vce physics unit 3

VCE PHYSICS UNIT 3 ÊÊÊÀ>Ê->`ÜVÊUÊÌÌÊ>À}>Û> Study Design 2009 © Science Press 2009 First published 2009 Science Press Private Bag 7023 Marrickville NSW 1475 Australia Tel: (02) 9516 1122 Fax: (02) 9550 1915 sales@sciencepress.com.au www.sciencepress.com.au 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 Science Press. ABN 98 000 073 861 Contents Introduction v Verbs to Watch vi Dot Points Motion in One and Two Dimensions vii Electronics and Photonics ix Einstein’s Special Theory of Relativity xi Materials and Their Use in Structures xiii Further Electronics xv Questions Motion in One and Two Dimensions 1 Electronics and Photonics 89 Einstein’s Special Theory of Relativity 129 Materials and Their Use in Structures 171 Further Electronics 215 Answers Motion in One and Two Dimensions 263 Electronics and Photonics 279 Einstein’s Special Theory of Relativity 287 Materials and Their Use in Structures 295 Further Electronics 303 Appendix Data Sheet 312 Science Press Dot Point VCE Physics Unit 3 iii Contents Notes ......................................................................................................................................................................................................................................................... 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Science Press Contents iv Dot Point VCE Physics Unit 3 Introduction What the book includes In this book you will find typical examination questions and answers for each dot point in the VCE Physics Study Design for the following topics in the Year 12 course: s -OTIONIN/NEAND4WO$IMENSIONS s %LECTRONICAND0HOTONICS s %INSTEINS3PECIAL4HEORYOF2ELATIVITY s -ATERIALSAND4HEIR5SEIN3TRUCTURES s &URTHER%LECTRONICS Format of the book The book has been formatted in the following way: 1.1 etc Area of Study knowledge statement. Note that the numbering of these statements is the authors’ choice and has been used to make referencing questions and answers clearer. The individual knowledge statements are not numbered in the study design, they are simply bulleted – hence our use of ‘dot points’ when we refer to them. 1.1.1 First typical question which could be asked in an examination for dot point 1.1 1.1.2 Second typical question which could be asked in an examinaton for dot point 1.1. Note also that some questions using the same stimulus diagrams may not relate to the same dot point as the first question using that diagram. How to use the book Completing all questions will provide you with an overview of all the work you need to know from the study design. 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, but not for the VCE. 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 to work you should spend more time revising later, and allow you to spend your study time more productively. Science Press Dot Point VCE Physics Unit 3 v Introduction Verbs to Watch account/account for State reasons for, report on, give an account of, narrate a series of events or transactions. distinguish Recognise or note/indicate as being distinct or different from, note difference between things. analyse Identify components and the relationships among them, draw out and relate implications. evaluate Make a judgement based on criteria. examine Inquire into. apply Use, utilise, employ in a particular situation. explain Relate cause and effect, make the relationship between things evident, provide why and/or how. appreciate Make a judgement about the value of something. extract Choose relevant and/or appropriate details. assess Make a judgement of value, quality, outcomes, results or size. extrapolate Infer from what is known. calculate Determine from given facts, figures or information. identify Recognise and name. clarify Make clear or plain. interpret Draw meaning from. classify Arrange into classes, groups or categories. investigate Plan, inquire into and draw conclusions about. compare Show how things are similar and different. justify Support an argument or conclusion. construct Make, build, put together items or arguments. outline Sketch in general terms; indicate the main features. contrast Show how things are different or opposite. predict Suggest what may happen based on available data. critically (analyse/evaluate) Add a degree or level of accuracy, depth, knowledge and understanding, logic, questioning, reflection and quality to an analysis or evaluation. propose Put forward (a point of view, idea, argument, suggestion etc) for consideration or action. deduce Draw conclusions. recall Present remembered ideas, facts or experiences. define State the meaning of and identify essential qualities. recommend Provide reasons in favour. demonstrate Show by example. recount Retell a series of events. describe Provide characteristics and features. summarise Express concisely the relevant details. discuss Identify issues and provide points for and against. synthesise Put together various elements to make a whole. Science Press Verbs to Watch vi Dot Point VCE Physics Unit 3 Motion in One and Two Dimensions Dot Point Page Dot Point Page 3 1.8 Analyse transformations of energy between kinetic energy, strain potential energy, gravitational potential energy, and energy dissipated to the environment. 63 Analyse the uniform circular motion of an object moving in a horizontal plane. 19 1.9 Apply gravitational field and gravitational force concepts. 73 79 Apply Newton’s second law to circular motion in a vertical plane, considering forces at the highest and lowest points only. 27 1.10 Apply the concepts of weight, apparent weight, weightlessness and apparent weightlessness. 1.11 Model satellite motion as uniform circular motion. 83 1.4 Investigate and analyse the motion of projectiles near the Earth’s surface including a qualitative description of the effects of air resistance. 33 1.12 Identify and apply safe and responsible practices when working with objects and equipment in investigations of motion. 