VCE PHYSICS UNITS 3 AND 4 • Brian Shadwick · PDF fileUnit 3 How Do Fields Explain Motion and Electricity? vi ... annotate Add brief notes to a diagram or graph. ... Dot Point VCE

VCE PHYSICS UNITS 3 AND 4

• Brian Shadwick •

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© Science Press 2017First published 2017

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Contents

Words to Watch iv

Introduction v

Dot Points

Unit 3 How Do Fields Explain Motion and Electricity? vi

Unit 4 How Can Two Contradictory Models Explain Both Light and Matter? xii

Questions

Unit 3 How Do Fields Explain Motion and Electricity? 1

Unit 4 How Can Two Contradictory Models Explain Both Light and Matter? 243

Answers

Unit 3 How Do Fields Explain Motion and Electricity? 354

Unit 4 How Can Two Contradictory Models Explain Both Light and Matter? 423

Appendices

Data Sheet 452

Periodic Table 453

Index 454

iii Contents

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Dot Point VCE Physics Units 3 and 4

account, account for State reasons for, report on,

give an account of, narrate a series of events or

transactions.

analyse Interpret data to reach conclusions.

annotate Add brief notes to a diagram or graph.

apply Put to use in a particular situation.

assess Make a judgement about the value of

something.

calculate Find a numerical answer.

clarify Make clear or plain.

classify Arrange into classes, groups or categories.

comment Give a judgement based on a given

statement or result of a calculation.

compare Estimate, measure or note how things are

similar or different.

construct Represent or develop in graphical form.

contrast Show how things are different or opposite.

create Originate or bring into existence.

deduce Reach a conclusion from given information.

define Give the precise meaning of a word, phrase or

physical quantity.

demonstrate Show by example.

derive Manipulate a mathematical relationship(s) to

give a new equation or relationship.

describe Give a detailed account.

design Produce a plan, simulation or model.

determine Find the only possible answer.

discuss Talk or write about a topic, taking into account

different issues or ideas.

distinguish Give differences between two or more

different items.

draw Represent by means of pencil lines.

estimate Find an approximate value for an unknown

quantity.

evaluate Assess the implications and limitations.

examine Inquire into.

explain Make something clear or easy to understand.

extract Choose relevant and/or appropriate details.

extrapolate Infer from what is known.

hypothesise Suggest an explanation for a group of facts or phenomena.

identify Recognise and name.

interpret Draw meaning from.

investigate Plan, inquire into and draw conclusions about.

justify Support an argument or conclusion.

label Add labels to a diagram.

list Give a sequence of names or other brief answers.

measure Find a value for a quantity.

outline Give a brief account or summary.

plan Use strategies to develop a series of steps or processes.

predict Give an expected result.

propose Put forward a plan or suggestion for consideration or action.

recall Present remembered ideas, facts or experiences.

relate Tell or report about happenings, events or circumstances.

represent Use words, images or symbols to convey meaning.

select Choose in preference to another or others.

sequence Arrange in order.

show Give the steps in a calculation or derivation.

sketch Make a quick, rough drawing of something.

solve Work out the answer to a problem.

state Give a specific name, value or other brief answer.

suggest Put forward an idea for consideration.

summarise Give a brief statement of the main points.

synthesise Combine various elements to make a whole.

Words to Watch

Dot Point VCE Physics Units 3 and 4iv

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Words to Watch

What the book includes

This book provides questions and answers for each dot point in the Victorian Certificate of Education Study Design for each core topic in the Year 12 Physics syllabus:

Unit 3 How Do Fields Explain Motion and Electricity?

• Area of Study 1 How Do Things Move Without Contact?

• Area of Study 2 How Are Fields Used to Move Electrical Energy?

• Area of Study 3 How Fast Can Things Go?

Unit 4 How Can Two Contradictory Models Explain Both Light and Matter?

• Area of Study 1 How Can Waves Explain the Behaviour of Light?

• Area of Study 2 How Are Light and Matter Similar?

Format of the book

The book has been formatted in the following way:

1.1 Subtopic from syllabus.

1.1.1 Assessment statement from syllabus.

1.1.1.1 First question for this assessment statement.

1.1.1.2 Second question for this assessment statement.

The number of lines provided for each answer gives an indication of how many marks the question might be worth in an examination. As a rough rule, every two lines of answer might be worth 1 mark.

How to use the book

Completing all questions will provide you with a summary of all the work you need to know from the syllabus. 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.

When working through the questions, write the answers you have to look up in a different colour to those you know without having to research the work. This will provide you with a quick reference for work needing further revision.

Introduction

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Dot Point VCE Physics Units 3 and 4 Introduction

Area of Study 1 How Do Things Move Without Contact?

Fields and interactions – gravitational fields

1.1 Describe gravitation using a field model. 5

1.1.1 Gravitational field model. 5

1.2 Investigate and compare theoretically 7 and practically gravitational fields about a point mass with reference to the direction and shape of the field.

1.2.1 Shape and direction of gravitational 7 fields.

1.3 Investigate theoretically and practically 9 gravitational fields, including directions and shapes of fields.

1.3.1 Falling objects – analysing an experiment. 9

1.4 Identify gravitational fields as static or 11 changing, and as uniform or non-uniform.

1.4.1 Static, changing, uniform and 11 non-uniform gravitational fields.

1.5 Describe the use of the inverse square 12 law to determine the magnitude of a gravitational field.

1.5.1 Gravitational field and the inverse 12 square law.

Fields and interactions – magnetic fields

1.6 Describe magnetism using a field 13 model.

1.6.1 Magnetic field model. 13

1.7 Investigate and compare theoretically 14 and practically magnetic fields, including directions and shapes of fields, attractive and repulsive fields, and the existence of dipoles and monopoles.

