Momentum

A tennis ball is dropped from a height above the ground.

Diagram 1 shows the tennis ball at the instant it is released.

Diagram 1

On diagram 1, draw a labelled arrow to show the force acting on the tennis ball at the instant it is released.

Diagram 2 shows the tennis ball at the instant it hits the ground.

Diagram 2

Just before hitting the ground, the tennis ball is moving downwards at a velocity of 2.5 m/s.

Just after hitting the ground, the tennis ball is moving upwards at a speed of 1.9 m/s.

The mass of the tennis ball is 0.057 kg.

Calculate the change in momentum of the tennis ball when it hits the ground.

Give the unit.

The ball is in contact with the ground for a time of 6.0 ms.

Calculate the force exerted on the ball by the ground.

Give the direction of this force.

The coefficient of restitution can be used to determine how high a ball will bounce. The higher the value of the coefficient of restitution, the higher the ball will bounce.

Diagram 3 shows a ball being dropped from a height (h₁) above the ground.

The ball hits the ground and bounces.

At the top of its bounce, the ball reaches a height (h₂) above the ground.

The coefficient of restitution can be determined using the formula

A student decides to do an investigation to compare the coefficient of restitution for different types of ball.

Design a method for the student’s investigation.

Your answer should include details of

• the variables in the investigation

• how to obtain accurate measurements

• how to obtain reliable results

You may add to diagram 3 or draw an additional diagram to help your answer.

State the principle of conservation of momentum.

The diagram shows object A and object B moving in opposite directions.

The arrows show the direction of the velocities of the two objects.

Before the collision object A has a momentum of 39 kg m/s.

After the collision object A and object B stick together and stop moving.

State the magnitude of the momentum of object B before the collision.

State the formula linking momentum, mass and velocity.

The mass of object A is 8.1 kg.

Calculate the velocity of object A before the collision.

The time taken for the collision is 0.56 s.

Calculate the average force on object A.

Give the direction and magnitude of the force on object B from object A.

The diagram shows the collision between two balls, A and B.

The masses and velocities of both balls are shown before and after the collision.

Ball B is stationary before the collision.

0.265 kg
0.265 kg

Before collision
After collision

When the balls collide, ball B applies a force on ball A, which causes the velocity of ball A to change.

Ball A also applies a force on ball B during the collision.

Describe how the force applied on ball A compares with the force applied on ball B during the collision.

Calculate the momentum of ball A before the collision.

momentum of ball A before collision =_........ kg m / s

Show that the velocity, v, of ball B after the collision is about 0.6 m / s.

A collision is considered elastic if the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

Using data from the diagram, deduce whether this collision is elastic.

This question is about momentum and forces.

State the principle of conservation of momentum.

The diagram shows an air track that can be used to investigate motion without friction.

Air comes out through a series of small holes in the air track. The air lifts the glider slightly above the track.

A small spacecraft engine floats at rest on a cushion of air.

State the momentum of the spacecraft engine when it is at rest.

The spacecraft engine ejects large numbers of xenon ions to the left.

A mass of 2.6 × 10⁻⁸kg of xenon ions leaves the engine with a mean speed of 26 km / s.

Calculate the momentum of all the ejected xenon ions.

momentum =_........ kg m / s

State the magnitude and direction of the spacecraft engine’s momentum after these xenon ions leave the engine.

The ions exert a force of 2.6 mN on the spacecraft engine.

The spacecraft engine has a mass of 1.2 kg.

Calculate the acceleration of the engine.

Give your answer to 2 significant figures.

acceleration =_........ m / s²

The engine is designed to accelerate a spacecraft while the spacecraft is travelling through space.

The spacecraft carries a mass of 0.75 kg of xenon ions for the engine.

When the engine is used, 9.9 × 10⁻⁸kg of xenon ions leave the engine each second.

A student suggests that this small spacecraft engine would not be useful because the acceleration it produces is very small.

Evaluate the student’s suggestion.

The diagram shows two birds, just before bird X catches the smaller bird Y.

Both birds are travelling horizontally at constant velocity.

mass = 0.41 kg

Show that the momentum of bird X is about 5 kg m / s.

The momentum of bird Y just before it is caught is 0.15 kg m / s.

Calculate the total momentum of the birds just before bird X catches bird Y.

momentum =_........ kg m / s

State the total momentum of the birds just after bird X has caught bird Y.

Bird Y has a mass of 0.17 kg.

Calculate the velocity of the birds just after bird X has caught bird Y.

The photograph shows a dummy during a test of the safety features of a car in a collision.

(Source: © fStop Images GmbH/Alamy Stock Photo)

Before the collision, the dummy in the car is travelling at a velocity of 14 m / s.

The dummy has a momentum of 1100 kg m / s.

State the formula linking momentum, mass and velocity.

Show that the mass of the dummy is approximately 80 kg.

The dummy is brought to rest during the collision by a mean force of 15 kN.

Calculate the time taken for the dummy to be brought to rest in the collision.

The car being tested is fitted with airbags.

Using ideas about momentum, explain how an airbag reduces the force experienced by the dummy in the collision.

A crumple zone is a safety feature in a car.

It is a part of the car that is designed to collapse during a collision.

A student investigates the effectiveness of crumple zones.

The student rolls two model cars down a ramp.

Each car comes to rest when it hits a large metal block.

A data logger measures the mean force applied to the car during the collision with the block.

The diagram shows the equipment used in the investigation.

Car 1 has a paper crumple zone at the front.

Car 2 has no paper crumple zone.

The table shows the student’s results.

The mass of each car is 0.074 kg.

Calculate the time taken for the velocity of car 1 to decrease from 3.0 m/s to 0.0 m/s.

