M1 January 2006 Q2
2.
(a) Two particles \(A\) and \(B\), of mass 3 kg and 2 kg respectively, are moving in the same direction on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of \(A\) is 4 m s\(^{-1}\) and the speed of \(B\) is 1.5 m s\(^{-1}\). In the collision, the particles join to form a single particle \(C\).
Find the speed of \(C\) immediately after the collision. (3)
Find the speed of \(C\) immediately after the collision. (3)
(b) Two particles \(P\) and \(Q\) have mass 3 kg and \(m\) kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table. Each particle has speed 4 m s\(^{-1}\), when they collide directly. In this collision, the direction of motion of each particle is reversed. The speed of \(P\) immediately after the collision is 2 m s\(^{-1}\) and the speed of \(Q\) is 1 m s\(^{-1}\). Find
(i) the value of \(m\), (3)
(ii) the magnitude of the impulse exerted on \(Q\) in the collision. (2)
| Scheme | Marks |
|---|---|
| CLM: \(3 \times 4 + 2 \times 1.5 = 5 \times v\) | M1 A1 |
| \(\Rightarrow v = 3\) m s\(^{-1}\) | A1 |
| (3) |
| Scheme | Marks |
|---|---|
| (i) CLM: \(3 \times 4 - m \times 4 = -3 \times 2 + m\,(\times 1)\) | M1 A1 |
| \(\Rightarrow m = 3.6\) | A1 |
| (3) | |
| (ii) \(I = 3.6(4 + 1)\) [or \(3(4 + 2)\)] | M1 |
| \(= 18\) Ns | A1ft |
| (2) | |
| (8 marks) |