1.7.1 Shapes and types of magnetic fields. 14


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1.8 Investigate and apply theoretically 15 and practically a vector field model to magnetic phenomena, including shapes and directions of fields produced by bar magnets, by current carrying wires, loops and solenoids.

1.8.1 Magnetic fields around straight 15 conductors.

1.8.2 Magnetic fields and solenoids. 18

1.9 Identify magnetic fields as static 20 or changing, and as uniform or non-uniform.

1.9.1 Static, changing, uniform and 20 non-uniform magnetic fields.

Fields and interactions – electric fields

1.10 Describe electricity using a field model. 21

1.10.1 Electrical field model. 21

1.11 Investigate theoretically and practically 25 electric fields, including directions and shapes of fields, attractive and repulsive fields, and the existence of dipoles and monopoles.

1.11.1 Shapes of fields. 25

1.12 Investigate and compare theoretically 27 and practically electrical fields about a point mass or charge (positive or negative) with reference to the direction and shape of the field.

1.12.1 Shapes and directions of fields. 27

1.12.2 Electric fields between parallel plates. 29

1.13 Identify electric fields as static or 31 changing, and as uniform or non-uniform.

1.13.1 Static, changing, uniform and 31 non-uniform electric fields.

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1.14 Describe the use of the inverse square 33 law to determine the magnitude of an electric field.

1.14.1 The use of the inverse square 33 law to determine the magnitude of an electric field.

Effects of fields – gravitational fields

1.15 The potential energy changes 34 (qualitative) of a point mass moving in a gravitational field.

1.15.1 Changes in gravitational potential 34 energy 1.

1.16 Analyse potential energy changes in a 35 uniform gravitational field: Eg = mgΔh.

1.16.1 Changes in gravitational potential 35 energy 2.

1.17 Analyse the change in gravitational 37 potential energy from area under a force-distance graph and area under a field-distance graph multiplied by mass.

1.17.1 Analysing force-distance graphs. 37

1.18 Describe that masses only attract 39 each other in gravitational fields.

1.19 Analyse the use of gravitational fields 39 to accelerate mass, including gravitational field and gravitational force concepts:

g = GM ____ r2

and Fg = GM1M2 ________ r2

.

1.18.1 Newton’s laws of gravity. 39

1.18.2 Gravitational fields. 41



Effects of fields – magnetic fields

1.20 Analyse the use of magnetic fields 43 to change the path of a charged particle with reference to the magnitude and direction of the force applied to an electron beam by a magnetic field: F = qvB, in cases where the directions of v and B are perpendicular or parallel and the radius of the path followed by a low velocity electron in a magnetic field: qvB = mv2 ____

r.

1.20.1 Moving charges in a magnetic field 1. 43



Effects of fields – electric fields

1.21 Apply electric field and electric 51 force concepts including E = k Q __

r2

and F = kq1 q2 _____

r2.

1.21.1 Electric field around a point charge. 51

1.21.2 Force between electrostatic charges. 53

1.22 Describe the interaction of two 53 electric fields, allowing that electric charges can either attract or repel.

Note that 1.22 has been combined with 1.11.

1.23 Analyse the use of a uniform electric 56 field to accelerate a charge, including F = qE = ma.

1.23.1 Charges in electric fields. 56

1.23.2 Charges between parallel plates. 57

1.24 Analyse potential energy changes 61 (qualitative) associated with a point mass or charge moving in a uniform electric field: W = qV and E = V ___

d.

1.24.1 Work done by electric fields. 61

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Application of field concepts – gravitational fields

1.25 Apply the concepts of force due 65 to gravity, Fg, and normal reaction force, FN, including satellites in orbit where the orbits are assumed to be uniform and circular.

1.25.1 Gravity and normal reaction forces. 65

1.26 Model satellite motion in a gravitational 67 field (artificial, Moon, planet) as uniform circular orbital motion: a = v

2 __ r

= 4π2r _____ T2

.

1.26.1 Circular motion and satellites. 67

Application of field concepts – magnetic fields

1.27 Describe the interaction of two magnetic 71 fields, allowing that magnetic poles and current carrying conductors can either attract or repel.

1.27.1 Force between parallel conductors. 71

1.28 Investigate and analyse theoretically 77 and practically the force on a current carrying conductor due to an external magnetic field, F = nILB , where I and B are either perpendicular or parallel to each other.

1.28.1 The motor effect 1. 77

1.28.2 The motor effect 2. 78

1.28.3 Forces on straight conductors in 81 magnetic fields 1.

1.28.4 Forces on straight conductors in 85 magnetic fields 2.

1.29 Investigate and analyse theoretically 87 and practically the operation of simple DC motors consisting of one coil, containing a number of loops of wire, which is free to rotate about an axis in a uniform magnetic field and including the use of a split ring commutator.

1.29.1 Torque on a coil in a magnetic field 1. 87

1.29.2 Torque on a coil in a magnetic field 2. 89

1.29.3 Simple DC motors. 92

Application of field concepts – electric fields

1.30 Model the acceleration of particles in 95 a particle accelerator (limited to linear acceleration by a uniform electric field and direction change by a uniform magnetic field).

