Brian Shadwick - Sciencepress · 2020. 4. 29. · Set 3 Projectile Motion Problems 1 4 Set 4...

Module 5 Advanced Mechanics

Module 6 Electromagnetism

Questions and Answers

NSW PHYSICSAQAQ+

Brian Shadwick

5 and 6

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Contents

Words to Watch vii

Module 5 Advanced Mecahnics

Projectile Motion

Analyse the motion of projectiles by resolving the motion into horizontal and vertical components, making the following assumptions: a constant vertical acceleration due to gravity and zero air resistance.

Set 1 Resolving Vectors Into Components 2Set 2 Finding Vector Components 3

Apply the modelling of projectile motion to quantitatively derive the relationships between the following variables initial velocity, launch angle, maximum height, time of flight, final velocity, launch height and horizontal range. Solve problems, create models and make quantitative predictions by applying the equations of motion relationships for uniformly accelerated and constant rectilinear motion.

Set 3 Projectile Motion Problems 1 4Set 4 Projectile Motion Problems 2 7Set 5 Projectile Motion Problems 3 11

Conduct a practical investigation to collect primary data in order to validate the relationships derived for projectile motion.

Set 6 Analysing Projectile Motion 13

Motion In Gravitational Fields

Apply qualitatively and quantitatively Newton’s law of universal gravitation to determine the force of

gravity between two objects: F = GMm ______ r 2

.

Set 7 Mass and Weight 16Set 8 Gravitational Field 17Set 9 Newton’s law Of Universal 19 Gravitation

Apply qualitatively and quantitatively Newton’s law of universal gravitation to investigate the factors that affect the gravitational field strength: g = GM ____

r 2.

Apply qualitatively and quantitatively Newton’s Law of Universal Gravitation to predict the gravitational field strength at any point in a gravitational field, including at the surface of a planet.

Set 10 Acceleration Due To Gravity – 21 An ExperimentSet 11 Acceleration Due To Gravity – 22 A Pendulum ExperimentSet 12 Acceleration Due To Gravity 23

Investigate the orbital motion of planets and artificial satellites when applying the relationships between the following quantities: gravitational force, centripetal force, centripetal acceleration, mass, orbital radius, orbital velocity and orbital period.

Set 13 Orbital Motion Of Planets 24

Predict quantitatively the orbital properties of planets and satellites in a variety of situations, including near the Earth and geostationary orbits, and relate these to their uses.

Set 14 Types Of Orbits 26

Derive quantitatively and apply the concepts of gravitational force and gravitational potential energy in radial gravitational fields to the concept

of escape velocity: vesc = 2GMr

.

Set 15 Escape Velocity 28

Derive quantitatively and apply the concepts of gravitational force and gravitational potential energy in radial gravitational fields to total potential energy

of a planet or satellite in its orbit: U = − GMm ______ r

.

Derive quantitatively and apply the concepts of gravitational force and gravitational potential energy in radial gravitational fields to total energy of a

planet or satellite in its orbit: E = − GMm ______ 2 r

.

Derive quantitatively and apply the concepts of gravitational force and gravitational potential energy in radial gravitational fields to energy changes that occur when satellites move between orbits.

Set 16 Gravitational Potential Energy 1 30Set 17 Gravitational Potential Energy 2 31Set 18 Total Energy Of an Orbiting Satellite 34

Module 5 Advanced MechanicsModule 6 Electromagnetism

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iiiQuestions and Answers NSW Physics Modules 5 and 6

Derive quantitatively and apply the concepts of gravitational force and gravitational potential energy in radial gravitational fields to Kepler’s laws of planetary motion. Investigate the relationship of Kepler’s laws of planetary motion to the forces acting on, and the total energy of, planets in circular and non-circular

orbits using: vo = 2 π r ____ T

and r 3 ___ T 2

= GM ____ 4 π 2

.

Set 19 Kepler’s Laws Of Planetary Motion 35Set 20 Kepler’s Third Law 36

Circular Motion

Conduct investigations to explain and evaluate, for objects executing uniform circular motion, the relationships that exist between centripetal force, mass, speed and radius of turn.

Set 21 Circular Motion 38

Analyse the forces acting on an object executing uniform circular motion for cars moving around horizontal circular bends. Analyse the forces acting on an object executing uniform circular motion for a mass on a string.