87 1.5 Apply laws of conservation of momentum and energy in isolated systems. 41 1.6 Analyse impulse in an isolated system, for collisions between objects moving in a straight line. 49 1.7 Apply the concept of work done by a constant force. 57 1.1 Apply Newton’s three laws of motion in situations where two or more coplanar forces act along a straight line and in two dimensions. 1.2 1.3 Answers to Motion in One and Two Dimensions 263 Science Press Dot Point VCE Physics Unit 3 vii Motion in One and Two Dimensions Space Notes ......................................................................................................................................................................................................................................................... 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Science Press Motion in One and Two Dimensions viii Dot Point VCE Physics Unit 3 Electronics and Photonics Dot Point Page 2.1 Apply the concepts of current, resistance, potential difference (voltage drop) and power to the operation of electronic circuits comprising diodes, resistors, thermistors and photonic transducers including LDRs, photodiodes and LEDs. 91 2.2 Calculate the effective resistance of circuits comprising parallel and series resistance and unloaded voltage dividers. 99 2.3 2.4 Describe energy transfers and transformations in opto-electronic devices. 107 Describe the transfer of information in analog form using light intensity modulation and demodulation. 111 Dot Point Page 2.5 Design, investigate and analyse circuits for particular purposes using technical specifications related to potential difference, current, resistance, power, temperature and illumination for electronic components such as diodes, resistors, thermistors, LDRs, photodiodes and LEDs. 115 2.6 Analyse voltage characteristics of amplifiers including linear voltage gain and clipping. 119 2.7 Identify and apply safe and responsible practices when conducting investigations involving electrical, electronic and photonic equipment. 127 Answers to Electronics and Photonics 279 Science Press Dot Point VCE Physics Unit 3 ix Electronics Motors and andGenerators Photonics Notes ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 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Science Press Electronics and Photonics x Dot Point VCE Physics Unit 3 From Ideas Einstein’s Special to Implementation Theory of Relativity Dot Point 3.1 3.2 3.3 Describe the prediction from Maxwell’s equations that the speed of light depends only on the electrical and magnetic properties of the medium through which it is passing, and not on the speed of the source or the speed of the medium. Page Dot Point 131 Compare the prediction from Maxwell’s 133 equations of an absolute speed of light with the classical principle of relativity, i.e. no absolute zero velocity; all velocity measurements are relative to the frame of reference. Describe Einstein’s two postulates for his special theory of relativity and compare them to classical theory: s T HELAWSOFPHYSICSARETHESAME in all inertial frames of reference s T HESPEEDOFLIGHTHASACONSTANT value for all observers regardless of their motion or the motion of the source. 3.6 Explain the concepts of proper time (to) and proper length (Lo) as quantities that are measured in the frame of reference in which the objects are at rest. 3.7 Explain the unfamiliar nature 151 of motion at speeds approaching c by mathematical modelling time dilation and length contraction using the equations: Interpret the results of the Michelson-Morley experiment in terms of Einstein’s second postulate. 139 3.5 Apply simple thought experiments to show that: 147 s T HETIMEINTERVALBETWEENTWO events differs depending on the motion of an observer relative to the events (non-simultaneity) s LENGTHCONTRACTIONOFANOBJECT occurs in the direction of its motion when observed from a different frame of reference. 149 t = toȖ and L = Lo/Ȗ where Ȗ= (1 – v2/c2)–½ 3.8 Apply Einstein’s prediction by showing that the total mass-energy of an object is given by Etot = Ek + Erest = mc2 where m = moȖ and so kinetic energy, Ek = (Ȗ – 1)mc2 163 3.9 Explain that mass can be converted into energy and vice versa, E = ǻmc2 165 135 3.4 Page 3.10 Explain the impossibility of motion faster than light in terms of relativistic mass m = mo at speeds approaching c. 169 Answers to Einstein’s Special Theory of Relativity 287 Science Press Dot Point VCE Physics Unit 3 xi Einstein’s From Special IdeasTheory to Implementation of Relativity Notes ......................................................................................................................................................................................................................................................... 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Science Press Einstein’s Special Theory of Relativity xii Dot Point VCE Physics Unit 3 From Ideas Materials and to Their Implementation Use in Structures Dot Point 4.1 4.2 4.3 4.4 Page Identify different types of external forces such as compression, tension and shear, that can act on a body, including gravitational forces. 173 Evaluate the suitability of different materials for use in structures, including beams, columns and arches, by comparing tensile and compressive strength and stiffness or flexibility under load. 177 Dot Point Analyse the behaviour of materials 181 under load in terms of extension and compression, including Young’s modulus, Y = σ . ε Calculate the stress and strain resulting 187 from the application of compressive and tensile forces and loads to materials in structures, σ = F , ε = Δl A Describe brittle and ductile failure and apply data to predict brittle or ductile failure under load. 4.6 Calculate the potential energy stored 191 in a material under load (strain energy) using area under the stress versus strain graph. 4.7 Evaluate the toughness of a material tested to the point of failure. 