- A particle \(A\) of mass \(2 m\) is moving in a straight line with speed \(3 u\) 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 \(2 u ( 1 + e )\).
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 \(\frac { 1 } { 2 }\)
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.