1.30.1 Particle accelerators. 95

Area of Study 2 How Are Fields Used to Move Electrical Energy?

Generation of electricity

2.1 Calculate magnetic flux when the 101 magnetic field is perpendicular to the area, and describe the qualitative effect of differing angles between the area and the field: ϕB = B A.

2.1.1 Magnetic flux and flux density. 101

2.2 Investigate and analyse theoretically 106 and practically the generation of electromotive force (emf) including AC voltage and calculations using

induced emf: ε = −N∆ϕβ ____ ∆t

, with

reference to the rate of change of magnetic flux, the number of loops through which the flux passes and direction of induced emf in a coil.

2.2.1 Faraday and induction. 106

2.2.2 Lenz’s law and electromagnetic 110 induction.

2.2.3 Lenz’s law and coils. 115

2.3 Explain the production of DC voltage 118 in DC generators and AC voltage in alternators, including the use of split ring commutators and slip rings respectively.

2.3.1 DC generators. 118

2.3.2 AC generators. 121

2.3.3 Comparing DC and AC generators 124 and motors.



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Transmission of electricity

2.4 Compare sinusoidal AC voltages 126 produced as a result of the uniform rotation of a loop in a constant magnetic field with reference to frequency, period, amplitude, peak to peak voltage (Vp–p) and to peak to peak current (Ip–p).

2.4.1 Comparing sinusoidal AC voltages. 126

2.5 Compare alternating voltage expressed 130 as the root mean square (RMS) to a constant DC voltage developing the same power in a resistive component.

2.5.1 RMS voltage. 130

2.6 Convert between RMS, peak and peak 132 to peak values of voltage and current.

2.6.1 RMS, peak and peak to peak voltage 132 and current.

2.6.2 Solve problems using peak and RMS 133 values.

2.7 Analyse transformer action with 136 reference to electromagnetic induction for an ideal transformer using N1 ___ N2

= V1 ___ V2

= I2 ___ I1

or V1I1 = V2I2.

2.7.1 Transformers. 136

2.8 Analyse the supply of power by 142 considering transmission losses across transmission lines.

2.8.1 Transformers and electricity 142 transmission.

2.9 Identify the advantage of the use of AC 145 power as a domestic power supply.

2.9.1 Impact of AC power. 145

Area of Study 3 How Fast Can Things Go?

Newton’s laws of motion

3.1 Investigate and apply theoretically 149 and practically Newton’s three laws of motion in situations where two or more coplanar forces act along a straight line and in two dimensions.

3.1.1 Newton’s first law – inertia. 149

3.1.2 Force and acceleration – Newton’s 151 second law.

3.1.3 More force vectors. 153

3.1.4 Objects on an inclined plane. 156

3.1.5 Newton’s third law of motion. 159

3.2 Investigate and analyse theoretically 163 and practically the uniform circular motion of an object moving in a

horizontal plane, Fnet = mv2 ____ r

.

3.2.1 Vehicles moving around a circular road. 163

3.2.2 Analysing a circular motion experiment. 166

3.2.3 Vehicles moving around a banked track. 168

3.2.4 Objects on the end of a string. 169

3.2.5 Satellites in circular motion. 172

3.2.6 Vertical circular motion. 174

3.3 Investigate and analyse theoretically 177 and practically the motion of projectiles near Earth’s surface, including a qualitative description of the effects of air resistance.

3.3.1 Projectile motion – free response. 177

3.3.2 Projectile motion – multiple choice. 179

3.3.3 Projectile motion – analysing results. 184

3.4 Investigate and apply theoretically 186 and practically the laws of energy and momentum conservation in isolated systems in one dimension.

3.4.1 Momentum set 1. 186

3.4.2 Momentum set 2. 189



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Relationships between force, energy and mass

3.5 Investigate and analyse theoretically 192 and practically impulse in an isolated system for collisions between objects moving in a straight line: FΔt = mΔv.

3.5.1 Impulse and momentum. 192

3.5.2 Momentum and force-time graphs. 194

3.6 Investigate and apply theoretically 198 and practically the concept of work done by a constant force using: work done = constant force × distance moved in direction of net force and work done = area under force-distance graph.

3.6.1 Work, energy and force. 198

3.6.2 Force-displacement graphs. 198

3.7 Analyse transformations of energy 201 including gravitational potential energy: Eg = mgΔh or from area under a force-distance graph and area under a field-distance graph multiplied by mass.

3.7.1 Gravitational potential energy (Eg). 201

3.7.2 Field-distance graphs. 202

3.8 Analyse transformations of energy 204 including kinetic energy at low speeds

using Ek = 1 __ 2

mv2 including elastic and

inelastic collisions with reference to conservation of kinetic energy.

3.8.1 Kinetic energy (Ek). 204

3.8.2 Conservation of energy. 205

3.8.3 Elastic and inelastic collisions. 209

3.9 Analyse transformations of energy 211 including strain potential energy: area under force-distance graph including ideal springs obeying Hooke’s law: Es = 1 __

2k∆x2.

3.9.1 Hooke’s law. 211

3.9.2 Energy stored in a stretched spring. 212

Einstein’s theory of special relativity

3.10 Describe Einstein’s two postulates 216 for his theory of special relativity that the laws of physics are the same in all inertial (non-accelerated) frames of reference and that the speed of light has a constant value for all observers regardless of their motion or the motion of the source.

