State the equation for momentum.
For the momentum equation in part (a) state the units of each variable.
Without calculation, state the momentum of an object at rest and explain your answer.
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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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 ....................
A ball with mass 5.0 kg is moving with velocity of 10 m/s.
Calculate the momentum of the ball.
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.
Explain your answer to part (c).
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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.
Trolley X collides with trolley Y.
If the two trolleys stick together, calculate their combined momentum after the collision.
Calculate the velocity of the two trucks after the collision.
State the direction the trolleys will move in, and explain your answer.
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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.
Calculate the momentum of the ball at the start, before it hits the wall.
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.
For the initial and final motion of the ball
Calculate the force exerted on the ball by the wall.
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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.
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.
For the golf ball in part (a) state the impulse exerted on the ball by the putter.
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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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.
[1]
Calculate the force required to give a mass of 71 kg an acceleration of 6.4 m/s2.
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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 = .........................................................
Calculate the average resultant force applied to the train as it slows down.
force = .........................................................
Suggest how the shape of the train helps it to travel at high speeds.
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.
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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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.
During the collision each truck experiences an impulse acting on it.
The trucks come to a stop after 3.0 minutes.
Calculate the deceleration of the joined trucks.
Explain why the trucks stop moving.
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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.
Calculate the velocity of the shell just after the rifle is fired.
Continue to calculate for the moment just after the rifle has been fired.
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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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.
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.
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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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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.
In a game of tennis, a player hits a stationary ball with his racquet.
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]
The mass of the ball is 0.056 kg.
Calculate the speed with which the ball leaves the racquet.
speed = ...........................................................[2]
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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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.
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.
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]
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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Define impulse.
The pellet has a mass of 1.1 × 10–4 kg.
Determine:
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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State the equation for impulse in terms of the velocity of an object. Define the variables used.
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.
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]
The mass of the ball is 0.450 kg.
Calculate the speed with which the ball leaves the mallet.
speed = ...........................................................[2]
Calculate the velocity of the mallet at the moment it hit the ball.
State the energy transfer that takes place:
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