determine the value of the acceleration due to gravity and identify reasons for possible variations from 9.8 m s Outline an experiment you have done to determine the acceleration due to gravity A group of students set up a pendulum and recorded the measurements shown in the table. Length of pendulum string (m) Time for 20 swings (s) Period of swing (s) (Period of swing) 2 (s 2 ) (a) Identify two factors which would have been kept constant if this experiment had been done correctly. (b) Complete the results table. Space 4 Dot Point HSC Physics

19 (c) What are these results telling us? (d) (e) Draw a graph of the period of swing (T) against the length of the pendulum (l). What conclusion can we draw from this graph? Explain your answer point and explain why it should be ignored. l T = 2π g (i) graph which does show the relationship between the period of a pendulum and its length. Use your graph to determine a value for the acceleration due to gravity as found by this experiment Dot Point HSC Physics 5 Space

20 1.4.3 Recall three reasons why the acceleration due to gravity at different places on the surface of the Earth varies slightly from the 9.8 m s 2 value we usually use. 1.5 Explain that a change in gravitational potential energy is related to work done Explain the relationship between the work done on an object which changes its position in a Identify the source of the work done when a satellite moves: (a) to a higher altitude orbit (b) to a lower altitude orbit A satellite has 4000 J of work done on it. Does it move to a higher or lower altitude orbit? Explain your answer. Space 6 Dot Point HSC Physics

21 1.5.4 A comet approaches the Sun and swings around it to travel back into the outer Solar System for years. The graphs show how the gravitational potential and kinetic energies of this comet change as it moves away from the Sun. Explain the shape of the two graphs KE E p Calculate the gravitational potential energy of a 2000 kg satellite which orbits the Earth at an altitude of km. The radius of Earth is 6378 km A satellite of mass 500 kg is boosted from an orbit of altitude km to one of altitude km. Given the diameter of Earth as km, its mass as kg, calculate the change in the gravitational potential energy of the satellite. Dot Point HSC Physics 7 Space

22 1.6.3 Explain, in terms of the principles of physics involved, why gravitational potential energy is a Satellite X has its orbit around Earth changed from an altitude of km to an altitude of km. Satellite Y has its orbit around Earth changed from an altitude of km to an altitude of km. Both satellites have a mass of 500 kg. (a) Predict the amount of work done on X compared to the amount done on Y and explain your reasoning. (b) Calculate the amount of work done on each satellite to see if your prediction was correct (a) Three spacecraft having masses m 1 > m 2 > m 3 are in the same stable orbit around planet X. Compare their gravitational potential energies and justify your answer. (b) The three spacecraft are now moved to an orbit with twice the radius relative to the centre of the planet. Compare the work which needs to be done on each. Justify your answer. (c) The three spacecraft each undergo orbital decay and fall to identical lower altitude orbits. Compare the changes in their kinetic energies. Justify your answer. Space 8 Dot Point HSC Physics

23 2. Many factors have to be taken into account to achieve a successful rocket launch, to maintain a stable orbit and to return to Earth. 2.1 Describe the trajectory of an object undergoing projectile motion within the Earth s Outline the characteristics of the motion of a projectile A projectile is launched at 40 m s 1 at 75º to the horizontal. Calculate the components of its launch velocity. 2.2 Describe Galileo s analysis of projectile motion The table shows the results of an experiment where a ball was rolled along a smooth, horizontal surface at 15 m s 1 and then over the edge of a 150 m drop. The ball left the surface and started to fall at time zero. Time (s) Speed of ball (m s 1 ) Dot Point HSC Physics 9 Space

24 2.3 Solve projectile motion problems using horizontal and vertical components and Newton s equations of motion from the top of a 196 m high cliff. Calculate: (b) its range (c) its velocity on hitting the ground (a) its horizontal velocity Space 10 Dot Point HSC Physics

25 (b) its maximum height (c) the velocity with which it is projected at an angle of 45 to the horizontal. Calculate the height at which the ball hits a vertical cliff 150 m away. 2.4 Explain the concept of escape velocity in terms of the gravitational constant, and the mass and radius of the planet show that escape velocity is independent of the mass of the object being put into orbit. Dot Point HSC Physics 11 Space

