Momentum (Cambridge O Level Physics)

Exam Questions

2 hours28 questions
1a
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1 mark

State the equation for momentum.

1b
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3 marks

For the momentum equation in part (a) state the units of each variable.

1c
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2 marks

Without calculation, state the momentum of an object at rest and explain your answer.

1d
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2 marks

Complete the sentence to state the principle of conservation of momentum.

 

In a closed system, the total momentum ........... an event is ........... to the total momentum after the event

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2a
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1 mark

Choose the word from the list which completes the sentence:

Momentum is a property of a moving object making it difficult for it to change ....................

 

direction      mass      speed      weight
2b
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3 marks

A ball with mass 5.0 kg is moving with velocity of 10 m/s.

   

Calculate the momentum of the ball.

2c
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2 marks

The ball in part (b) hits a wall and rebounds in the opposite direction. The speed of the ball does not change.

                 

Without further calculation, state the momentum of the ball in part (b) after it rebounds.

2d
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3 marks

Explain your answer to part (c).

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3a
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3 marks

A trolley X with mass of 4.0 kg is moving on a track with velocity of 2.0 m/s towards a stationary trolley Y with mass of 8.0 kg as shown in Fig. 1.

1-6-3a-e-momentum-trolleys

Fig. 1

Calculate the initial momentum of trolley X.

3b
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1 mark

Trolley X collides with trolley Y. 

If the two trolleys stick together, calculate their combined momentum after the collision.

3c
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3 marks

Calculate the velocity of the two trucks after the collision.

3d
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2 marks

State the direction the trolleys will move in, and explain your answer.

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4a
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3 marks

A squash ball is hit towards a wall at a velocity of 44 m/s. The ball has mass 0.025 kg.

The motion of the ball is shown in Fig. 1.

1-6-4a-e-squash-momentum
Fig. 1.
       

Calculate the momentum of the ball at the start, before it hits the wall.

4b
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3 marks

The ball is in contact with the wall for 0.1 s and then rebounds with velocity 42 m/s

Calculate the momentum of the ball at the end of the motion, after the impact with the wall.

Consider the direction of motion in your answer.

4c
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4 marks

For the initial and final motion of the ball

  
(i)
Calculate the change in momentum.
[3]
(ii)
State the impulse on the ball.
[1]
4d
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3 marks

Calculate the force exerted on the ball by the wall.

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5a
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3 marks

A golf ball with mass 0.05 kg is at rest on the grass as shown in Fig. 1.

1-6-5a-e-momentum-impulse-golf

Fig. 1

The ball is hit with a putter so that the ball moves off with velocity of 2.0 m/s

Calculate the momentum of the ball after being hit with the putter.

5b
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3 marks

After hitting the golf ball the putter immediately stops moving. The mass of the putter is 0.5 kg. 

   

Calculate the velocity of the putter at the moment it hit the ball.

5c
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2 marks

For the golf ball in part (a) state the impulse exerted on the ball by the putter.

5d
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3 marks

The putter is in contact with the ball for 0.6 seconds.

Calculate the force exerted on the ball by the putter.

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1
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3 marks

A tennis player is practicing by hitting a ball many times against a wall.   The ball hits the wall 20 times in 60 s.

The average change in momentum for each collision with the wall is 4.2 kg m/s.

Calculate the average force that the ball exerts on the wall.

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2a
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1 mark

The velocity of an object of mass m increases from u to v.

State, in terms of m, u and v, the change of momentum of the object.

2b
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6 marks

In a game of tennis, a player hits a stationary ball with his racquet.

 
(i)

The racquet is in contact with the ball for 6.0 ms. The average force on the ball during this time is 400 N.

Calculate the impulse on the tennis ball.

 

 

impulse = ...........................................................[2]

(ii)

The mass of the ball is 0.056 kg.

Calculate the speed with which the ball leaves the racquet.

 

 

speed = ...........................................................[2]

(iii)

State the energy transfer that takes place:

 
1. as the ball changes shape during the contact between the racquet and the ball

2. as the ball leaves the racquet.

[2]

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3a
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2 marks

Complete Fig. 2.1 by writing in the right-hand column the name of the quantity given by the product in the left-hand column.

q2a
3b
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5 marks

Fig. 2.2 shows a man hitting a ball with a golf club.

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The ball has a mass of 0.046 kg. The golf club is in contact with the ball for 5.0 × 10–4 s and the ball leaves the golf club at a speed of 65 m/s.

 
(i)

Calculate:

1. the momentum of the ball as it leaves the golf club

 

 

momentum = ...........................................................[2]

 

2. the average resultant force acting on the ball while it is in contact with the golf club.

 

 

average force = ...........................................................[2]

 

(ii)

While the golf club is in contact with the ball, the ball becomes compressed and changes shape.

Name the energy store being filled whilst the ball is in contact with the golf club.

[1]

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4a
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1 mark

Fig. 3.1 shows a shooting competition, where air rifles fire soft metal pellets at distant targets.

screenshot-2022-11-04-at-09-59-42
When an air rifle is fired, it exerts an impulse of 0.019 N s on the pellet.
  

Define impulse.

4b
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5 marks

The pellet has a mass of 1.1 × 10–4 kg.

  

Determine: 

   
(i)
the speed with which the pellet leaves the rifle
   
   
 speed = ........................................................ [2]
    
(ii)
the kinetic energy of the pellet as it leaves the rifle.
   
   
kinetic energy = ........................................................ [3]
4c
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3 marks

The pellet melts when it strikes the target.

Describe how the molecular structure of the liquid metal differs from that of the solid metal.