Set 22 Forces In Circular Motion 41

Analyse the forces acting on an object executing uniform circular motion for objects on banked tracks.

Set 23 Circular Motion On a Banked Curve 43

Solve problems, model and make quantitative predictions about objects executing uniform circular motion in a variety of situations, using the

relationships: a = v 2 __ r

, ΣF = mv 2 ____ r

and ω = Δθ ___ t

.

Set 24 More Circular Motion Problems 44

Investigate the relationship between the total energy and work done on an object executing uniform circular motion.

Set 25 Total Energy Of a Satellite and 46 Work Done

Investigate the relationship between the rotation of mechanical systems and the applied torque: τ = rF⊥ = rF sin θ.

Set 26 Rotational Torque 48

Module 6 Electromagnetism

Charged Particles, Conductors and Electric and Magnetic Fields

Investigate and quantitatively derive and analyse the interaction between charged particles and uniform electric fields, including the electric field between

parallel charged plates: E = − V __ d

.

Investigate and quantitatively derive and analyse the interaction between charged particles and uniform electric fields, including acceleration of charged particles by the electric field: F = ma, F = qE.

Set 27 Electrostatic Charges 52Set 28 Electric Fields 54Set 29 Force On a Charge In an Electric Field 56Set 30 Electric Field Diagrams – Revision 58Set 31 Electric Field Strength Between 59 Parallel Plates

Investigate and quantitatively derive and analyse the interaction between charged particles and uniform electric fields, including the work done on the charge: W = qV, W = qEd, KE = 1 _

2 mv2.

Set 32 Work Done By a Field 61

Model qualitatively and quantitatively the trajectories of charged particles in electric fields and compare them with the trajectories of projectiles in a gravitational field.

Set 33 Shapes Of Trajectories 64

Analyse the interaction between charged particles and uniform magnetic fields, including the acceleration, perpendicular to the field, of charged particles. Analyse the interaction between charged particles and uniform magnetic fields, including the force on the charge: F = qvB sin θ. Compare the interaction of charged particles moving in magnetic fields to the interaction of charged particles with electric fields.

Set 34 Moving Charges In a Magnetic Field 1 65Set 35 Moving Charges In a Magnetic Field 2 66Set 36 Moving Charges In a Magnetic Field 3 68


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iv Questions and Answers NSW Physics Modules 5 and 6

Compare the interaction of charged particles moving in magnetic fields to other examples of uniform circular motion.

Set 37 Other Examples Of Uniform Circular 70 Motion

The Motor Effect

Investigate qualitatively and quantitatively the interaction between a current carrying conductor and a uniform magnetic field (F = BIL sin θ) to establish conditions under which the maximum force is produced, the relationship between the directions of the force, magnetic field strength and current, and conditions under which no force is produced on the conductor.

Set 38 The Motor Effect 1 72Set 39 The Motor Effect 2 73Set 40 Conductors In Magnetic Fields 1 75Set 41 Analysing Experimental Results 76Set 42 Conductors In Magnetic Fields 2 77

Conduct a quantitative investigation to demonstrate the interaction between two parallel current carrying wires. Analyse the interaction between two parallel current

carrying wires ( F __ L

= μ0 ___ 2π

× I1 I2 ____ r ) and determine the

relationship between the International System of Units (SI) definition of an ampere and Newton’s third law of motion.

Set 43 Forces Between Parallel 79 Conductors 1Set 44 Forces Between Parallel 81 Conductors 2Set 45 Another Practical Analysis 83

Electromagnetic Induction

Describe how magnetic flux can change, with reference to the relationship ɸ = BA.

Set 46 Magnetic Flux and Flux Density 84

Analyse qualitatively and quantitatively, with reference to energy transfers and transformations, examples

of Faraday’s law and Lenz’s law (ε = −ΔΦ ____ Δt ), including

but not limited to the generation of an electromotive force (emf) and evidence for Lenz’s law produced by the relative movement between a magnet, straight conductors, metal plates and solenoids or changes in current in one solenoid in the vicinity of another solenoid.

Set 47 Faraday and Induction 86Set 48 Lenz’s Law and Electromagnetic 88 InductionSet 49 Lenz’s Law and Coils 90

Analyse quantitatively the operation of ideal transformers through the application of Vp __ Vs

= Np ___ Ns

and VpIp = VsIs.

