CfE Higher Physics Tutorial Questions

Curriculum For Excellence Higher Physics Tutorial Questions

Compiled and edited by F. Kastelein

Source – GWC, LTS, ES

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Boroughmuir High School

City of Edinburgh Council




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Vector problems

1. Complete a table with the headings “vectors” and “scalars” with 4 physical quantities in each column.

2. Write a simple description, in your own words, to distinguish between vector and scalar quantities.

3. What was the velocity of the runner in lane 1 in the women’s 400m final at the London

Olympics?

4. What is your average velocity from 3a.m. Monday to 3a.m. Tuesday? Give a reason for your answer.

5. A car travels 50 km due north and then returns 30 km due south. The whole journey takes

2 hours.

Calculate:

(a) the total distance travelled by the car

(b) the average speed of the car

(c) the resultant displacement of the car

(d) the average velocity of the car.

6. A girl delivers newspapers to three houses, X, Y and Z, as shown in the diagram. She starts at X and walks directly from X to Y and then to Z.

(a) Calculate the total distance the girl walks.

(b) Calculate the girl’s final displacement from X.

(c) The girl walks at a steady speed of 1 m s -1 .

(i) Calculate the time she takes to get from X to Z.

(ii) Calculate her resultant velocity.

Equations of Motion (s u v a t)

1. An object is travelling at a speed of 8·0 ms -1 . It then accelerates uniformly at 4·0 ms -2 for

10 s. How far does the object travel in this 10 s?

2. A car is travelling at a speed of 15·0 ms

-1

. It accelerates uniformly at 6·0 ms

-2 and travels a distance of 200 m while accelerating. Calculate the velocity of the car at the end of the 200 m.

3. A ball is thrown vertically upwards to a height of 40 m above its starting point. Calculate the speed at which it was thrown.

4. A car is travelling at a speed of 30·0 ms -1 . It then slows down at 1·80 ms -2 until it comes to rest. It travels a distance of 250 m while slowing down. What time does it take to travel the

250 m?

5. A stone is thrown with an initial speed 5·0 ms -1 vertically down a well. The stone strikes the water 60 m below where it was thrown. Calculate the time taken for the stone to reach the surface of the water. (The effects of friction can be ignored).



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6. A tennis ball launcher is 0·60 m long. One tennis ball leaves the launcher at a speed of

30 ms

-1

.

(a) Calculate the average acceleration of the tennis ball in the launcher.

(b) Calculate the time the ball accelerates in the launcher.

7. In an experiment to find ‘g’ a steel ball falls from rest through a distance of 0·40 m. The time taken to fall this distance is 0·29 s. What is the value of ‘g’ calculated from the data of this experiment?

8. A trolley accelerates uniformly down a slope. Two light gates connected to a motion computer are spaced 0·50 m apart on the slope. The speeds recorded as the trolley passes the light gates are 0·20 ms

-1 and 0·50 ms

-1

.

(a) Calculate the acceleration of the trolley.

(b) What time does the trolley take to travel the 0·5 m between the light gates?

9. A helicopter is rising vertically at a speed of 10·0 ms

-1 when a wheel falls off. The wheel hits the ground 8·00 s later. Calculate the height of the helicopter above the ground when the wheel came off. The effects of friction can be ignored.

10. A ball is thrown vertically upwards from the edge of a cliff as shown in the diagram. The effects of friction can be ignored.

(a) (i) What is the height of the ball above sea level 2·0 s after being thrown?

(ii) What is the velocity of the ball 2·0 s after being thrown?

(b) What is the total distance travelled by the ball from launch to landing in the sea?

Free Falling Objects

1. Draw a diagram to show the forces acting on a 3kg mass at the instant it is released.

2. What will the initial acceleration of the object be?

3. What happens to the magnitude of the air resistance acting on the object as it falls? Explain your answer.

4. Describe what happens to the acceleration of the object as it falls, you must justify your answer.

5. Give an example of a situation when the air resistance is greater than the weight of a falling object.

6. Why can the air resistance not exceed the weight of the object for any length of time?

What would happen if this situation did occur?

7. Sketch a velocity time graph for the motion of an object that experiences air resistance; assume it is falling from a very large height.



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Displacement –Time Graphs

1. Draw a displacement time graph to represent the following information:

Billy walks 50m East, at a constant rate, in a time of 40s. He then turns and walks 30m West in 30s. He stops for 20s before continuing West for another 50m in a time of 20s.

2. Draw Billy’s corresponding velocity time graph.

3. The graph shows how the displacement of an object varies with time.

(a) Calculate the velocity of the object between 0 and 1 s.

(b) What is the velocity of the object between 2 and 4 s from the start?

(c) Draw the corresponding distance against time graph for the movement of this object.

(d) Calculate the average speed of the object for the 8 seconds shown on the graph.

(e) Draw the corresponding velocity against time graph for the movement of this object.

4. The graph shows how the displacement of an object varies with time.

(a) Calculate the velocity of the object during the first second from the start.

(b) Calculate the velocity of the object between 1 and 5 s from the start.

(c) Draw the corresponding distance against time graph for this object.

(d) Calculate the average speed of the object for the 5 seconds.

(e) Draw the corresponding velocity against time graph for this object.

(f) What are the displacement and the velocity of the object 0·5 seconds after the start?

(g) What are the displacement and the velocity of the object 3 seconds after the start?



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5. The graph shows the displacement against time graph for the movement of an object.

(a) Calculate the velocity of the object between 0 and 2 s.

(b) Calculate the velocity of the object between 2 and 4 s from the start.

(c) Draw the corresponding distance against time graph for this object.

(d) Calculate the average speed of the object for the 4 seconds.

(e) Draw the corresponding velocity against time graph for this object.

(f) What are the displacement and the velocity of the object 0·5 s after the start?

(g) What are the displacement and the velocity of the object 3 seconds after the start?

6. Sketch velocity time graphs for the displacement time graphs below. No numerical values are required. [Hint: think of the gradient!]

Velocity – Time Graphs

1. An object starts from a displacement of 0 m. The graph shows how the velocity of the object varies with time from the start.

(a) Calculate the acceleration of the object between 0 and 1 s.

(b) What is the acceleration of the object between 2 and 4 s from the start?

(c) Calculate the displacement of the object 2 seconds after the start.

(d) What is the displacement of the object 8 seconds after the start?

(e) Sketch the corresponding displacement against time graph for the movement of this object.



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2. An object starts from a displacement of 0 m. The graph shows how the velocity of the object varies with time from the start.

(a) Calculate the acceleration of the object between 0 and 2 s.

(b) Calculate the acceleration of the object between 2 and 4 s from the start.

(c) Draw the corresponding acceleration against time graph for this object.

(d) What are the displacement and the velocity of the object 3 seconds after the start?

(e) What are the displacement and the velocity of the object 4 seconds after the start?

(f) Sketch the corresponding displacement against time graph for the movement of this object.

3. The velocity-time graph for an object is shown.

A positive value indicates a velocity due north and a negative value indicates a velocity due south. The displacement of the object is 0 at the start of timing.

(a) Calculate the displacement of the object:

(i) 3 s after timing starts

(ii) 4 s after timing starts

(iii) 6 s after timing starts.

(b) Draw the corresponding acceleration–time graph.



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Curriculum For Excellence Higher Physics

4. The graph shows the velocity of a ball that is dropped and bounces on a floor.

Tutorial Questions

(a) Which direction is represented by a positive velocity?

(b) In which direction is the ball travelling during section OB of the graph?

(c) Describe the velocity of the ball as represented by section CD of the graph.

(d) Describe the velocity of the ball as represented by section DE of the graph.

(e) What happened to the ball at the time represented by point B on the graph?

(f) What happened to the ball at the time represented by point C on the graph?

(g) How does the speed of the ball immediately before rebound from the floor compare with the speed immediately after rebound?

(h) Sketch a graph of acceleration against time for the movement of the ball.

Acceleration – Time Graphs

1. The graph shows how the acceleration a, of an object, starting from rest, varies with time.

Draw a graph to show how the velocity of the object varies with time for the 10 seconds of the motion.

2. The graph shows how the acceleration of an object changes with time. The object begins at rest.

(a) Calculate the speed of the object after 4 seconds.

(b) Calculate the speed of the object after 7 seconds.

(c) Draw a velocity time graph for the 10s of motion.



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Thinking Questions

1. Describe a situation where a runner has a displacement of 100 m due north, a velocity of 3 m s -1 due north and an acceleration of 2 ms -2 due south. Your description should include a diagram. [TQ]

2. Is it possible for an object to be accelerating but have a constant speed? You must justify your answer. [TQ]

3. Is it possible for an object to move with a constant speed for 5 s and have a displacement of 0 m?

You must justify your answer. [TQ]

4. Is it possible for an object to move with a constant velocity for 5 s and have a displacement of 0 m?

You must justify your answer. [TQ]

5. The following questions relate to the graph shown below. This velocity time graph represents the motion of a ball dropped from rest onto a surface.

(a). Why will the acceleration of the ball be the same when it is moving upwards as when it is moving downwards?

(b). What will the acceleration be if this experiment was conducted on Earth?

(c). Why will the velocity of the ball immediately after rebounding be less than the initial velocity of the ball?

(d). Sketch a graph showing the velocity time graph if the time of contact during rebound was not zero.

(e). Sketch a graph showing the velocity time graph if the air resistance was not zero.



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Forces questions revisited

1. State Newton’s 1st Law of Motion.

2. A lift of mass 500 kg travels upwards at a constant speed.

Calculate the tension in the cable that pulls the lift upwards.

3. A fully loaded oil tanker has a mass of 2·0 × 10 8 kg.

As the speed of the tanker increases from 0 to a steady maximum speed of 8.0 m s propellers remains constant at 3.0 × 10 6 N.

-1 the force from the

(a) (i) Calculate the acceleration of the tanker just as it starts from rest.

(ii) What is the size of the force of friction acting on the tanker when it is moving at a steady speed of 8.0 ms -1 ?

(b) When its engines are stopped, the tanker takes 50 minutes to come to rest from a speed of 8.0 m s -1 . Calculate its average deceleration.

4. The graph shows how the speed of a parachutist varies with time after having jumped from an aeroplane.

With reference to the origin of the graph and the letters A, B, C, D and E explain the variation of speed with time for each stage of the parachutist’s fall.

5. Two girls push a car of mass 2000 kg. Each applies a force of 50 N and the force of friction is 60 N.

Calculate the acceleration of the car.

6. A boy on a skateboard rides up a slope. The total mass of the boy and the skateboard is 90 kg. He decelerates uniformly from 12 ms -1 to 2 ms -1 in 6 seconds. Calculate the resultant force acting on him.

7. A box of mass 30 kg is pulled along a rough surface by a constant force of 140 N. The acceleration of the box is 4·0 ms -2 .

(a) Calculate the magnitude of the unbalanced force causing the acceleration.

(b) Calculate the force of friction between the box and the surface.



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8. A car of mass 800 kg is accelerated from rest to 18 ms -1 in 12 seconds.

(a) What is the size of the resultant force acting on the car?

(b) How far does the car travel in these 12 seconds?

(c) At the end of the 12 seconds period the brakes are operated and the car comes to rest in a distance of 50 m. What is the size of the average frictional force acting on the car?

Higher Forces

9. A rocket of mass 4·0 × 10 4 kg is launched vertically upwards from the surface of the Earth. Its engines produce a constant thrust of 7·0 × 10 5 N.

(a) (i) Draw a diagram showing all the forces acting on the rocket just after take-off.

(ii) Calculate the initial acceleration of the rocket.

(b) As the rocket rises the thrust remains constant but the acceleration of the rocket increases. Give three reasons for this increase in acceleration.

(c) Explain in terms of Newton’s laws of motion why a rocket can travel from the

Earth to the Moon and for most of the journey not burn up any fuel.

10. A rocket takes off from the surface of the Earth and accelerates to 90 ms -1 in a time of 4·0 s. The resultant force acting on it is 40 kN upwards.

(a) Calculate the mass of the rocket.

(b) The average force of friction is 5000 N. Calculate the thrust of the rocket engines.

11. A helicopter of mass 2000 kg rises upwards with an acceleration of 4·00 ms -2 . The force of friction caused by air resistance is 1000N. Calculate the upwards force produced by the rotors of the helicopter.

12. A crate of mass 200 kg is placed on a balance, calibrated in newtons, in a lift.

(a) What is the reading on the balance when the lift is stationary?

(b) The lift now accelerates upwards at 1·50 ms balance?

-2 . What is the new reading on the

(c) The lift then travels upwards at a constant speed of 5·00 ms -1 . What is the new reading on the balance?

(d) For the last stage of the journey the lift decelerates at 1·50 ms -2 while going up.

Calculate the reading on the balance.

13. A small lift in a hotel is fully loaded and has a total mass of 250 kg. For safety reasons the tension in the pulling cable must never be greater than 3500 N.

(a) What is the tension in the cable when the lift is:

(i) at rest

(ii) moving up at a constant speed of 1 ms -1

(iii) moving up with a constant acceleration of 2 ms -2

(iv) moving down with a constant acceleration of 2 ms -2 .

(b) Calculate the maximum permitted upward acceleration of the fully loaded lift.

(c) Describe a situation where the lift could have an upward acceleration greater than the value in (b) without breaching safety regulations.



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14. A package of mass 4·00 kg is hung from a spring (Newton) balance attached to the ceiling of a lift.

The lift is accelerating upwards at 3·00 ms -2 . What is the reading on the spring balance?

15. The graph shows how the downward speed of a lift varies with time.

(a) Draw the corresponding acceleration against time graph.

(b) A 4.0 kg mass is suspended from a spring balance inside the lift. Determine the reading on the balance at each stage of the motion.

16. Two trolleys joined by a string are pulled along a frictionless flat surface as shown.

(a) Calculate the acceleration of the trolleys.

(b) Calculate the tension, T, in the string joining the trolleys.

17. A car of mass 1200 kg tows a caravan of mass 1000 kg. The frictional forces on the car and caravan are 200 N and 500 N, respectively. The car accelerates at 2.0 ms -2 .

(a) Calculate the force exerted by the engine of the car.

(b) What force does the tow bar exert on the caravan?

(c) The car then travels at a constant speed of 10 ms -1 . Assuming the frictional forces to be unchanged, calculate:

(i) the new engine force

(ii) the force exerted by the tow bar on the caravan.

(d) The car brakes and decelerates at 5·0 ms -2 . Calculate the force exerted by the brakes

(assume the other frictional forces remain constant).

18. A log of mass 400 kg is stationary. A tractor of mass 1200 kg pulls the log with a tow rope. The tension in the tow rope is 2000 N and the frictional force on the log is 800 N. How far will the log move in 4 s?



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19. A force of 60 N is used to push three blocks as shown.

Each block has a mass of 8·0 kg and the force of friction on each block is 4·0 N.

Tutorial Questions

(a) Calculate:

(i) the acceleration of the blocks

(ii) the force that block A exerts on block B

(iii) the force block B exerts on block C.

(b) The pushing force is then reduced until the blocks move at constant speed.

(i) Calculate the value of this pushing force.

(ii) Does the force that block A exerts on block B now equal the force that block B exerts on block C? Explain.

20. A 2·0 kg trolley is connected by string to a 1·0 kg mass as shown. The bench and pulley are frictionless.

(a) Calculate the acceleration of the trolley.

(b) Calculate the tension in the string.

Resolution of Forces

1. A man pulls a garden roller with a force of 50 N.

(a) Find the effective horizontal force applied to the roller.

(b) Describe and explain how the man can increase this effective horizontal force without changing the size of the force applied.

2. A barge is dragged along a canal as shown below.

What is the size of the component of the force parallel to the canal?



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3. A toy train of mass 0·20 kg is given a push of 10 N along the rails at an angle of 30º above the horizontal.

Calculate:

(a) the magnitude of the component of force along the rails

(b) the acceleration of the train.

4. A barge of mass 1000 kg is pulled by a rope along a canal as shown.

The rope applies a force of 800 N at an angle of 40º to the direction of the canal. The force of friction between the barge and the water is 100 N. Calculate the acceleration of the barge.

5. A crate of mass 100 kg is pulled along a rough surface by two ropes at the angles shown.

(a) The crate is moving at a constant speed of 1·0 ms friction?

-1 . What is the size of the force of

(b) The forces are now each increased to 140 N at the same angle. Assuming the friction force remains constant, calculate the acceleration of the crate.

6. A 2·0 kg block of wood is placed on a slope as shown.

The block remains stationary. What are the size and direction of the frictional force on the block?