3.10.1 Frames of reference. 216

3.10.2 Einstein’s postulates. 219

3.11 Compare Einstein’s theory of 220 special relativity with the principles of classical physics.

3.11.1 Classical versus Einstein’s physics. 220

3.11.2 Relativistic mathematics – extension. 222

3.12 Describe proper time (t0 ) as the time 224 interval between two events in a reference frame where the two events occur at the same point in space.

3.13 Model mathematically time dilation 224 at speeds approaching c using the

equations: t = t0γ and γ = (1 – v2 __

c2 )

− 1 __ 2 .

3.12.1 Time dilation 1. 224

3.12.1 Time dilation 2. 227

3.14 Describe proper length (L0 ) as 229 the length that is measured in the frame of reference in which objects are at rest.

3.15 Model mathematically length 229 contraction at speeds approaching

c using the equations: L = L0 ___ γ

and

γ = (1 – v2 __

c2 )

− 1 __ 2 .

3.14.1 Length contraction 1. 229

3.14.2 Length contraction 2. 230



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3.16 Interpret Einstein’s prediction by 233 showing that the total ‘mass-energy’ of an object is given by: Etot = Ek + E0 = γmc2 where E0 = mc2, and where kinetic energy can be calculated by: Ek = (γ − 1)mc2.

3.16.1 Relativistic mass 1. 233

3.16.2 Relativistic mass 2. 235

3.16.3 Mass-energy equivalence. 236

3.17 Explain why muons can reach 239 Earth even though their half-lives would suggest that they should decay in the outer atmosphere.

3.17.1 Muons and special relativity. 239

3.18 Describe how matter is converted 241 to energy by nuclear fusion in the Sun, which leads to its mass decreasing and the emission of electromagnetic radiation.

3.18.1 Energy and the Sun. 241

Answers to How Do Fields Explain Motion 354 and Electricity?

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Area of Study 1 How Can Waves Explain the Behaviour of Light?

Properties of mechanical waves

1.1 Explain a wave as the transmission 247 of energy through a medium without the net transfer of matter.

1.1.2 Waves and energy. 247

1.2 Distinguish between transverse 248 and longitudinal waves.

1.2.1 Transverse matter waves. 248

1.2.2 Longitudinal matter waves. 251

1.3 Identify the amplitude, wavelength, 253 period and frequency of waves.

1.3.1 Properties of waves. 253

1.4 Calculate the wavelength, frequency, 257 period and speed of travel of waves using: v = fλ = λ __

T.

1.4.1 Using the wave equation. 257

1.4.2 Analysing wave diagrams 1. 258

1.4.3 Analysing wave diagrams 2. 260

1.5 Investigate and analyse theoretically 262 and practically constructive and destructive interference from two sources with reference to coherent waves and path difference:

nλ and (n − 1 __ 2

) λ respectively.

1.5.1 Superposition of waves. 262

1.6 Explain qualitatively the Doppler effect. 265

1.6.1 The Doppler effect. 265

1.7 Explain resonance as the superposition 267 of a travelling wave and its reflection, and with reference to a forced oscillation matching the natural frequency of vibration.

1.7.1 Mechanical resonance. 267

1.8 Analyse the formation of standing 269 waves in strings fixed at one or both ends.

1.8.1 Standing waves in strings. 269

1.9 Investigate and explain theoretically 271 and practically diffraction as the directional spread of various frequencies with reference to different gap width or obstacle size, including the qualitative

effect of changing the λ __ w

ratio.

1.9.1 Diffraction. 271

Light as a wave

1.10 Describe light as an electromagnetic 273 wave which is produced by the acceleration of charges, which in turn produces changing electric fields and associated changing magnetic fields.

1.11 Identify that all electromagnetic 273 waves travel at the same speed, c, in a vacuum.

1.10.1 Electromagnetic waves. 273

1.12 Compare the wavelength and 276 frequencies of different regions of the electromagnetic spectrum, including radio, microwave, infra-red, visible, ultraviolet, X-ray and gamma, and identify the distinct uses each has in society.

1.12.1 Properties of electromagnetic 276 radiations.



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1.13 Explain polarisation of visible light and 278 its relation to a transverse wave model.

1.13.1 Polarisation. 278

1.14 Investigate and analyse theoretically 280 and practically the behaviour of waves including refraction using Snell’s law: n1 sin (θ1) = n2 sin (θ2) and n1v1 = n2v2.

1.14.1 Refraction 1. 280




1.15 Investigate and analyse theoretically 288 and practically the behaviour of waves including total internal reflection and critical angle including applications: n1 sin (θc) = n2 sin (90°).

1.15.1 Total internal reflection. 288

1.16 Investigate and explain theoretically 290 and practically colour dispersion in prisms and lenses with reference to refraction of the components of white light as they pass from one medium to another.

1.16.1 Dispersion by a prism. 290

1.16.2 Dispersion by lenses. 290

1.17 Explain the results of Young’s double 292 slit experiment.

1.17.1 Evidence for the wave-like nature 292 of light.

1.17.2 Constructive and destructive 292 interference in terms of path differences: nλ and (n − 1 __

2) λ

respectively.

1.17.3 Effect of wavelength, distance of 293 screen and slit separation on

interference patterns: ∆x = λL __ d

.

Area of Study 2 How Are Light and Matter Similar?

Behaviour of light

2.1 Investigate and describe theoretically 297 and practically the effects of varying the width of a gap or diameter of an obstacle on the diffraction pattern produced by light and apply this to limitations of imaging using light.