Set 50 Transformers 92

Evaluate qualitatively the limitations of the ideal transformer model and the strategies used to improve transformer efficiency, including but not limited to incomplete flux linkage and resistive heat production and eddy currents. Analyse applications of step-up and step-down transformers, including but not limited to the distribution of energy using high voltage transmission lines.

Set 51 Transformers and Electricity 95 Transmission


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vQuestions and Answers NSW Physics Modules 5 and 6

Applications Of the Motor Effect

Investigate the operation of a simple DC motor to analyse the functions of its components and the production of a torque (τ = nBA cos θ) and the effects of back emf.

Set 52 Torque On a Coil 1 97Set 53 Torque On a Coil 2 99Set 54 Simple DC Motors 100Set 55 Improving the Simple Motor 101Set 56 Back Emf In Motors 102

Analyse the operation of simple DC and AC generators and AC induction motors.

Set 57 The DC Generator 103Set 58 The AC Generator 105Set 59 Comparing DC and AC Generators 107 and MotorsSet 60 The AC Induction Motor 108

Relate Lenz’s law to the law of conservation of energy and apply the law of conservation of energy to DC motors and magnetic braking.

Set 61 Lenz’s Law and the Conservation 109 Of Energy

Answers 111Data Sheet 167Formula Sheet 168Periodic Table 169


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vi Questions and Answers NSW Physics Modules 5 and 6

account, account for State reasons for, report on,

give an account of, narrate a series of events or

transactions.

analyse Interpret data to reach conclusions.

annotate Add brief notes to a diagram or graph.

apply Put to use in a particular situation.

assess Make a judgement about the value of

something.

calculate Find a numerical answer.

clarify Make clear or plain.

classify Arrange into classes, groups or categories.

comment Give a judgement based on a given

statement or result of a calculation.

compare Estimate, measure or note how things are

similar or different.

construct Represent or develop in graphical form.

contrast Show how things are different or opposite.

create Originate or bring into existence.

deduce Reach a conclusion from given information.

define Give the precise meaning of a word, phrase or

physical quantity.

demonstrate Show by example.

derive Manipulate a mathematical relationship(s) to

give a new equation or relationship.

describe Give a detailed account.

design Produce a plan, simulation or model.

determine Find the only possible answer.

discuss Talk or write about a topic, taking into account

different issues or ideas.

distinguish Give differences between two or more

different items.

draw Represent by means of pencil lines.

estimate Find an approximate value for an unknown

quantity.

evaluate Assess the implications and limitations.

examine Inquire into.

explain Make something clear or easy to understand.

extract Choose relevant and/or appropriate details.

extrapolate Infer from what is known.

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

identify Recognise and name.

interpret Draw meaning from.

investigate Plan, inquire into and draw conclusions about.

justify Support an argument or conclusion.

label Add labels to a diagram.

list Give a sequence of names or other brief answers.

measure Find a value for a quantity.

outline Give a brief account or summary.

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

predict Give an expected result.

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

recall Present remembered ideas, facts or experiences.

relate Tell or report about happenings, events or circumstances.

represent Use words, images or symbols to convey meaning.

select Choose in preference to another or others.

sequence Arrange in order.

show Give the steps in a calculation or derivation.

sketch Make a quick, rough drawing of something.

solve Work out the answer to a problem.

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

suggest Put forward an idea for consideration.

summarise Give a brief statement of the main points.

synthesise Combine various elements to make a whole.

Words to Watch


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viiQuestions and Answers NSW Physics Modules 5 and 6

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viii Questions and Answers NSW Physics Modules 5 and 6


Science Press

1

Module 5 Advanced Mechanics

FOCUSCONTENT In this module you will:

~ Describe and analyse qualitatively and quantitatively circular motion and motion in a gravitational field, in particular, the projectile motion of particles.

~ Explain and analyse motion in one dimension at constant velocity or constant acceleration.

~ Extend your study of motion into examples involving two or three dimensions that cause the net force to vary in size or direction.

~ Develop an understanding that all forms of complex motion can be explained by analysing the forces acting on a system, including the energy transformations taking place within and around the system.

~ Apply new mathematical techniques to model and predict the motion of objects within systems. You will examine two-dimensional motion, including projectile motion and uniform circular motion, along with the orbital motion of planets and satellites, which are modelled as an approximation to uniform circular motion.

~ Engage with all the Working Scientifically skills for practical investigations involving the focus content to examine trends in data and to solve problems related to advanced mechanics.