26 2.4.2 The escape velocity of Earth is 11.2 kps. That for Neptune is 23.6 kps. Give possible reasons to account for this difference Mercury has a mass of kg and a diameter of 4880 km. Venus has a mass of kg and a diameter of km. Predict which has the greater escape velocity and explain your reasoning. 2.5 Outline Newton s concept of escape velocity Identify why the term g-forces is used to explain the forces acting on an astronaut A rocket is accelerating from the launch pad at m s Space 12 Dot Point HSC Physics

27 2.6.3 A rocket is accelerating from between Mars and Jupiter at m s 2 on a 60 kg astronaut The diagram shows a stroboscopic photograph of a projectile which was released from (a) Calculate the horizontal component of the projectile as it left the track (b) Calculate the vertical component of the projectile as it left the track (c) Calculate the velocity of the projectile as it left the track. (d) Determine the maximum height of the projectile above the end of the track. Dot Point HSC Physics 13 Space

28 (f) Calculate the range of the projectile. 2.8 Analyse the changing acceleration of a rocket during launch in terms of the Law of Conservation of Momentum and the forces experienced by astronauts A rocket has a mass of 400 kg, 75% being fuel. It develops a thrust of 8000 N. (a) Calculate its initial acceleration. (b) Calculate its acceleration when half its fuel has been consumed. Space 14 Dot Point HSC Physics

29 2.8.2 are used to put astronauts into space A rocket has a mass of kg, including kg of fuel. It develops N of thrust. Calculate: (b) the theoretical maximum acceleration of the rocket Dot Point HSC Physics 15 Space

30 2.8.5 Explain, in terms of the Law of Conservation of Momentum, how a rocket takes off. 2.9 Discuss the effect of the Earth s orbital and rotational motion on the launch of a rocket Recall the optimum position on Earth and orientation of a launch in order to place a satellite in orbit around the Earth Justify your answer to above Space 16 Dot Point HSC Physics

31 2.10 Analyse the forces involved in uniform circular motion for a range of objects, including satellites orbiting Earth Choose an object which undergoes uniform circular motion (do not choose a satellite in orbit). With the aid of a labelled diagram, describe the forces acting on this object State the forces acting on a satellite in a stable orbit around Earth Solve problems to calculate the centripetal force acting on a satellite in orbit about Earth using: A 3000 kg satellite is orbiting Earth at an altitude of 250 km. Its orbital speed is kph. and the diameter of Earth is km. Calculate: (a) the centripetal force acting on it (b) its centripetal acceleration Dot Point HSC Physics 17 Space

32 A 150 kg satellite is orbiting Earth at an altitude of 272 km. Its orbital period is 90 minutes. Given that the diameter of Earth is km, and its mass is kg, calculate the centripetal force on the satellite Compare qualitatively, low Earth and geostationary orbits Recall a use for low Earth orbit and geostationary satellites Explain why each type of satellite is ideal for the use you have given in above Complete the table to compare low Earth and geostationary satellites. Low Earth satellites Geostationary satellites Space 18 Dot Point HSC Physics

33 2.13 Outline the contribution of one of the following to the development of space exploration: Tsiolkovsky, Oberth, Goddard, Esnault-Pelterie, O Neill or von Braun. the mass of the planet, the mass of the satellite and the radius of the orbit qualitatively and quantitatively Imagine satellites orbiting Earth and Jupiter, both at altitudes of 2000 km. Compare their Three moons around planet X have masses M, 9 M and 16 M. speeds. Dot Point HSC Physics 19 Space

34 R, 9 R and 16 R respectively, calculate the ratio of their orbital speeds Three identical moons are in orbit around planets of masses M, 9 M and 16 M. The planets have the same radii Calculate the orbital speed of the Earth around the Sun given the mass of the Sun is kg, and its diameter is km. The mass of the Earth is kg, its diameter is km, and the distance between the Sun and Earth is km. Space 20 Dot Point HSC Physics