2.1.1 Factors affecting diffraction patterns. 297

2.2 Analyse the photoelectric effect with 301 reference to the evidence for the particle-like nature of light.

2.2.1 Max Planck – the beginning of 301 quantum theory.

2.2.2 Albert Einstein – the photoelectric 304 effect.

2.2.3 Quantum theory and the 307 photoelectric effect.

2.3 Analyse the photoelectric effect with 309 reference to experimental data in the form of graphs of photocurrent versus electrode potential, and of kinetic energy of electrons versus frequency.

2.3.1 Analysing experimental data. 309

2.4 Analyse the photoelectric effect with 319 reference to kinetic energy of emitted photoelectrons: Ek max = hf – ϕ, using energy units of joule and electron volt.

2.4.1 Solve problems using E = hf and 319 c = fλ.

2.5 Analyse the photoelectric effect with 323 reference to the effects of intensity of incident irradiation on the emission of photoelectrons.

2.5.1 Photoemission and incident frequency. 323

2.5.2 Incident intensity and photoemission. 325


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2.6 Describe the limitation of the wave 328 model of light in explaining experimental results related to the photoelectric effect.

2.6.1 Limits of particle model and 328 photoelectric effect.

Matter as particles or waves

2.7 Interpret electron diffraction patterns 329 as evidence for the wave-like nature of matter.

2.8 Distinguish between the diffraction 329 patterns produced by photons and electrons.

2.7.1 Diffraction – a wave property? 329

2.9 Calculate the de Broglie wavelength 331

of matter: λ = h __ p

.

2.9.1 De Broglie’s hypothesis. 331

2.9.2 De Broglie wavelength of matter: 332

λ = h __ p

.

Similarities between light and matter

2.10 Compare the momentum 333 of photons and of matter of the same wavelength including calculations using: p = h __

λ.

2.10.1 Using de Broglie’s equation. 333

2.11 Explain the production of atomic 335 absorption and emission line spectra, including those from metal vapour lamps.

2.11.1 Atomic spectra. 335

2.11.2 The hydrogen spectrum. 337

2.11.3 Other spectra. 338

2.12 Interpret spectra and calculate the 340 energy of absorbed or emitted photons: ∆E = hf.

2.13 Analyse the absorption of photons by 340 atoms, with reference to the change in energy levels of the atom due to electrons changing state.

2.14 Analyse the absorption of photons by 340 atoms, with reference to the frequency and wavelength of emitted photons: E = hf = hc ___

λ.

2.12.1 Analysing spectra. 340

2.15 Describe the quantised states of the 342 atom with reference to electrons forming standing waves, and explain this as evidence for the dual nature of matter.

2.15.1 Quantised states of atoms. 342

2.16 Interpret the single photon/electron 344 double slit experiment as evidence for the dual nature of light/matter.

2.16.1 Interference supports the dual 344 wave/particle model.

2.17 Explain how diffraction from a single 348 slit experiment can be used to illustrate Heisenberg’s uncertainty principle.

2.17.1 Heisenberg uncertainty and diffraction. 348

2.18 Explain why classical laws of physics 350 are not appropriate to model motion at very small scales.

2.18.1 Limitations of classical physics. 350

Production of light from matter

2.19 Compare the production of light in 351 lasers, synchrotrons, LEDs and incandescent lights.

2.19.1 Production of light. 351

Answers to How Can Two Contradictory 423 Models Explain Both Light and Matter?



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DOT POINT

How Do Fields Explain Motion and Electricity?

Unit 3

1 How Do Fields Explain Motion and Electricity?

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How Do Things Move Without Contact?

DOT POINT

AREA OF STUDY 1


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1.1 Describe gravitation using a field model.

1.1.1 Gravitational field model.

1.1.1.1

(a) In general, in physics, what is a field? ��

��

(b) More specifically, what is a gravitational field? ��

��

(c) Where do we find gravitational fields? ��

(d) Define gravitational field strength. ��

��

(e) Give the mathematical equation for gravitational field strength. ��

(f) What are the units for gravitational field strength? ��

(g) What do we commonly refer to gravitational field as? ��

1.1.1.2

(a) What two properties of a mass changes if its position in a gravitational field changes?

��

(b) State the relationship between the work done on an object and its changing position in a gravitational field.

��

(c) Explain why the gravitational field strength at the surface of the Earth is not constant.

��

��

1.1.1.3 Compare the gravitational field strength at sea level on Earth with the field strength on top of Mount Everest. Explain your answer.

��

��


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1.1.1.4

(a) Explain, in terms of gravitational field strength, why all objects, regardless of mass, will fall towards the Earth at the same rate when they are dropped from the same height.

��

��

��

��

(b) Will the rate at which they fall change if they are dropped from a significantly higher height? Justify your answer.

��

��

��

1.1.1.5

(a) Describe what happens to the gravitational field strength as a mass approaches closer to the surface of a planet.

��

(b) Explain how you could determine the truth of your answer to (a) experimentally, indicating what the results would show if your answer was correct.

��

��

1.1.1.6 What would be the magnitude of the gravitational field midway between two identical planets?

(A) Zero.

(B) Depends on their masses.

(C) Depends on the total distance between them.

(D) Infinite.

1.1.1.7 The gravitational field lines are shown for planet X. Planet Y is smaller, but more massive than X. Which statement about a similar diagram for Y is correct?

(A) It would have more field lines.

(B) It would have fewer field lines.

(C) It would have the same number of field lines.

(D) More information is required.

1.1.1.8 What is the effect of a gravitational field on a mass placed in it?

(A) It gives the mass an acceleration.