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NSW PHYSICS 5and 6

Questions and Answers NSW Physics Modules 5 and 6

FOCUSCONTENT Analyse the motion of projectiles by resolving the motion

into horizontal and vertical components, making the following assumptions: a constant vertical acceleration due to gravity and zero air resistance.

SET 1 Resolving Vectors Into Components

1. Calculate the missing values in the table.

2. Find the horizontal and vertical components of each of the following vectors. All vectors are drawn to a scale where 1 cm = 10 m. All answers to one decimal place.

(c)(a)

(d)

(e)

(f)

(g)

(b)

Vector Magnitude Angle of inclination

from horizontalHorizontal component

Vertical component

1 60 24 A = B =

2 66 66 C = D =

3 E = 42 68 F =

4 G = H = 46 87

5 350 I = J = 200

Projectile Motion


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2 Questions and Answers NSW Physics Modules 5 and 6

SET 2 Finding Vector Components

1. The boxes indicate several pairs of perpendicular vector components. Sketch vector diagrams to combine them to find the resultant vectors.

(a) Horizontal component = 38 m E

Vertical component = 46 m N

(b) Horizontal component = 26 m W

Vertical component = 72 m S

(c) Horizontal component = 35 m E


(d) Horizontal component = 62 m W


(e) Horizontal component = 55 m E


(f) Horizontal component = 75 m E



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3Questions and Answers NSW Physics Modules 5 and 6

FOCUSCONTENT

Apply the modelling of projectile motion to quantitatively derive the relationships between the following variables initial velocity, launch angle, maximum height, time of flight, final velocity, launch height and horizontal range. Solve problems, create models and make quantitative predictions by applying the equations of motion relationships for uniformly accelerated and constant rectilinear motion.

SET 3 Projectile Motion Problems 1

1. An aeroplane is flying horizontally at 240 m s−1 at an altitude of 1500 m. A small parcel is dropped from the aeroplane.

(a) What is the initial horizontal velocity of the parcel?

(b) What is the initial vertical velocity of the parcel?

(c) How long does it take the parcel to reach the ground?

(d) What horizontal distance will it travel in this time?

(e) What is the final horizontal velocity of the parcel (just as it hits the ground)?

(f) What its final vertical velocity?

(g) Find the final velocity of the parcel.

2. A car is driving at 12 m s−1 on a flat road towards the edge of a cliff. Its brakes fail just as it approaches the edge of the cliff. It goes over the edge and hits the ground at the bottom 3.5 s later.

(a) What was its initial vertical velocity?

(b) How far out from the edge of the cliff does it hit the bottom?

(c) What is the height of the cliff?

(d) With what velocity does it hit the ground at the bottom of the cliff?

3. A ball moving horizontally at 6 m s−1 rolls off the edge of a 125 m cliff.

(a) How long will it take the ball to hit the water at the bottom of the cliff?

(b) How far out from the edge does the ball hit the water?

(c) Find its velocity on hitting the water.

4. A ball is thrown horizontally with a speed of 14.0 m s−1 from a height of 2.0 m above the ground.

(a) Find its initial horizontal velocity.

(b) Find its initial vertical velocity.

(c) How long does it take to reach the ground?

(d) What horizontal distance will it travel in this time?

(e) Find the final horizontal velocity of the ball just as it hits the ground.

(f) Find its final vertical velocity.

(g) What is the final velocity of the ball?

5. A gun is aimed directly at the centre of the bullseye in a target 60 m away. It fires a bullet horizontally at 300 m s−1 directly at the bullseye. Where does the bullet hit the target?

6. Two balls are thrown at the same time horizontally outwards from the top of a 147 m high building. Ball A is thrown at 15 m s−1 and ball B at 17.5 m s−1.

(a) Which ball will hit the ground first, and by how much?

(b) How far apart will the balls be when they hit the ground?

(c) What will be the vertical velocity of ball A just as it hits the ground?

(d) What will be the vertical velocity of ball B just as it hits the ground?


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7. An arrow is fired horizontally at 30 m s−1 at an apple in a tree. Just as the arrow starts its flight, the apple falls from the tree. If the arrow and the apple are 15 m above the ground at the start, and the apple is 45 m from the archer, find:

(a) How long it takes the arrow to reach the apple.

(b) How far above the ground the arrow is after travelling the 45 m.