7. A runway is 2·0 m long and raised 0·30 m at one end. A trolley of mass 0·50 kg is placed on the runway. The trolley moves down the runway with constant speed. Calculate the magnitude of the force of friction acting on the trolley. [Hint: draw a sketch of the set up]



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8. A car of mass 900 kg is parked on a hill. The slope of the hill is 15º to the horizontal. The brakes on the car fail. The car runs down the hill for a distance of 50 m until it crashes into a hedge. The average force of friction on the car as it runs down the hill is 300 N.

(a) Calculate the component of the weight acting down the slope.

(b) Find the acceleration of the car.

(c) Calculate the speed of the car just before it hits the hedge.

9. A trolley of mass 2·0 kg is placed on a slope which makes an angle of 60º to the horizontal.

(a) A student pushes the trolley and then releases it so that it moves up the slope. The force of friction on the trolley is 1·0 N.

(i) Why does the trolley continue to move up the slope after it is released?

(ii) Sketch a diagram to show the forces acting on the trolley after the pushing force is removed.

(iv) Calculate acceleration of the trolley as it moves up the slope.

(iii) Calculate the unbalanced force on the trolley as it moves up the slope, after the pushing force is removed.

(b) The trolley eventually comes to rest then starts to move down the slope.

(i) Sketch a diagram to show the forces acting on the trolley as it moves down the slope.

(ii) Calculate the unbalanced force on the trolley as it moves down the slope.

(iii) Calculate the acceleration of the trolley down the slope.

Work, Potential and Kinetic Energy[recap]

1. A small ball of mass 0·20 kg is dropped from a height of 4·0 m above the ground. The ball rebounds to a height of 2·0 m.

(a) Calculate total loss in energy of the ball.

(b) Calculate the speed of the ball just before it hits the ground.

(c) Calculate the speed of the ball just after it leaves the ground.

2. A box of mass 70 kg is pulled along a horizontal surface by a horizontal force of 90 N. The box is pulled a distance of 12 m. There is a frictional force of 80 N between the box and the surface.

(a) Calculate the total work done by the pulling force.

(b) Calculate the amount of kinetic energy gained by the box.



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3. A box of mass 2·0 kg is pulled up a frictionless slope as shown.

Tutorial Questions

(a) Calculate the gravitational potential energy gained by the box when it is pulled up the slope.

(b) The block is now released.

(i) Use conservation of energy to find the speed of the box at the bottom of the slope.

(ii) Use another method to confirm your answer to (i).

4. A winch driven by a motor is used to lift a crate of mass 50 kg through a vertical height of 20 m.

(a) Calculate the size of the minimum force required to lift the crate.

(b) Calculate the minimum amount of work done by the winch while lifting the crate.

(c) The power of the winch is 2·5 kW. Calculate the minimum time taken to lift the crate to the required height.

5. A train has a constant speed of 10 ms -1 over a distance of 2·0 km.

The driving force of the train engine is 3·0 × 10 4 N.

What is the power developed by the train engine?

6. An arrow of mass 22 g has a speed of 30 ms -1 as it strikes a target. The tip of the arrow goes

3·0 × 10 -2 m into the target.

(a) Calculate the average force of the target on the arrow.

(b) What is the time taken for the arrow to come to rest after striking the target, assuming the target exerts a constant force on the arrow?

Collisions and Explosions

1. What is the momentum of the objects in each of the following situations?



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2. A trolley of mass 2·0 kg is travelling with a speed of 1·5 ms -1 . The trolley collides and sticks to a stationary trolley of mass 2·0 kg.

(a) Calculate the velocity of the trolleys immediately after the collision.

(b) Show that the collision is inelastic.

3. A target of mass 4·0 kg hangs from a tree by a long string. An arrow of mass 100 g is fired at the target and embeds itself in the target. The speed of the arrow is 100 ms

-1 just before it strikes the target.

4. A trolley of mass 2·0 kg is moving at a constant speed when it collides and sticks to a second stationary trolley.

The graph shows how the speed of the 2·0 kg trolley varies with time.

Determine the mass of the second trolley.

5. In a game of bowls a bowl of mass 1·0 kg is travelling at a speed of 2·0ms -1 when it hits a stationary jack ‘straight on’. The jack has a mass of

300 g. The bowl continues to move straight on with a speed of 1·2 ms -1 after the collision.

(a) What is the speed of the jack immediately after the collision?

(b) How much kinetic energy is lost during the collision?

6. Two space vehicles make a docking maneuver (joining together) in space. One vehicle has a mass of 2000 kg and is travelling at 9·0 ms -1 . The second vehicle has a mass of 1500 kg and is moving at

8·0 ms -1 in the same direction as the first.

Determine their common velocity after docking.

7. Two cars are travelling along a race track. The car in front has a mass of 1400 kg and is moving at

20 ms -1 . The car behind has a mass of 1000 kg and is moving at 30ms -1 . The cars collide and as a result of the collision the car in front has a speed of 25 ms -1 .

(a) Determine the speed of the rear car after the collision.

(b) Show clearly whether this collision is elastic or inelastic.



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8. One train carriage approaches another from behind as shown.

Tutorial Questions

The carriage at the rear is moving faster than the one in front and they collide. This causes the carriage in front to be ‘nudged’ forward with an increased speed. Determine the speed of the rear carriage immediately after the collision.

9. A trolley of mass 0·8 kg is travelling at 1·5 ms -1 . It collides head-on with another vehicle of mass

1·2 kg travelling at 2·0 ms -1 in the opposite direction. The vehicles lock together on impact.

Determine the speed and direction of the vehicles after the collision.

10. A firework is launched vertically and when it reaches its maximum height it explodes into two pieces.

One of the pieces has a mass of 200 g and moves off with a speed of 10 ms -1 . The other piece has a mass of 120 g. What is the velocity of the second piece of the firework?

11. Two trolleys initially at rest and in contact move apart when a plunger on one trolley is released.

One trolley with a mass of 2 kg moves off with a speed of 4 ms -1 . The other moves off with a speed of

2 ms -1 , in the opposite direction. Calculate the mass of this trolley.

12. A man of mass 80 kg and woman of mass 50 kg are skating on ice. At one point they stand next to each other and the woman pushes the man. As a result of the push the man moves off at a speed of

0·5 ms -1 . What is the velocity of the woman as a result of the push?

13. Two trolleys initially at rest and in contact fly apart when a plunger on one of them is released.

One trolley has a mass of 2·0 kg and moves off at a speed of 2·0 ms -1 . The second trolley has a mass of 3·0 kg. Calculate the velocity of this trolley.

14. A cue exerts an average force of 7·00 N on a stationary snooker ball of mass 200 g. The impact of the cue on the ball lasts for 45·0 ms. What is the speed of the ball as it leaves the cue?

15 A football of mass 500 g is stationary. When a girl kicks the ball her foot is in contact with the ball for a time of 50 ms. As a result of the kick the ball moves off at a speed of 10 ms -1 . Calculate the average force exerted by her foot on the ball.

16. A stationary golf ball of mass 100 g is struck by a club. The ball moves off at a speed of 30 ms -1 .

The average force of the club on the ball is 100 N. Calculate the time of contact between the club and the ball.



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17. The graph shows how the force exerted by a hockey stick on a stationary hockey ball varies with time.

The mass of the ball is 150 g. Determine the speed of the ball as it leaves the stick.

18. A ball of mass 100 g falls from a height of 0·20 m onto concrete. The ball rebounds to a height of

0·18 m. The duration of the impact is 25 ms. Calculate:

(a) the change in momentum of the ball caused by the ‘bounce’

(b) the impulse on the ball during the bounce

(c) the average unbalanced force exerted on the ball by the concrete

(d) the average unbalanced force of the concrete on the ball.

(e) What is in the total average upwards force on the ball during impact?

19. A rubber ball of mass 40·0 g is dropped from a height of 0·800 m onto the pavement. The ball rebounds to a height of 0·450 m. The average force of contact between the pavement and the ball is

2·80 N.

(a) Calculate the velocity of the ball just before it hits the ground and the velocity just after hitting the ground.

(b) Calculate the time of contact between the ball and pavement.

20. A ball of mass 400 g travels falls from rest and hits the ground. The velocity-time graph represents the motion of the ball for the first 1·2 s after it starts to fall.

(a) Describe the motion of the ball during sections

AB, BC, CD and DE on the graph.

(b) What is the time of contact of the ball with the ground?

(c) Calculate the average unbalanced force of the ground on the ball.

(d) How much energy is lost due to contact with the ground?



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21. Water with a speed of 50 ms -1 is ejected horizontally from a fire hose at a rate of 25 kgs -1 . The water hits a wall horizontally and does not rebound from the wall. Calculate the average force exerted on the wall by the water.

22. A rocket ejects gas at a rate of 50 kgs -1 , ejecting it with a constant speed of 1800 ms -1 . Calculate magnitude of the force exerted by the ejected gas on the rocket.

23. Describe in detail an experiment that you would do to determine the average force between a football boot and a football as the ball is being kicked. Draw a diagram of the apparatus and include all the measurements taken and details of the calculations carried out.

24. A 2·0 kg trolley travelling at 6·0 ms -1 collides with a stationary 1·0 kg trolley. The trolleys remain connected after the collision.

(a) Calculate:

(i) the velocity of the trolleys just after the collision

(ii) the momentum gained by the 1·0 kg trolley

(iii) the momentum lost by the 2·0 kg trolley.

(b) The collision lasts for 0·50 s. Calculate the magnitude of the average force acting on each trolley.

25. In a problem two objects, having known masses and velocities, collide and stick together. Why does the problem ask for the velocity immediately after collision to be calculated? [TQ]

26. A Newton’s cradle apparatus is used to demonstrate conservation of momentum. Four steel spheres, each of mass 0.1 kg, are suspended so that they are in a straight line. Sphere 1 is pulled to the side and released, as shown in diagram I.

When sphere 1 strikes sphere 2 (as shown by the dotted lines) then sphere 4 moves off the line and reaches the position shown by the dotted lines.

The student estimates that sphere 1 has a speed of 2ms -1 when it strikes sphere 2. She also estimates that sphere 4 leaves the line with an initial speed of 2 ms -1 . Hence conservation of momentum has been demonstrated.

A second student suggests that when the demonstration is repeated there is a possibility that spheres 3 and 4, each with a speed of 0·5 ms -1 , could move off the line as shown in diagram II.

Use your knowledge of physics to show this is not possible. [TQ]



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Projectiles

1. A plane is travelling with a horizontal velocity of 350 ms -1 at a height of 300 m. A box is dropped from the plane. The effects of friction can be ignored.

(a) Calculate the time taken for the box to reach the ground.

(b) Calculate the horizontal distance between the point where the box is dropped and the point where it hits the ground.

(c) What is the position of the plane relative to the box when the box hits the ground?

2. A projectile is fired horizontally with a speed of 12·0 ms -1 from the edge of a cliff. The projectile hits the sea at a point 60·0 m from the base of the cliff.

(a) Calculate the time of flight of the projectile.

(b) What is the height of the starting point of the projectile above sea level?

State any assumptions you have made.

3. A ball is thrown horizontally with a speed of 15 ms -1 from the top of a vertical cliff. It reaches the horizontal ground at a distance of 45 m from the foot of the cliff.

(a) (i) Draw a graph of vertical speed against time for the ball for the time from when it is thrown until it hits the ground.

(ii) Draw a graph of horizontal speed against time for the ball.

(b) Calculate the velocity of the ball 2 s after it is thrown. (Magnitude and direction are required.)

4. A football is kicked up at an angle of 70º above the horizontal at 15 ms -1 . Calculate:

(a) the horizontal component of the velocity

(b) the vertical component of the velocity.



23




5. A projectile is fired across level ground and takes 6 s to travel from A to B.

The highest point reached is C. Air resistance is negligible.

Tutorial Questions

Velocity-time graphs for the flight are shown below. V

H vertical velocity. is the horizontal velocity and V

V is the

(a) Describe:

(i) the horizontal motion of the projectile

(ii) the vertical motion of the projectile.

(b) Use a vector diagram to find the speed and angle at which the projectile was fired from point A.

(c) Find the speed at position C. Explain why this is the smallest speed of the projectile. [TQ]

(d) Calculate the height above the ground of point C.

(e) Find the horizontal range of the projectile.

6. A ball of mass 5·0 kg is projected with a velocity of 40 ms -1 at an angle of 30º to the horizontal.

Calculate:

(a) the vertical component of the initial velocity of the ball

(b) the maximum vertical height reached by the ball

(c) the time of flight for the whole trajectory

(d) the horizontal range of the ball.

7. A launcher is used to fire a ball with a velocity of

100 ms -1 at an angle of 60º to the ground. The ball strikes a target on a hill as shown.

(a) Calculate the time taken for the ball to reach the target.

(b) What is the height of the target above the launcher?



24




8. A stunt driver attempts to jump across a canal of width 10 m. The vertical drop to the other side is

2 m as shown.

(a) Calculate the minimum horizontal speed required so that the car reaches the other side.

(b) Explain why your answer to (a) is the minimum horizontal speed required. [TQ]

(c) State any assumptions you have made. [TQ]

9. A ball is thrown horizontally from a cliff. The effect of friction can be ignored.

(a) Is there any time when the velocity of the ball is parallel to its acceleration? Justify your answer. [TQ]

(b) Is there any time when the velocity of the ball is perpendicular to its acceleration?

Justify your answer. [TQ]

10. A ball is thrown at an angle of 45º to the horizontal. The effect of friction can be ignored.

(a) Is there any time when the velocity of the ball is parallel to its acceleration? Justify your answer. [TQ]

(b) Is there any time when the velocity of the ball is perpendicular to its acceleration?

Justify your answer. [TQ]

11. A small ball of mass 0·3 kg is projected at an angle of

60º to the horizontal. The initial speed of the ball is 20 ms -1 .

Show that the maximum possible gain in potential energy of the ball is 45 J.

12. A ball is thrown horizontally with a speed of 20 ms -1 from a cliff. The effects of air resistance can be ignored. How long after being thrown will the velocity of the ball be at an angle of 45º to the horizontal?



25




Gravity and Mass

In the following questions, when required, use the following data:

Gravitational constant = 6·67 × 10 -11 N m 2 kg -2

1. State the inverse square law of gravitation.

2. Show that the force of attraction between two large ships, each of mass 5·00 × 10

7 kg and separated by a distance of 20 m, is 417 N.

3. Calculate the gravitational force between two cars parked 0·50 m apart. The mass of each car is 1000 kg.

4. In a hydrogen atom an electron orbits a proton with a radius of 5·30 × 10 an electron is 9·11 × 10

-31 kg and the mass of a proton is 1·67 × 10

-27 kg.

-11 m. The mass of

Calculate the gravitational force of attraction between the proton and the electron in a hydrogen atom.

5. The distance between the Earth and the Sun is 1·50 × 10

5·98 × 10

24 kg and the mass of the Sun is 1·99 × 10

11 m. The mass of the Earth is

30 kg. Calculate the gravitational force between the Earth and the Sun.

6. Two protons exert a gravitational force of 1·16 × 10

-55

N on each other. The mass of a proton is 1·67 × 10 -27 kg. Calculate the distance separating the protons.



26




Special Relativity

1. A river flows at a constant speed of 0·5 ms -1 south. A canoeist is able to row at a constant speed of

1·5 ms -1 .

(a) Determine the velocity of the canoeist relative to the river bank when the canoeist is paddling north.

(b) Determine the velocity of the canoeist relative to the river bank when the canoeist is paddling south.

2. In an airport, passengers use a moving walkway. The moving walkway is travelling at a constant speed of 0·8 ms -1 and is travelling east.

For the following people, determine the velocity of the person relative to the ground:

(a) a woman standing at rest on the walkway

(b) a man walking at 2·0 ms -1

in the same direction as the walkway is moving

(c) a boy running west at 3·0 ms -1 .

3. The steps of an escalator move upwards at a steady speed of 1·0 ms -1

relative to the stationary side of the escalator.

(a) A man walks up the steps of the escalator at 2·0 ms -1 . Determine the speed of the man relative to the side of the escalator.

(b) A boy runs down the steps of the escalator at 3·0 ms -1 relative to the side of the escalator.

. Determine the speed of the boy

4. In the following sentences the words represented by the letters A, B, C, D, E, F and G are missing:

In A Theory of Special Relativity the laws of physics are the B for all observers, at rest or moving at constant velocity with respect to each other ie C acceleration.

An observer, at rest or moving at constant D has their own frame of reference.

In all frames of reference the E , c, remains the same regardless of whether the source or observer is in motion.

Einstein’s principles that the laws of physics and the speed of light are the same for all observers leads to the conclusion that moving clocks run F (time dilation) and moving objects are G (length contraction).