(B) It causes the mass to move towards the centre of curvature.

(C) It gives the object weight.

(D) It produces the mass of the object.

X

Dot Point VCE Physics Units 3 and 46How Do Fields Explain Motion and Electricity?

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1.2 Investigate and compare theoretically and practically gravitational fields about a point mass with reference to the direction and shape of the field.

1.2.1 Shape and direction of gravitational fields.

1.2.1.1 The field diagrams represent the relative strengths of the gravitational fields of two planets X and Y. The planets have the same radii.

Which statement about these two planets is correct?

(A) The gravitational field strength at the surface of each planet is the same.

(B) The mass of planet X must be greater than the mass of planet Y.

(C) The gravitational field at the surface of X will be less than the field at the surface of Y.

(D) The gravitational field above the surface of X will be less than the gravitational field at the same distance above the surface of Y.

1.1.2.2 A mass is moving in a gravitational field. Which statement correctly identifies the direction of movement of the mass?

(A) It will move in the direction of the field.

(B) It will move in the opposite direction to the field.

(C) The direction depends on whether the field is uniform or not.

(D) If the field strength is zero, it will not move.

1.1.2.3 Which statement best describes the motion of a mass which is free to fall in a uniform gravitational field?

(A) It will move with constant speed.

(B) It will move with constant velocity.

(C) It will move with constant acceleration.

(D) It will move with increasing acceleration.

1.1.2.4 Consider the two, isolated point masses, X and Y shown in the diagram. Draw the gravitational field lines around each mass. Note that one point mass has mass M and the other has mass 2M.

X = mass = M Y = mass = 2M

X

Y


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1.1.2.5 Consider a mass, free to move, in a gravitational field.

(a) What will the mass do? Justify your answer.

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(b) On the diagram draw vectors to indicate: (i) The direction of the gravitational field

around the satellite (represented by the black circle).

(ii) Its instantaneous orbital velocity.

(iii) The net force due to the gravitational field. Its orbital path is also shown (dotted line).

1.1.2.6 Diagram X shows the surface of the Earth and the space above it for a distance of, say, 100 m. Diagram Y shows the surface of the Earth and the space above it for a distance of, say, 1000 m.

(a) Complete each diagram to show the gravitational field lines in each space above the surface.

X Y

(b) Describe each field in terms of the terms static, changing, uniform and non-uniform.

X = ��

Y = ��

(c) Account for the difference in your answers. ��

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1.3 Investigate theoretically and practically gravitational fields, including directions and shapes of fields.

1.3.1 Falling objects – analysing an experiment.

The information in the table was obtained from an experiment where the time it took an object to fall from different heights was measured. Use the information to answer the questions.

1.3.1.1 Suggest a purpose of this experiment.

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1.3.1.2 Identify four factors which would have been controlled.

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1.3.1.3 Identify the factors that varied. ��

1.3.1.4 Graph the information on the axes provided.

0

2

4

6

8

10

12

14

16

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Time to fall various distances (s)

Time (s)

Dis

tanc

e fa

llen

(m)

1.3.1.5 Predict the time to fall 5.0 m. ��

1.3.1.6 Predict the time to fall 25 m. ��

Distance fallen (m)

Time to fall (s)

(Time to fall)2 (s2)

0 0

2 0.64

4 0.90

6 1.11

8 1.28

10 1.43

12 1.56

14 1.69


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1.3.1.7 Comment on the accuracy and reliability of your predictions above. Explain your answer.

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1.3.1.8 If it took 1.5 seconds to hit the ground, predict the height it fell from. ��

1.3.1.9 Can you write a conclusion from this graph? Explain your answer. ��

1.3.1.10 Complete the third column headed (Time to fall)2.

1.3.1.11 Graph distance fallen against (Time to fall)2 on the grid provided.

0

2

4

6

8

10

12

14

16

0 0.5 1 1.5 2 2.5 3

Distance fallen versus (Time to fall)2

(Time to fall)2 (s)2

Dis

tanc

e fa

llen

(m)

1.3.1.12 What does this tell you about the rate at which the object falls? ��

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1.3.1.13 Given that twice the gradient of your graph is equal to the acceleration of the falling object, calculate the acceleration of the falling object.

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1.3.1.14 Is this object falling on Earth? Justify your answer. ��

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1.3.1.15 Write a conclusion for the experiment. ��

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1.3.1.16 Suggest at least one way this experiment could be improved. ��

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1.4 Identify gravitational fields as static or changing, and as uniform or non-uniform.

1.4.1 Static, changing, uniform and non-uniform gravitational fields.

1.4.1.1

(a) What do we mean by a static field? ��

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(b) Where would you expect to find a static gravitational field? Justify your answer.

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1.4.1.2

(a) What do we mean by a changing field? ��

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(b) Give an example of where we might find a changing gravitational field? Justify your answer.

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1.4.1.3

(a) What do we mean by a uniform field? ��

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(b) Where would you expect to find a uniform gravitational field? Justify your answer. ��

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1.4.1.4

(a) What do we mean by a non-uniform field? ��

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(b) Where would you expect to find a non-uniform gravitational field? Justify your answer.

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1.4.1.5 Consider a satellite in a stable, circular orbit around the Earth. Classify each statement about this satellite below as true or false. Justify each answer.

(a) It is a static gravitational field. ��

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(b) It is a changing gravitational field. ��

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(c) It is a uniform gravitational field. ��

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(d) It is a non-uniform gravitational field. ��


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1.5 Describe the use of the inverse square law to determine the magnitude of a gravitational field.

