AQA AS Physics

Topic Questions

4.5 Linear Momentum & Conservation

1a2 marks
(i)
Write an equation for the momentum of an object in words 
(ii)
State the SI units of momentum.

1b3 marks

A railway carriage, C1, of mass 1100 kg is rolling along a horizontal track at a speed of 6 m s-1 towards a stationary carriage, C2, as shown in Figure 1.  Carriage C2 has a mass of  3 300 kg. 

Figure 1

4-5-s-q--q1a-easy-aqa-a-level-physics

State or calculate: 

(i)         The initial momentum of carriage C1 before the collision 

(ii)        The initial momentum of carriage C2 before the collision.

1c3 marks

At the moment of collision, both carriages C1 and C2, become joined. 

The joined carriages move off with a velocity, v, as shown in Figure 2.  

                                                                     Figure 2

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Use your answers from part (b), and the conservation of momentum, to calculate the total momentum of C1 and C2 after they have become joined.

1d3 marks

Use your answer to part (c) to calculate the velocity, v, at which the carriages C1 and C2 move after becoming joined.

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2a3 marks

A film stuntman, of mass 85.0 kg, is being trained to jump off high objects.

In one scene he steps off a roof and falls vertically to the ground below. Just before he hits the ground he has a velocity of 9.08 m s-1.  After he has landed on the ground he remains at rest.

Calculate the momentum of the stuntman

(i)         Just before he hits the ground

(ii)        After he has landed.

2b2 marks

Using your answers to part (a), calculate the change of momentum of the stuntman during the landing.

2c2 marks

Hence state the impulse experienced by the stuntman during landing. 

Give an appropriate unit with your answer.

2d3 marks

If the stuntman keeps his legs fully rigid, the time for the impact is 4.20 ms.  

Calculate the magnitude of the average resultant force acting on the stuntman’s legs during this time.

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3a2 marks

A bullet, of mass 20 g, leaves the barrel of a rifle, of mass 1.9 kg, with a momentum 4.0 kg m s–1.

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

3b3 marks

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

3c4 marks

Immediately 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 bullet
(ii)
Calculate the recoil momentum of the rifle      
3d4 marks

The bullet has a momentum of 3 kg m s–1 just before it hits a target.  

It takes 2.5 ms for the bullet to the stopped by the target. 

Calculate the average force needed to stop the bullet.

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4a6 marks

Zorbing is an activity which involves a person running inside an inflatable ball, called a ‘zorb’.  Two zorbs, A and B, collide head on with each other, as shown in Figure 1.  The total mass of zorb A and its occupant is 75 kg and the total mass of zorb B and its occupant is 60 kg.  Before the collision, zorb A is travelling at 2.0 m s-1 and zorb B is travelling at 1.5 m s-1. 

Figure 1

4-5-s-q--q4b-easy-aqa-a-level-physics

Calculate:   

(i)   The momentum of zorb A before the collision    

(ii)   The momentum of zorb B before the collision 

(iii)   The total momentum of both zorbs before the collision. 

    
4b6 marks

After the collision both zorbs bounce off each other and move in opposite directions, as shown in Figure 2.  Zorb A travels at 0.8 m s–1 and zorb B travels at 2.0 m s–1. 

Figure 2

4-5-s-q--q4c-easy-aqa-a-level-physics

Calculate: 

(i)         The momentum of zorb A after the collision 

(ii)        The momentum of zorb B after the collision 

(iii)       The total momentum of both zorbs after the collision.

4c4 marks

Calculate:           

            (i)         The total kinetic energy of the zorbs before the collision 

            (ii)        The total kinetic energy of the zorbs after the collision.

4d3 marks

State whether: 

            (i)         Momentum is conserved during the collision of the zorbs 

            (ii)        Kinetic energy is conserved during the collision of the zorb 

            (iii)       The collision of the zorbs is elastic or inelastic.

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5a3 marks

A collision can be described as elastic or inelastic. 

Place a ‘’ in Table 1 below to show which quantities are conserved in each type of collision, provided there are no external forces acting. 

Table 1 

Quantity

Elastic Collision

Inelastic Collision

Momentum

 

 

Total Energy

 

 

Kinetic Energy

 

 

 

5b2 marks

During a safety test, a car or mass 1 250 kg travels at 0.5 m s–1 towards a wall. 

Calculate the momentum of the car before it collides with the wall.

5c3 marks

The car has a force sensor attached to the bumper which detects the force exerted on the front of the car.  The graph shown in Figure 1 shows the variation of force with time for the during of the collision. 

Figure 1

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Use the graph to show that the impulse of the collision is 625 N s.

5d2 marks

All cars are designed to with a crumple zone to protect passengers if they are involved in a collision. 