State the magnitude and direction of the force on the metal block, when car 2 collides with the block.

Explain why the mean force from the block on car 1 is smaller than the mean force on car 2.

Which of these is a device used to measure force?

Airbags are safety devices used in cars to protect the driver if there is a crash.

State the formula linking momentum, mass and velocity.

A person inside a car has a mass of 72 kg and a velocity of 13 m/s.

Show that the momentum of the person is about 900 kg m/s.

The person experiences a crash and comes to rest in 0.29 s.

Calculate the force on the person.

Which statement explains how airbags protect the driver?

Cricket is a sport played with bats and balls.

A cricket player hits a ball with a bat. Before the ball is hit, it is moving to the left with a momentum of 4.2 kg m/s.

The bat is in contact with the ball for 0.012 s.

After the ball is hit, it moves to the right with a momentum of 6.7 kg m/s.

Calculate the mean force the bat exerts on the ball and state the direction of the force.

State the magnitude and direction of the mean force the ball exerts on the bat.

The cricket player wears padded protective equipment.

This protective equipment reduces the risk of injury to the player if they are struck by the cricket ball.

Explain how this protective equipment reduces the risk of injury to the player.

Use ideas about momentum in your answer.

The diagram shows an air track that can be used to investigate motion without friction.

Air comes out through a series of small holes in the air track, which lifts the gliders slightly above the track.

There are two gliders on the track.

Each glider has a magnet.

The poles of the magnets nearest each other are alike.

Explain the direction of the force acting on magnet A from magnet B.

The gliders collide and the magnets cause them to rebound.

Before the collision, the momentum of glider A is 0.045 kg m/s to the right and glider B is at rest.

State the total momentum of glider A and glider B after the collision.

After the collision, the momentum of glider A is 0.021 kg m/s to the left.

Calculate the momentum of glider B after the collision.

momentum of glider B =_........ kg m/s

The time taken for glider B to change its momentum is 0.19 seconds.

Calculate the average force on glider B that causes this change in momentum.

Give the direction of the force on glider B from glider A.

The diagram shows a child’s toy for accelerating steel balls.

This is how the toy works.

• the toy uses three identical steel balls, each with a mass of 4.1 g

• ball A moves towards the magnet

• ball B is in contact with the magnet

• balls B and C are initially at rest and are in contact with each other

• when ball A collides with the magnet, ball C moves away from the magnet

Ball A moves towards the magnet with an initial velocity of 0.15 m/s.

Calculate the initial momentum of ball A.

initial momentum =_........ kg m/s

Ball A is attracted to the magnet.

Explain how this attraction affects the momentum of ball A as it approaches the magnet.

When ball A collides with the magnet, a force of 1.3 N is exerted on ball C for a time of 0.0025 s.

This causes ball C to move away from the magnet.

Calculate the change in velocity of ball C due to this force.

Curling is a sport played on ice.

A player slides stone A across the ice towards a scoring zone.

The ice reduces friction so that there is negligible friction when the stone is sliding.

Stone A leaves the player’s hand with a velocity of 2.90 m/s.

The mass of stone A is 17 kg.

State the formula linking momentum, mass and velocity.

Show that the momentum of stone A is approximately 50 kg m/s.

Stone A slides towards the scoring zone.

In the scoring zone, stone A collides with a stationary stone, B.

After the collision, both stones move in the same direction as the initial direction of stone A.

The velocity of stone A after the collision is 0.40 m/s.

Calculate the velocity of stone B after the collision.

[mass of stone B = 19 kg]

When the stones collided, they were in contact for a time of 25 ms.

Calculate the magnitude of the force stone A exerted on stone B in this collision.

This question is about momentum.

Diagram 1 shows a neutron approaching a uranium-235 nucleus.

State the formula linking momentum, mass and velocity.

Calculate the momentum of the neutron.

Give a unit with your answer.

[mass of neutron = 1.67 × 10^–27kg]

State what is meant by the term conservation of momentum.

Diagram 2 shows that when the neutron collides with the uranium-235 nucleus, they combine to give a uranium-236 nucleus.

Use conservation of momentum to calculate the velocity, v, of the uranium-236 nucleus.

[mass of uranium-235 nucleus = 3.99 × 10^–25kg]

[mass of uranium-236 nucleus = 4.01 × 10^–25kg]

A metalworker uses a hammer of mass 1.8 kg to deform a piece of metal on an anvil.

Calculate the increase in the hammer’s gravitational potential energy (GPE) store when the hammer is raised through a height of 0.95 m above the metal.

[GPE gained = mass × gravitational field strength × height]

The metalworker moves the hammer down to strike the metal.

The hammer must have at least 21 J of energy in its kinetic energy (KE) store as it hits the metal to deform it.

Explain why the metalworker must do at least 4 J of mechanical work on the hammer to deform the metal.

Calculate the velocity of the hammer just before it strikes the metal.

[KE of hammer = 21 J]

When the hammer hits the metal, the hammer comes to rest without rebounding.

Calculate the mean (average) force needed to bring the hammer to rest in a time of 0.12 s.

A game is played on a table with balls of different colours.

The diagram shows the white ball moving across a flat surface.

State the formula linking momentum, mass and velocity.

The white ball has a mass of 170 g.

Calculate the momentum of the white ball.

momentum =_........ kgm/s

The white ball collides with a stationary black ball.

white ball
black ball
white ball
black ball

before collision
after collision

The black ball has a mass of 160 g.

After the collision, the black ball moves away from the white ball with a velocity of 5.0 m/s.

Calculate the velocity of the white ball after the collision.

During the collision, the white ball exerts a force of 80 N on the black ball.

The direction of this force is to the right.

State the magnitude and direction of the force the black ball exerts on the white ball during the collision.