1.5.1 Gravitational field and the inverse square law.

1.5.1.1

(a) State the inverse square law as it applies to gravitational field. ��

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(b) List three quantities in physics that obey the inverse square law. ��

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1.5.1.2 The gravitational field strength at the surface of the Earth, radius R, is g and the weight of an object on the surface is W.

The object is now taken to a distance of 3R from the centre of the Earth.

Which choice gives the correct new values for the gravitational field and the weight of the object?

1.5.1.3 The graph shows how the gravitational field varies with distance from the centre of a planet.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 1 2 3 4 5 6 7Distance from centre (r)

Gra

vita

tiona

l fie

ld (N

kg−

1 )

(a) Explain the shape of this graph. ��

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(b) Estimate the value of the gravitational field on the surface of this planet. ��

Gravitational field Weight

(A)g __ 3

W __ 3

(B)g __ 3

W __ 9

(C)g __ 4

W __ 4

(D)g __ 9

W __ 9


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1.6 Describe magnetism using a field model.

1.8 Investigate and apply theoretically and practically a vector field model to magnetic phenomena.

1.6.1 Magnetic field model.

1.6.1.1 Complete the sentences.

(a) Magnetic fields are produced by �� or �� .

(b) A magnetic field is a region in which a magnetic substance will experience a �� .

(c) Magnetic field is also directed from magnetic �� towards magnetic �� .

(d) Magnetic field can be represented by �� or ��

�� drawn from north towards south.

(e) The direction of the magnetic field at any point in a field is given by the direction of the ��

to the field lines at that point.

(f) The geographic north pole of Earth is actually a magnetic �� .

(g) Like magnetic poles �� .

(h) Unlike magnetic poles �� .

(i) The intensity of a magnetic field is represented in a field diagram by how �� the field

lines are together.

(i) A diagram representing a strong field will show the field lines �� than if the field is weaker.

1.6.1.2 Given that magnetic fields, like gravitational and electric fields are vectors, determine the direction of the magnetic field at each of the points P, Q, R, S, T and U in the diagrams below. Consider the magnetic poles in each part of the question to be point monopoles. Note, black = north monopole, dotted = south monopole.

P

Q

S

R

T

U


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1.7 Investigate and compare theoretically and practically, magnetic fields, including directions and shapes of fields, attractive and repulsive fields, and the existence of dipoles and monopoles.

1.8 Investigate shapes and directions of fields produced by bar magnets.

1.7.1 Shapes and types of magnetic fields.

1.7.1.1

(a) What is a monopole? Give an example. ��

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(b) What is a magnetic dipole? Give an example. ��

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(c) Comment on the existence of magnetic monopoles and dipoles. ��

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1.7.1.2

(a) Complete the diagrams by drawing in the field lines between and around the magnets.

A B

C

N S N

N N

S

(b) Describe the nature of the magnetic fields you have drawn in B and C. ��

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DOT POINT

Answers

353 Answers

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1.1.1.1 (a) A field is a region in which something experiences a force.

(b) A gravitational field is a region in which masses experience forces.

(c) Gravitational fields are found around all masses.

(d) Gravitational field strength is the force per unit mass an object experiences when placed in the field.

(e) g = F __ m

(f) N kg−1 or m s−2

(g) Acceleration due to gravity.

1.1.1.2 (a) Its gravitational potential energy.

(b) Work done equals the change in the gravitational potential energy.

(c) The Earth is not a perfect sphere, and gravitational field strength depends partly on the distance the object is from the centre (of mass) of the Earth.

1.1.1.3 The gravitational field on top of Mount Everest would be less than that at sea level because the top of Mount Everest is further from the centre of mass of the Earth (taken as being at the centre of the Earth).

1.1.1.4 (a) The motion of an object in a gravitational field is described by Newton’s three equations of motion, and the mass of an object is not one of the factors affecting that motion. However, in order to fall at the same rate, a larger object will need a larger force acting on it, so the gravitational force will be larger (equal to mass × gravitational field). This ensures that the rate of fall for all masses is the same.

(b) If the height is significant, then the value of the gravitational field (g) will be less, and therefore the initial rate of fall will also be less. As the object falls closer to the Earth, and gravitational field increases, the rate at which its downwards velocity increases will also increase (note that we are ignoring air resistance here).

1.1.1.5 (a) The gravitational field increases in strength.

(b) Determine the acceleration of the same object at varying altitudes which are significantly different. At higher altitudes, the acceleration (i.e. the gravitational field) will be less.

1.1.1.6 C

1.1.1.7 A

1.1.1.8 C (Answer A is also true provided it is free to move, which it may not be, so C is the better answer because it is always correct).

1.2.1.1 B

1.2.1.2 A

1.2.1.3 C

1.2.1.4

1.2.1.5 (a) It will accelerate towards the centre of mass of the object causing the gravitational field.

(b)

X Y

FieldNet force

Instantaneous velocity

354Answers Dot Point VCE Physics Units 3 and 4

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1.2.1.6 (a)

(b) X is static and uniform.

Y is static and non-uniform.

(c) The difference is only due to our approximating the nature af the field close to the Earth’s surface. Because the field is directed towards the centre of the Earth, the field lines in X will be slightly out of parallel, so the field in X is technically also non uniform.

1.3.1.1 To examine the relationship between the time it takes an object to fall from various heights and the height from which it is dropped or, to examine the rate at which an object falls.