193 4.8 Describe elastic or plastic behaviour of materials under load and the resulting energy transformed to heat 195 4.9 Evaluate the suitability of a composite material for its use in a structure by considering its properties and the properties of the component materials (maximum of three components). 197 4.10 Calculate torque, . 201 4.11 Analyse translational and rotational 205 forces (torques) in simple structures, including uniform columns, struts, ties, beams, cables, but not including trusses, modelled as two-dimensional structures in static equilibrium. 4.12 Identify safe and responsible practices 213 when working with structures, materials and associated measuring equipment in investigations of materials. l 4.5 Page 189 Answers to Materials and Their Use in Structures 295 Science Press Dot Point VCE Physics Unit 3 xiii Materials andFrom Their Quanta Use in Structures to Quarks Notes ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 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Science Press Materials and Their Use in Structures xiv Dot Point VCE Physics Unit 3 From Ideas Further Electronics to Implementation Dot Point 5.1 Page Design and investigate an AC to DC voltage regulated power supply system, given a range of AC input voltages (specified as RMS, peak and peak-to-peak), smoothing conditions and resistive loads. 217 Describe the role of a transformer, including the analysis of voltage ratio, N1/N2 = V1/V2, but not including induction. 219 5.3 Describe effects on the DC power supply system of changes to the components used. 221 5.4 Interpret information from the display of an oscilloscope in terms of voltage as a function of time. 227 5.5 Analyse circuits, including fault diagnosis, following selection and use of appropriate measuring devices, including analog meters, multimeters, and oscilloscope. 229 5.2 5.6 5.7 Dot Point Evaluate the operation of a circuit in 231 terms of its design brief by selecting measurements of potential difference (voltage drop) and current (using analog meters, multimeters and oscilloscope) in the DC power supply circuit. Explain the function of diodes in half-wave and full-wave bridge rectification. Page 5.8 Explain the effect of capacitors in terms of: 239 s POTENTIALDIFFERENCEVOLTAGEDROP and current when charging and discharging s TIMECONSTANTFORCHARGINGAND discharging, Ĳ = RC s SMOOTHINGFOR$#POWERSUPPLIES 5.9 Apply the current-voltage characteristics of voltage regulators, including Zener diodes and integrated circuits, to circuit design. 245 5.10 Describe, qualitatively, the effect on the magnitude of the ripple voltage of changing the effective load, the capacitance and input supply voltage (magnitude and period). 251 5.11 Describe the use of heat sinks in electronic circuits. 255 5.12 Calculate power dissipation in circuit elements, P = VI, P = I2R, P = V 2/R. 257 5.13 Identify and apply safe and responsible responsible practices when undertaking investigations involving electrical and electronic equipment. 259 Answers to Further Electronics 303 235 Science Press Dot Point VCE Physics Unit 3 xv Further Astrophysics Electronics Notes 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Science Press Further Electronics xvi Dot Point VCE Physics Unit 3 DOT POINT ÌÊÊ"iÊ>`Ê/ÜÊiÃÃ Science Press Dot Point VCE Physics Unit 3 1 Motion in One and Two Dimensions Notes ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 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Science Press Motion in One and Two Dimensions 2 Dot Point VCE Physics Unit 3 1.1 Apply Newton’s three laws of motion in situations where two or more coplanar forces act along a straight line and in two dimensions. 1.1.1 Recall Newton’s first law of motion. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.1.2 Explain the relationship between Newton’s first law of motion and the concept of inertia. 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1.1.3 Explain, in terms of the principles of physics involved, why it is potentially dangerous to leave loose objects on the back shelf of a car. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.1.4 Explain, in terms of the principles of physics involved why it is dangerous to drive a car without wearing a seatbelt. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.1.5 Identify two real-life situations where Newton’s first law of motion is apparent, and explain how this affects the person involved. ......................................................................................................................................................................................................................................................... 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Science Press Dot Point VCE Physics Unit 3 3 Motion in One and Two Dimensions 1.1.6 Identify two real-life situations where Newton’s first law of motion is not apparent, and explain why it is not apparent. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.1.7 Explain the role of the inertia of passengers in each of the following situations. For each situation, outline what forces do act on the passenger (ignore weight force and reaction to weight force). (a) The school bus turning a corner. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ........................................................................................................................................................................................................................................................ ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (b) A plane accelerating down the runway. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (c) A lift in a high-rise building starting to move upwards. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (d) A lift in a high rise building starting to move downwards. