1

1.When a body is accelerating, the resultant force acting on it is equal to its

A.change of momentum.

B.rate of change of momentum.

C.acceleration per unit of mass.

D.rate of change of kinetic energy.

(1)

2.The velocity of a body of mass m changes by an amount Dv in a time Dt. The impulse given to the body is equal to

A.mDt.

B.

.

t

v

D

D

C.

.

t

v

m

D

D

D.mDv.

(1)

3.A ball is held at rest at point X and is then released. It drops on to a flat horizontal surface and rebounds to a maximum height at point Y.

point X

point Y

before

after

Which one of the following graphs best shows the variation with time t of the momentum p of the ball as it moves between point X and point Y?

A.

B.

C.

D.

p

t

0

0

p

t

0

0

p

t

0

0

p

t

0

0

(1)

4.An object on the end of a light flexible string rotates in a circle as shown below.

object

T

The tension in the string is T when the string is at angle to the vertical. Which of the following is true?

State

Resultant force

A.

not in equilibrium

T

B.

not in equilibrium

T sin

C.

in equilibrium

T

D.

in equilibrium

T sin

(1)

5.A sphere of mass m strikes a vertical wall and bounces off it, as shown below.

momentum

p

momentum

p

B

A

wall

The magnitude of the momentum of the sphere just before impact is pB and just after impact is pA. The sphere is in contact with the wall for time t. The magnitude of the average force exerted by the wall on the sphere is

A.

(

)

t

p

p

A

B

.

B.

(

)

t

p

p

A

B

+

.

C.

(

)

mt

p

p

A

B

.

D.

(

)

mt

p

p

A

B

+

.

(1)

6.An object is moving at constant velocity. Which one of the following quantities must have zero magnitude?

A.Weight of object

B.Momentum of object

C.Kinetic energy of object

D.Resultant force on object

(1)

7.A ball of weight W is dropped on to the pan of a top pan weighing balance and rebounds off the pan.

pan

00.00

At the instant that the ball has zero velocity when in contact with the pan, the scale will read

A.zero.

B.a value less than W but greater than zero.

C.W.

D.a value greater than W.

(1)

8.A small boat in still water is given an initial horizontal push to get it moving. The boat gradually slows down. Which of the following statements is true for the forces acting on the boat as it slows down?

A.There is a forward force that diminishes with time.

B.There is a backward force that diminishes with time.

C.There is a forward force and a backward force both of which diminish with time.

D.There is a forward force and a backward force that are always equal and opposite.

(1)

9.If the resultant external force acting on a particle is zero, the particle

A.must have constant speed.

B.must be at rest.

C.must have constant velocity.

D.must have zero momentum.

(1)

10.A horse pulls a boat along a canal at constant speed in a straight-line as shown below.

boat

L

P

F

horse

direction of travel

The horse exerts a constant force F on the boat. The water exerts a constant drag force L and a constant force P on the boat. The directions of F, L and P are as shown. Which one of the following best represents a free-body diagram for the boat?

A.

B.

C.

D.

F

L

P

F

L

P

F

L

P

F

L

P

(1)

11.An elevator (lift) is used to either raise or lower sacks of potatoes. In the diagram, a sack of potatoes of mass 10 kg is resting on a scale that is resting on the floor of an accelerating elevator. The scale reads 12 kg.

10 kg

elevator

scale

The best estimate for the acceleration of the elevator is

A.2.0 m s2 downwards.

B.2.0 m s2 upwards.

C.1.2 m s2 downwards.

D.1.2 m s2 upwards.

(1)

12.A general expression for Newtons second law of motion is

F =

t

p

What condition is applied so that the law may be expressed in the form F = ma?

A.The mass m is constant.

B.The acceleration a is constant.

C.The force F is constant.

D.The direction of the force F is constant.

(1)

13.A ball of mass m, travelling in a direction at right angles to a vertical wall, strikes the wall with a speed v1. It rebounds at right angles to the wall with a speed v2. The ball is in contact with the wall for a time t. The magnitude of the force that the ball exerts on the wall is

A.