State how a crumple zone: 

            (i)         affects the impact time of a collision 

            (ii)        affects the force exerted on the car during a collision.

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1a3 marks

Figure 1 shows a jet engine.

Figure 1

4-5-s-q--q1a-hard-aqa-a-level-physics

Air enters the engine at A and is heated before leaving B at a much higher speed. 

By referring to the momentum of the air as it passes through the engine, explain using appropriate laws of motion, why the air exerts a force on the engine in the forward direction.

1b2 marks

In one second, a mass of 350 kg of air enters at A. The speed of this mass of air increases by 590 m s−1 as it passes through the engine.

Calculate the force that the air exerts on the engine.

1c4 marks

Hot air flows out of the exhaust of the engine at B through a cross–sectional area of 6.2 × 106 mm2. 

The density of the hot air is 456.5 g m–3. 

Calculate the volume of air leaving the engine every second.

1d4 marks

When an aircraft lands, its jet engines exert a decelerating force on the aircraft by making use of deflector plates. 

These cause the air leaving the engines to be deflected at an angle to the direction the aircraft is travelling as shown in Figure 2. 

Figure 2

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The speed of the air leaving B is the same as the speed of the deflected air. 

Explain why the momentum of the air changes, and suggest why in practice the decelerating force provided by the deflector plates may not remain constant.

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2a6 marks

A tennis ball is raised from the ground and dropped onto a hard plate to test the properties of the ball. A sensor measures the force exerted by the plate on the ball during its collision with the plate. 

The graph in Figure 1 shows the variation of force exerted on the tennis ball with time. 

Figure 1

4-5-s-q--q2a-hard-aqa-a-level-physics

Explain how the ball’s momentum varies, and using the axes below, sketch a graph to show how the momentum of the ball varies in the first 30 ms. 

You may be awarded marks for the quality of written communication in your answer.

4-5-s-q--q2a-fig1-hard-aqa-a-level-physics

2b3 marks

The ball strikes the plate with a speed of 14.2 m s−1 and has a mass of 90 g. It leaves the plate with a speed of 7.8 m s−1. 

Show that this is consistent with the impulse from Figure 1.

2c3 marks

The ball continues to bounce, each time losing the same fraction of its energy when it strikes the plate. Air resistance is negligible.

Determine the percentage of the original gravitational potential energy of the ball that remains when it reaches its maximum height after bouncing four times.

2d3 marks

Explain, with reference to the conservation of momentum, the effect that the motion of the tennis ball has on the motion of the Earth from the instant it is released until it bounces at the plate.

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3a3 marks

A stationary uranium nucleus decays by emitting an ɑ particle and thorium nucleus as shown in Figure 1. 

Figure 1

4-5-s-q--q3a-hard-aqa-a-level-physics

Discuss how the principle of conservation of momentum applies in this instance.

3b4 marks

Assume that all of the energy released in the emission process is transferred as kinetic energy to the α particle and the recoiling nucleus and is equal to 6.46 MeV. 

Calculate the kinetic energy of the Thorium nucleus and alpha particle in MeV.

3c3 marks

Show that momentum has been conserved in this decay.

3d4 marks

Collisions can occur between neutrons and stationary Uranium nuclei, for example, during nuclear fission. 

Discuss how this collision would be if this was inelastic as opposed to elastic.

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4a5 marks

A popular demonstration of the conservation of momentum and conservation of energy is the  Newton’s cradle. 

It features several identical polished steel balls hung in a straight line in contact with each other. 

If one ball is pulled back and allowed to strike the line, one ball is released from the other end whilst the rest are stationary. If two are pulled out, two are released on the other end and so forth as shown in Figure 1. 

Figure 1

4-5-s-q--q5a-hard-aqa-a-level-physics

Explain, with energy and momentum considerations, why swinging one ball from the left will not release two balls on the right. 

Assume the Newton’s cradle is in a vacuum.

4b5 marks

The speed of an air rifle pellet is measured by firing it into a wooden block suspended from a rigid support. 

The wooden block can swing freely at the end of a light inextensible string of length 2 m measured from the pivot to the centre of the block, as shown in Figure 2 below. 

Figure 2

4-5-s-q--q5b-hard-aqa-a-level-physics

A pellet of mass 2.81 g strikes a stationary wooden block and is completely embedded in it. The centre of mass of the block rises by h at an angle of 35º to the vertical. The wooden block has a mass of 520 g. 

Determine the speed of the pellet when it strikes the wooden block.

4c5 marks

The wooden block is replaced by a steel block of the same mass. The experiment is repeated with the steel block and an identical pellet. The pellet rebounds after striking the block. 

