4 Two model railway trucks, A of mass 0.1 kg and B of mass 0.2 kg , are constrained to move on a smooth straight level track.
Initially B is stationary and A is moving towards B with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) before they collide. The coefficient of restitution between A and B is \(e\).
- Find the speed of A and the speed of B after the collision, giving your answers in terms of \(e\) and \(u\).
- Show that the loss of kinetic energy in the collision is \(\frac { 1 } { 30 } u ^ { 2 } \left( 1 - e ^ { 2 } \right)\).
- For the case in which the loss of kinetic energy is least
- state the value of \(e\)
- state the loss in kinetic energy
- describe the subsequent motion of the trucks.
- For the case in which the loss of kinetic energy is greatest
- state the value of \(e\)
- state the loss in kinetic energy
- describe the subsequent motion of the trucks.