(

)

t

v

v

m

D

+

2

1

.

B.m(v1 + v2)t.

C.

(

)

t

v

v

m

D

-

2

1

.

D.m(v1 v2)t.

(1)

14.A truck collides head on with a less massive car moving in the opposite direction to the truck. During the collision, the average force exerted by the truck on the car is FT and the average force exerted by the car on the truck is FC. Which one of the following statements is correct?

A.FT will always be greater in magnitude than FC.

B.FT will always be equal in magnitude to FC.

C.FT will be greater in magnitude than FC only when the speed of the car is less than the speed of the truck.

D.FT will be equal in magnitude to FC only when the speed of the truck is equal to the speed of the car.

(1)

15.A light inextensible string has a mass attached to each end and passes over a frictionless pulley as shown.

pulley

string

mass

m

mass

M

The masses are of magnitudes M and m, where m < M. The acceleration of free fall is g. The downward acceleration of the mass M is

A.

(

)

(

)

m

M

g

m

M

+

-

.

B.

(

)

M

g

m

M

-

.

C.

(

)

(

)

m

M

g

m

M

-

+

.

D.

(

)

m

M

Mg

+

.

(1)

16.Two blocks having different masses slide down a frictionless slope.

Which of the following correctly compares the accelerating force acting on each block and also the accelerations of the blocks down the slope?

Accelerating force

Acceleration

A.

Equal

Equal

B.

Equal

Different

C.

Different

Equal

D.

Different

Different

(1)

17.This question is about conservation of momentum and conservation of energy.

(a)State Newtons third law.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(1)

(b)State the law of conservation of momentum.

.....................................................................................................................................

.....................................................................................................................................

(2)

The diagram below shows two identical balls A and B on a horizontal surface. Ball B is at rest and ball A is moving with speed V along a line joining the centres of the balls. The mass of each ball is M.

A

B

v

Before collision

During the collision of the balls, the magnitude of the force that ball A exerts on ball B is FAB and the magnitude of the force that ball B exerts on ball A is FBA.

(c)On the diagram below, add labelled arrows to represent the magnitude and direction of the forces FAB and FBA.

A

B

During the collision

(3)

The balls are in contact for a time t. After the collision, the speed of ball A is +vA and the speed of ball B is +vB in the directions shown.

A

B

After the collision

v

A

v

B

As a result of the collision, there is a change in momentum of ball A and of ball B.

(d)Use Newtons second law of motion to deduce an expression relating the forces acting during the collision to the change in momentum of

(i)ball B.

...........................................................................................................................

...........................................................................................................................

(2)

(ii)ball A.

...........................................................................................................................

...........................................................................................................................

(2)

(e)Apply Newtons third law and your answers to (d), to deduce that the change in momentum of the system (ball A and ball B) as a result of this collision, is zero.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(4)

(f)Deduce, that if kinetic energy is conserved in the collision, then after the collision, ball A will come to rest and ball B will move with speed V.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(3)

(Total 17 marks)

18.This question is about modelling the thermal processes involved when a person is running.

When running, a person generates thermal energy but maintains approximately constant temperature.

(a)Explain what thermal energy and temperature mean. Distinguish between the two concepts.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(4)

The following simple model may be used to estimate the rise in temperature of a runner assuming no thermal energy is lost.

A closed container holds 70 kg of water, representing the mass of the runner. The water is heated at a rate of 1200 W for 30 minutes. This represents the energy generation in the runner.

(b)(i)Show that the thermal energy generated by the heater is 2.2 106 J.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(2)

(ii)Calculate the temperature rise of the water, assuming no energy losses from the water. The specific heat capacity of water is 4200 J kg1 K1.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(3)

(c)The temperature rise calculated in (b) would be dangerous for the runner. Outline three mechanisms, other than evaporation, by which the container in the model would transfer energy to its surroundings.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(6)

A further process by which energy is lost from the runner is the evaporation of sweat.

