Momentum & Impulse (Edexcel A Level Further Maths: Further Mechanics 1): Exam Questions

A small ball of mass 0.3 kg is released from rest from a point 3.6 m above horizontal ground.
The ball falls freely under gravity, hits the ground and rebounds vertically upwards.

In the first impact with the ground, the ball receives an impulse of magnitude 4.2 Ns. The ball is modelled as a particle.

Find the speed of the ball immediately after it first hits the ground.

Find the kinetic energy lost by the ball as a result of the impact with the ground.

A particle P, of mass 0.5 kg, is moving with velocity when it receives an impulse  of magnitude 2.5 Ns.

As a result of the impulse, the direction of motion of P is deflected through an angle of 45°.

Given that  Ns, find all the possible pairs of values of and . 

A particle of mass 0.5 kg is moving with velocity  when it receives an impulse  Ns. Immediately after receiving the impulse, is moving with velocity . 

Find the magnitude of .

The angle between the direction of the impulse and the direction of motion of immediately before receiving the impulse is .

Find the value of .

A particle  has mass 0.5 kg. It is moving in the  plane with velocity  when it receives an impulse , where  is a positive constant.

The angle between the direction of motion of immediately before receiving the impulse and the direction of motion of immediately after receiving the impulse is 

Immediately after receiving the impulse, is moving with speed .

Find

i) the value of  

ii) the value of

A particle of mass and a particle of mass are moving along the same straight line on a smooth horizontal surface. The particles are moving in opposite directions towards each other when they collide directly.

Immediately before the collision, the speed of is and the speed of is .
Immediately after the collision, the speed of is and the speed of is .

The magnitude of the impulse received by in the collision is .

Find in terms of only.

Find the two possible values of .

A particle of mass 0.5 kg is moving in a straight line with speed 2.8 m s⁻¹ when it receives an impulse of magnitude 3 Ns.
The angle between the direction of motion of immediately before receiving the impulse and the line of action of the impulse is , where , as shown in Figure 2.

Find the speed of immediately after receiving the impulse.

A particle of mass 2 kg is moving with velocity when it receives an impulse .

Find the speed of immediately after receiving the impulse.

The angle through which the direction of motion of has been deflected by the impulse is .

Find the value of

[In this question, and are horizontal perpendicular unit vectors.]

A particle has mass 3 kg and a particle has mass 2 kg.

The particles are moving on a smooth horizontal plane when they collide directly.

Immediately before the collision, the velocity of is and the velocity of is

Immediately after the collision the velocity of A is:

Find the total kinetic energy of the two particles before the collision.

Find, in terms of and , the impulse exerted on by in the collision.

Find, in terms of and , the velocity of immediately after the collision.