1.3.1.2 Object being dropped, stopwatch used, place where object dropped, air temperature, altitude.

1.3.1.3 Height object dropped from.

1.3.1.4

1.3.1.5 About 1.0 s.

1.3.1.6 Difficult to do – author’s estimate is 2.4 s (theoretical value is 2.26 s).

1.3.1.7 The interpolation at 5 m is more accurate and reliable than the extrapolation at 25 m. Extrapolations rely on the trend shown by the graph continuing and this may not happen. It also involves estimating beyond the limits of the graph grid which causes inaccuracy.

1.3.1.8 About 11 m (theoretical answer is 11.025 m).

1.3.1.9 No. Conclusion can only be drawn from a straight line graph.

1.3.1.10

YX

Time to fall various distances (s)

0

2

4

6

8

10

12

14

16

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8Time (s)

Dis

tanc

e fa

llen

(m)

Distance fallen (m)

Time to fall (s)

(Time to fall)2 (s2)

0 0 0

2 0.64 0.41

4 0.90 0.81

6 1.11 1.23

8 1.28 1.64

10 1.43 2.04

12 1.56 2.43

14 1.69 2.86

355 Answers

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1.3.1.11

1.3.1.12 Time to fall squared is directly proportional to height dropped from.

1.3.1.13 9.8 m s–2

1.3.1.14 Yes, (unless coincidentally the planet it is on has the same gravitational field as Earth). Gravity on Earth is 9.8 m s–2 or very close to this, depending on altitude.

1.3.1.15 Time to fall squared is directly proportional to height dropped from.

1.3.1.16 Use average times to fall, repeat with objects of different mass, measure distances several times and use averages.

1.4.1.1 (a) A static field is one which is constant at any point in space in both magnitude and direction.

(b) The Earth’s gravitational field would be considered a static field because at any point in space around the Earth, the direction and the magnitude of the field will both be constant.

1.4.1.2 (a) A changing field is one which is varying in magnitude and/or direction.

(b) At an isolated point in space which is stationary relative to the Sun, the gravitational field due to Earth will change in both magnitude and direction as the Earth orbits the Sun.

1.4.1.3 (a) A uniform field is constant in both magnitude and direction – it will be represented by parallel field lines.

(b) Given that gravitational fields act towards the centre of mass of an object, we could consider the field very close to the Earth’s surface over a small area of surface to be uniform although technically the field lines will not be quite parallel.

1.4.1.4 (a) Non-uniform fields will vary in magnitude and/or direction.

(b) The Earth’s magnetic field is not uniform. Its magnitude varies with altitude and its direction, towards the centre of Earth, is different according to position in space.

1.4.1.5 Only (a) and (c) are correct.

(a) The field is static – although its direction is in a different direction at different points around the orbit neither its direction (towards the centre of mass of the planet) nor magnitude at any point changes.

(b) No. This is incorrect because the field at any point has constant magnitude and direction at that point. (Note that we take ‘towards the centre of mass of the planet’ as the direction, and this will always be the same, although, if observed from free space, it could be taken as a different direction).

(c) If the orbital altitude remains constant, then the magnitude of the field will also be constant.

(d) This is incorrect – see (b) and (c).

1.5.1.1 (a) The intensity of a gravitational field at any point in space is inversely proportional to the distance from the source of the field squared.

(b) Gravitational field, electric field, electromagnetic radiations.

1.5.1.2 D

1.5.1.3 (a) The graph shape reflects the inverse squared relationship between the variables.

(b) 4.8 N kg−1 (Note that reading the value at r = 2 and multiplying it by 4 is the more accurate way of estimating this value.)

1.6.1.1 (a) Magnets or current carrying coils

(b) Force

(c) North, south

(d) Field lines, vector lines

(e) Tangent

(f) South

(g) Repel

(h) Attract

(i) Close

(j) Closer

0

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0 0.5 1 1.5 2 2.5 3

Distance fallen versus (time to fall)2

(Time to fall )2 (s2)

Dis

tanc

e fa

llen

(m)

356Answers Dot Point VCE Physics Units 3 and 4

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1.6.1.2 In the answers below, the full arrows represent the fields due to the magnetic poles and the dotted lines represent the resultant force, and hence the direction of that force. Note that relative sizes of the forces need to take into account the distances of each point from the poles. According to our definition of field direction, we imagine a north monopole at each of the points and draw in the forces of repulsion or attraction as needed.

P

Q

S

R

T

U

1.7.1.1 (a) A magnetic monopole would consist of an isolated north or south magnetic pole.

(b) A magnetic dipole consists of a north-south magnetic pole pair, as in a bar magnet, or the poles of the Earth.

(c) Magnetic monopoles have not been found to exist. Obviously, magnetic dipoles exist – wherever there is a magnetic north pole, there will be a matching magnetic south pole.

1.7.1.2 (a)

(b) B = attractive field

C = repulsive field

1.8.1.1 We use the right hand grip rule, where the extended thumb indicates the direction of current flow in the wire and the curled fingers show the circular direction of the magnetic field around the wire.

1.8.1.2 Note that the relative numbers of dots and crosses should reflect the 2 A and 5 A current difference.

N N

N

A

C

B

S N S

Thumb(current)

Fingers(magnetic field)

2 A 5 A

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VCE PHYSICS UNITS 3 AND 4 • Brian Shadwick · PDF fileUnit 3 How Do Fields Explain Motion and Electricity? vi ... annotate Add brief notes to a diagram or graph. ... Dot Point VCE