(d)(i)Describe, in terms of molecular behaviour, why evaporation causes cooling.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(3)

(ii)Percentage of generated energy lost by sweating: 50%Specific latent heat of vaporization of sweat: 2.26 106 J kg1

Using the information above, and your answer to (b) (i), estimate the mass of sweat evaporated from the runner.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(3)

(iii)State and explain two factors that affect the rate of evaporation of sweat from the skin of the runner.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(4)

(Total 25 marks)

19.This question is about an experiment designed to investigate Newtons second law.

In order to investigate Newtons second law, David arranged for a heavy trolley to be accelerated by small weights, as shown below. The acceleration of the trolley was recorded electronically. David recorded the acceleration for different weights up to a maximum of 3.0 N. He plotted a graph of his results.

heavy trolley

acceleration

pulley

weight

(a)Describe the graph that would be expected if two quantities are proportional to one another.

.....................................................................................................................................

.....................................................................................................................................

(2)

(b)Davids data are shown below, with uncertainty limits included for the value of the weights. Draw the best-fit line for these data.

1.40

1.20

1.00

0.80

0.60

0.40

0.20

0.00

0.00

0.50

1.00

1.50

2.00

2.50

weight / N

acceleration

/ ms

2

(2)

(c)Use the graph to

(i)explain what is meant by a systematic error.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(2)

(ii)estimate the value of the frictional force that is acting on the trolley.

...........................................................................................................................

(1)

(iii)estimate the mass of the trolley.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(2)

(Total 9 marks)

20.This question is about momentum and the kinematics of a proposed journey to Jupiter.

(a)State the law of conservation of momentum.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(2)

A solar propulsion engine uses solar power to ionize atoms of xenon and to accelerate them. As a result of the acceleration process, the ions are ejected from the spaceship with a speed of 3.0104 m s1.

xenon ions

speed = 3.010 m s

4

2

1

spaceship

mass = 5.410 kg

(b)The mass (nucleon) number of the xenon used is 131. Deduce that the mass of one ion of xenon is 2.2 1025 kg.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(2)

(c)The original mass of the fuel is 81 kg. Deduce that, if the engine ejects 77 1018 xenon ions every second, the fuel will last for 1.5 years. (1 year = 3.2 107 s)

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(2)

(d)The mass of the spaceship is 5.4 102 kg. Deduce that the initial acceleration of the spaceship is 8.2 105 m s2.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(5)

The graph below shows the variation with time t of the acceleration a of the spaceship. The solar propulsion engine is switched on at time t = 0 when the speed of the spaceship is 1.2103 m s1.

a

/ 10 m s

5

7

2

t

/ 10 s

10.0

9.5

9.0

8.5

8.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

(e)Explain why the acceleration of the spaceship is increasing with time.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(2)

(f)Using data from the graph, calculate the speed of the spaceship at the time when the xenon fuel has all been used.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(4)

(g)The distance of the spaceship from Earth when the solar propulsion engine is switched on is very small compared to the distance from Earth to Jupiter. The fuel runs out when the spaceship is a distance of 4.7 1011 m from Jupiter. Estimate the total time that it would take the spaceship to travel from Earth to Jupiter.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(2)

(Total 19 marks)

21.This question is about a balloon used to carry scientific equipment.

The diagram below represents a balloon just before take-off. The balloons basket is attached to the ground by two fixing ropes.

balloon

basket

fixing rope

fixing rope

50

50

ground

There is a force F vertically upwards of 2.15 103 N on the balloon. The total mass of the balloon and its basket is 1.95 102 kg.

(a)State the magnitude of the resultant force on the balloon when it is attached to the ground.

...................................................................................................................................

