M1 June 2008 Q1
1. Two particles \(P\) and \(Q\) have mass 0.4 kg and 0.6 kg respectively. The particles are initially at rest on a smooth horizontal table. Particle \(P\) is given an impulse of magnitude 3 N s in the direction \(PQ\).
(a) Find the speed of \(P\) immediately before it collides with \(Q\). (3)
Immediately after the collision between \(P\) and \(Q\), the speed of \(Q\) is 5 m s\(^{-1}\).
(b) Show that immediately after the collision \(P\) is at rest. (3)
| Scheme | Marks |
|---|---|
| \(I = mv\ \ \Rightarrow\ \ 3 = 0.4 \times v\) | M1 A1 |
| \(v = 7.5\ \left(\text{ms}^{-1}\right)\) | A1 |
| (3) |
| Scheme | Marks |
|---|---|
| LM \(0.4 \times 7.5 = 0.4v + 0.6 \times 5\) | M1 A1 |
| \(0 = 0.4v\ \ \Rightarrow\ \ v = 0\) \(\ast\) cso | A1 |
| (3) | |
| (6 marks) |