(c) How far the apple has fallen by the time the arrow has travelled 45 m.

(d) Whether or not the arrow hits the apple. Justify your answer.

8. Ball X is fired horizontally from a 1.2 m high table at 2.6 m s−1. Ball Y is projected vertically out from the edge of the table at 1.5 m s−1.

(a) How much further out from the edge of the table does ball Y land? About:

(A) 0.5 m

(B) 0.7 m

(C) 1.0 m

(D) 1.25 m

(b) With what velocity will X hit the floor?

(A) 4.85 m s−1

(B) 5.08 m s−1

(C) 5.50 m s−1

(D) 23.52 m s−1

9. A ball is rolled at different speeds along a horizontal benchtop until it falls over the edge towards the floor. Which graph best shows the velocity of the ball as it falls to the floor?

(A) (B) (C) (D)

v v v v

t t t t

10. A ball is rolled at constant speed along a horizontal benchtop until it falls over the edge towards the floor. Which graph best shows the acceleration of the ball as it falls to the floor?

(A) (B) (C) (D)

a a a a

t t t t

Ball X

Ball Y


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5Questions and Answers NSW Physics Modules 5 and 6

11. A student rolls two balls X and Y, X with mass m and Y with mass 2m across a benchtop so that they leave the edge at the same time and with the same speed.

Four students made statements about the flight of the two balls:

Jacinta: Y hits the ground before X.

Chin: X and Y hit the ground at the same time.

Mario: X hits the ground twice as far away from the table compared to Y.

Pasqual: X hits the ground the same distance from the table as Y.

Whose statement about the two balls is correct?

(A) Mario and Jacinta.

(B) Mario and Chin.

(C) Pasqual and Jacinta.

(D) Pasqual and Chin.

12. Several balls are rolled at different speeds along a benchtop until they fall over the edge towards the floor. Which statement about these balls is correct?

(A) All four balls will hit the floor at the same time.

(B) The slowest ball will hit the floor first; the fastest will hit it last.

(C) The fastest ball will hit the floor first; the slowest will hit it last.

(D) All balls will land in the same position at the same time.

13. A cannon was fired at an elevation of 40°. It was then loaded with an identical charge and ball and fired again at an elevation of 50°. Which statement about the two cannonballs is correct?

(A) The first cannonball will have a shorter time of flight.

(B) The first cannonball will have a longer time of flight.

(C) The first cannonball will have the longer range.

(D) The first cannonball will have the shorter range.

X

Y

Mass m


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Questions and Answers NSW Physics Modules 5 and 6 111

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NSW PHYSICS 5and 6

Answers

Set 1 Resolving Vectors Into Components

1. A = 54.8

B = 24.4

C = 26.8

D = 60.3

E = 91.5

F = 61.2

G = 98

H = 62o

I = 55.2°

J = 287.5

2.

Set 2 Finding Vector Components

1. (a) 59.7 m bearing 040° (all to nearest degree)

(b) 76.6 m s−1 bearing 200°

(c) 91.9 m s−1 bearing 022°

(d) 65.8 m bearing 250°

(e) 105.5 m s−1 bearing 149°

(f) 87.5 m bearing 015°

Set 3 Projectile Motion Problems 1

1. (a) 240 m s−1

(b) 0

(c) 17.5 s

(d) 4199 m

(e) 240 m s−1

(f) 171.5 m s−1

(g) 295 m s−1 at 35.5° below the horizontal

2. (a) 0

(b) 42 m

(c) 60 m

(d) 36.3 m s−1 at 70.7° down from horizontal (or 19.3° to the vertical)

3. (a) 5.05 s

(b) 30.3 m

(c) 49.85 m s−1 at 6.9° to the vertical

4. (a) 14.0 m s−1

(b) 0

(c) 0.64 s

(d) 8.96 m

(e) 14.0 m s−1

(f) 6.26 m s−1

(g) 15.34 m s−1 at 24.1° down from horizontal

Horizontal component = vector cos θ Vertical component = vector sin θ

(a) 4.9 3.4

(b) 2.9 3.4

(c) 6.6 2.4

(d) 3.5 4.2

(e) 8.6 6.0

(f) 2.4 6.6

(g) 14.1 5.1


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Brian Shadwick - Sciencepress · 2020. 4. 29. · Set 3 Projectile Motion Problems 1 4 Set 4...

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