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5a
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2 marks

State the equation for impulse in terms of the velocity of an object. Define the variables used.

5b
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5 marks

In a game of croquet, a player hits a ball which was initially at rest with a mallet.

The mallet has mass of 1.36 kg.

 
(i)

The mallet is in contact with the ball for 11 ms. The average force on the ball during this time is 200 N.

Calculate the impulse on the croquet ball.

 

 

impulse = ...........................................................[3]

(ii)

The mass of the ball is 0.450 kg.

Calculate the speed with which the ball leaves the mallet.

 

 

speed = ...........................................................[2]

5c
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3 marks

Calculate the velocity of the mallet at the moment it hit the ball.

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1a
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3 marks

Fig. 2.1 shows an athlete crossing the finishing line in a race. As she crosses the finishing line, her speed is 10.0 m/s. She slows down to a speed of 4.0 m/s.      

runners

The mass of the athlete is 71 kg. Calculate the impulse applied to her as she slows down.

 
 
 impulse = ............................................... 
1b
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3 marks
(i)
Define impulse in terms of force and time.

[1]

     

(ii)
The athlete takes 1.2 s to slow down from a speed of 10.0 m/s to a speed of 4.0 m/s.
 
Calculate the average resultant force applied to the athlete as she slows down.
 
 
force = ........................................................ [2]
1c
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2 marks

Calculate the force required to give a mass of 71 kg an acceleration of 6.4 m/s2.

 
 
force = ........................................................

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2a
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3 marks

Fig. 2.1 shows a train.

 may-june-2020-42-q2

The total mass of the train and its passengers is 750 000 kg. The train is travelling at a speed of 84 m/s. The driver applies the brakes and the train takes 80 s to slow down to a speed of 42 m/s.

 

Calculate the impulse applied to the train as it slows down.

 

 

impulse = .........................................................

2b
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2 marks

Calculate the average resultant force applied to the train as it slows down.

 

force = .........................................................

2c
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1 mark

Suggest how the shape of the train helps it to travel at high speeds.

2d
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1 mark

The train took 80 s to reduce its speed from 84 m/s to 42 m/s. Explain why, with the same braking force, the train takes more than 80 s to reduce its speed from 42 m/s to zero.

2e1 mark

On a wet day, the train travels a greater distance before it stops along the same track. The train has the same speed of 84 m / s before the brakes are applied.

 
Suggest a reason for this.

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3a
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4 marks

Fig. 1 shows two railway trucks A and B travelling towards each other on the same railway line which is straight and horizontal.

4-5---q1

 

Fig. 1 

The trucks are involved in a collision. They join when they collide and then move together.

Truck A has a total mass of 27 000 kg and truck B has a total mass of 22 000 kg.

Just before the collision, truck A was moving at a speed of 3.6 m s–1 and truck B was moving at a speed of 2.4 m s–1.

Calculate the speed of the joined trucks immediately after the collision.

3b
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4 marks

During the collision each truck experiences an impulse acting on it.

  
(i)
Calculate the impulse that acts on each truck during the collision.
[2]
(ii)
State two possible units for your answer.
[2]
3c
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2 marks

The trucks come to a stop after 3.0 minutes.

Calculate the deceleration of the joined trucks.

3d
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2 marks

Explain why the trucks stop moving.

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4a
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2 marks

A shell, of mass 30 g, is fired from the barrel of a rifle, of mass 1.9 kg, with a momentum 36 kg m/s.

State the total momentum of the rifle and the bullet before the rifle is fired and give a reason for your answer.

4b
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3 marks

Calculate the velocity of the shell just after the rifle is fired.

4c
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6 marks

Continue to calculate for the moment just after the rifle has been fired.

(i)
Use the principle of conservation of momentum, and your answer to part (a), to state the total momentum of the rifle and the shell.
[2]
(ii)
Calculate the recoil momentum of the rifle.
[4]
4d
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4 marks

The shell has a momentum of 9.8 kg m/s just before it hits a target.

It takes 4.5 ms for the bullet to the stopped by the target.

Calculate the average force needed to stop the bullet.

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5
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5 marks

Until the second half of the 20th century, cars were designed as strong rigid boxes, which designers thought would protect passengers in accidents. In fact, although average speeds were much slower than today, passengers were often very badly injured.

Modern cars are designed with safety features including 'crumple zones'. The crumple zones are at the front and rear of the car but do not include the passenger section. In a crash, the crumple zone is designed so that it deforms and bends. This is shown in Fig. 1.1.

HIVZR74H_1-6-5a-h-momentum-crumple-zone

The use of crumple zones explains why the front and rear of cars are badly damaged during accidents.

Another safety feature of modern cars is air bags. During a collision, air bags quickly inflate, filling the space between the driver and the steering wheel and windscreen. This is shown in Fig. 1.2.

1-6-5b-h-momentum-crumple-zone

Two cars are crash-tested to assess how much protection air bags provide in a road-traffic accident.

Car A does not have an air bag, whilst car B does.

Car A has a mass of 1200 kg and car B has a mass of 1500 kg.

Both cars have a driver of mass 70 kg and they both crash to a stop from an initial speed of 30 m/s.

At the moment of impact, the drivers are thrown forwards, taking different amounts of time to come to a stop. The driver of car A takes 0.3 seconds to stop, while the driver of car B takes 0.7 seconds to stop.

 

Using this information, calculate the forces which would be experienced by the drivers due to the impact.

   
(i)
For the driver in car A
Force = .................................... N [3]
  
(ii)
For the driver in car B
Force = .................................... N [2]

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