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Motion in One and Two Dimensions 4 Dot Point VCE Physics Unit 3 1.1.8 Assess the relative effectiveness of lap, lap-sash and harness seatbelts in reducing the effects of inertia in collisions. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.1.9 Assess reasons for the introduction of lower speed limits for vehicles in built-up areas. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.1.10 Outline how airbags work to reduce the effects of inertia. ......................................................................................................................................................................................................................................................... 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1.1.12 The inertia of a spacecraft in deep space keeps it travelling towards its destination. The inertia of a moving car does not – it slows and stops. Explain the reasons for the difference. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Dot Point VCE Physics Unit 3 5 Motion in One and Two Dimensions 1.1.13 Recall Newton’s second law of motion. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.1.14 Recall the mathematical equation which governs Newton’s second law of motion. ......................................................................................................................................................................................................................................................... 1.1.15 Calculate the force acting on a 5.0 kg mass which accelerates for 3.0 s. During this time its velocity changes from 2.5 m s–1 east to 17.5 m s–1 west. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.1.16 A 12 N force acts on a body and accelerates it from rest to 4.5 m s–1 south. This takes 15 s. Calculate the mass of the body. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.1.17 An 80 g object is initially at rest. A 0.16 N force to the north acts on it for 5 s. Calculate: (a) The acceleration produced by the force. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (b) The final velocity of the object. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (c) Its displacement after 5 s. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Motion in One and Two Dimensions 6 Dot Point VCE Physics Unit 3 1.1.18 Consider the two blocks shown in the diagram. They are resting on a surface which provides a frictional force of 0.25 N kg–1. Y X 18 N (a) 2.5 kg 5.5 kg Calculate the acceleration of the system. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (b) Calculate the net force on each block. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (c) Calculate the force block X puts on block Y. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (d) Calculate the force block Y puts on block X. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.1.19 Consider the two blocks shown in the diagram. They are resting on a smooth surface. Y X 36 N (a) 3.0 kg 6.0 kg Calculate the acceleration of the system. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Dot Point VCE Physics Unit 3 7 Motion in One and Two Dimensions (b) Calculate the net force on each block. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (c) Calculate the force tension in the string. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.1.20 Consider the object shown in the diagram. Several forces act on this object which is at rest on a smooth, horizontal surface. (a) Calculate the net force on the object. 15 N 26 N 4 kg 6N ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (b) Calculate the acceleration of the object. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (c) Calculate its velocity after 5.0 s ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (d) Calculate its displacement after 5 s. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Motion in One and Two Dimensions 8 Dot Point VCE Physics Unit 3 1.1.21 Consider the two blocks shown in the diagram. They are connected by a light string over a frictionless pulley. X 2 kg Y 4 kg (a) Label all the forces acting in this pulley system, then calculate: (b) The acceleration of the system. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (c) The net force on each block. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (d) The tension in the string connecting the blocks. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Dot Point VCE Physics Unit 3 9 Motion in One and Two Dimensions 1.1.22 Consider the two blocks shown in the diagram. They are connected by a light string over a frictionless pulley. Block X is resting on a smooth surface. X 2 kg Y 5 kg (a) Label all the forces acting in this pulley system. (b) Calculate the acceleration of the system. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (c) Calculate the net force on each block. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (d) Calculate the tension in the string connecting the blocks. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.1.23 A 3 kg mass is resting on a newton balance in an elevator. Complete the table to show the reading on the balance under the conditions of movement of the elevator given. Movement of elevator Reading on newton balance (a) Stationary (b) Moving up at 2.0 m s–1 (c) Moving down at 2.0 m s–1 (d) Moving up at 2.0 m s–2 (e) Moving down at 2.0 m s–2 Science Press Motion in One and Two Dimensions 10 Dot Point VCE Physics Unit 3 1.1.24 Two masses are connected by a string and are hanging from the ceiling of an elevator as shown. Complete the table to show the tensions in each string under the conditions of movement of the elevator given. Movement of elevator Tension in string 1 (N) Tension in string 2 (N) (a) Stationary (b) Moving up at 3.0 m s–1 (c) Moving down at 3.0 m s–1 (d) Moving up at 3.0 m s–2 (e) Moving down at 3.0 m s–2 1.1.25 A ball is hanging by a string from the ceiling of a bus. Describe the motion of the bus when the string is: (a) Hanging straight