6. A smooth sphere \(P\) of mass \(m\) is moving in a straight line with speed \(u\) on a smooth horizontal table. Another smooth sphere \(Q\) of mass \(2 m\) is at rest on the table. The sphere \(P\) collides directly with \(Q\). After the collision the direction of motion of \(P\) is unchanged. The spheres have the same radii and the coefficient of restitution between \(P\) and \(Q\) is \(e\). By modelling the spheres as particles,

1. show that the speed of \(Q\) immediately after the collision is \(\frac { 1 } { 3 } ( 1 + e ) u\),
2. find the range of possible values of \(e\). Given that \(e = \frac { 1 } { 4 }\),
3. find the loss of kinetic energy in the collision.
4. Give one possible form of energy into which the lost kinetic energy has been transformed.