(1)

(b)Calculate the tension in either of the fixing ropes.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(3)

(c)The fixing ropes are released and the balloon accelerates upwards. Calculate the magnitude of this initial acceleration.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(2)

(d)The balloon reaches a terminal speed 10 seconds after take-off. The upward force F remains constant. Describe how the magnitude of air friction on the balloon varies during the first 10 seconds of its flight.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(2)

(Total 8 marks)

22.Kinematics

(a)State the principle of conservation of energy.

...................................................................................................................................

...................................................................................................................................

(1)

(b)An aircraft accelerates from rest along a horizontal straight runway and then takes-off. Discuss how the principle of conservation of energy applies to the energy changes that take place while the aircraft is accelerating along the runway.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(3)

(c)The mass of the aircraft is 8.0 103 kg.

(i)The average resultant force on the aircraft while travelling along the runway is 70 kN. The speed of the aircraft just as it lifts off is 75 m s1. Estimate the distance travelled along the runway.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(3)

(ii)The aircraft climbs to a height of 1250 m. Calculate the potential energy gained during the climb.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(1)

When approaching its destination, the pilot puts the aircraft into a holding pattern. This means the aircraft flies at a constant speed of 90 m s1 in a horizontal circle of radius 500 m as shown in the diagram below.

500 m

(d)For the aircraft in the holding pattern,

(i)calculate the magnitude of the resultant force on the aircraft;

.........................................................................................................................

.........................................................................................................................

(2)

(ii)state the direction of the resultant force.

.........................................................................................................................

.........................................................................................................................

(1)

(Total 11 marks)

23.Linear momentum

(a)Define

(i)linear momentum;

.........................................................................................................................

.........................................................................................................................

(1)

(ii)impulse.

.........................................................................................................................

.........................................................................................................................

(1)

(b)Explain whether momentum and impulse are scalar or vector quantities.

...................................................................................................................................

...................................................................................................................................

(1)

(c)By reference to Newtons laws of motion, deduce that when two particles collide, momentum is conserved.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(5)

A rubber ball of mass 50 g is thrown towards a vertical wall. It strikes the wall at a horizontal speed of 20 m s1 and bounces back with a horizontal speed of 18 m s1 as shown below.

speed before

=

20 m s

1

speed after

=

18 m s

1

The ball is in contact with the wall for 0.080 s.

(d)(i)Calculate the change in momentum of the ball.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(2)

(ii)Calculate the average force exerted by the ball on the wall.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(2)

(iii)Suggest, in terms of Newtons laws of motion, why a steel ball of the same mass and the same initial horizontal speed exerts a greater force on the wall.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(3)

(Total 15 marks)

24.This question is about Newtons laws of motion, the dynamics of a model helicopter and the engine that powers it.

(a)Explain how Newtons third law leads to the concept of conservation of momentum in the collision between two objects in an isolated system.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(4)

(b)The diagram illustrates a model helicopter that is hovering in a stationary position.

rotating

blades

downward motion of air

0.70 m

0.70 m

The rotating blades of the helicopter force a column of air to move downwards. Explain how this may enable the helicopter to remain stationary.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(3)

(c)The length of each blade of the helicopter in (b) is 0.70 m. Deduce that the area that the blades sweep out as they rotate is 1.5 m2. (Area of a circle = pr2)

...................................................................................................................................

...................................................................................................................................

(1)

(d)For the hovering helicopter in (b), it is assumed that all the air beneath the blades is pushed vertically downwards with the same speed of 4.0 m s1. No other air is disturbed.

The density of the air is 1.2 kg m3.

Calculate, for the air moved downwards by the rotating blades,

(i)the mass per second;

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(2)

(ii)the rate of change of momentum.

.........................................................................................................................

.........................................................................................................................

(1)

(e)State the magnitude of the force that the air beneath the blades exerts on the blades.

...................................................................................................................................

(1)

(f)Calculate the mass of the helicopter and its load.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(2)

(g)In order to move forward, the helicopter blades are made to incline at an angle q to the horizontal as shown schematically below.

While moving forward, the helicopter does not move vertically up or down. In the space provided below draw a free body force diagram that shows the forces acting on the helicopter blades at the moment that the helicopter starts to move forward. On your diagram, label the angle q.