A student makes an assumption that the angle that the steel block makes with the vertical will be greater than 35º because the block doesn’t have the additional mass of the pellet embedded within it. 

Discuss the validity of the student’s assumption.

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1a1 mark

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

Figure 1

4-5-s-q--q1a-medium-aqa-a-level-physics

The trucks are involved in an inelastic 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. 

   State what is meant by an ‘inelastic collision’.

1b3 marks

Show that the speed of the joined trucks immediately after the collision is about 0.9 m s–1.

1c2 marks

Calculate the impulse that acts on each truck during the collision. 

Give an appropriate unit for your answer.

1d2 marks

Explain, without doing a calculation, how the motion of the trucks immediately after the collision would be different for a collision that is perfectly elastic.

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2a4 marks

Figure 1 below shows a neutron about to collide inelastically with a stationary plutonium–238 nucleus. During the collision, the neutron will be absorbed by the plutonium nucleus to initiate the fission process. 

Figure 1

4-5-s-q--q2a-medium-aqa-a-level-physics

Calculate the kinetic energy of the plutonium nucleus immediately after the neutron has been absorbed.

2b4 marks

The neutron and plutonium atom now collides elastically with the plutonium nucleus still initially at rest. 

As the neutron rebounds to the left and the plutonium nucleus continues to the right with a velocity of 1.5 × 106 m s–1.

If the neutron still has the same initial speed, calculate the speed at which the neutron rebounds to the left.

2c2 marks

A different plutonium–238 decays into a uranium nucleus and an  particle after around 87 years, shown in Figure 2. 

Figure 2

4-5-s-q--q2c-medium-aqa-a-level-physics

Calculate the mass of the uranium nucleus and ∝ particle in kg.

2d3 marks

The alpha particle has a speed of 1.6 × 107 m s–1 immediately after it has been emitted. 

Hence, or otherwise, calculate the speed of recoil of the uranium nucleus immediately after the alpha particle has been emitted. Assume the plutonium nucleus is initially at rest.

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3a2 marks

Figure 1 shows a sketch drawn by an accident investigator following a head–on collision between two vehicles. 

Figure 1

4-5-s-q--q3a-medium-aqa-a-level-physics

From the skid marks and debris on the road the investigator knows that the collision took place at the point marked X. The vehicles locked together on impact and vehicle A was pushed backwards a distance of 12.1 m. 

For the road conditions and vehicle masses the average frictional force between the road and the vehicles immediately after the collision was known to be 8200 N 

   State the principle of conservation of momentum.

3b4 marks

Vehicle A was known to be moving at 15.5 m s–1 just before the impact. 

Calculate the speed of vehicle just before impact.

3c4 marks

The drivers of both vehicles have the same mass. 

State and explain which driver is likely to experience the higher force during the impact.

3d4 marks

Most cars manufactured in recent years have been fitted with air bags as a safety feature. In a collision the bag inflates automatically to protect the driver as air is released from a compressed air cylinder. 

Explain why the driver would be less seriously injured in a collision if the air bag inflates than he would be if unrestrained.

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4a4 marks

Figure 1 shows how the momentum of two colliding railway trucks varies with time. Truck has a mass of 5.2 × 103 kg and truck has a mass of 6.7 × 103 kg. The trucks are travelling in the same direction. 

Figure 1

4-5-s-q--q4a-medium-aqa-a-level-physics

Show that momentum is conserved in this collision.

4b3 marks

Calculate the acceleration of truck B during the collision.

4c2 marks

Complete Table 1 to show the initial and final velocities and kinetic energies of the trucks. 

Table 1

 

Initial
velocity / m s–1

Final
velocity / m s–1

Initial kinetic
energy / J

Final kinetic
energy / J

truck A

 

 

 

 

truck B

 

 

 

 

4d2 marks

Using Table 1, explain whether the collision of the two trucks is an example of an elastic or inelastic collision.

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5a5 marks

Most cars manufactured in recent years have been fitted with crumple zones as a safety feature. 

Explain how crumple zones protect a driver from serious injury in a collision.

5b4 marks

Two cars are crash tested. Car A doesn’t 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 crashing at 30 m s–1. Cars A takes 0.3 seconds and 0.7 seconds to stop respectively. 

Using this information, deduce whether air bags are a necessary safety feature.

5c2 marks

Cars are also fitted with both seat belts and air bags as additional safety features. 

Explain why it would be safer for a car to be fitted with just air bags than fitted only with seat belts.

5d4 marks

Both cars A and B are now collided head on. Car A initially travels to the right with a velocity of 45 m s–1. After the crash, both car A and car B travel to the left with a velocity 41 m s–1. 

Calculate the velocity of car B before the collision.

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