35 2.15 Solve problems using Kepler s Law of Periods: Calculate the orbital period of Deimos, one of the two moons of Mars. Its average distance from Mars is km and its irregular shape averages about 13 km across. The mass of Mars is kg, and its diameter is 6794 km Calculate the altitude of an Earth satellite with a period of 12 hours. The mass of the Earth is kg of Periods to calculate the missing data in the following table: Moon Radius of orbit (km) Orbital period (Earth days) Miranda A 1.41 Ariel B Titania C 8.71 Oberon Dot Point HSC Physics 21 Space

36 (a) the period of a satellite which orbits with a radius of km (b) the orbital radius of a satellite which has an orbital period of 4.0 hours Io, closest to the planet, Europa, Ganymede and Callisto, furthest from the planet, are the four moons of Jupiter discovered by Galileo in There is an interesting relationship between the orbital period (T from the planet. In other words: T Io = 0.5 T Europa T Europa = 0.5 T Ganymede Given the mass of Jupiter as kg and the orbital radius of Ganymede as km, calculate: (a) the orbital radius of Io Space 22 Dot Point HSC Physics

37 2.16 Account for the orbital decay of satellites in LEO Explain, in terms of the principle of physics involved why satellites in low Earth orbits will eventually fall to Earth Two students are discussing orbital decay. Maria says that frictional forces between the spacecraft and the atmosphere are responsible. Edward says that this is incorrect and that statements Discuss issues associated with safe re-entry into the Earth s atmosphere and landing on the Earth s surface (b) on the space shuttle Dot Point HSC Physics 23 Space

38 Explain the concept of Identify that there is an optimum angle for re-entry of a spacecraft into the Earth s atmosphere and the consequences of failing to achieve this Space 24 Dot Point HSC Physics

39 3. The Solar System is held together by gravity calculate its magnitude. 3.3 Solve problems and analyse information using: Calculate the gravitational force between the Moon and the Earth. The mass of the Moon is kg, that of the Earth is kg, the diameter of the Moon is 3467 km, that of the Earth is km and the distance between them is about km. Dot Point HSC Physics 25 Space

40 3.3.2 The mass of Jupiter is kg. Its diameter is km. Calculate: (a) the weight of a 10 kg object on its surface (b) the value of its acceleration due to gravity at its surface The radius of the Earth is 6378 km and its mass is kg. Calculate the acceleration at an altitude of m Two moons have masses M and 4 M and radii R and 4 R respectively. Compare their accelerations due to gravity The mass of Mercury is kg. Its diameter is 4880 km. Compare its gravitational acceleration with that of Pluto, mass kg, diameter 2320 km. Space 26 Dot Point HSC Physics

41 3.3.6 Calculate the gravitational force between two 60 kg students two metres apart. 3.4 Discuss factors affecting the strength of the gravitational force Predict the effect on the gravitational force between two objects of: (a) halving the distance between them... (b) doubling both masses... (c) doubling one mass and halving the distance between them Calculate how far an astronaut would need to be away above the Earth in order for his weight (a) An astronaut is in a satellite orbiting the Earth at an altitude of one Earth radius. What is the gravitational force acting on him compared to his weight on the surface of the Earth? Justify your answer. (b) The satellite is boosted to double this altitude. What is the new gravitational force acting on the astronaut? (c) Calculate the orbital velocity of the astronaut in this higher orbit. Dot Point HSC Physics 27 Space

42 3.5 Discuss the importance of Newton s Law of Universal Gravitation in understanding and calculating the motion of satellites Given that the gravitational force holding an orbiting satellite in a stable orbit is also the centripetal force acting on it due to its orbital speed, determine the relationship between the orbital speed and the mass of the satellite A satellite has an orbital period of T and an orbital radius of R formula. 3.6 Identify that a slingshot effect can be provided by planets for space probes Explain the slingshot effect Explain the role of gravitational attraction between a spacecraft and a planet as the spacecraft moves around the planet and accelerated due to the slingshot effect. Space 28 Dot Point HSC Physics

43 4. Current and emerging understanding about time and space has been dependent upon earlier models of the transmission of light. 4.1 Outline the features of the aether model for the transmission of light List the properties of the aether as predicted by scientists in the 1800s, and justify their perception of the need for each property. Property of the aether Justification 4.2 Describe and evaluate the Michelson-Morley experiment Dot Point HSC Physics 29 Space

