- Particle \(P\) has mass \(3 m\) and particle \(Q\) has mass \(k m\). The particles are moving towards each other on the same straight line on a smooth horizontal surface.
The particles collide directly.
Immediately before the collision, the speed of \(P\) is \(2 u\) and the speed of \(Q\) is \(3 u\). Immediately after the collision, the speed of \(P\) is \(u\) and the speed of \(Q\) is \(v\).
The direction of motion of \(P\) is unchanged by the collision.
- Show that \(v = \frac { ( 3 - 3 k ) } { k } u\)
- Find, in terms of \(m\) and \(u\), the magnitude of the impulse received by \(Q\) in the collision.
The coefficient of restitution between \(P\) and \(Q\) is \(e\).
Given that \(v \neq u\) - find the range of possible values of \(k\).