IGCSE
Cambridge (CIE)
Physics
2 hours
15 questions
Theory Questions
Momentum
Momentum / Impulse
Easy (5 questions)
/46
Medium (5 questions)
/41
Hard (5 questions)
/51
Total Marks
/138
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1
Easy Questions
1 (a) Extended tier only
State the equation for momentum.
(1 mark)
(b) Extended tier only
For the momentum equation in part (a) state the units of each variable.
(3 marks)
(c) Extended tier only
Without calculation, state the momentum of an object at rest and explain your answer.
(2 marks)
(d) Extended tier only
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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(2 marks)
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2 (a) Extended tier only
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
(1 mark)
(b) Extended tier only
A ball with mass 5.0 kg is moving with velocity of 10 m/s.
Calculate the momentum of the ball.
(3 marks)
(c) Extended tier only
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.
(2 marks)
(d) Extended tier only
Explain your answer to part (c).
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(3 marks)
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3 (a) Extended tier only
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.
Fig. 1
Calculate the initial momentum of trolley X.
(3 marks)
(b) Extended tier only
Trolley X collides with trolley Y.
If the two trolleys stick together, calculate their combined momentum after the collision.
(1 mark)
(c) Extended tier only
Calculate the velocity of the two trucks after the collision.
(3 marks)
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(d) Extended tier only
State the direction the trolleys will move in, and explain your answer.
(2 marks)
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4 (a) Extended tier only
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.
Fig. 1.
Calculate the momentum of the ball at the start, before it hits the wall.
(3 marks)
(b) Extended tier only
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.
(1 mark)
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(c) Extended tier only
For the initial and final motion of the ball
(i) Calculate the change in momentum.
[3]
(ii) State the impulse on the ball.
[1]
(4 marks)
(d) Extended tier only
Calculate the force exerted on the ball by the wall.
(1 mark)
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5 (a) Extended tier only
A golf ball with mass 0.05 kg is at rest on the grass as shown in Fig. 1.
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.
(3 marks)
(b) Extended tier only
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.
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(3 marks)
(c) Extended tier only
For the golf ball in part (a) state the impulse exerted on the ball by the putter.
(2 marks)
(d) Extended tier only
The putter is in contact with the ball for 0.6 seconds.
Calculate the force exerted on the ball by the putter.
(3 marks)
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11
Medium Questions
1 Extended tier only
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.
(3 marks)
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2 (a) Extended tier only
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.
(1 mark)
(b) Extended tier only
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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(6 marks)
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3 (a) Extended tier only
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.
product
quantity
mass × acceleration
force × time
Fig 2.1
(2 marks)
(b) Extended tier only
Fig. 2.2 shows a man hitting a ball with a golf club.
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:
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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]
(5 marks)
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4 (a) Extended tier only
Fig. 3.1 shows a shooting competition, where air rifles fire soft metal pellets at distant
targets.
When an air rifle is fired, it exerts an impulse of 0.019 N s on the pellet.
Define impulse.
(1 mark)
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(b) Extended tier only
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]
(5 marks)
(c) 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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(3 marks)
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5 (a) Extended tier only
State the equation for impulse in terms of the velocity of an object. Define the variables
used.
(2 marks)
(b) Extended tier only
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]
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(5 marks)
(c) Extended tier only
After making contact with the ball the mallet stops moving. Calculate the velocity of the
mallet at the moment it hit the ball.
(3 marks)
(d) State the energy transfer that takes place:
(i) As the ball changes shape during the contact between the mallet and the ball.
[2]
(ii) As the ball leaves the mallet.
[1]
(5 marks)
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Hard Questions
1 (a) Extended tier only
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.
The mass of the athlete is 71 kg. Calculate the impulse applied to her as she slows down.
Give your answer to 2 significant figures.
impulse = ...............................................
(3 marks)
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(b) Extended tier only
(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]
(3 marks)
(c) Extended tier only
Calculate the force required to give a mass of 71 kg an acceleration of 6.4 m/s2.
force = ........................................................
(2 marks)
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2 (a) Extended tier only
Fig. 2.1 shows a train.
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 = .........................................................
(3 marks)
(b) Extended tier only
Calculate the average resultant force applied to the train as it slows down.
force = .........................................................
(2 marks)
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(c) Suggest how the shape of a modern electric train helps it to travel at high speeds.
(1 mark)
(d) 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 less than 80 s to reduce its speed from 42 m/s to
zero.
(1 mark)
(e) 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.
(1 mark)
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3 (a) Extended tier only
Fig. 1 shows two railway trucks A and B travelling towards each other on the same
railway line which is straight and horizontal.
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.
(4 marks)
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(b) Extended tier only
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]
(1 mark)
(c) Extended tier only
The trucks come to a stop after 3.0 minutes.
Calculate the deceleration of the joined trucks.
(2 marks)
(d) Explain why two trucks on rail tracks stop moving after they have collided.
(2 marks)
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4 (a) Extended tier only
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.
(2 marks)
(b) Extended tier only
Calculate the velocity of the shell just after the rifle is fired.
(3 marks)
(c) Extended tier only
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]
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(6 marks)
(d) Extended tier only
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.
(4 marks)
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5 (a) Extended tier only
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.
The use of crumple zones explains why the front and rear of cars are badly damaged
during accidents.
Use your knowledge of momentum and impulse forces to suggest why a car with a
crumple zone protects the driver and passengers from serious injury better than one
which is a strong, rigid box.
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(6 marks)
(b) Extended tier only
Two cars are crash-tested, with crash test dummy 'drivers' wearing seatbelts, to assess
the force reduction that crumple zones provide in a road-traffic accident.
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 front ends of the cars crumple, taking different amounts of
time to come to a stop. Car A takes 0.3 seconds to stop, while car B takes 0.7 seconds to
stop.
Using this information, calculate the forces which would be experienced by the cars due
to the impact.
(i) For car A
Force = .................................... N [3]
(ii)
For car B
Force = .................................... N [2]
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(5 marks)
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