Linear Momentum & Conservation (AQA A Level Physics)

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

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’.

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

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

Figure 1

Show that momentum is conserved in this collision.

Calculate the acceleration of truck B during the collision.

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

Table 1

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

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.

Both cars A and B are now collided head on, without the drivers. 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.

Figure 1 shows a jet engine.

Figure 1

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.

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.

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

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.

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

Figure 1

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

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.

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

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.

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 2.0 m measured from the pivot to the centre of the block, as shown in Figure 2 below. 

Figure 2

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.

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.