44 Interpret the results of the Michelson-Morley experiment Discuss the role of the Michelson-Morley experiment in making determinations about competing theories that time. 4.5 Outline the nature of inertial frames of reference Space 30 Dot Point HSC Physics

45 4.5.2 An astronaut tied her mascot to a string and hung it from the ceiling. One day she noticed that instead of hanging straight down, it hung at an angle. (a) Account for this. (b) Identify the frame of reference when it hangs straight down. Justify your answer Identify the frame of reference of the spaceship when the mascot hangs at an angle. Justify your answer. 4.6 Perform an investigation to distinguish between non-inertial and inertial frames of reference of reference If you are in an inertial frame of reference you cannot tell if you are moving at a constant velocity or if you are stationary. Why not? Dot Point HSC Physics 31 Space

46 4.7 Discuss the principle of relativity Explain the principle of relativity. speed of light Outline the essential problem with light, the aether and the principle of relativity. 4.9 Analyse and interpret some of Einstein s thought experiments involving mirrors and trains and discuss the relationship between thought and reality Space 32 Dot Point HSC Physics

47 4.10 Identify that if c is constant, then space and time become relative metre standard Explain why the standard of length changed from being the distance between two lines on a 4.12 Analyse information to discuss the relationship between theory and the evidence supporting it using Einstein s predictions based on relativity that were made many years before evidence was available to support it theory of relativity. Outline one piece of evidence in support of his theory Dot Point HSC Physics 33 Space

48 4.13 Explain qualitatively the consequence of special relativity in relation to the relativity of simultaneity Explain qualitatively the consequence of special relativity in relation to the equivalence between mass and energy Solve problems using: Explain why the concept of rest mass is needed. Space 34 Dot Point HSC Physics

49 A proton has a rest mass of kg. Calculate its rest energy That is, in all exothermic or endothermic chemical processes, the energy involved is actually a result of mass to energy or from energy to mass. (a) This would seem to contradict the law of conservation of energy and the law of conservation of mass. Comment on this statement. Comment on this idea. (c) Which way would the energy/mass conversion work for: (i) an endothermic process? (ii) an exothermic process? 4.16 Explain qualitatively the consequence of special relativity in relation to mass. Dot Point HSC Physics 35 Space

50 4.17 Solve problems using: The mass of an electron at rest is kg. Calculate its mass in a TV tube when it is moving at 0.15 c Calculate the mass of a proton, rest mass kg in a linear accelerator when it is moving at 0.8 c Explain qualitatively the consequence of special relativity in relation to length contraction Solve problems using: c. Calculate the apparent length of the spacecraft as seen from Earth stationary length. Calculate how fast it is travelling. Space 36 Dot Point HSC Physics

51 c. Describe its shape as seen by an observer on Earth Explain qualitatively the consequence of special relativity in relation to time dilation Solve problems using: An astronaut travelling at 0.5 c takes 10 hours ship time to reach his destination. Calculate how much time has passed on Earth c. The pilot and his girlfriend on the planet each wave at the other for 4.0 seconds. (a) Calculate how long the pilot sees his girlfriend waving. (b) Calculate how long the girlfriend sees the pilot waving. (c) Account for these answers being the same value. Dot Point HSC Physics 37 Space

52 Star X is 8.0 ly from Earth. A spaceship travels at 0.5 c to reach the star. (a) Calculate how long the trip takes as measured by an observer on Earth. (b) Calculate how long the trip takes as measured by the astronauts in the ship. (c) Calculate the distance travelled as measured by the astronauts. (d) Calculate the speed of the ship as measured by the astronauts Discuss the implications of mass increase, time dilation, and length contraction for space travel. Space 38 Dot Point HSC Physics