Match each letter with the correct word from the list below: acceleration different lengthened Newton’s slow speed of light

Einstein’s same fast shortened velocity zero

5. An observer at rest on the Earth sees an aeroplane fly overhead at a constant speed of 2000 km h -1 .

At what speed, in km h -1 , does the pilot of the aeroplane see the Earth moving? [TQ]

6. A scientist is in a windowless lift. Can the scientist determine whether the lift is moving with a:

(a) uniform velocity

(b) uniform acceleration? speed does spaceship B see the light beam from spaceship A pass?

7. Spaceship A is moving at a speed of 2·4 × 10 8 ms -1 . It sends out a light beam in the forwards direction. Meanwhile another spaceship B moves towards spaceship A at 2·4 × 10 8 ms -1 . At what



27




8. A spacecraft is travelling at a constant speed of 7·5 × 10 7 ms -1 . It emits a pulse of light when it is

3·0 × 10 10 m from the Earth as measured by an observer on the Earth. Calculate the time taken for the pulse of light to reach the Earth according to a clock on the Earth when the spacecraft is moving:

(a) away from the Earth

(b) towards the Earth.

9. A spaceship is travelling away from the Earth at a constant speed of 1·5 × 10 8 ms -1 . A light pulse is emitted by a lamp on the Earth and travels towards the spaceship. Find the speed of the light pulse according to an observer on:

(a) the Earth

(b) the spaceship.

10. Convert the following fraction of the speed of light into a value in ms -1 :

(a) 0·1 c

(b) 0·5 c

(c) 0·6 c

(d) 0·8 c

11. Convert the following speeds into a fraction of the speed of light:

(a) 3·0 × 10 8 ms

-1

(b) 2·0 × 10 8 ms

-1

(c) 1·5 × 10 8 ms

-1

(d) 1·0 × 10 8 ms

-1

Time dilation

1. Write down the relationship involving the proper time t and dilated time t’ between two events which are observed in two different frames of reference moving at a speed, v, relative to one another

(where the proper time is the time measured by an observer at rest with respect to the two events and the dilated time is the time measured by another observer moving at a speed, v, relative to the two events).

2. In the table shown, use the relativity equation for time dilation to calculate the value of each missing quantity (a) to (f) for an object moving at a constant speed relative to the Earth.

Dilated time

(a)

(b)

1400 s

1.40 x 10 -4 s

Proper Time

20 h

10 years

(c)

(d)

Speed of Object (ms -1 )

1.00 x 10 8

2.25 x 10 8

2.00 x 10 8

1.00 x 10 8

84 s 60 s (e)

21 minutes 20 minutes (f)

3. Two observers P, on Earth, and Q, in a rocket, synchronise their watches at 11.00 am just as observer Q passes the Earth at a speed of 2 × 10 8 ms -1 .

(a) At 11.15 am according to observer P’s watch, observer P looks at Q’s watch through a telescope. Calculate the time, to the nearest minute, that observer P sees on Q’s watch.

(b) At 11.15 am according to observer Q’s watch, observer Q looks at P’s watch through a telescope. Calculate the time, to the nearest minute, that observer Q sees on P’s watch.



28




4. The lifetime of a star is 10 billion years as measured by an observer at rest with respect to the star.

The star is moving away from the Earth at a speed of 0·81 c. Calculate the lifetime of the star according to an observer on the Earth.

5. A spacecraft moving with a constant speed of 0·75 c passes the Earth. An astronaut on the spacecraft measures the time taken for Usain Bolt to run 100 m in the sprint final at the 2008 Olympic

Games. The astronaut measures this time to be 14·65 s. Calculate Usain Bolt’s winning time as measured on the Earth.

6. A scientist in the laboratory measures the time taken for a nuclear reaction to occur in an atom.

When the atom is travelling at 8·0 × 10 7 ms -1 the reaction takes 4·0 × 10 -4 s. Calculate the time for the reaction to occur when the atom is at rest.

7. The light beam from a lighthouse sweeps its beam of light around in a circle once every 10 s. To an astronaut on a spacecraft moving towards the Earth, the beam of light completes one complete circle every 14 s. Calculate the speed of the spacecraft relative to the Earth.

8. A rocket passes two beacons that are at rest relative to the Earth. An astronaut in the rocket measures the time taken for the rocket to travel from the first beacon to the second beacon to be

10·0 s. An observer on Earth measures the time taken for the rocket to travel from the first beacon to the second beacon to be 40·0 s. Calculate the speed of the rocket relative to the Earth.

9. A spacecraft travels to a distant planet at a constant speed relative to the Earth. A clock on the spacecraft records a time of 1 year for the journey while an observer on Earth measures a time of

2 years for the journey. Calculate the speed, in ms -1 , of the spacecraft relative to the Earth.

Length Contraction

1. Write down the relationship involving the proper length l and contracted length l’ of a moving object observed in two different frames of reference moving at a speed, v, relative to one another

(where the proper length is the length measured by an observer at rest with respect to the object and the contracted length is the length measured by another observer moving at a speed, v, relative to the object).

2. In the table shown, use the relativity equation for length contraction to calculate the value of each missing quantity (a) to (f) for an object moving at a constant speed relative to the Earth.

Contracted length Proper Length Speed of Object (ms -1 )

(a)

(b)

5.00 m

15.0 m

1.00 x 10 8

2.00 x 10 8

0.15 km

150 km

(c)

(d)

2.25 x 10 8

1.04 x 10 8

30 m 35 m (e)

10 m 11 m (f)

3. A rocket has a length of 20 m when at rest on the Earth. An observer, at rest on the Earth, watches the rocket as it passes at a constant speed of 1·8 × 10 8 ms -1 . Calculate the length of the rocket as measured by the observer.

4. A pi meson is moving at 0·90 c relative to a magnet. The magnet has a length of 2·00 m when at rest to the Earth. Calculate the length of the magnet in the reference frame of the pi meson.

5. In the year 2050 a spacecraft flies over a base station on the Earth. The spacecraft has a speed of

0·8 c. The length of the moving spacecraft is measured as 160 m by a person on the Earth. The spacecraft later lands and the same person measures the length of the now stationary spacecraft.

Calculate the length of the stationary spacecraft.



29




6. A rocket is travelling at 0·50 c relative to a space station. Astronauts on the rocket measure the length of the space station to be 0.80 km. Calculate the length of the space station according to a technician on the space station.

7. A metre stick has a length of 1·00 m when at rest on the Earth. When in motion relative to an observer on the Earth the same metre stick has a length of 0·50 m. Calculate the speed, in ms -1 , of the metre stick.

8. A spaceship has a length of 220 m when measured at rest on the Earth. The spaceship moves away from the Earth at a constant speed and an observer, on the Earth, now measures its length to be 150 m.

Calculate the speed of the spaceship in ms -1 .

9. The length of a rocket is measured when at rest and also when moving at a constant speed by an observer at rest relative to the rocket. The observed length is 99·0 % of its length when at rest.

Calculate the speed of the rocket.

Relativity Miscellaneous

1. Two points A and B are separated by 240 m as measured by metre sticks at rest on the Earth. A rocket passes along the line connecting A and B at a constant speed. The time taken for the rocket to travel from A to B, as measured by an observer on the Earth, is 1·00 × 10 -6 s.

(a) Show that the speed of the rocket relative to the Earth is 2·40 × 10 ms -1 .

(b) Calculate the time taken, as measured by a clock in the rocket, for the rocket to travel from A to B.

8

(c) What is the distance between points A and B as measured by metre sticks carried by an observer travelling in the rocket?

2. A spacecraft is travelling at a constant speed of 0·95 c. The spacecraft travels at this speed for

1 year, as measured by a clock on the Earth.

(a) Calculate the time elapsed, in years, as measured by a clock in the spacecraft.

(b) Show that the distance travelled by the spacecraft as measured by an observer on the spacecraft is 2·8 × 10 15 m.

(c) Calculate the distance, in m, the spacecraft will have travelled as measured by an observer on the Earth.

3. A pi meson has a mean lifetime of 2·6 × 10 -8 s when at rest. A pi meson moves with a speed of

0·99 c towards the surface of the Earth.

(a) Calculate the mean lifetime of this pi meson as measured by an observer on the

Earth.

(b) Calculate the mean distance travelled by the pi meson as measured by the observer on the

Earth.

4. A spacecraft moving at 2·4 × 10 8 ms -1 passes the Earth. An astronaut on the spacecraft finds that it takes 5·0 × 10 -7 s for the spacecraft to pass a small marker which is at rest on the Earth.

(a) Calculate the length, in m, of the spacecraft as measured by the astronaut.

(b) Calculate the length of the spacecraft as measured by an observer at rest on the

Earth.



30




5. A neon sign flashes with a frequency of 0·2 Hz.

(a) Calculate the time between flashes.

(b) An astronaut on a spacecraft passes the Earth at a speed of 0·84 c and sees the neon light flashing. Calculate the time between flashes as observed by the astronaut on the spacecraft.

6. When at rest, a subatomic particle has a lifetime of 0·15 ns. When in motion relative to the Earth the particle’s lifetime is measured by an observer on the Earth as 0·25 ns. Calculate the speed of the particle.

7. A meson is 10·0 km above the Earth’s surface and is moving towards the Earth at a speed of

0·999 c.

(a) Calculate the distance, according to the meson, travelled before it strikes the Earth.

(b) Calculate the time taken, according to the meson, for it to travel to the surface of the

Earth.

8. The star Alpha Centauri is 4·2 light years away from the Earth. A spacecraft is sent from the Earth to Alpha Centauri. The distance travelled, as measured by the spacecraft, is 3·6 light years.

(a) Calculate the speed of the spacecraft relative to the Earth.

(b) Calculate the time taken, in seconds, for the spacecraft to reach Alpha Centauri as measured by an observer on the Earth.

(c) Calculate the time taken, in seconds, for the spacecraft to reach Alpha Centauri as measured by a clock on the spacecraft.

9. Muons, when at rest, have a mean lifetime of 2·60 × 10 -8 s. Muons are produced 10 km above the

Earth. They move with a speed of 0·995 c towards the surface of the Earth.

(a) Calculate the mean lifetime of the moving muons as measured by an observer on

(b) Calculate the mean distance travelled by the muons as measured by an observer on the

Earth.

(c) Calculate the mean distance travelled by the muons as measured by the muons.

The Expanding Universe

In the following questions, when required, use the approximation for speed of sound in air = 340 ms -1 .

1. In the following sentences the words represented by the letters A, B, C and D are missing:

A moving source emits a sound with frequency f s

. When the source is moving towards a stationary observer, the observer hears a A frequency f o

. When the source is moving away from a stationary observer, the observer hears a B frequency f o

. This is known as the C D .

Match each letter with the correct word from the list below:

Doppler effect higher louder lower quieter softer

2. Write down the expression for the observed frequency f o

, detected when a source of sound waves in air of frequency f s moves:

(a) towards a stationary observer at a constant speed, v s

(b) away from a stationary observer at a constant speed, v s

.



31




3. In the table shown, calculate the value of each missing quantity (a) to (f), for a source of sound moving in air relative to a stationary observer.

Frequency Heard by Stationary observer

(Hz)

Frequency of

Source

(Hz)

Speed of source moving towards observer

(ms -1 )

Speed of source moving away from observer

(ms -1 )

(a)

(b)

850

1020

400

400

(c)

(d)

10

-

20

-

-

10

-

5

2125

170

2000

200

(e)

-

-

(f)

4. A girl tries out an experiment to illustrate the Doppler effect by spinning a battery-operated siren around her head. The siren emits sound waves with a frequency of 1200 Hz. Describe what would be heard by a stationary observer standing a few metres away.

5. A police car emits sound waves with a frequency of 1000 Hz from its siren. The car is travelling at

20 ms -1 .

(a) Calculate the frequency heard by a stationary observer as the police car moves towards her.

(b) Calculate the frequency heard by the same observer as the police car moves away from her.

6. A student is standing on a station platform. A train approaching the station sounds its horn as it passes through the station. The train is travelling at a speed of 25 ms -1 . The horn has a frequency of

200 Hz.

(a) Calculate the frequency heard as the train is approaching the student.

(b) Calculate the frequency heard as the train is moving away from the student.

7. A man standing at the side of the road hears the horn of an approaching car. He hears a frequency of 470 Hz. The horn on the car has a frequency of 450 Hz. Calculate the speed of the car.

8. A source of sound emits waves of frequency 500 Hz. This is detected as 540 Hz by a stationary observer as the source of sound approaches. Calculate the frequency of the sound detected as the source moves away from the stationary observer.

9. A whistle of frequency 540 vibrations per second rotates in a circle of radius 0·75 m with a speed of 10 ms -1 . Calculate the lowest and highest frequency heard by a listener some distance away at rest with respect to the centre of the circle.

10. A woman is standing at the side of a road. A lorry, moving at 20 ms -1 , sounds its horn as it is passing her. The lorry is moving at 20 ms -1 and the horn has a frequency of 300 Hz.

(a) Calculate the wavelength heard by the woman when the lorry is approaching her.

(b) Calculate the wavelength heard by the woman when the lorry is moving away from her.



32




11. A siren emitting a sound of frequency 1000 vibrations per second moves away from you towards the base of a vertical cliff at a speed of 10 ms -1 .

(a) Calculate the frequency of the sound you hear coming directly from the siren.

(b) Calculate the frequency of the sound you hear reflected from the cliff.

12. A sound source moves away from a stationary listener. The listener hears a frequency that is 10% lower than the source frequency. Calculate the speed of the source.

13. A bat flies towards a tree at a speed of 3·60 ms -1 while emitting sound of frequency 350 kHz. A moth is resting on the tree directly in front of the bat.

(a) Calculate the frequency of sound heard by the bat.

(b) The bat decreases its speed towards the tree. Does the frequency of sound heard by the moth increase, decrease or stays the same? Justify your answer.

(c) The bat now flies directly away from the tree with a speed of 4·50 ms -1 while emitting the same frequency of sound. Calculate the new frequency of sound heard by the moth.

14. The siren on a police car has a frequency of 1500 Hz. The police car is moving at a constant speed of 54 km h -1 .

(a) Show that the police car is moving at 15 ms -1 .

(b) Calculate the frequency heard when the car is moving towards a stationary observer.

(c) Calculate the frequency heard when the car is moving away from a stationary observer.

15. A source of sound emits a signal at 600 Hz. This is observed as 640 Hz by a stationary observer as the source approaches. Calculate the speed of the moving source.

16. A battery-operated siren emits a constant note of 2200 Hz. It is rotated in a circle of radius 0·8 m at 3·0 revolutions per second. A stationary observer, standing some distance away, listens to the note made by the siren.

(a) Show that the siren has a constant speed of 15·1 ms -1 .

(b) Calculate the minimum frequency heard by the observer.

(c) Calculate the maximum frequency heard by the observer.

17. You are standing at the side of the road. An ambulance approaches you with its siren on. As the ambulance approaches, you hear a frequency of 460 Hz and as the ambulance moves away from you, a frequency of 410 Hz. The nearest hospital is 3 km from where you are standing. Estimate the time for the ambulance to reach the hospital. Assume that the ambulance maintains a constant speed during its journey to the hospital.

18. On the planet Lots, a poobah moves towards a stationary glonk at 10 ms -1 . The poobah emits sound waves of frequency 1100 Hz. The stationary glonk hears a frequency of 1200 Hz.

Calculate the speed of sound on the planet Lots.



33




19. In the following sentences the words represented by the letters A, B, C, D and E are missing:

A hydrogen source gives out a number of emission lines. λ for one of these lines is measured. When the light source is at rest, the value of this wavelength is λ rest

. When the same emission line is observed in light coming from a distant star the value of the wavelength is λ observed

. When a star is moving away from the Earth λ observed is _ A_ than λ rest

. This is known as the _B_ shift.

When the distant star is moving towards the Earth λ observed

__D__ shift. is __C__ than λ rest

. This is known as the

Measurements on many stars indicate that most stars are moving _E__ from the Earth.

Match each letter with the correct word from the list below:

away

red blue shorter longer towards.

20. In the table shown, calculate the value of each missing quantity.

Fractional change in Wavelength of light on Wavelength of light observed wavelength, z

(a)

Earth, λ rest

(nm)

365 from star, λ observed

(nm)

402

(b)

8.00 x 10 -2

4.00 x 10

-2

5.00 x 10 -2

1.00 x 10

-1

Hubble’s Law

434

486

656

(e)

(f)

456

(c)

(d)

456

402

In the following questions, when required, use the approximation for

H o

= 2·4 × 10 -18 s -1

1. Convert the following distances in light years into distances in metres.

(a) 1 light year

(b) 50 light years

(c) 100, 000 light years

(d) 16, 000, 000, 000 light years

2. Convert the following distances in metres into distances in light years.

(a) Earth to our Sun = 1·44 × 10 11 m.

