M1 January 2008 Q1
1. Two particles \(A\) and \(B\) have masses 4 kg and \(m\) kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of \(A\) is 5 m s\(^{-1}\) and the speed of \(B\) is 3 m s\(^{-1}\). Immediately after the collision, the direction of motion of \(A\) is unchanged and the speed of \(A\) is 1 m s\(^{-1}\).
(a) Find the magnitude of the impulse exerted on \(A\) in the collision. (2)
Immediately after the collision, the speed of \(B\) is 2 m s\(^{-1}\).
(b) Find the value of \(m\). (4)
| Scheme | Marks |
|---|---|
| \(I = 4(5 - 1) = 16\) Ns | M1 A1 |
| (2) |
| Scheme | Marks |
|---|---|
| CLM: \(4 \times 5 - m \times 3 = 4 \times 1 + m \times 2\) | M1 A1 |
| \(\Rightarrow\ \ m = 3.2\) | DM1 A1 |
| (4) | |
| (6 marks) |
or
| \(16 = m(3 + 2)\) | M1 A1 |
| \(\Rightarrow\ \ m = 3.2\) | DM1 A1 |