53 DOT POINT Answers Dot Point HSC Physics 235 Answers

54 Notes Answers 236 Dot Point HSC Physics

55 Space Weight on Jupiter will be 2.53 times greater than its weight on Earth (124 N compared to 49 N) Amount of matter in an object Measured in kilograms Does not vary Cannot be zero Is a scalar quantity Mass Weight Measure of gravitational force on an object Measured in newtons Varies as gravitational acceleration varies Can be zero Is a vector quantity N, N m s 2, N The bathroom scales are calibrated in kilograms, but actually measure weight because they work by the mass on them force is only about one sixth that of Earth, so the spring will only compress about one sixth as much. The scales therefore read 1.6 kg instead of 10 kg Correct values for (a) and (b) given in table. Your estimates may be different, but see how close you were. Gravitational Object Mass of object (kg) Diameter of object (km) Rank of gravitational force (smallest (=1) to largest (=12)) Gravitational acceleration (m s 2 ) The Sun Mercury Venus Earth The Moon Mars Jupiter Saturn Uranus Neptune Pluto (a) 60 kg (b) (c) (d) (e) 588 N N 60 kg 1470 N Answers will vary check with your teacher if unsure. Dot Point HSC Physics 237 Space

56 1.4.2 A group of students set up a pendulum and recorded the measurements shown in the table. Length of pendulum string (m) Time for 20 swings (s) Period of swing (s) (Period of swing) 2 (s 2 ) (a) (b) (c) (d) (e) (f) The mass of the pendulum bob (although this would not affect the results), the angle of swing, the person doing the timing, the timer used. See above. As the length of the pendulum increases, the period of swing increases. See graph (right). Only that as length increases, period of swing increases we cannot express this as a not a straight line. The period for pendulum length 0.75 m seems to be incorrect. It should be treated as an (g) g 2 l/t 2 (h) You should graph length of the pendulum versus period 2. 2 /gradient of this graph = 9.49 m s 2. Period squared (s 2 ) Length (m) Value for acceleration due to gravity will vary as altitude varies, because the Earth is not a perfect sphere, so at sea level at poles), type of, and amount of rock in the crust underneath the object could cause very slight variations Work is done on an object whenever an applied force causes a change in energy of the object. When a gravitational force (or the gravitational potential energy the object loses (or gains) (a) external force (thrust from engines) (b) gravity gravity, then it moves to a lower orbit. If the source is its engines and these are providing an impulse away from the Earth, then it moves to a higher orbit. gravitational force as it travels away from the Sun, so its kinetic energy decreases and will also become zero if it reaches J J falls towards the planet, its gravitational potential energy will decrease (its kinetic energy increases). If GPE decreases from zero, it must become negative in value (a) Your prediction could be anything less for X, less for Y, same for each. The most logical is the same for each based on the fact that they both have their orbit increased by the same amount. Space 238 Dot Point HSC Physics

57 (b) Calculations show that the initial E P of X is J for an increase of J. The initial E P of Y is J also for an increase of J (a) The gravitational potential energy of m 1 > m 2 > m 3 proportional to the masses of the objects. (b) (c) The work needed to put the three spacecraft into a higher, identical orbit is directly proportional to their masses also (W = Fs = mgs. Note that g is the value of the acceleration due to gravity of planet X at the altitude of the orbit). This makes the work done on m 1 > m 2 > m 3. As the objects fall to a lower orbit they lose gravitational potential energy and gain kinetic energy. If they all end up at the same altitude, then the loss of E P and gain in KE for each will be the same, but E P loss will depends on their masses, so KE gain will also. Therefore, KE of m 1 > m 2 > m Horizontal component of its motion is constant velocity (zero acceleration), while the vertical component is accelerated by gravity Horizontal component is m s 1, vertical component is m s Horizontal and vertical components of the motion of a projectile are independent of each other. Horizontal component of its motion is constant velocity (zero acceleration). Vertical component is constantly accelerated (by gravity) Using Pythagoras, at t = 1, = vector sum of v y + 15 so 2 v y = therefore v y = 9.8 m s 1 at t = 2, = vector sum of v y + 15 so 2 v y = therefore v y = 19.6 m s 1 at t = 3, = vector sum of v y + 15 so 2 v y = therefore v y = 29.4 m s 1 at t = 4, = vector sum of v y + 15 so 2 v y = therefore v y = 39.2 m s 1 So, change in velocity each second = 9.8 m s 1, so acceleration is constant at 9.8 m s (a) 6.32 s (b) (c) m 162 m s 1 at 22.5º down from the horizontal (a) 160 m s 1 (b) (c) 68.9 m up at m s 1 at 12.9º to the horizontal m Given E P = Gm 1 m 2 /r = ½m 1 v 2 (m 2 = mass planet, m 1 = mass satellite) v 2 = 2Gm 1 m 2 /m 1 r i.e. v Gm 2 /r i.e. escape velocity is independent of the mass of the satellite Either the mass of Neptune is larger than the mass of Earth, or its radius is smaller, or the combination mass/radius is larger for Neptune than for Earth For Mercury, mass/radius = , for Venus this ratio is , therefore this would indicate escape velocity for 1, for Venus it is m s 1.) Dot Point HSC Physics 239 Space