(b) Earth to next nearest star Alpha Centauri = 3.97 × 10 16 m.

(c) Earth to a galaxy in the constellation of Virgo = 4·91 × 10 23 m.

3. In the table shown, calculate the value of each missing quantity.

Speed of galaxy relative to

Earth (ms -1 )

(a)

(c)

1.70 x10 6

2.21 x10 6

Approximate distance from

Earth to galaxy (m)

7.10 x10 22

1.89 x10 24

(e)

(g)

Fractional change in wavelength, z

(b)

(d)

(f)

(h)



34




4. Light from a distant galaxy is found to contain the spectral lines of hydrogen. The light causing one of these lines has a measured wavelength of 466 nm. When the same line is observed from a hydrogen source on Earth it has a wavelength of 434 nm.

(a) Calculate the Doppler shift, z, for this galaxy.

(b) Calculate the speed at which the galaxy is moving relative to the Earth.

(c) In which direction, towards or away from the Earth, is the galaxy moving?

5. Light of wavelength 505 nm forms a line in the spectrum of an element on Earth. The same spectrum from light from a galaxy in Ursa Major shows this line shifted to correspond to light of wavelength 530 nm.

(a) Calculate the speed that the galaxy is moving relative to the Earth.

(b) Calculate the approximate distance, in metres, the galaxy is from the Earth.

6. A galaxy is moving away from the Earth at a speed of 0·074 c.

(a) Convert 0·074 c into a speed in ms -1 .

(b) Calculate the approximate distance, in metres, of the galaxy from the Earth.

7. A distant star is travelling directly away from the Earth at a speed of 2·4 × 10 7 ms -1 .

(a) Calculate the value of z for this star.

(b) A hydrogen line in the spectrum of light from this star is measured to be 443 nm.

Calculate the wavelength of this line when it observed from a hydrogen source on the

Earth.

8. A line in the spectrum from a hydrogen atom has a wavelength of 489 nm on the Earth. The same line is observed in the spectrum of a distant star but with a longer wavelength of 538 nm.

(a) Calculate the speed, in ms -1 , at which the star is moving away from the Earth.

(b) Calculate the approximate distance, in metres and in light years, of the star from the Earth.

9. The galaxy Corona Borealis is approximately 1 000 million light years away from the Earth.

Calculate the speed at which Corona Borealis is moving away from the Earth.

10. A galaxy is moving away from the Earth at 3·0 × 10 7 ms -1 . The frequency of an emission line coming from the galaxy is measured. The light forming the same emission line, from a source on

Earth, is observed to have a frequency of 5·00 × 10 14 Hz.

(a) Show that λ for the light of the emission line from the source on the Earth is

6·00 × 10 -7 m.

(b) Calculate the frequency of the light forming the emission line coming from the galaxy.

11. A distant quasar is moving away from the Earth. Hydrogen lines are observed coming from this quasar. One of these lines is measured to be 20 nm longer than the same line, of wavelength 486 nm from a source on Earth.

(a) Calculate the speed at which the quasar is moving away from the Earth.

(b) Calculate the approximate distance, in millions of light years, that the quasar is from the Earth.

12. A hydrogen source, when viewed on the Earth, emits a red emission line of wavelength 656 nm.

Observations, for the same line in the spectrum of light from a distant star, give a wavelength of 660 nm. Calculate the speed of the star relative to the Earth.



35




13. Due to the rotation of the Sun, light waves received from opposite ends of a diameter on the Sun show equal but opposite Doppler shifts. The relative speed of rotation of a point on the end of a diameter of the Sun relative to the Earth is 2 kms -1 . Calculate the wavelength shift for a hydrogen line of wavelength 486·1 nm on the Earth.

The Big Bang Theory

1. The graphs below are obtained by measuring the energy emitted at different wavelengths from an object at different temperatures.

(a) Which part of the x-axis, P or Q, corresponds to ultraviolet radiation?

(b) What do the graphs show happens to the amount of energy emitted at a certain wavelength as the temperature of the object increases?

(c) What do the graphs show happens to the total energy radiated by the object as its temperature increases?

(d) Each graph shows that there is a wavelength λ max at which the maximum amount of energy is emitted.

(i) Explain why the value of λ max decreases as the temperature of the object increases.

The table shows the values of λ max at different temperatures of the object.

Temperature (K) Max Wavelength λ max

(nm)

6000 4.8 x 10

-7

5000

4000

3000

5.8 x 10

-7

7.3 x 10

-7

9.7 x 10

-7

(ii) Use this data to determine the relationship between temperature T and λ max

.

(e) Use your answer to (d) (ii) to calculate:

(i) T of the star Sirius where λ max

(ii) the value of λ max is 2·7 × 10 -7 m for the star Alpha Crucis which has a temperature of 23,000 K

(iii) T of the present universe when λ max

1·1 × 10 -3 m. for the cosmic microwave radiation is measured as

(iv) the approximate wavelength and type of the radiation emitted by your skin, assumed to be at a temperature of 33º C.



36




Orders of magnitude

1. The diagram shows a simple model of the atom.

Tutorial Questions

Match each of the letters A, B, C and D with the correct word from the list below. electron neutron nucleus proton

2. In the following table the numbers or words represented by the letters A, B, C,

D, E, F and G are missing.

Order of magnitude/m

10

−15

Object

A

10

−14

10 −10

B

Diameter of hydrogen atom

10

−4

10

0

10

3

10

7

C

D

E

Diameter of Earth

10

9

10 13

10

21

F

Diameter of solar system

G

Match each letter with the correct words from the list below. diameter of nucleus diameter of proton distance to nearest galaxy height of Ben Nevis size of dust particle your height diameter of Sun



37




The standard model of fundamental particles and interactions

1.

Name the particles represented by the following symbols.

(a) p (b) p (c) e (d) e

(e) n (f) n (g) v (h) ν

2. A particle can be represented by a symbol X where M represents the mass number, A the atomic number and X identifies the type of particle, for example a proton can be represented by p

1 following particles.

. Give the symbols, in this form, for the

(a) p (b) e (c) e (d) n (e) n

3. Copy and complete the table by placing the fermions in the list below in the correct column of the table. bottom charm neutrino muon down electron muon neutrino tau neutrino top electron strange up tau

Quarks Leptons

4. (a) State the difference between a hadron and a lepton in terms of the type of force experienced by each particle.

(b) Give one example of a hadron and one example of a lepton.



38




5. Information on the sign and charge relative to proton charge of six types of quarks (and their corresponding antiquarks) is shown in the table.

Quark name Charge relative to size of proton charge

Antiquark name Charge relative to size of proton charge up +2/3 antiup –2/3 charm top

+2/3

+2/3 anticharm antitop

–2/3

–2/3 down strange

–1/3

–1/3 antidown antistrange

+1/3

+1/3 bottom –1/3 antibottom +1/3

Calculate the charge of the following combinations of quarks:

(a) two up quarks and one down quark

(b) one up quark and two down quarks

(c) two antiup quarks and one antidown quark

(d) one antiup quark and two antidown quarks.

6. Neutrons and protons are considered to be composed of quarks.

(a) How many quarks are in each neutron and in each proton?

(b) Comment briefly on the different composition of the neutron and proton.

7. (a) Briefly state any differences between the ‘strong’ and ‘weak’ nuclear forces.

(b) Give an example of a particle decay associated with the weak nuclear force.

(c) Which of the two forces, strong and weak, acts over the greater distance?



39




Electric fields

1. Draw the electric field pattern for the following point charges and pair of charges:

(a) (b) (c)

2. Describe the motion of the small test charges in each of the following fields.

(a) (b)

(c) (d)

3. An electron volt (eV) is a unit of energy. It represents the change in potential energy of an electron that moves through a potential difference of 1 V (the size of the charge on an electron is

1· 6 × 10

−19

C).

What is the equivalent energy of 1 eV in joules?

4. An electron has energy of 5 MeV. Calculate its energy in joules.

5. The diagram shows an electron accelerates between two parallel conducting plates A and B.

The p.d. between the plates is 500 V. (mass of electron = 9· 1 × 10 −31 kg, charge on electron = 1· 6 × 10

−19

C)

(a) Calculate the electrical work done in moving the electron from plate A to plate B.

(b) How much kinetic energy has the electron gained in moving from A to B?

(c) What is the speed of the electron just before it reaches plate B?



40




6. Electrons are ‘fired’ from an electron gun at a screen.

Tutorial Questions

The p.d. across the electron gun is 2000 V. The electron gun and screen are in a vacuum. After leaving the positive plate the electrons travel at a constant speed to the screen. Calculate the speed of the electrons just before they hit the screen.

7. A proton is accelerated from rest across a p.d. of 400 V. Calculate the increase in speed of the proton.

8. In an X-ray tube electrons forming a beam are accelerated from rest and strike a metal target. The metal then emits X-rays. The electrons are accelerated across a p.d. of 25 kV. The beam of electrons forms a current of 3· 0 mA.

(a) (i) Calculate the kinetic energy of each electron just before it hits the target.

(ii) Calculate the speed of an electron just before it hits the target.

(iii) Find the number of electrons hitting the target each second.

(mass of electron = 9· 1 × 10

−31 kg, charge on electron = 1· 6 × 10 −19 C)

(b) What happens to the kinetic energy of the electrons?

9. Sketch the paths which

(a) an alpha-particle

(b) a beta-particle

(c) a neutron would follow if each particle, with the same velocity, enters the electric fields shown in the diagrams.



41




Charged particles in a magnetic field

1. An electron travelling with a constant velocity enters a region where there is a uniform magnetic field. There is no change in the velocity of the electron.

What information does this give about the magnetic field?

2. The diagram shows a beam of electrons as it enters the magnetic field between two magnets. The electrons will:

A be deflected to the left (towards the N pole)

B be deflected to the right (towards the S pole)

C be deflected upwards

D be deflected downwards

E have their speed increased without any change in direction.

3. The diagrams show particles entering a region where there is a uniform magnetic field. (X denotes magnetic field into page and • denotes magnetic field out of page.)

Use the terms: up, down, into the paper, out of the paper, left, right, no change in direction to describe the deflection of the particles in the magnetic field.

4. An electron enters a region of space where there is a uniform magnetic field.

As it enters the field the velocity of the electron is at right angles to the magnetic field lines.

The energy of the electron does not change although it accelerates in the field.

Use your knowledge of physics to explain this effect.



42




Particle accelerators

In the following questions, when required, use the following data:

Charge on electron = –1·60 × 10 −19 C

Charge on proton = 1· 60 × 10

−19

C

Mass of electron = 9·11 × 10 −31 kg

Mass of proton = 1· 67 × 10

−27

kg

1. In an evacuated tube, an electron initially at rest is accelerated through a p.d. of

500 V.

(a) Calculate, in joules, the amount of work done in accelerating the electron.

(b) How much kinetic energy has the electron gained?

(c) Calculate the final speed of the electron.

2. In an electron gun, electrons in an evacuated tube are accelerated from rest through a potential difference of 250 V.

(a) Calculate the energy gained by an electron.

(b) Calculate the final speed of the electron.

3. Electrons in an evacuated tube are ‘fired’ from an electron gun at a screen. The p.d. between the cathode and the anode of the gun is 2000 V. After leaving the anode, the electrons travel at a constant speed to the screen. Calculate the maximum speed at which the electrons will hit the screen.

4. A proton, initially at rest, in an evacuated tube is accelerated between two charged plates A and B. It moves from A, where the potential is 10 kV, to B, where the potential is zero.

Calculate the speed of the proton at B.

5. A linear accelerator is used to accelerate a beam of electrons, initially at rest, to high speed in an evacuated container. The high- speed electrons then collide with a stationary target. The accelerator operates at 2· 5 kV and the electron beam current is 3 mA.

(a) Calculate the gain in kinetic energy of each electron.

(b) Calculate the speed of impact of each electron as it hits the target.

(c) Calculate the number of electrons arriving at the target each second.

(d) Give a reason for accelerating particles to high speed and allowing them to collide with a target.

6. The power output of an oscilloscope (cathode-ray tube) is estimated to be

30 W. The potential difference between the cathode and the anode in the evacuated tube is 15 kV.

(a) Estimate the number of electrons striking the screen per second.

(b) Calculate the speed of an electron just before it strikes the screen, assuming that it starts from rest and that its mass remains constant.



43




7. In an oscilloscope electrons are accelerated between a cathode and an anode and then travel at constant speed towards a screen. A p.d. of 1000 V is maintained between the cathode and anode. The distance between the cathode and anode is 5· 0 × 10 −2 m. The electrons are at rest at the cathode and attain a speed of 1· 87 × 10

7

m s

−1

on reaching the anode. The tube is evacuated.

(a) (i) Calculate the work done in accelerating an electron from the cathode to the anode.

(ii) Show that the average force on the electron in the electric field is

3· 20 × 10

−15

N.

(iii) Calculate the average acceleration of an electron while travelling from the cathode to the anode.

(iv) Calculate the time taken for an electron to travel from cathode to anode.

(v) Beyond the anode the electric field is zero. The anode to screen distance is 0· 12 m. Calculate the time taken for an electron to travel from the anode to the screen.

(b) Another oscilloscope has the same voltage but a greater distance between cathode and anode.

(i) Would the speed of the electrons be higher, lower or remain at

1· 87 × 10

7

m s

−1

? Explain your answer.

(ii) Would the time taken for an electron to travel from cathode to anode be increased, decreased or stay the same as in (a) (iv)? Explain your answer.

8. In an X-ray tube a beam of electrons, initially at rest, is accelerated through a potential difference of 25 kV. The electron beam then collides with a stationary target. The electron beam current is 5 mA.

(a) Calculate the kinetic energy of each electron as it hits the target.

(b) Calculate the speed of the electrons at the moment of impact with the target assuming

that the electron mass remains constant.

(c) Calculate the number of electrons hitting the target each second.

(d) What happens to the kinetic energy of the electrons?



44




9. In the following descriptions of particle accelerators, some words and phrases have been replaced by the letters A to R.

In a linear accelerator groups of charged particles are accelerated by a series of A . The final energy of the particles is limited by the length of the accelerator.

This type of accelerator is used in B experiments.

In a cyclotron the charged particles are accelerated by C . The particles travel in a D as a result of a E , which is F to the spiral. The radius of the spiral increases as the energy of the particles G .

The diameter of the cyclotron is limited by the H of the magnet. The resultant energy of the particles is limited by the diameter of the cyclotron and by I .

This type of accelerator is used in J experiments.

In a synchrotron groups of charged particles travel in a K as a result of C shaped magnets whose strength L . The particles are accelerated by M . As the energy of the particles increases the strength of the magnetic field is N to maintain the radius of the path of the particles.

In synchrotron accelerators the particles can have, in theory, an unlimited series of accelerations as the particles can transit indefinitely around the ring.

There will be a limit caused by O .

In this type of accelerator particles with P mass and Q charge can circulate in opposite directions at the same time before colliding. This increases the energy of impact. This type of accelerator is used in D experiments.

Letter

A, C, E, M

B, J, R

D, K

List of replacement word or phrase constant magnetic field, alternating magnetic fields, alternating electric fields, constant electric fields colliding-beam, fixed-target spiral of decreasing radius, spiral of increasing radius, circular path of fixed radius perpendicular, parallel F

G

H

I, O

L

N

P, Q decreases, increases physical size, strength gravitational effects, relativistic effects can be varied, is constant decreases, increases the same, different



45




Fission and fusion

1. The following is a list of atomic numbers:

(a) 6

(b) 25

(c) 47

(d) 80

(e) 86

(f) 92

Use a periodic table to identify the elements that have these atomic numbers.

2. The list shows the symbols for six different isotopes.

(i)

7

3

Li

(iv)

131

54

Xe

(ii)

(v)

64

330

Zn

239

94

Pu

(iii)

109

47

Ag

(vi)

257

103

Lw

For each of the isotopes state:

(a) the number of protons

(b) the number of neutrons.

3. The incomplete statements below illustrate four nuclear reactions.

Identify the missing particles or nuclides represented by the letters A, B, C and

D.

4. Part of a radioactive decay series is represented below:

235

92

U →

231

90

Th →

231

91

Pa →

227

89

Ac

Identify the particle emitted at each stage of the decay.

Such a series does not always give a complete picture of the radiations emitted by each nucleus. Give an explanation why the picture is incomplete.

5. For a particular radionuclide sample 8 × 10

7

disintegrations take place in 40 s.

Calculate the activity of the source.

