Impulse and momentum

A particle A has mass 4m and a particle B has mass 3m. The particles are moving along the same straight line on a smooth horizontal table. The particles are moving in opposite directions towards each other when they collide directly.

As a result of the collision, the direction of motion of each particle is reversed.

Immediately before the collision, the speed of A is u and the speed of B is ku, where k is a constant.

Immediately after the collision, the speed of A is 2v and the speed of B is 3v.

The magnitude of the impulse received by A in the collision is 20mv.

Find u in terms of v only.

Find the exact value of k.

A particle P of mass 0.4 k moving with velocity 7i ms¹ when it receives

Find the two possible values of λ

Three small balls, A, B and C, have masses 2m, 3m and 4m respectively.

The balls are initially at rest in a straight line on a smooth horizontal surface, with B between A and C, as shown in Figure 2.

Ball A is projected towards B with speed 5u and A and B collide directly. Immediately after the collision, the speed of B is 3 u

The balls are modelled as uniform spheres with equal radii.

Find, in terms of u, the speed of A immediately after the collision with B.

Find the coefficient of restitution between A and B.

After the collision between A and B, ball C is projected towards B with speed u Balls B and C collide directly. The coefficient of restitution between B and C is f

Given that there is a second direct collision between A and B

find the complete range of possible values of f

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

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

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

Immediately before the collision, the velocity of A is (3i – j) m s^–1 and the velocity of B is (–6i + 2j) m s^–1 Immediately after the collision the velocity of A is 2i m s

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

Find, in terms of i and j, the impulse exerted on A by B in the collision.

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

A particle A of mass 2m is moving in a straight line with speed 3u on a smooth horizontal plane. Particle A collides directly with a particle B of mass m which is at rest on the plane.

The coefficient of restitution between A and B is e, where e 0

Show that the speed of B immediately after the collision is 2u(1 + e).

After the collision, B hits a smooth fixed vertical wall which is perpendicular to the direction of motion of B.

Show that there will be a second collision between A and B.

The coefficient of restitution between B and the wall is

Find, in simplified form, in terms of m, u and e,

the magnitude of the impulse received by B in its collision with the wall,

the loss in kinetic energy of B due to its collision with the wall.

A particle P of mass 2 kg is moving with velocity (4i 3j) m s¹when it receives an impulse (6i 42j) N s.

Find the speed of P immediately after receiving the impulse.

The angle through which the direction of motion of P has been deflected by the impulse is α °

Find the value of α

Two particles, A and B, are moving in opposite directions along the same straight line on a smooth horizontal surface when they collide directly.

Particle A has mass 5m and particle B has mass 3m.

The coefficient of restitution between A and B is e, where e 0

Immediately after the collision the speed of A is v and the speed of B is 2v.

Given that A and B are moving in the same direction after the collision,

find the set of possible values of e.

Given also that the kinetic energy of A immediately after the collision is 16% of the kinetic energy of A immediately before the collision,

find

the value of e,

the magnitude of the impulse received by A in the collision, giving your answer in terms of m and v.

A particle P has mass 0.5 kg. It is moving in the xy plane with velocity 8im s⁻¹ when it receives an impulse λ (− i + j) N s, where λ is a positive constant.

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

Find (i) the value of λ

the value of θ

[In this question, i and j are perpendicular unit vectors in a horizontal plane.]

Figure 3 represents the plan view of part of a smooth horizontal floor, where AB is a fixed smooth vertical wall. The direction of AB is in the direction of the vector (i + j)

A small ball of mass 0.25 kg is moving on the floor when it strikes the wall AB. Immediately before its impact with the wall AB, the velocity of the ball is (8i + 2j)m s⁻¹

Immediately after its impact with the wall AB, the velocity of the ball is vm s⁻¹ The coefficient of restitution between the ball and the wall is

By modelling the ball as a particle,

show that v = 4i + 6j

Find the magnitude of the impulse received by the ball in the impact.

A particle P of mass 0.5 kg is moving with velocity (4i + 3j) m s^–1 when it receives an impulse J N s. Immediately after receiving the impulse, P is moving with velocity (–i + 6j) m s^–1.

Find the magnitude of J.

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

Find the value of α

[In this question, i and j are perpendicular unit vectors in a horizontal plane.]

Figure 1 represents the plan view of part of a smooth horizontal floor, where AB represents a fixed smooth vertical wall.

A small ball of mass 0.5 kg is moving on the floor when it strikes the wall.

Immediately before the impact the velocity of the ball is (7i + 2j) m s^–1.

Immediately after the impact the velocity of the ball is (i + 6j) m s^–1.

The coefficient of restitution between the ball and the wall is e.

Show that AB is parallel to (2i + 3j).

Find the value of e.