down. ......................................................................................................................................................................................................................................................... (b) Hanging down towards the rear of the bus. ......................................................................................................................................................................................................................................................... (c) Hanging down towards the front of the bus. ......................................................................................................................................................................................................................................................... Science Press Dot Point VCE Physics Unit 3 11 Motion in One and Two Dimensions 1.1.26 A 3.0 kg ball is hanging by a string from the ceiling of a bus as shown in the diagram. (a) Label the forces acting on the ball. 10º 3 kg ball (b) Using an appropriate vector diagram, calculate the tension in the string when the ball is in the position shown. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (c) Calculate the acceleration of the bus. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (d) At what angle would the ball and string hang if the bus was breaking at 2.5 m s–2? ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Motion in One and Two Dimensions 12 Dot Point VCE Physics Unit 3 1.1.27 Analysing an experiment 1. Trolley Pulley Mass In this experiment, a trolley of mass 1.5 kg was placed on the bench accelerated by a force attached to it by a string, which passed over a pulley. The mass of the trolley was kept constant and different forces used to accelerate it from rest across the benchtop. The time it took the trolley to travel 1.0 m across the benchtop was measured. The results are shown in the table. Run Accelerating force (N) Time to travel Initial speed of 1.0 m (s) trolley (m s–1) 1 F 0.89 2 2F 0.63 3 3F 0.52 4 4F 0.45 5 5F 0.40 Average speed of trolley (m s–1) Final speed of trolley (m s–1) Acceleration of trolley (m s–2) (a) Complete the table by calculating values for all missing data. (b) Draw a graph to show the relationship between the force and acceleration produced. (Place force on the y-axis.) (c) Use your graph to write a conclusion for the experiment. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Dot Point VCE Physics Unit 3 13 Motion in One and Two Dimensions 1.1.28 Analysing an experiment 2. The students did another experiment using the same apparatus. This time they kept the accelerating force constant, and changed the mass of the trolley. They measured how long it took the trolley to move 1.0 m across the benchtop. Run Trolley mass (kg) Time to travel 1.0 m (s) 1 1.0 1.83 2 2.0 2.58 3 3.0 3.16 4 4.0 3.65 5 5.0 4.08 Initial speed of trolley (m s–1) Average speed of trolley (m s1) Final speed Acceleration of trolley of trolley (m s–2) (ms–1) (a) Complete the table of results by calculating values for all missing quantities. (b) Graph mass vs. (acceleration)–1. (c) Use your graph to write a conclusion for the experiment. (Acceleration)–1 ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Motion in One and Two Dimensions 14 Dot Point VCE Physics Unit 3 Combining your conclusions for experiments 1 and 2 (d) Use the conclusions you have written to write a mathematical equation, which shows the relationship between the mass of an object, the force acting on it and the acceleration the force produces. ......................................................................................................................................................................................................................................................... (e) Use the results of the experiments to find the value of the accelerating forces in the two experiments above. Experiment 1 ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Experiment 2 ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.1.29 Maria is riding her skateboard, total mass 60 kg, down a slight incline at a constant speed of 12 m s–1. The air is providing a resistance of 40 N and the wheels of the skates provide another 6 N of frictional force. (a) What is the net force acting on Maria? Justify your answer. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (b) If the incline is at 10° what is the component of the weight force of Maria and her skateboard down the incline? ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (c) What force does the ground exert on the wheels of the skateboard in opposition to its motion? ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Dot Point VCE Physics Unit 3 15 Motion in One and Two Dimensions 1.1.30 A cyclist of mass 65 kg pedals a 35 kg bike up a 15° incline at a constant speed. (a) Draw a diagram and label all the forces acting in this situation. (b) What is the net force on the cyclist as he pedals up the incline? ......................................................................................................................................................................................................................................................... (c) If the frictional forces against motion are 40 N, what force does the cyclist exert on the bike to ride it up the incline? ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (d) When he reaches the top, the rider turns around and coasts down the incline. His acceleration is 1.5 m s–2. What frictional forces oppose his motion? ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Opposing force (N) 1.1.31 A 1500 kg boat accelerates at a constant rate across the surface of a lake. As its speed increases, the opposing forces applied to it by the water and air resistance change as shown in the graph. After travelling 500 m it travels at constant speed. 