(4)

(h)Use your diagram in (g) opposite to explain why a forward force F now acts on the helicopter and deduce that the initial acceleration a of the helicopter is given by

a = g tan q

where g is the acceleration of free fall.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(5)

(i)Suggest why, even though the forward force F does not change, the acceleration of the helicopter will decrease to zero as it moves forward.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(2)

(Total 25 marks)

25.This question is about Newtons laws of motion, the dynamics of a model helicopter and the engine that powers it.

(a)Explain how Newtons third law leads to the concept of conservation of momentum in the collision between two objects in an isolated system.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(4)

(b)The diagram illustrates a model helicopter that is hovering in a stationary position.

rotating

blades

downward motion of air

0.70 m

0.70 m

The rotating blades of the helicopter force a column of air to move downwards. Explain how this may enable the helicopter to remain stationary.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(3)

(c)The length of each blade of the helicopter in (b) is 0.70 m. Deduce that the area that the blades sweep out as they rotate is 1.5 m2. (Area of a circle = pr2)

...................................................................................................................................

...................................................................................................................................

(1)

(d)For the hovering helicopter in (b), it is assumed that all the air beneath the blades is pushed vertically downwards with the same speed of 4.0 m s1. No other air is disturbed.

The density of the air is 1.2 kg m3.

Calculate, for the air moved downwards by the rotating blades,

(i)the mass per second;

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(2)

(ii)the rate of change of momentum.

.........................................................................................................................

.........................................................................................................................

(1)

(e)State the magnitude of the force that the air beneath the blades exerts on the blades.

...................................................................................................................................

(1)

(f)Calculate the mass of the helicopter and its load.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(2)

(g)In order to move forward, the helicopter blades are made to incline at an angle q to the horizontal as shown schematically below.

While moving forward, the helicopter does not move vertically up or down. In the space provided below draw a free body force diagram that shows the forces acting on the helicopter blades at the moment that the helicopter starts to move forward. On your diagram, label the angleq.

(4)

(h)Use your diagram in (g) to explain why a forward force F now acts on the helicopter and deduce that the initial acceleration a of the helicopter is given by

a = g tanq

where g is the acceleration of free fall.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(5)

(i)The helicopter is driven by an engine that has a useful power output of 9.0 102 W. The engine makes 300 revolutions per second. Deduce that the work done in one cycle is 3.0 J.

...................................................................................................................................

...................................................................................................................................

(1)

(j)The diagram below shows the relation between the pressure and the volume of the air in the engine for one cycle of operation of the engine.

A

B

C

D

pressure

volume

(i)State the name given to the type of process represented by DA.

.........................................................................................................................

(1)

(ii)During one cycle of the engine, the gas absorbs Q1 units of thermal energy and Q2 units of thermal energy are transferred from the gas. On the diagram above, draw labelled arrows to show these energy transfers.

(2)

(iii)The efficiency of the engine is 60%. Using your answer to question (i), calculate the values of Q1 and Q2.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(3)

(Total 30 marks)

26.Linear motion

At a sports event, a skier descends a slope AB. At B there is a dip BC of width 12 m. The slope and dip are shown in the diagram below. The vertical height of the slope is 41 m.

A

B

C

D

41m

slope

(not to scale)

1.8m

dip

12m

The graph below shows the variation with time t of the speed v down the slope of the skier.

25.0

20.0

15.0

10.0

5.0

0.0

8.0

7.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

v

/ ms

1

t

/ s

The skier, of mass 72 kg, takes 8.0 s to ski, from rest, down the length AB of the slope.

(a)Use the graph to

(i)calculate the kinetic energy EK of the skier at point B.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(2)

(ii)determine the length of the slope.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(4)

(b)(i)Calculate the magnitude of the change DEP in the gravitational potential energy of the skier between point A and point B.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(2)

(ii)Use your anwers to (a)(i) and (b)(i) to determine the ratio

(

)

.