6. How much energy is released when the following ‘decreases’ in mass occur in various fission reactions?

(a) 3· 25 × 10

−28

kg

(b) 2· 01 × 10

−28

kg

(c) 1· 62 × 10

−28

kg

(d) 2· 85 × 10

−28

kg



46




7. The following statement represents a nuclear reaction involving the release of energy.

3

1

H ! H → He ! n

The masses of these particles are given below.

Mass of

3

1

H = 5· 00890 × 10 −27 kg Mass of

4

2

He = 6· 64632 × 10 −27 kg

Mass of

2

1

H = 3· 34441 × 10

−27

kg Mass of

1

0 n = 1· 67490 × 10

−27

kg

(a) Calculate the decrease in mass that occurs when this reaction takes place.

(b) Calculate the energy released in this reaction.

(c) What is the name given to this type of nuclear reaction?

(d) Calculate the number of reactions required each second to produce a power of 25 MW.

8. Plutonium can undergo the nuclear reaction represented by the statement below:

239

94

Pu ! n !

100

42

Mo ! 3 n

The masses of the nuclei and particles involved in the reaction are as follows.

Particle n Pu Te Mo

Mass/kg 1· 675 × 10

−27

396· 741 × 10

−27

227· 420 × 10

−27

165· 809 × 10

−27

(a) What kind of reaction is represented by the statement?

(b) State the mass number and atomic number (a) and (b) of the nuclide Te in the reaction.

(c) Calculate the decrease in mass that occurs in this reaction.

(d) Calculate the energy released in this reaction.



47




Photoelectric effect

1. A ‘long wave’ radio station broadcasts on a frequency of 252 kHz.

(a) Calculate the period of these waves.

(b) What is the wavelength of these waves?

2. Green light has wavelength 546 nm.

(a) Express this wavelength in metres (using scientific notation).

(b) Calculate:

(i) the frequency of these light waves

(ii) the period of these light waves.

3. Ultraviolet radiation has a frequency 2· 0 × 10

15

Hz.

(a) Calculate the wavelength of this radiation.

(b) Calculate the period of this radiation.

4. Blue light has a frequency of 6· 50 × 10 14 Hz. Calculate the energy of one photon of this radiation.

5. Red light has a wavelength of 6· 44 × 10

−7

m. Calculate the energy of one photon of this light.

6. A photon of radiation has an energy of 3· 90 × 10

-19

J. Calculate the wavelength of this radiation in nm.

7. In an investigation into the photoelectric effect a clean zinc plate is attached to a coulombmeter, as shown. The threshold frequency of radiation for zinc is

6· 50 × 10 14 Hz.

(a) The zinc plate is initially negatively charged.

A lamp is used to shine ultraviolet radiation of frequency

6· 7 × 10

14

Hz onto the zinc plate.

Describe and explain what happens to the reading on the coulombmeter.

(b) The zinc plate is again negatively charged.

Describe and explain the effect each of the following changes has on the reading on the coulombmeter:

(i) moving the ultraviolet lamp further away from the zinc plate

(ii) using a source of red light instead of the uv lamp. this has on the positive reading on the coulombmeter.

(d) The zinc plate is now positively charged. The uv lamp is again used to irradiate the zinc plate. Describe and explain the effect



48




8. In a study of photoelectric currents, the graph shown was obtained.

(a)

(b)

What name is given to the frequency f o

?

Explain why no current is detected when the frequency of the incident radiation is less than f o

.

9. For a certain metal, the energy required to eject an electron from the atom is

3· 30 × 10

−19

J.

(a) Calculate the minimum frequency of radiation required to emit a photoelectron from the metal.

(b) Explain whether or not photoemission would take place using radiation of:

(i) frequency 4 × 10

14

(ii) wavelength 5 × 10

Hz

−7

m.

10. The minimum energy required to remove an electron from zinc is

6· 10 × 10

−19

J.

(a)

(b)

(c)

What is the name is given to this minimum energy?

Calculate the value of f o

for zinc.

Photons with a frequency of 1· 2 × 10 15 Hz strike a zinc plate, causing an electron to be ejected from the surface of the zinc.

(i) Calculate the amount of energy the electron has after it is released from the zinc.

(ii) What kind of energy does the electron have after it is released?

11. Radiation of frequency 5· 0 × 10

14

Hz can eject electrons from a metal surface.

(a)

(b)

Calculate the energy of each photon of this radiation.

Photoelectrons are ejected from the metal surface with a kinetic energy of

7· 0 × 10 −20 J. Calculate the work function of this metal.



49




12.

An argon laser is used in medicine to remove fatty deposits in arteries by passing the laser light along a length of optical fibre. The energy of this light is used to heat up a tiny metal probe to a sufficiently high temperature to vaporise the fatty deposit.

The laser has a power of 8· 0 W. It emits radiation with a wavelength of 490nm.

(a) How much energy is delivered from the laser in 5 s?

(b) Calculate the number of photons of this radiation required to provide the 5 s pulse of energy from the 8· 0 W laser.

13. The apparatus shown is used to investigate photoelectric emission from a metal plate when electromagnetic radiation is shone on the plate. The irradiance and frequency of the incident radiation can be varied as required.

(a)

(b)

(c)

Explain what is meant by ‘photoelectric emission’ from a metal.

What is the name given to the minimum frequency of the radiation that produces a current in the circuit?

A particular source of radiation produces a current in the circuit. Explain why the current in the circuit increases as the irradiance of the incident radiation increases.

14. State whether each of the following statements is true or false.

(a) Photoelectric emission from a metal occurs only when the frequency of the incident radiation is greater than the threshold frequency for the metal.

(b) The threshold frequency depends on the metal from which photoemission takes place.

(c) When the frequency of the incident radiation is greater than the threshold frequency for a metal, increasing the irradiance of the radiation will cause photoemission from the metal to increase.



50




(d) When the frequency of the incident radiation is greater than the threshold frequency for a metal, increasing the irradiance of the radiation will increase the maximum energy of the electrons emitted from the metal.

(e) When the frequency of the incident radiation is greater than the threshold frequency for a metal, increasing the irradiance of the incident radiation will increase the photoelectric current from the metal.

Interference and diffraction

1. Explain how it is possible for interference to occur in the following situations:

(a) a single loudspeaker emitting sound in a room with no other objects in the room

(b) receiving radio reception in a car when passing large buildings.

2. In an experiment on interference of sound, two loudspeakers A and B are connected in such a way that they emit coherent sound waves.

The loudspeakers are placed 2 m apart.

As a girl walks from X to Y she hears a point of maximum loudness at point P and the next maximum of loudness at point Q.

(a)

(b)

(c)

Calculate the distances AQ and BQ.

Calculate the wavelength of the sound.

Calculate the frequency of the sound. (speed of sound in air is 340 m s

−1

)



51




3. A microwave transmitter is placed in front of a metal plate that has two slits A and B as shown.

A microwave detector is moved along the line from C to D.

The zero- order maximum of radiation is detected at C and the first-order maximum is detected at D.

AD = 0· 52 m and BD = 0· 55 m.

(a)

(b)

(c)

Calculate the path difference between paths AD and BD.

What is the wavelength of the microwaves?

Calculate the path difference from slits A and B to the second-order maximum.

Calculate the path difference from slits A and B to the minimum of (d)

(e) intensity between C and D.

Calculate the path difference from slits A and B to the next minimum after D.

(f) What is the path difference from slits A and B to point C?

4. A microwave interference experiment is set up as shown.

E and F are two slits in a metal plate. A microwave detector is moved along the line GH.

H is the second minimum from the straight through point at G. (This is sometimes called the first-order (m = 1) minimum, the first minimum being the zero order m = 0)

Measurement of distances EH and FH gives: EH = 0· 421 m and FH = 0· 466 m.

Calculate the wavelength and frequency of the microwaves used.



52




5. A microwave experiment is set up as shown.

Tutorial Questions

The waves reflected from the metal reflector plate interfere with the incident waves from the source. As the reflector is moved away from the detector, a series of maxima and minima are recorded by the detector.

A maximum is found when the reflector is at a distance of 0· 25 m from the detector. A further eight maxima are found as the reflector is moved to a distance of 0· 378 m from the detector.

(a)

(b)

(c)

Calculate the average distance between the maxima.

Calculate the wavelength of the microwaves.

Calculate the frequency of the microwaves.

6. A source of microwaves is placed in front of a metal sheet that has two slits S

1 and S

2

as shown.

A microwave detector shows a minimum at P. P is the position of the firstorder minimum, ie it is the second minimum from the centre.

S

1

P = 0· 421 m S

2

P = 0· 466 m

Calculate the wavelength of the microwaves.

7. A grating has 400 lines per millimetre.

Calculate the spacing between the lines on this grating.

8. A grating with 600 lines per millimetre is used with a monochromatic source of light. The first-order maximum is produced at an angle of 20· 5° to the straight through position.

(a)

(b)

Calculate the wavelength of the light from the source.

A grating with 1200 lines per millimetre is now used.

Calculate the angle between the zero maximum and the new first-order maximum.

9. Light of wavelength 600 nm is shone onto a grating having 400, 000 lines per metre. Calculate the angle between the zero maximum and first-order maximum.



53




10. Light of wavelength 6· 50 × 10

−7

m is shone onto a grating. The angle between the zero- and third-order maxima is 31.5°.

(a) Calculate the spacing between the slits on the grating.

(b) Calculate the number of lines per mm on the grating.

11. Light of wavelength 500 nm is used with a grating having 500 lines per millimetre.

Calculate the angle between the first- and second-order maxima.

12. White light, with a range of wavelengths from 440 nm to 730 nm, is shone onto a grating having 500 lines per millimetre. A screen is placed behind the grating.

(a)

(b)

(c)

Describe the pattern seen on the screen.

Explain the type of pattern produced.

Calculate the angle between the extremes of the first-order maximum, ie the angle between violet and red.

13. A source of white light is set up in front of a grating. A green filter is placed between the source and the grating. The grating has 300 lines per millimetre.

A pattern of bright and dark bands is produced on a screen.

(a)

(b)

What is the colour of the bright bands produced on the screen?

Explain what happens to the spacing between the bright bands on the screen when each of the following changes is made:

(i) using a blue filter instead of a green filter

(ii) using a grating with 600 lines per millimetre

(iii) using a source producing a greater irradiance of light

(iv) moving the screen closer to the grating.



54




Section 6: Refraction of light

1. A ray of monochromatic light passes from air into rectangular blocks of different materials A, B and C as shown.

Calculate the refractive index n of each of the materials for this light.

2. A ray of monochromatic light passes from air into a thin glass walled container of water, a rectangular block of ice and a rectangular block of diamond as shown in the diagrams.

Calculate the values of the angles x, y and z in each of the diagrams.

3.

A ray of monochromatic light passes from air into a certain material as shown.

The refractive index of the material is 1· 35.

(a)

(b)

Calculate the value of angle r.

Calculate the velocity of the light in the material.



55




4. A ray of light of wavelength 6· 00 × 10

−7

m passes from air into glass as shown.

(a) Calculate the refractive index of the glass for this light.

(b)

(c)

Calculate the speed of this light in the glass.

Calculate the wavelength of this light in the glass.

(d)

(e)

Calculate the frequency of this light in air.

State the frequency of this light in the glass.

5.

A ray of light of wavelength 500 nm passes from air into perspex.

The refractive index of the perspex for this light is 1· 50.

(a)

(b)

(c)

Calculate the value of angle r.

Calculate the speed of light in the perspex.

Calculate the wavelength of this light in the perspex.

6. The refractive index for red light in crown glass is 1· 513 and for violet light it is 1· 532.

(a) Using this information, explain why white light can produce a spectrum when passed through crown glass.

(b) A ray of white light passes through a semi-circular block of crown glass as shown and produces a spectrum.

(c) Which exit ray is red and which exit ray is violet?

(d) Calculate the angle of refraction in air for each of the exit rays.

(e) Find angle x, the angle between the red and violet rays.



56




7. A ray of white light is dispersed, by a glass prism, producing a spectrum S.

The angle x is found to be 0· 7°.

The refractive index for red light in this glass is 1· 51. Calculate the refractive index for blue light.

8. Calculate the critical angle for each material using the refractive n index given in the table below.

Material n

Glass

Ice

1· 54

1· 31

Perspex 1· 50

9. A beam of infrared radiation is refracted by a type of glass as shown.

(a)

(b)

Calculate the refractive index of the glass for infrared.

Calculate the critical angle of infrared radiation for this glass.



57




10. A ray of light enters a glass prism of absolute refractive index 1· 52, as shown.

(a)

(b)

(c)

(d)

(e)

Explain why the ray does not change direction on entering the glass prism.

Calculate the value of angle X.

Why does the ray undergo total internal reflection at O?

Redraw the complete diagram showing the angles at O with their values.

Explain what would happen when the experiment is repeated with a prism of material with refractive index 1· 30.

11. The absolute refractive indices of water and diamond are 1· 33 and 2· 42, respectively.

(a) Calculate the critical angles for light in each of these materials when surrounded by air.

(b) Comment on the effect of the small critical angle of diamond on the beauty of a well-cut diamond.

Irradiance and inverse square law

1. A satellite is orbiting the Earth. The satellite has solar panels, with a total area of 15 m 2 , directed at the Sun. The Sun produces an irradiance of 1· 4 kW m −2 on the solar panels. Calculate the power received by the solar panels.

2. A 100 W light source produces an irradiance of 0· 2 W m −2 at a distance of 2 m.

The light source can be considered to be a point source.

Calculate the irradiance produced at a distance of:

(a)

(b)

1 m from the source

4 m from the source.



58




3. An experiment is performed to measure the irradiance produced at different distances from a point source of light. The results obtained are shown in the table.

Distance from point source d /m

Irradiance I /W m −2

1· 0 1· 4 2· 2 2· 8 3· 0

85 43 17· 6 10· 8 9· 4

(a) Sketch the apparatus that could be used to obtain these results.

(b) Use an appropriate format to show the relationship between the irradiance

I and the distance d.

(c) Calculate the irradiance at a distance of 5 m from the source.

(d) At what distance from the source is the irradiance

150 W m

−2

?

4. The radiation from the Sun produces an irradiance of 200 W m −2 at a certain point on the surface of the Earth.

(a)

(b)

What area of solar cells would be required to produce a power output of 1

MW when the cells are considered to be 100% efficient?

The cells are only 15% efficient. What additional area of solar cells is required to produce a power output of 1 MW?

5. An experiment is set up in a darkened laboratory with a small lamp L1 with a power P. The irradiance at a distance of 0· 50 m from the lamp is 12 W m

−2

. The experiment is repeated with a different small lamp L2 that emits a power of 0· 5

P.

Calculate the irradiance at a distance of 0· 25 m from this lamp.

Line and continuous spectra

1. When the light emitted by a particular material is observed through a spectroscope, it appears as four distinct lines.

(a)

(b)

(c)

(d)

What name is given to this kind of emission spectrum?

Explain why a series of specific, coloured lines is observed.

The red line in the spectrum coincides with a wavelength of 680 nm.

Calculate the energy of the photons of light that produced this line.

The spectroscope is now used to examine the light emitted from a torch bulb (filament lamp). What difference is observed in the spectrum when compared with the one in the diagram?



59




2. The diagram shows some of the energy levels for two atoms X and Y.

(a) (i) How many downward transitions are possible between these energy levels of each atom?

(ii) How many lines could appear in the emission spectrum of each element as a result of these energy levels?

(iii) Copy the diagram of the energy levels for each atom and show the possible transitions.

(b) Which transition in each of these diagrams gives rise to the emitted radiation of:

(i) lowest frequency

(ii) shortest wavelength?

3. The diagram shows some of the electron energy levels of a particular element.

.

(a) How many lines could appear in the emission spectrum of this element as a result of these levels?

(b) Calculate the frequencies of the photons arising from:

(i) the largest energy transition

(ii) the smallest energy transition.

(iii) Show whether any of the emission lines in the spectrum correspond to frequencies within the visible spectrum.

(iv) Explain which transition would produce the photons most likely to cause photoemission in a metal.



60




4. The diagram shows some of the electron energy levels in a hydrogen atom.

(a) How many emission lines are possible from electron transitions between these energy levels?

(b) Which of the following radiations could be absorbed by the electrons in a hydrogen atom?

(i) frequency 2· 92 × 10

15

Hz

(ii) frequency 1· 57 × 10 15 Hz

(iii) wavelength 4· 89 × 10

−7

m.

5. Explain why the absorption spectrum of an atom has dark lines corresponding to frequencies present in the emission spectrum of the atom.

6. (a) Explain the presence of the Fraunhofer lines, the dark lines that appear in the spectrum of sunlight.

