Momentum & collisions

Determine the value of e.

After this collision, Q goes on to collide directly with the wall. The coefficient of restitution between Q and the wall is .

Determine whether there will be a subsequent collision between P and Q.

Two identical spheres, A and B, each of mass m kg, are moving directly towards each other along the same straight line on a smooth horizontal surface until they collide. Just before they collide, the speeds of A and B are 20 ms^-1 and 10 ms^-1 respectively. The coefficient of restitution between A and B is e.

By finding, in terms of e, an expression for the velocity of B after the collision, show that the

direction of motion of B is reversed by the collision.

After the collision between A and B, which is not perfectly elastic, B goes on to collide directly with a fixed, vertical wall. The coefficient of restitution between B and the wall is . After the collision between B and the wall, there are no further collisions between A and B.

Determine the range of possible values of e.

Two smooth circular discs A and B are moving on a smooth horizontal plane when they collide. The mass of A is 5 kg and the mass of B is 3 kg.

At the instant before they collide,

• the velocity of A is 4 ms^-1 at an angle of 60° to the line of centres,

• the velocity of B is 6 ms^-1 along the line of centres

(see diagram).

The coefficient of restitution for collisions between the two discs is

Determine the angle that the velocity of A makes with the line of centres after the collision.

Two smooth circular discs, A and B, have equal radii and are free to move on a smooth horizontal plane. The masses of A and B are 1 kg and m kg respectively. B is initially placed at rest with its centre at the origin, O. A is projected towards B with a velocity of u m s^-1 at an angle of θ to the negative y‑axis where tan θ = . At the instant of collision the line joining their centres lies on the x ‑axis.

There are two straight vertical walls on the plane. One is perpendicular to the x ‑axis and the other is perpendicular to the y ‑axis. The walls are an equal distance from O (see diagram).

After A and B have collided with each other, each of them goes on to collide with a wall. Each then rebounds and they collide again at the same place as their first collision, with disc B again at O.

The coefficient of restitution between A and B is denoted by e. The coefficient of restitution between A and the wall that it collides with is also e while the coefficient of restitution between B and the wall that it collides with is . It is assumed that any resistance to the motion of A and B may be ignored.

Explain why it must be the case that the collision between A and the wall that it collides with

is not inelastic.

State one limitation of the model used.

Two smooth circular discs A and B are moving on a horizontal plane. The masses of A and B are 3 kg and 4 kg respectively. At the instant before they collide

• the velocity of A is 2ms^-1 at an angle of 60° to the line joining their centres,

• the velocity of B is 5ms^-1 towards A along the line joining their centres (see Fig. 6).

Given that the velocity of A after the collision is perpendicular to the velocity of A before the collision, find

the coefficient of restitution between A and B,

the total loss of kinetic energy as a result of the collision.