P

K

P

E

E

E

D

-

D

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(2)

(iii)Suggest what this ration represents.

.........................................................................................................................

.........................................................................................................................

(1)

(c)At point B of the slope, the skier leaves the ground. He flies across the dip and lands on the lower side at point D. The lower side C of the dip is 1.8 m below the upper side B.

(i)Calculate the time taken for an object to fall, from rest, through a vertical distance of 1.8 m. Assume negligible air resistance.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(2)

(ii)The time calculated in (c)(i) is the time of flight of the skier across the dip. Determine the horizontal distance travelled by the skier during this time, assuming that the skier has the constant speed at which he leaves the slope at B.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(2)

(Total 15 marks)

27.Linear motion

At a sports event, a skier descends a slope AB. At B there is a dip BC of width 12 m. The slope and dip are shown in the diagram below. The vertical height of the slope is 41 m.

A

B

C

D

41m

slope

(not to scale)

1.8m

dip

12m

The graph below shows the variation with time t of the speed v down the slope of the skier.

25.0

20.0

15.0

10.0

5.0

0.0

8.0

7.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

v

/ ms

1

t

/ s

The skier, of mass 72 kg, takes 8.0 s to ski, from rest, down the length AB of the slope.

(a)Use the graph to

(i)calculate the kinetic energy EK of the skier at point B.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(2)

(ii)determine the length of the slope.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(4)

(b)(i)Calculate the change DEP in the gravitational potential energy of the skier between point A and point B.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(2)

(ii)Use your answers to (a) and (b)(i) to determine the average retarding force on the skier between point A and point B.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(3)

(iii)Suggest two causes of the retarding force calculated in (ii).

1................................................................................................................

2................................................................................................................

(2)

(c)At point B of the slope, the skier leaves the ground. He flies across the dip and lands on the lower side at point D. The lower side C of the dip is 1.8 m below the upper side B.

Determine the distance CD of the point D from the edge C of the dip. Air resistance may be assumed to be negligible.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(4)

(d)The lower side of the dip is altered so that it is inclined to the horizontal, as shown below.

slope

B

C

D

dip

12m

1.8m

(i)State the effect of this change on the landing position D.

.........................................................................................................................

.........................................................................................................................

(1)

(ii)Suggest the effect of this change on the impact felt by the skier on landing.

.........................................................................................................................

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.........................................................................................................................

(2)

(Total 20 marks)

28.This question is about the breaking distance of a car and specific heat capacity.

(a)A car of mass 960 kg is free-wheeling down an incline at a constant speed of 9.0 m s1.

15

speed = 9.0 m s

-1

The slope makes an angle of 15 with the horizontal.

(i)Deduce that the average resistive force acting on the car is 2.4103N.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(2)

(ii)Calculate the kinetic energy of the car.

...........................................................................................................................

...........................................................................................................................

(1)

(b)The driver now applies the brakes and the car comes to rest in 15 m. Use your answer to (a)(ii) to calculate the average braking force exerted on the car in coming to rest.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(2)

(c)The same braking force is applied to each rear wheel of the car. The effective mass of each brake is 5.2 kg with a specific heat capacity of 900 J kg1 K1. Estimate the rise in temperature of a brake as the car comes to rest. State one assumption that you make in your estimation.

estimate:

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.....................................................................................................................................

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.....................................................................................................................................

.....................................................................................................................................

assumption:

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(4)

(Total 9 marks)

29.Two identical springs A and B each have a force constant (force per unit extension) of 2.5Ncm1. One end of each spring is attached to a trolley and the other ends are attached to rigid supports, as shown.

support

trolley

spring A

spring B

The springs are horizontal and, when the trolley is at rest, the extension of each spring is 3.0 cm. The trolley is displaced 1.2 cm to the right.

support

trolley

spring B

displacement 1.2 cm

spring A

(a)Calculate the magnitude of the force on the trolley due to

(i)spring A alone.