12 000 10 000 8000 6000 4000 2000 0 0 (a) 100 200 300 Distance (m) 400 500 What total force do the engines apply to the boat after it has travelled 500 m? ......................................................................................................................................................................................................................................................... (b) What is the net force acting on the boat after it has travelled 500 m? ......................................................................................................................................................................................................................................................... Science Press Motion in One and Two Dimensions 16 Dot Point VCE Physics Unit 3 (c) What is the force exerted by the engines as the boat reaches the 200 m mark? ......................................................................................................................................................................................................................................................... (d) Calculate the acceleration of the boat at the instant is reaches the 300 m mark. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.1.32 A police officer measured the skid marks of a 1200 kg car which crashed into a barrier across the road at 75 m long. She estimates that the frictional forces between the car and the road while it skidded into the barrier averaged 15 000 N. If the speed limit in the area was 90 kph, and assuming the driver applied the brakes where the skid marks start, by how much was the driver breaking the speed limit when he first applied the brakes? ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.1.33 State Newton’s third law of motion. ......................................................................................................................................................................................................................................................... 1.1.34 Describe an example of Newton’s third law of motion. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.1.35 Two students are riding in a dodgem car (X) when the car behind (Y) crashes into their car. Describe the forces on the students during this collision and indicate which of Newton’s laws of motion apply. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Dot Point VCE Physics Unit 3 17 Motion in One and Two Dimensions Notes ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 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Science Press Motion in One and Two Dimensions 18 Dot Point VCE Physics Unit 3 1.2 Analyse the uniform circular motion of an object moving in a horizontal plane. 1.2.1 Two 60 kg boys on 20 kg bikes are riding at 15 m s–1 directly towards a wall which is 30 m from them. X continues towards the wall, but slams on his brakes applying a 400 N force. Y does not put on his brakes, but turns his bike with the same force in a circular path in the hope of not hitting the wall. Analyse this information to determine whether or not the boys hit the wall. (a) For X ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (b) For Y ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.2.2 A toy racing car of mass 150 g is racing around a circular track of diameter 80 cm. It takes 8.4 s to do one lap of the track. Calculate: (a) The speed of the car. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (b) The acceleration of the car. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (c) The centripetal force acting on the car. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Dot Point VCE Physics Unit 3 19 Motion in One and Two Dimensions 1.2.3 A 1500 kg racing car goes around a circular track of radius 200 m at a constant speed of 270 kph. (a) Calculate the speed of the car in m s–1. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (b) Calculate the acceleration of the car. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (c) What force holds the car to the road as it speeds around this corner. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (d) Calculate the value of this force. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (e) State the direction this force acts. ......................................................................................................................................................................................................................................................... (f) Predict the value of this force if the speed of the car was to halve. ......................................................................................................................................................................................................................................................... 1.2.4 A toy train of mass 600 g moves around a circular track of diameter 3.0 m. The maximum frictional force experienced by the train is 0.16 N. What is the maximum speed of the train so that it stays on the tracks? ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Motion in One and Two Dimensions 20 Dot Point VCE Physics Unit 3 1.2.5 A particular horse on a merry-go-round is 3.5 m from the centre. A 20 kg child sits on the horse as it goes around, completing 16 revolutions in the 4-minute ride time. (a) What acceleration does the child experience? ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (b) Calculate the average acceleration experienced by the child during each complete revolution. ......................................................................................................................................................................................................................................................... (c) Calculate the horizontal speed of the child while the merry-go-round is working. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.2.6 The tracks at velodromes are banked to allow cyclists to travel at very fast speeds. A particular track is banked at 20o and has a radius of curvature of 105 m. The diagram represents a cyclist and her bike, total mass 75 kg, travelling at constant speed on this track. (a) Draw and label any forces acting on the cyclist. (b) What is the component of the weight force of the cyclist and her bike down the incline on the banked track? ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (c) If the track surface itself provides 15 N against slippage down the bank, what is the maximum speed this cyclist can travel at safely? ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.2.7 A cycling track in a park is totally flat and provides 125 N of sideways friction on each of the wheels of a 15 kg bike ridden by a 20 kg child at each corner. The radius of the curve at each of the four corners is 15 m. Calculate the maximum safe speed the child can be going as he turns the corners. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Dot Point VCE Physics Unit 3 21 Motion in One and Two Dimensions 1.2.8 A racing car, mass 750 kg, moving with constant speed, experiences a horizontal force of 15 000 N as it turns an unbanked corner of radius 35 m. (a) What is the net force acting on the car? ......................................................................................................................................................................................................................................................... (b) Calculate the speed of the car around the corner. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (c) What provides this force? ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (d) What will be the average force on each tyre? ......................................................................................................................................................................................................................................................... 1.2.9 The diagram represents a front view of the wheels of a train which is travelling towards you (out of the page). The train is about to turn towards its left (right as you look at it). Wheel X Wheel Y Train about to turn this way Rail X Rail Y (a) On the diagram label the force(s) that cause the train to turn in the direction shown. (b) Referring to the principles of physics involved, justify your answer. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Motion in One and Two Dimensions 22 Dot Point VCE Physics Unit 3 1.2.10 The diagram represents a car travelling at constant speed around a circular track. On this diagram draw a labelled vector to indicate each of the following: (a) The instantaneous velocity of the car. (b) The acceleration of the car. (c) The net force acting on the car. 1.2.11 An object is travelling in uniform circular motion in a circle of radius 0.25 m. The diagram represents a stroboscopic photograph taken of the object over a 0.5 s interval. (a) What is the speed of the object? ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... (b) What is its acceleration? ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... (c) A student now adjusts the stroboscope so that it flashes twice as fast. Complete the diagram (above) to show what would be observed on the photograph for the next half revolution of the object. (d) What would be the acceleration of the object now? ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Dot Point VCE Physics Unit 3 23 Motion in One and Two Dimensions 1.2.12 A toy train of mass 250 g is travelling on a circular track of radius 50 cm, on a frictionless, horizontal table. (a) What is the magnitude and direction of the force of the table on the mass? ......................................................................................................................................................................................................................................................... (b) If the car comes off the tracks when the centripetal force is just greater than 3 × 10–2 N, what is its maximum possible speed around the track? ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (c) If a carriage of mass 200 g was coupled to the engine, what would be its maximum frequency of rotation? ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... 1.2.13 A pilot in an aircraft will black out if his plane turns in a circle with too small a radius. The average acceleration air force pilots can withstand is about 4 g or 39.2 m s–2. What is the tightest horizontal circle a pilot in an aircraft flying at 950 kph can make? ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Motion in One and Two Dimensions 24 Dot Point VCE Physics Unit 3 1.2.14 Two balls, X and Y are attached to the ends of light strings as shown in the diagram. They are swung in a horizontal circle, each completing that circle in the same time despite that fact that the radius of the circle for X is 0.3 m and that for Y is 0.2 m. Point of suspension X Y 0.2 m 0.3 m (a) Determine the value of the ratio of the angular speed of X to that of Y. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (b) Determine the value of the ratio of the linear speed of X to that of Y. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (c) Determine the value of the ratio of the centripetal accelerations of X and Y. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... (d) If X has a mass twice that of Y, determine the value of the ratio of the centripetal forces acting on X and Y. ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... ......................................................................................................................................................................................................................................................... Science Press Dot Point VCE Physics Unit 3 25 Motion in One and Two Dimensions

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