58 2.6.1 It is simpler to use than an absolute force scale, and communicates the same relative forces acting on astronauts of different masses (a) (b) (a) m s 1 (b) m s 1 (c) (d) (e) (f) 2.43 m s 1 at 75.1º up from horizontal 0.28 m 0.84 s m (a) 10.2 m s 2 (b) 22.2 m s 2 (c) discarded, lessening the mass for the second stage engines and so making their thrust more effective and it also reduces the 4 g-force t Time after lift-off As fuel is used the mass of the rocket decreases and because the thrust is constant, the force on the rocket stays the same, so the acceleration (as per F = ma) must increase (a) 2.2 m s 2 (b) 62.2 m s 2 (c) which causes the upwards acceleration of the rocket. rotational speed is greatest. Space 240 Dot Point HSC Physics

59 2.9.3 If the rocket is launched too early, or in the wrong direction, it will reach its destination before Mars gets to the same position. If launched too late, Mars will have passed the intercept point before the rocket gets there For example: An electron in orbit about a nucleus is moving with uniform circular motion. The centripetal force is provided by the electrostatic force of attraction between the positive charge on the protons in the nucleus and the negative charge on the electrons Gravitational attraction towards the Earth (= centripetal force) (a) N towards the centre of the Earth (b) 8.98 m s 2 towards the centre of the Earth N towards the centre of the Earth LEO spy satellites, geostationary communications LEO satellites cover the entire surface of the Earth at least once per day and, being much lower, can see more detail in the things they observe (reading car number plates, identifying faces, seeing a golf ball on a golf green). They are therefore useful for spy activities. therefore able to be used to predict weather in other places Low Earth satellites Altitude km Period 90 minutes to 4 or 5 hours Usually polar orbit Not fixed relative to Earth s surface Used for spying Geostationary satellites Altitude km Period 23 hours 65 min 4 sec Equatorial orbit Stay over same position on Earth s surface Used for communications and weather forecasting 2.13 Answers will vary according to the scientist chosen check your text for details. Dot Point HSC Physics 241 Space

60 The orbital speed of the satellite around Jupiter would have to be greater than that of the satellite around Earth if both are to be in stable orbits because the gravitational pull of Jupiter is greater than that of Earth (a) 1 : 1 : 1 (orbital speed is independent of the mass of the satellite) (b) 12 : 4 : (a) 1 : 9 : 16 (b) 1 : 3 : m s 1 = kph s = 37 hours km A = km B = 2.51 days C = km (a) hours (b) km (a) km (b) m s 1 = 4750 kph Friction between the satellite and the atmosphere reduces the speed of the satellite, so gravitational forces can attract it closer to Earth where the denser atmosphere will provide greater frictional forces which will slow it even more and allow gravity to pull it even closer to Earth, and so on Both students are correct in that each factor contributes to orbital decay, but both are incorrect in assuming that their factor is the only one involved. Both frictional forces to slow the craft and gravity are needed before orbital decay can occur. Without the slowing of the craft due to friction, gravity will simply keep it in a stable orbit, and without gravity, the craft would not be pulled to Earth (a) Because air is one of the best heat insulators, the most effective heat protection is the cushion of air that builds up in that absorb much of the heat energy as they vaporise. shuttles. These are 90% air (an excellent insulator) and are painted with a waterproof silicon sealant between each survival of the astronauts or the craft Every object in the Universe attracts every other object with a gravitational force. The force is directly proportional to the masses of the objects. Space 242 Dot Point HSC Physics