...........................................................................................................................

...........................................................................................................................

(2)

(ii)spring B alone.

...........................................................................................................................

...........................................................................................................................

(1)

(b)The trolley is released. Determine the initial acceleration of the trolley of mass 0.75 kg.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(2)

(Total 5 marks)

30.This question is about energy and momentum.

A train carriage A of mass 500 kg is moving horizontally at 6.0 m s1. It collides with another train carriage B of mass 700 kg that is initially at rest, as shown in the diagram below.

1

6.0m s

train carriage A

500kg

train carriage B

700kg

The graph below shows the variation with time t of the velocities of the two train carriages before, during and after the collision.

6.0

5.0

4.0

3.0

2.0

1.0

0.0

1.0

2.0

10.0

9.0

8.0

7.0

6.0

5.0

4.0

3.0

2.0

1.0

train carriage B

train carriage A

t

/ s

v

/ ms

1

(a)Use the graph to deduce that

(i)the total momentum of the system is conserved in the collision;

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(2)

(ii)the collision is elastic.

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(2)

(b)Calculate the magnitude of the average force experienced by train carriage B.

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(3)

(Total 7 marks)

31.This question is about momentum.

(a)Define

(i)linear momentum.

...........................................................................................................................

...........................................................................................................................

(1)

(ii)impulse.

...........................................................................................................................

...........................................................................................................................

(1)

(b)In a ride in a pleasure park, a carriage of mass 450 kg is travelling horizontally at a speed of 18 m s1. It passes through a shallow tank containing stationary water. The tank is of length 9.3 m. The carriage leaves the tank at a speed of 13 m s1.

18 m s

carriage, mass 450 kg

9.3m

water-tank

13 m s

1

1

As the carriage passes through the tank, the carriage loses momentum and causes some water to be pushed forwards with a speed of 19 m s1 in the direction of motion of the carriage.

(i)For the carriage passing through the water-tank, deduce that the magnitude of its total change in momentum is 2250N s.

...........................................................................................................................

...........................................................................................................................

(1)

(ii)Use the answer in (b)(i) to deduce that the mass of water moved in the direction of motion of the carriage is approximately 120 kg.

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(2)

(iii)Calculate the mean value of the magnitude of the acceleration of the carriage in the water.

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...........................................................................................................................

(3)

(c)For the carriage in (b) passing through the water-tank, determine

(i)its total loss in kinetic energy.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(3)

(ii)the gain in kinetic energy of the water that is moved in the direction of motion of the carriage.

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(1)

(d)By reference to the principles of conservation of momentum and of energy, explain your answers in (c).

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.....................................................................................................................................

(3)

(Total 15 marks)

32.Block on an inclined plane

A block is held stationary on a frictionless inclined plane by means of a string as shown below.

string

block

inclined plane

(a)(i)On the diagram draw arrows to represent the three forces acting on the block.

(3)

(ii)The angle q of inclination of the plane is 25. The block has mass 2.6 kg. Calculate the force in the string. You may assume that g = 9.8 m s2.

.........................................................................................................................

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(2)

(b)The string is pulled so that the block is now moving at a constant speed of 0.85 m s1 up the inclined plane.

(i)Explain why the magnitude of the force in the string is the same as that found in (a)(ii).

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.........................................................................................................................

(2)

(ii)Calculate the power required to move the block at this speed.

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(2)

(iii)State the rate of change of the gravitational potential energy of the block. Explain your answer.

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(2)

(Total 11 marks)

33.Motion of a ball

A ball of mass 0.25 kg is projected vertically upwards from the ground with an initial velocity of 30 m s1. The acceleration of free fall is 10 m s2, but air resistance cannot be neglected.

The graph below shows the variation with time t of the velocity v of this ball for the upward part of the motion.

30.0

25.0

20.0

15.0

10.0

5.0

0.0

3.0

2.5

2.0

1.5

1.0

0.5

0.0

v

/ ms

1

t

/s

(a)State what the area under the graph represents.