(b) How are Fraunhofer lines used to determine the gases that are present in the solar atmosphere?

7. The light from a star can be analysed to show the presence of different elements in the star. How can the positions of the spectral lines for the elements be used to determine the speed of the star?



61




8. A bunsen flame is placed between a sodium vapour lamp and a screen as shown.

A sodium ‘pencil’ is put into the flame to produce vaporised sodium in the flame.

(a)

(b)

Explain why a dark shadow of the flame is seen on the screen.

The sodium vapour lamp is now replaced with a cadmium vapour lamp.

Explain why there is now no dark shadow of the flame on the screen.



62




A.C./D.C.

1. (a) What is the peak voltage of the 230 V mains supply?

(b) The frequency of the mains supply is 50 Hz. How many times does the voltage fall to zero in

1 second?

2. The circuit below is used to compare a.c. and d.c. supplies.

The variable resistor is used to adjust the brightness of the lamp until the lamp has the same brightness when connected to either supply.

(a) Explain why the brightness of the lamp changes when the setting on the variable resistor is altered.

(b) What additional apparatus would you use to ensure the brightness of the lamp is the same when connected to either supply?

(c) The time-base of the oscilloscope is switched off. Diagram 1 shows the oscilloscope trace obtained when the switch is in position B. Diagram 2 shows the oscilloscope trace obtained when the switch is in position A. Y gain set to 1 V cm -1

Using information from the oscilloscope traces, find the relationship between the root mean square (r.m.s.) voltage and the peak voltage of a voltage supply.

(d) The time-base of the oscilloscope is now switched on. Redraw diagrams 1 and 2 to show what happens to the traces.

3. The root mean square voltage produced by a low voltage power supply is 10 V.

(a) Calculate the peak voltage of the supply.

(b) An oscilloscope, with its time-base switched off, is connected across the supply. The Ygain of the oscilloscope is set to 5 Vcm -1 . Describe the trace seen on the oscilloscope screen.



63




4. (a) A transformer has a peak output voltage of 12 V. Calculate the r.m.s. value of this voltage.

(b) An oscilloscope, with the time base switched off, is connected across another a.c. supply.

The Y gain of the oscilloscope is set to 20 Vcm -1 . A vertical line 6 cm high appears on the

oscilloscope screen. Calculate:

(i) the peak voltage of the input

(ii) the r.m.s. voltage of the input.

5. An oscilloscope is connected across a signal generator. The time-base switch is set at

2·5 ms cm -1 . The diagram shows the trace on the oscilloscope screen.

6.

(a) (i) What is the frequency of the output from the signal generator?

(ii) What is the uncertainty in the frequency to the nearest Hz?

(b) The time base switch is now changed to:

(i) 5 ms cm -1

(ii) 1·25 ms cm -1

Sketch the new traces seen on the screen.

An a.c. signal of frequency 20 Hz is connected to an oscilloscope. The time-base switch on the oscilloscope is set at 0.01 s cm -1 .

Calculate the distance between the neighbouring peaks of this waveform when viewed on the screen.

Circuits

1. There is a current of 40 mA in a lamp for 16 s. Calculate the quantity of charge that passes any point in the circuit in this time.

2. A flash of lightning lasts for 1 ms. The charge transferred between the cloud and the ground in this time is 5 C. Calculate the value of the average current in this flash of lightning.

3. The current in a circuit is 2 ⋅ 5 × 10 -2 A. How long does it take for 500 C of charge to pass any given point in the circuit?

4. There is a current of 3 mA in a 2 k Ω resistor. Calculate the p.d. across the resistor.



64




5. Calculate the values of the readings on the meters in the following circuits

6. Calculate the unknown values R of the resistors in the following circuits.



65




7. Calculate the total resistance between X and Y for the following combinations of resistors.

8. In the following circuit the reading on the ammeter is 2 mA. Calculate the reading on the voltmeter.



66




9. Calculate the power in each of the following situations.

(a) A 12 V battery is connected to a motor. There is a current of 5 A in the motor.

(b) A heater of resistance 60 Ω that is connected across a 140V supply.

(c) A current of 5 A in a heater coil of resistance 20 Ω .

10. The heating element in an electric kettle has a resistance of 30 Ω .

(a) What is the current in the heating element when it is connected to a 230 V supply?

(b) Calculate the power rating of the element in the kettle.

11. A 15 V supply produces a current of 2 A in a lamp for 5 minutes. Calculate the energy supplied in this time.

12. Calculate the readings on the ammeter and the voltmeter in the circuit shown below.

13. Each of the four cells in the circuit shown is identical. Calculate

(a) the reading on the ammeter

(b) the current in the 20 Ω resistor

(c) the voltage across the 2 Ω resistor.

14. A voltage of 12 V is applied across a resistor. The current in the resistor is 50 mA. Calculate the resistance of the resistor.



67




15. The LED in the circuit below is to emit light.

Tutorial Questions

(a) What is the required polarity of A and B when connected to a 5 V supply so that the LED emits light?

(b) What is the purpose of the resistor R in the circuit?

(c) The LED rating is 20 mA at 1·5 V. Calculate the value of resistor R.

16. Write down the series and parallel circuit rules for

(a) potential differences (b) currents .

17. What is the name given to the circuit shown?

Write down the relationship between V

1

, V

2

, R

1 and R

2

.

18. Calculate the values of V

1 and V

2 of the circuit in question 17 when:

(a) R

1

= 1 k Ω R

2

= 49 k Ω

(b) R

1

= 5 k Ω R

2

= 15 k Ω

19. The light dependent resistor in the circuit is in darkness.

Light is now shone on the LDR.

Explain what happens to the readings on V

1 and V

2



68




20. Calculate the p.d. across resistor R

2 in each of the following circuits.

Tutorial Questions

21. Calculate the p.d. across AB (voltmeter reading) in each of the following circuits

22. A circuit consisting of two potential dividers is set up as shown.

(a) Calculate the reading on the voltmeter.

(b) (i) Suggest a value of a resistor to replace the 9 k Ω resistor that would give a reading of 0 V on the voltmeter.

(ii) Suggest a value of resistor to replace the 3 k Ω resistor that would give a reading of 0 V on the voltmeter.



69




23. In the circuits shown the reading on the voltmeters is zero. Calculate the value of the unknown resistors X and Y in each of the circuits

Electrical sources and internal resistance

1. State what is meant by:

(a) the e.m.f. of a cell

(b) the p.d. between two points in a circuit.

2. A circuit is set up as shown.

(a) Calculate the total resistance of the circuit.

(b) Calculate the readings on the ammeters.

(c) What is the value of the p.d. between X and Y?

(d) Calculate the power supplied by the battery.

3. The circuit shown uses a 230 V alternating mains supply.

Calculate the current in each resistor when:

(a) switch S is open

(b) switch S is closed



70




4. An electric cooker has two settings, high and low.

This involves two heating elements, R

1 and R

2

.

Tutorial Questions

On the low setting the current from the supply is 1 A.

On the high setting the current from the supply is 3 A.

(a) Calculate the resistance of R

1 and R

2

.

(b) What is the power consumption at each setting?

5. A lamp is rated at 12 V, 36 W. It is connected in a circuit as shown.

(a) Calculate the value of the resistor R that allows the lamp to operate at its normal rating.

(b) Calculate the power dissipated in the resistor.

6. In the circuit shown, r represents the internal resistance of the cell and R represents the external resistance (or load resistance) of the circuit.

When S is open, the reading on the voltmeter is 2·0 V.

When S is closed, the reading on the voltmeter is 1·6 V and the reading on the ammeter is 0·8 A.

(a) What is the value of the e.m.f. of the cell?

(b) When S is closed what is the terminal potential difference across the cell?

(c) Calculate the values of r and R.

(d) The resistance R is now halved in value. Calculate the new readings on the ammeter and voltmeter.



71




7. The battery in the circuit shown has an e.m.f. of 5·0 V. The current in the lamp is 0·20 A and the reading on the voltmeter is 3·0 V. Calculate the internal resistance of the battery.

8. A battery of e.m.f. 4·0 V is connected to a load resistor with a resistance of 15 Ω . There is a current of 0 2 A in the load resistor. Calculate the internal resistance of the battery.

9. A signal generator has an e.m.f. of 8·0 V and an internal resistance of 4·0 Ω . A load resistor is connected across the terminals of the generator. The current in the load resistor is 0·50 A. Calculate the resistance of the load resistor.

10. A cell is connected in a circuit as shown.

(a) Calculate the terminal p.d. across the cell.

(b) The resistance of the variable resistor R is now increased. cell.

(i) Describe and explain what happens to the current in the circuit.

(ii) Describe and explain what happens to the p.d. across the terminals of the

11. A cell has an e.m.f. 1·5 V and an internal resistance of 2·0 Ω . A 3·0 Ω resistor is connected across the terminals of the cell. Calculate the current in the circuit.

12. A student is given a voltmeter and a torch battery. When the voltmeter is connected across the terminals of the battery the reading on the voltmeter is 4·5 V.

When the battery is connected across a 6·0 Ω resistor the reading on the voltmeter decreases to 3·0 V.

(a) Calculate the internal resistance of the battery.

(b) What value of resistor when connected across the battery reduces the reading on the voltmeter to 2·5 V?



72




13. In the circuit shown, the battery has an e.m.f. of 6·0 V and an internal resistance of 1·0 Ω .

When the switch is closed, the reading on the ammeter is 2·0 A. What is the corresponding reading on the voltmeter?

14. To find the internal resistance of a cell a load resistor is connected across the terminals of the cell.

A voltmeter is used to measure V tpd

, the voltage measured across the terminals of the cell. An ammeter is used to measure I, the current in the variable resistor. The table below shows the results obtained as the resistance of the variable resistor is changed.

V t.p.d.

(V) 1.02 0.94 0.85 0.78 0.69 0.60

I (A) 0.02 0.04 0.06 0.08 0.10 0.12

(a) Draw a diagram of the circuit used to produce these results.

(b) Plot a graph of the results and from it determine:

(i) the e.m.f. of the cell

(ii) the internal resistance of the cell

(iii) the short circuit current of the cell.

15. A variable resistor is connected across a power supply. A voltmeter is used to measure

V tpd

, the voltage measured across the terminals of the supply. An ammeter is used to measure

I, the current in the variable resistor. The table below shows the results obtained as the resistance of the variable resistor is changed.

V t.p.d.

(V) 5.5 5.6 5.7 5.8 5.9

I (A) 5.0

Plot a graph of V tpd

. against I.

4.0 3.0

(a) What is the value of the open circuit p.d.?

(b) Calculate the internal resistance of the power supply.

(c) Calculate the short circuit current of the power supply.

2.0 1.0

(d) The variable resistor is now removed from the circuit and a lamp of resistance 1·5 connected across the terminals of the supply. Calculate:

(i) the terminal p.d.

(ii) the power delivered to the lamp.

Ω is



73




16. A circuit is set up as shown to investigate the properties of a battery.

Tutorial Questions

The variable resistor provides known values of resistance R. For each value of resistance R, the switch is closed and the current I noted. The table shows the results obtained.

R( Ω ) 0 2 4 6 8 10 12

I(A)

1/I(A -1 )

6.80 3.78 2.62 2.00 1.62 1.36 1.17

(a) Show that the relationship E = I(R + r) can be put in the form: R =

E

I

(b) Complete the third row in the table.

(c) Use the values of R and 1/I to plot a graph.

(d) Use the information in the graph to find:

(i) the internal resistance of the battery

(ii) the e.m.f. of the battery.

(e) The battery is now short circuited. Calculate the current in the battery when this happens.

- r

17. A student uses the following circuit to investigate the conditions for transferring the maximum power into a load resistor.

For each setting of the variable resistor the current in the circuit is recorded. The table below shows the results obtained.

R ( Ω )

I (A)

Power in R (W)

1

2.40

2

2.00

3

1.71

4

1.50

5

1.33

6

1.20

(a) Complete the table by calculating the power in the load for each value of R.

(b) Sketch a graph to show how the power in the load resistor R varies with R.

(c) In order to achieve maximum transfer of power, what is the relationship between the internal resistance of the power source and the resistance of the load resistor?



74




18. An automotive electrician needed to accurately measure the resistance of a resistor.

She set up a circuit using an analogue milliammeter and a digital voltmeter.

(a) What are the readings on the ammeter and the voltmeter?

(b) What is the nominal resistance calculated from these readings?

(c) What is the smallest division on the milliammeter?

(d) What is the absolute uncertainty on the milliammeter?

(e) What is the absolute uncertainty on the voltmeter?

(f) What is the percentage uncertainty on the milliammeter?

(g) What is the percentage uncertainty on the voltmeter?

(h) Which is the greatest percentage uncertainty?

(i) What is the percentage uncertainty in the resistance?

(j) What is the absolute uncertainty in the resistance?

(k) Express the final result as (resistance ± uncertainty) Ω

(l) Round both the result and the uncertainty to the relevant number of significant figures or decimal places.

Capacitors

1. A 50 µ F capacitor is charged until the p.d. across it is 100 V.

(a) Calculate the charge on the capacitor when the p.d. across it is 100 V.

(b) The capacitor is now ‘fully’ discharged in a time of 4·0 milliseconds.

(i) Calculate the average current during this time.

(ii) Why is this average current?

2. A capacitor stores a charge of 3·0 × 10 -4 C when the p.d. across its terminals is 600 V. What is the capacitance of the capacitor?

3. A 30 µ F capacitor stores a charge of 12 × 10 -4 C.

(a) What is the p.d. across its terminals?

(b) The tolerance of the capacitor is ± 0·5 µ F. Express this uncertainty as a percentage.

4. A 15 µ F capacitor is charged using a 1·5 V battery. Calculate the charge stored on the capacitor when it is fully charged.

5. (a) A capacitor stores a charge of 1·2 × 10 -5 C when there is a p.d. of 12 V across it. Calculate the capacitance of the capacitor.

(b) A 0·10 µ F capacitor is connected to an 8·0 V d.c. supply. Calculate the charge stored on the capacitor when it is fully charged.



75



Curriculum For Excellence

6. A circuit is set up as shown.

Higher Physics Tutorial Questions

The capacitor is initially uncharged. The switch is now closed. The capacitor is charged with a constant charging current of 2·0 × 10 -5 A for 30 s. At the end of this time the p.d. across the capacitor is 12 V.

(a) What has to be done to the value of the variable resistor in order to maintain a current constant for the 30 s?

(b) Calculate the capacitance of the capacitor.

7. A 100 µ F capacitor is charged using a 20 V supply.

(a) How much charge is stored on the capacitor when it is fully charged?

(b) Calculate the energy is stored in the capacitor when it is fully charged.

8. A 30 µ F capacitor stores 6·0 × 10

–3

C of charge. How much energy is stored in the capacitor?

9. The circuit below is used to investigate the charging of a capacitor.

The battery has negligible internal resistance.

The capacitor is initially uncharged. The switch is now closed.

(a) Describe what happens to the reading on the ammeter from the instant the switch is closed.

(b) How can you tell when the capacitor is fully charged?

(c) What would be a suitable range for the ammeter?

(d) The 10 k Ω resistor is now replaced by a larger resistor and the investigation repeated.

What is the maximum voltage across the capacitor now?



76




10. In the circuit below the neon lamp flashes at regular intervals. The neon lamp requires a potential difference of 100 V across it before it conducts and flashes. It continues to glow until the potential difference across it drops to 80 V. While lit, its resistance is very small compared with the resistance of R.

(a) Explain why the neon bulb flashes.

(b) Suggest two methods of decreasing the flash rate.

11. In the circuit below the capacitor C is initially uncharged.

Switch S is now closed. By carefully adjusting the variable resistor R a constant charging current of

1·0 mA is maintained. The voltmeter reading is recorded every 10 seconds. The results are shown in the table below.

Time (s) 0 10 20 30 40

V (V) 0 1.9 4.0 6.2 8.1

(a) Plot a graph of the charge on the capacitor against the p.d. across the capacitor.

(b) Use the graph to calculate the capacitance of the capacitor.



77




12. The circuit below is used to charge and discharge a capacitor.

Tutorial Questions

The battery has negligible internal resistance. The capacitor is initially uncharged. V

R is the p.d. across the resistor and V

C is the p.d. across the capacitor.

(a) What is the position of the switch:

(i) to charge the capacitor

(ii) to discharge the capacitor?

(b) Sketch graphs of V

R against time for the capacitor charging and discharging. Show numerical values for the maximum and minimum values of V

R

.

(c) Sketch graphs of V

C against time for the capacitor charging and discharging. Show numerical values for the maximum and minimum values of V

C

.

