A particle \(P\) of mass \(2 m\) is moving with speed \(2 u\) in a straight line on a smooth horizontal plane. A particle \(Q\) of mass \(3 m\) is moving with speed \(u\) in the same direction as \(P\). The particles collide directly. The coefficient of restitution between \(P\) and \(Q\) is \(\frac { 1 } { 2 }\).
Show that the speed of \(Q\) immediately after the collision is \(\frac { 8 } { 5 } u\).
Find the total kinetic energy lost in the collision.
After the collision between \(P\) and \(Q\), the particle \(Q\) collides directly with a particle \(R\) of mass \(m\) which is at rest on the plane. The coefficient of restitution between \(Q\) and \(R\) is \(e\).
Calculate the range of values of \(e\) for which there will be a second collision between \(P\) and \(Q\).