...................................................................................................................................

(1)

(b)Estimate the maximum height reached by the ball.

...................................................................................................................................

...................................................................................................................................

(1)

(c)Determine, for the ball at t = 1.0 s,

(i)the acceleration;

.........................................................................................................................

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.........................................................................................................................

(3)

(ii)the magnitude of the force of air resistance.

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(2)

(d)Use the graph to explain, without any further calculations, that the force of air resistance is decreasing in magnitude as the ball moves upward.

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...................................................................................................................................

(2)

(e)The diagram below is a sketch graph of the upward motion of the ball.

Draw a line to indicate the downward motion of the ball. The line should indicate the motion from the maximum height of the ball until just before it hits the ground.

30

20

10

0.0

10

20

30

4.0

2.0

0.0

t

/ s

v

/ ms

1

(2)

(f)State and explain, by reference to energy transformations, whether the speed with which the ball hits the ground is equal to 30 m s1.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(2)

(g)Use your answer in (f) to state and explain whether the ball takes 2.0 s to move from its maximum height to the ground.

...................................................................................................................................

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...................................................................................................................................

(2)

(Total 15 marks)

34.This question is about units and momentum.

(a)Distinguish between fundamental units and derived units.

.....................................................................................................................................

.....................................................................................................................................

(1)

(b)The rate of change of momentum R of an object moving at speed v in a stationary fluid of constant density is given by the expression

R = kv2

where k is a constant.

(i)State the derived units of speed v.

...........................................................................................................................

(1)

(ii)Determine the derived units of R.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(2)

(iii)Use the expression and your answers in (b)(i) and (b)(ii) to determine the derived units of k.

...........................................................................................................................

...........................................................................................................................

(1)

(c)Define

(i)linear momentum.

...........................................................................................................................

...........................................................................................................................

(1)

(ii)impulse.

...........................................................................................................................

...........................................................................................................................

(1)

(d)In a ride in a pleasure park, a carriage of mass 450 kg is travelling horizontally at a speed of 18 m s1. It passes through a shallow tank containing stationary water. The tank is of length 9.3 m. The carriage leaves the tank at a speed of 13 m s1.

18 m s

carriage, mass 450 kg

9.3m

water-tank

13 m s

1

1

As the carriage passes through the tank, the carriage loses momentum and causes some water to be pushed forwards with a speed of 19 m s1 in the direction of motion of the carriage.

(i)For the carriage passing through the water-tank, deduce that the magnitude of its total change in momentum is 2250N s.

...........................................................................................................................

...........................................................................................................................

(1)

(ii)Use the answer in (d)(i) to deduce that the mass of water moved in the direction of motion of the carriage is approximately 120 kg.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(2)

(iii)Calculate the mean value of the magnitude of the acceleration of the carriage in the water.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(3)

(e)For the carriage in (d) passing through the water-tank, determine

(i)its total loss in kinetic energy.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(3)

(ii)the gain in kinetic energy of the water that is moved in the direction of motion of the carriage.

...........................................................................................................................

...........................................................................................................................

(1)

(f)By reference to the principles of conservation of momentum and of energy, explain your answers in (e).

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(3)

(Total 20 marks)

35.This question is about linear and circular motion.

A car moves along a straight road. At time t = 0 the car starts to move from rest and oil begins to drip from the engine of the car. One drop of oil is produced every 0.80 s. Oil drops are left on the road. The position of the oil drops are drawn to scale on the grid below such that 1.0 cm represents 4.0 m. The grid starts at time t = 0.

direction of motion

1.0cm

(a)(i)State the feature of the diagram above which indicates that, initially, the car is accelerating.

...........................................................................................................................

(1)

(ii)On the grid above, draw further dots to show where oil would have dripped if the drops had been produced from the time when the car had started to move.

(2)

(iii)Determine the distance moved by the car during the first 5.6 s of its motion.

...........................................................................................................................

...........................................................................................................................

(1)

(b)Using information from the