(d) (i) When the capacitor is charging what is the direction of the electrons between points A and B in the wire?

(ii) When the capacitor is discharging what is the direction of the electrons between points A and B in the wire?

(e) The capacitor has a capacitance of 4·0 µ F. The resistor has resistance of

2·5 M Ω . Calculate:

(i) the maximum value of the charging current

(ii) the charge stored by the capacitor when the capacitor is fully charged.



78




13. A capacitor is connected in a circuit as shown.

Tutorial Questions

The power supply has negligible internal resistance. The capacitor is initially uncharged. V

R is the p.d. across the resistor and V

C is the p.d. across the capacitor. The switch S is now closed.

(a) Sketch graphs of:

(i) V

C against time during charging. Show numerical values for the maximum and minimum values of V

C

(ii) V

R

. against time during charging. Show numerical values for the maximum and minimum values of V

R

.

(b) (i) What is the p.d. across the capacitor when it is fully charged?

(ii) Calculate the charge stored by the capacitor when it is fully charged.

(c) Calculate the maximum energy stored by the capacitor.

14. A capacitor is connected in a circuit as shown.

The power supply has negligible internal resistance.

The capacitor is initially uncharged. The switch S is now closed.

(a) Calculate the value of the initial current in the circuit.

(b) At a certain instant in time during charging the p.d. across the capacitor is 3 V.

Calculate the current in the resistor at this time.

15. The circuit shown is used to charge a capacitor. The power supply has negligible internal resistance. The capacitor is initially uncharged. The switch S is now closed.

At a certain instant in time the charge on the capacitor is 20 µ C.

Calculate the current in the circuit at this time.



79




16. The circuit shown is used to investigate the charge and discharge of a capacitor.

The switch is in position 1 and the capacitor is uncharged.

The switch is now moved to position 2 and the capacitor charges.

The graphs show how V

C

, the p.d. across the capacitor, V

R

, the p.d. across the resistor, and I, the current in the circuit, vary with time.

(a)The experiment is repeated with the resistance changed to 2 k Ω . Sketch the original graphs again and on each graph sketch the new lines which show how VC, VR and I vary with time.

(b)The experiment is repeated with the resistance again at 1 k Ω but the capacitor replaced with one of capacitance 20 mF. Sketch the original graphs again and on each graph sketch the new lines which show how VC, VR and I vary with time.

(c) (i) What does the area under the current against time graph represent?

(ii)Compare the areas under the current versus time graphs in the original graphs and in your answers to (a) and (b). Give reasons for any differences in these areas.

(d) At any instant in time during the charging what should be the value of (VC + VR)?

(e)The original values of resistance and capacitance are now used again and the capacitor fully charged. The switch is now moved to position 1 and the capacitor discharges. Sketch graphs of VC,

VR and I from the instant the switch is moved until the capacitor is fully discharged.



80




17. A student uses the circuit shown to investigate the charging of a capacitor.

The capacitor is initially uncharged.

The student makes the following statements:

(a) When switch S is closed the initial current in the circuit does not depend on the internal resistance of the power supply.

(b) When the capacitor has been fully charged the p.d. across the capacitor does not depend on the internal resistance of the power supply.

Use your knowledge of capacitors to comment on the truth or otherwise of these two statements.

Electrons at work

1. In the following descriptions of energy levels in metals, insulators and semiconductors some words and phrases have been replaced by the letters A to N.

From the table below choose the correct words or phrases to replace the letters.

In a metal the A band is completely filled and the B band is partially filled.

The electrons in the C band are free to move under the action of D so the metal has a E conductivity.

In an insulator there are no free electrons in the F band. The energy gap between the two bands is large and there is not enough energy at room temperature to move electrons from the G band into the H band.

Insulators have a very I conductivity.

In a pure semiconductor the energy gap between the valence and conduction bands is J than in a metal. At room temperature there is enough energy to move some electrons from the K band into the L band. As the temperature is increased the number of electrons in the conduction band M so the conductivity of the semiconductor N .

Letter

A, B, C, F, G, H, K, L

D

E, I

J

M, N

List of replacement words/phrases conduction, valence an electric field, a magnetic field low, high bigger, smaller decreases, increases



81




2. The conductivity of a semiconductor material can be increased by ‘doping’.

(a) Explain what is meant by the ‘conductivity’ of a material.

(b) Explain, giving an example, what is meant by ‘doping’ a semiconductor.

(e) Why does ‘doping’ decrease the resistance of a semiconductor material?

3. (a) A sample of pure germanium (four electrons in the outer shell) is doped with phosphorus (five electrons in the outer shell). What kind of semiconductor is formed?

(b) Why does a sample of n-type semiconductor still have a neutral overall charge?

4. Describe the movement of the majority charge carriers when a current flows in:

(a) an n-type semiconductor material

(b) a p-type semiconductor material.

5. A p-n junction diode is connected across a d.c. supply as shown.

7.

6.

(a) Is the diode connected in forward or reverse bias mode

(b) Describe the movement of the majority charge carriers across the p-n junction.

(c) What kind of charge is the only one that actually moves across the junction?

When positive and negative charge carriers recombine at the junction of ordinary diodes and LEDs, quanta of radiation are emitted from the junction.

(a) Does the junction have to be forward biased or reverse biased for radiation to be emitted?

(b) What form does this emitted energy take when emitted by:

(i) an LED

(ii) an ordinary junction diode?

A particular LED is measured as having a recombination energy of 3· 12 × 10 –19 J.

(a) Calculate the wavelength of the light emitted by the LED.

(b) What colour of light is emitted by the LED?

(c)What factor about the construction of the LED determines the colour of the emitted light?



82




8. (a) State two advantages of an LED over an ordinary filament lamp.

(b) An LED is rated as follows: operating p.d. 1· 8 V, forward current 20 mA

The LED is to be operated from a 6 V d.c. power supply.

(i) Draw a diagram of the circuit, including a protective resistor, which allows the LED to operate at its rated voltage.

(ii) Calculate the resistance of the protective resistor that allows the

LED to operate at its rated voltage.

9. The diagram shows a photodiode connected to a voltmeter.

(a) In which mode is the photodiode operating?

(b) Light is now incident on the photodiode.

(i) Explain how an e.m.f. is created across the photodiode.

(ii) The irradiance of the light incident on the photodiode is now increased. Explain why this increases the e.m.f. of the photodiode.

10. A photodiode is connected in reverse bias in a series circuit as shown.

(a) In which mode is the photodiode is operating?

(b) Why is the photodiode connected in reverse bias?

(c) What is the current in the circuit when the photodiode is in darkness? Explain your answer.

(d) The irradiance of the light on the photodiode is now increased.

(i) What is the effect on the current in the circuit?

(ii) What happens to the effective ‘resistance’ of the photodiode? Explain



83




TUTORIAL SOLUTIONS

Vector Problems

3. 0ms -1 , runner starts and finishes on start line so displacement for the race is zero.

4. 0ms -1 still in same place in bed!

5. (a) 80 km

6. (a) 70 m

(b) 40 km h -1 (c) 20 km north (d) 10 km h -1 north

(b) 50 m bearing 037 (c) (i) 70 s (ii) 0·71 m s -1 bearing 037

Equations of Motion (suvat)

1. 280 m

2. 51·2 ms -1

3. 28 ms -1

4. 16·7 s

5. 3·0 s

6. (a) 750 ms -2

7. 9·5 ms -2

8. (a) 0·21 ms -2

(b) 0·04 s

(b) 1·4 s

9. 234 m

10. (a) (i) 21·4 m (ii) 15·6 ms -1

downwards

(b) 34·6 m

Free Falling Objects

2. 9.8ms

-2 downwards

3. increases, air resistance increases with velocity

4. decreases, unbalanced force reduces as air resistance increases.

5. parachutist, just after the parachute is opened.

6. The object could stop moving before it hit the ground. It could even start to go upwards.

Displacement –Time Graphs

3. (a) 2 ms -1 due north (b) 0 ms -1

4. (a) 4 ms -1 due north (b) 1·0 ms -1

(d) 0·75 ms -1 due south (d) 1·6 ms -1

(f) displacement 2 m due north, velocity 4 m s -1 due north

(g) displacement 2 m due north, velocity 1 ms

5. (a) 1 ms -1 due north (b) 2 ms -1

-1 due south

due south

(d) 1.5 ms -1

(f) displacement 0·5 m due north, velocity 1 ms -1 due north

(g) displacement 0, velocity 2 ms -1

4. (a) 2 ms -2 due north (b) 0 ms -2

due south

(c) 4 m due north

5. (a) 1 ms -2 due north (b) 2 ms -2 due south

(d) 32 m due north

(d) displacement 3 m due north, velocity 0 ms -1

(e) displacement 2 m due north, velocity 2 ms -1 due south

Velocity – Time Graphs

1. (a) 2 ms -2 due north (b) 0 ms -2 (c) 4 m due north

2. (a) 1 ms -2 due north (b) 2 ms -2 due south

(d) displacement 3 m due north, velocity 0 ms -1

(e) displacement 2 m due North, velocity 2 ms -1 due south

3. (a)(i) 17·5 m due north (ii) 22·5 m due north

(d) 32 m due north

(iii) 17·5 m due north



84




4. (a) upwards (b) downwards (c) velocity is decreasing upwards

(d) velocity is increasing downwards (e) it hits the ground

(f) it starts to travel upwards

Acceleration – Time Graphs

2. (a) 24ms -1 (b) 33ms -1

(g) speed before is greater

Forces questions revisited

1. An object will remain at rest or move with constant velocity unless an unbalanced force acts upon it.

2. 4900 N

3. (a) (i) 1·5 × 10 -2 ms

5. 0·02 ms -2

-2 (ii) 3·0 × 10 6 N (b) –2·7 × 10 -3 ms -2

6. 150 N

7. (a) 120 N

8. (a) 1200 N

9. (a) (ii) 7·7 ms -2

(b) 20 N

(b) 108 m (c) 2590 N

10. (a) 1·78 × 10 3 kg

11. 2·86 × 10 4 N

(b) 6.2 × 10 4 N

12. (a) 1·96 × 10 3 N (b) 2.26 × 10 3

13. (a) (i) 2·45 × 10 3

N (c) 1.96 × 10

N (ii) 2·45 × 10 3 N (iii) 2·95 × 10

3 N (d) 1.66 × 10 3 N

3 N (iv) 1·95 × 10 3 N (b) 4·2 ms -2

14. 51·2 N

15. (b) 0·4 s reading 37·2 N

16. (a) 8 ms -2 (b) 16 N

4 s to 10 s reading 39·2 N

17. (a) 5·1 × 10 3 N (b) 2·5 × 10 3 N (c) (i) 700 N (ii) 500 N

10 s to 12 s reading 43·2 N

(d) 1·03 × 10 4 N

18. 24 m

19. (a) (i) 2 ms -2

20. (a) 3·27 ms -2

(ii) 40 N

(b) 6·54 N

(iii) 20 N (b) (i) 12 N

Resolution of Forces

1. (a) 43·3 N

2. 354 N

3. (a) 8·7 N

4. 0·513 ms -2

(b) 43·5 ms -2

5. (a) 226 N

6. 9·8 N up the slope

(b) 0·371 ms -2

7. 0·733 N

8. (a) 2283 N (b) 2·2 ms -2 (c) 14·8 ms -1

9. (a) (iii) 18 N down the slope (iv) 9 ms

(b) (ii) 16 N down the slope (iii) 8 ms

-2

-2 down the slope down the slope

Work, Potential and Kinetic Energy[recap]

1. (a) 3·92 J

2. (a) 1080 J

3. (a) 9·8 J

(b) 8·9 ms -1 (c) 6·3 ms -1

(b) 120 J

(b) (i) 3·1 ms -1 (ii) suvat

(b) 9·8 × 10 3 J (c) 3·9 s 4. (a) 490 N

5. 3·0 × 10 5 W

6. (a) 330 N (b) 2·0 × 10 -3 s



85




Collisions and Explosions

1. (a) 20 kg ms

2. (a) 0·75 ms

3. 2·4 ms -1

-1 to the right (b) 500 kg ms -1 downwards (c) 9 kg ms

-1 in the direction in which the first trolley was moving

-1 to the right

4. 3·0 kg

5. (a) 2·7 ms -1 (b) 0·19 J

6. 8·6 ms -1 in the original direction of travel

7. (a) 23 ms -1

8. 8·7 ms -1

9. 0·6 ms -1 in the original direction of travel of the 1·2 kg trolley

10. 16·7 ms -1 in the opposite direction to the first piece

11. 4 kg

12. 0·8 ms

13. 1·3 ms

-1

-1 in the opposite direction to the velocity of the man in the opposite direction to the velocity of the first trolley

14. 1·58 ms -1

15. 100 N

16. 3·0 × 10 -2 s

17. 2·67 ms -1

18 (a) + 0·39 kg ms -1 if you have chosen upwards directions to be positive

(b) + 0·39 N s if you have chosen upwards directions to be positive

(c) 15·6 N downwards (d) 15·6 N upwards

19. (a) v before = 3·96 ms -1 downwards; v after = 2·97 ms

(e) 16·6 N upwards

-1 upwards

(b) 9·9 × 10 -2 s

20.(b) 0·2 s (c) 20 N upwards (or –20 N for the sign convention used in the graph)

(d) 4·0 J

21. 1·25 × 10 3 N towards the wall

22. 9·0 × 10 4 N

24. (a) (i) 4·0 ms -1 in the direction the 2·0 kg trolley was travelling

(ii) 4·0 kg ms -1 in the direction the 2·0 kg trolley was travelling

(iii) 4·0 kg ms -1 in the opposite direction the 2·0 kg trolley was travelling

(b) 8·0 N

Projectiles

1. (a) 7·8 s

2. (a) 5·0 s

3. (b) 24·7 ms -1

(b) 123 m at an angle of 37º below the horizontal

4. (a) v

H

= 5·1 ms -1 , v

V

= 14·1 ms -1

5. (b) 50 ms -1 at 36.9º above the horizontal

(c) 40 ms -1 (d) 45 m

6. (a) 20 ms -1 (b) 20.4 m

(e) 240 m

(c) 4·1 s

7. (a) 8 s

8. (a) 15·6 ms -1

(b) 2730 m

(b) 379 m

(c) directly above box

(d) 142 m

12. 2 s

Gravity and mass

2. 417 N 3. 2·67 × 10 -4 N

6. 4·00 × 10 -15 m

4. 3·61 × 10 -47 N 5. 3·53 × 10 22 N



86




Special relativity

1. (a) 1·0 ms -1 north (b) 2·0 ms -1 south

2. (a) 0·8 ms -1 east (b) 2·8 ms -1

3. (a) 3·0 ms -1 (b) 2·0 ms -1

east

4. A = Einstein’s B = same

(c) 2·2 ms -1 west

C = zero D = velocity E = speed of light F = slow

G = shortened

5. 2000 km h -1

6. (a) No

7. 3 × 10 8 ms -1

(b) Yes

8. (a) 100 s

9. (a) 3 × 10 8 ms -1

10. (a) 0·3 × 10 8 ms -1

11. (a) c (b) 0·67 c

(b) 100 s

(b) 3 × 10 8

ms

-1

(b) 1·5 × 10 8 ms -1

(c) 0·5 c

Time dilation

(c) 1·8 × 10 8 ms -1

(d) 0·33 c

(d) 2·4 × 10 8 ms -1

2. (a) 21·2 h

(e) 2·10 × 10 8 ms -1

(b) 15·1 year

(f) 9·15 × 10 7 ms -1

5. 9·69 s

6. 3·9 × 10 -4 s

8 ms -1 or 0·70 c 7. 2·1 × 10

8. 2·90 10 8 ms

9. 2·60 × 10 8

-1 ms or 0·97 c

-1

(c) 1043 s (d) 1·32 × 10

3. (a) 11.11 am (b) 11.11 am or 11.20 am depending on interpretation of question

4. 17·1 billion years

-4 s

Length contraction

2. (a) 4·71 m

(e) 1·55 × 10 8 ms -1

3. 16 m

4. 0·872 m

5. 267 m

(b) 11·2 m

(f) 1·25 × 10 8 ms -1

(c) 0·227 km (d) 160 mm

6. 0·92 km

7. 2·60 × 10

8 ms -1

8. 2·19 × 10

8

9. 4·23 × 10

7 ms -1 ms -1 or 0.14 c

Relativity Miscellaneous

1 (b) 6 × 10 -7 s (c) 144 m

2. (a) 0·31 of a year (b) 2.8 x 10 15 m

3. (a) 1·84 × 10 -7 s (b) 54·6 m

4. (a) 120 m

5. (a) 5 s

(b) 72 m

(b) 9·22 s

6. 0·8 c

7. (a) 447 m

8. (a) 0·52 c

(b) 1·49 × 10 -6 s

(b) 2·58 × 10 8 s

9. (a) 2·60 × 10 -7 s (b) 77·6 m

(c) 8·99 × 10 15 m

(c) 2·21 × 10 8 s

(c) 7·75 m



87




The Expanding Universe

1. A = higher; B= lower; C = Doppler; D = effect

3. (a) 412 Hz

(e) 20 ms -1

(b) 389 Hz

(f) 60 ms -1

(c) 800 Hz

5. (a) 1063 Hz (b) 944 Hz

6. (a) 216 Hz

7. 14·5 ms -1

(b) 186 Hz

8. 466 Hz

9. 556 Hz, 525 Hz

10. (a) 1·07 m (b) 1·2 m

11. (a) 971 Hz (b) 1030 Hz

12. 37·8 ms -1

(d) 1035 Hz

13. (a) 354 kHz (b) Decrease – denominator is larger (c) 346 kHz

14. (a) 15 ms -1

15. 21·3 ms -1

16. (a) 15.1 ms -1

(b) 1569 Hz

(b) 2106 Hz

(c) 1437 Hz

(c) 2302 Hz

17. 154 s

18. 120 ms -1

19. A = longer; B = red; C = shorter; D = blue; E = away

20. (a) 1·01 × 10 -1 (b) 5·07 × 10 -2 (c) 525 nm

(e) 434 nm (f) 365 nm

(d) 682 nm

Hubble’s Law

1. (a) 9·46 × 10 15

2. (a) 1·52 × 10 -5 m (b) 4·75 × 10 17 light years m (c) 9·46 × 10 20

(b) 4·2 light years m (d) 1·51 × 10 26 m

(c) 5·19 × 10 7 light years

4. (a) 7·37 × 10 -2

5. (a) 1·49 × 10 7 ms -1

(b) 2·21 × 10 7 ms

(b) 6·21 × 10 ms -1 (b) 9·25 × 10

24

24

m m

(c) Away

6. (a) 2·22 × 10 7

7. (a) 8 × 10 -2

8. (a) 3·0 × 10 7

9. 2·27 × 10 7 ms ms

-1

(b) 410 nm

-1 (b) 1·25 × 10 25 m, 1·32 × 10 9

10. (a) Teacher Check (b) 4·55 × 10 14 Hz

11. (a) 1·23 × 10 7

12. 1·83 × 10 6 ms -1 ms

13. 3·24 × 10 -12 m

-1 (b) 542 million light years light years


1. (a) P (b) Energy emitted increases (c) Increases

(d) (ii) T λ max

= 2·9 × 10 -3 m K

(e) (i) T =11, 000 K (ii) λ max

= 1·3 × 10 -7 m (iii) T = 2·6 K

(iv) λ = 9·5 × 10 -6 m, infrared

3. v / ms -1 d / m z

1·70 × 10

4·54 × 10 6

5 7·10 × 10 22

1·89 × 10 24

5·67 × 10 -4

1·51 × 10 -2

1·70 × 10 6

2·21 × 10 6

7·08 × 10 23

9·21 × 10 23

5·667 × 10 -3

7·37 × 10 -3



88




4. (a) 7·37 × 10 -2

5. (a) 1·49 × 10 7 ms ms

-1

-1 6. (a) 2·22 × 1 07

7. (a) 8 × 10 -2

8. (a) 3·0 × 10 7 ms -1

9. 2·27 × 10 7 ms -1

10. (b) 4·55 × 10 14 Hz

11. (a) 1·23 × 10 7 ms -1

12. 1·83 × 10 6 ms -1

13. 3·24 × 10 -12 m


(b) 2·21 × 10 7 ms

(b) 6·21 × 10 24

(b) 9·25 × 10 24 m m

(c) Away

(b) 410 nm

(b) 1·25 × 10 25 m, 1·32 × 10 9 light years

(b) 542 million light years

1. (a) P (b) Energy emitted increases (c) Increases (d) (ii) T λ max

= 2·9 × 10 -3 m K

(e) (i) T =11, 000 K

(ii) λ max

= 1·3 × 10

(iii) T = 2·6 K

-7 m

(iv) λ = 9·5 × 10 -6 m, infrared

Orders of magnitude

1. A= electron; B = proton; C = nucleus; D = neutron

2. A = diameter of proton; B = diameter of nucleus; C = size of dust particle;

D = your height; E = height of Ben Nevis; F = diameter of Sun;

G = distance to nearest galaxy

The standard model of fundamental particles and interactions

1. (a) proton (b) antiproton (c) electron (d) positron

(e) neutron (f) antineutron (g) neutrino (f) antineutrino

2. (a)

1

-1 p (b)

0

-1 e (c)

0

1 e (d)

1

0 n (e)

1

0 n

3. Quarks: bottom, charm, down, strange, top, up

Leptons: electron, electron neutrino, muon, muon neutrino, tau, tau neutrino

4. (a) Leptons are particles that are acted on by the weak nuclear force but not by the strong nuclear force. Hadrons are particles that are acted on by the weak and strong nuclear force.

(b) Leptons – any one of electron, electron neutrino, muon, muon neutrino, tau and tau neutrino. Hadron – proton or neutron (or any combination of quarks which produce a integer charge).

5. (a) +e (b) 0 (c) −e (d) 0

6. (a) 3

(b) For the neutron the three quarks must give a charge of zero. For the proton the three quarks must give a charge of +e.



89




7. (a) Strong force has a range of less than 10

−14

m; weak force has a range of less than 10

−17

m.

(b) Beta decay

(c) Strong force.

Electric fields

3. 1· 6 × 10

−19

J

4. 8· 0 × 10

−13

J

5. (a) 8· 0 × 10

−17

J

6. 2· 65 × 10 7 m s −1

(b) 8· 0 ×10

−17

J

7. 2· 76 × 10

5

m s

−1

8. (a) (i) 4· 0 × 10

-15

J

(iii) 1· 9 × 10

16 electrons

(ii) 9· 4 × 10

Charged particles in a magnetic field

7

m s

−1

(c) 1· 3 × 10

7

m s

−1

1. Magnetic field is in the same plane and in the same or opposite direction to the velocity of the electron.

2. C: be deflected upwards

3. (a) no change in direction

(c) into the paper

(e) up

(g) left

Particle accelerators

1. (a) 8 × 10

−17

J

2. (a) 4.0 × 10

−17

J

3. 2· 65 × 10

7

m s

−1

4.

1· 38 × 10 6 m s −1

(b) out of the paper

(d) no change in direction

(f) left

(h) down

(b) 8 × 10

−17

(b) 9· 37 × 10

J (c) 1· 33 × 10

7

6

m s

−1

m s

−1

5. (a) 4 × 10

−16

J (b) 2· 96 × 10

7

m s

−1

(c) 1· 9 × 10

16

electrons

6. (a) 1· 25 × 10

16

(b) 7· 26 × 10

7

m s

−1

7. (a) (i) 1· 6 × 10

−16

J (ii) 3.2 x 10

-15

N (iii) 3· 52 × 10

15

m s

−2

(iv) 5· 34 × 10 −9 s (v) 6· 42 × 10 −9 s

(b) (i) Same since Q and V same (ii) Longer since acceleration is smaller



90




8. (a) 4· 0 × 10

−15

J (b) 9· 37 × 10

7

m s

−1

(d) Heat and X-rays are produced

(c) 3· 12 × 10

9. (a) Electron accelerated towards positive plate

16 electrons

(b) Proton accelerated towards negative plate but less curved than that of electron

(c) Neutron straight through.

10. (a) Negative (b) Positive (c) Positive (d) Negative

11. A = alternating electric fields; B = fixed-target; C = alternating electric fields;

D = spiral of increasing radius; E = constant magnetic field;

F = perpendicular; G = increases;

H = physical size; I = relativistic effects;

J = fixed-target;

L = can be varied;

N = increased;

P = the same;

R = colliding beam.

Fission and fusion

1. a) 6 Carbon C

K = circular path of fixed radius;

M = alternating magnetic fields;

O = relativistic effects;

Q = opposite; b) c)

25

47

Manganese

Silver

Mn

Ag d) 80 Mercury e) 86 Radon

Hg

Rn f) 92 Uranium U

2. (i)

(ii)

( a)

( a)

3

30

(b)

(b)

4

34

(iii) ( a) 47 (b) 62

(iv) (a) 54 (b) 77

(v) (a) 94 (b) 145

(vi) (a) 103 (b) 154

3. A is

4

2

He or α B is

216

284

Po C is

0

-1 e or β

5. A = 2 × 10

6

Bq

D is

223

88

Ra

6. (a) 2· 93 × 10

(c) 1· 46 × 10

−11

−11

J

J

(b) 1· 81 × 10

−11

J

(d) 2· 57 × 10

−11

J

7. (a) 3· 209 × 10 −29 kg (b) 2· 89 × 10 −12 J

(d) α then β then

(d) 8· 65 × 10 18

α

8. (b) mass number 137, atomic number 52

(c) 1· 62 × 10 −28 kg

(d) 1· 46 × 10

−11

J



91




Photoelectric effect

1. (a) 3· 97 × 10

−6

s

2. (a) 5· 46 × 10

−7

m

3. (a) 1· 5 × 10 −7 m

(b) 1· 19 × 10

(b) (i) 5· 49 × 10

3

14

m

Hz (ii) 1· 82 × 10

−15

(b) 5· 0 × 10 −16 s

4. 4· 31 × 10

−19

J

5. 3· 12 × 10 −19 J (3· 09 × 10 −19 J if calculated first and rounded)

s

6.

510 nm

9. (a) 4· 98 × 10

14

Hz

10. (b) 9.20 × 10 14 Hz

11. (a) 3· 3 × 10

−19

J

(c) (i) 1.86 × 10

(b) 2· 6 × 10

−19

J

−19 J

12. (a) 40 J

Interference and diffraction

19

2. (a) AQ = 12· 4 m, BQ = 13 m

3.

(a) 3· 0 × 10 −2 m

(d) 1· 5 × 10

−2

m

(b) 0· 6 m

(b) 3· 0 × 10

(e) 4· 5 × 10

−2 m

−2

m

4. Wavelength = 3· 0 × 10 −2 m

(c) 550 Hz

(c) 6· 0 × 10

(f) 0 m

Frequency = 1· 0 × 10

−2 m

10 Hz

5. (a) 0· 016 m

6. 0· 03 m

(b) 9· 9 × 10

(b) 3· 2 × 10

−2

m (c) 9· 4 × 10

9

Hz

7. 2· 5 × 10

−6

m

8. (a) 5· 84 × 10

−7

m

9. 13· 9º

10. (a) 3· 73 × 10

−6

m

11. 15· 5º

(b) 44· 5º

(b) 268

12. (c) 8· 7º



92




Refraction of light

1. material A n = 1· 27 material B n = 1· 37 material C n = 1· 53

2. (a) x = 32· 1º (b) y = 40· 9 º (c) z = 55· 9 º

3. (a) 21· 7 º (b) 2· 2 × 10 8 m s −1

4. (a) 1· 52

(d) 3.3 × 10

14

Hz

5. (a) 30· 7º

(b) 2.00 × 10

(e) 3.3 × 10

14

8

Hz

(b) 2.00 × 10

8

m s

−1

m s

−1

(c) 4.00 × 10

(c) 3.33 × 10

−7

m

−7

m

6. (b) (ii) ray 1 = 61· 49º, ray 2 = 60· 20º (iii) 1· 29º

7. 1· 54

8. glass = 40· 5º

9. (a) 1· 4

10. (b) 45º

11. (a) water = 48· 8º ice = 49· 8º

(b) 46º

Irradiance and inverse square law diamond = 24· 4º perspex = 41· 8º

1. 21 kW

2. (a) 0· 8 W m −2

3. (c) 3· 4 W m

−2

4. (a) 5000 m 2

(b) 0· 05 W m

(d) 0· 75 m

5. 24 W m

−2

Line and continuous spectra

1. (c) 2· 93 × 10

−19

J

2. (a) (i) X 3; Y 6

4. (a) 6 lines

(b) (i) X

2

to X

1

: Y

3

to Y

2

3. (a) 6 lines

(b) (i) 2· 0 × 10 15 Hz

−2

(b) 28333 m 2

(ii) X 3; Y 6

(ii) X

2

to X o

(ii) 2· 2 × 10

; Y

14

3

to Y

Hz o



93




Monitoring and measuring a.c.

1. (a) 325 V (b)

2 (c) V r. m.s

.

= 0.71 V peak

100 times

3. (a) 14 V

4. (a) 8.5 V (b) (i) 60 V (ii) 42 V

5. (a) (i) 100 Hz (ii) ±2 Hz

6. 5 cm

Current, voltage, power and resistance

1. 0.64 C

2. 5 × 10 3 A

3. 2· 0 × 10 4 s

4. 6 V

5. (a) I = 0· 1 A

6. (a) 5 Ω

(b) 6 Ω

(b) I = 0· 5 A, V = 4· 5 V (c) I = 2 A, V = 10 V

7.(a) 25 Ω (b) 25 Ω (c) 24· 2 W (d) 13· 3 Ω (e) 22· 9 Ω (f) 14· 7 Ω .

8. 3· 75 × 10 –3 V

9. (a) 60 W (b) 327 W

10. (a) 7· 7 A (b) 1763 W

(c) 500 W

11. 9000 J

12. I = 0· 67 A, V = 4 V

13. (a) 0· 67 A

14. 240 Ω

(b)

15. (c) 175 Ω

18. (a) V

1

= 0· 2 V, V

2

= 9· 8 V

0· 13 A (c) 1· 32 V

(b) V

1

= 2· 5 V, V

2

= 7· 5 V



94




20. (a) 4 V

21. (a) 3 V

22. (a) 0· 6 V

(b) 1 V

(b) -0· 8 V

(b) (i) 12 k Ω

23. X = 9 W Y = 45 W

Electrical sources and internal resistance

(c) 3 V

(c) 0 V

(ii) 4 k Ω

2. (a) 6 Ω (b) A

1

= 2 A, A

4. (a) R

1

= 230 Ω R

2

= 115 Ω

2

= 1· 5 A (c) 6 V (d)

(b)

24 W

Low 230 W high 690 W

5. (a) 4 Ω (b) 36 W

6. (a) 2· 0 V

(d)

(b)

1· 3 A, 1· 3 V

1· 6 V

7. 10 Ω

8. 5 Ω

(c) r = 0· 5 Ω R = 2 Ω

9. 12 Ω

10. (a) 1· 3 V

11. 0· 30 A

12. (a) 3· 0 Ω

13. 4· 0 V

(b) 3· 75 Ω

14. (b) (i) 1· 1 V, the intercept on the y-axis

(ii) 4· 2 Ω , the gradient of the line

(iii) 0· 26 A

15 (a) 6 V (b) 0· 1 W (c) 60 A

16. (b) 0· 147, 0· 264, 0· 382, 0· .500, 0· 617, 0· 735, 0· 855

(d) (i) 2· 5 Ω (ii) 17 V

(e) 6· 8 A

18. (a) Ammeter 1· 76 mA, voltmeter 1· 3 V

(b) 740 W (c) 0· 02 mA

(e) ± 0· 1 V (f) 0· 6 %

(h) 8%

(k) (740± 59) Ω

(i) 8%

(j) (740 ± 60) Ω

(d) ±0· 01 mA

(g) 8%

(j) 59 Ω



95




Capacitors

1. (a) 5· 0 × 10 –3 C

2. 50 µ F

3 (a) 40 V

4. 2· 25 × 10 –5 C

5. (a) 1· 0 µ F

6. (b) 50 µ F

7. (a) 2· 0 × 10 –3 C

8. 0· 60 J

(b)

(b)

(b)

(b)

(i)

1· 7%

0· 8 µ

1· 25 A

C

0· 020 J

9. (b) Reading on ammeter is 0 A

(c) 0 to 2 mA (max. current 1· 2 mA)

(d) 12 V

11. (b) 4· 9 mF

12. (e) (i) 4.0 x 10 -5 A

13. (b) (i) 3 V

14. (a) 2 mA (b)

(ii)

(ii)

9 mC

1· 5 mA

4· 0 mC

(c) 1· 35 × 10 –5 J

15. 2 mA

Electrons at work

1. A = valence; B = conduction; C = conduction; D = an electric field; E = high;

F = conduction; G = valence; H = conduction; I = low; J = smaller;

K = valence; L = conduction; M = increases; N = increases.

7. (a) 638 nm (b) Red

8. (b) (ii) 210 Ω



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