M1 June 2005 Q2
2. Two small steel balls \(A\) and \(B\) have mass 0.6 kg and 0.2 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 8 m s\(^{-1}\) and the speed of \(B\) is 2 m s\(^{-1}\). Immediately after the collision, the direction of motion of \(A\) is unchanged and the speed of \(B\) is twice the speed of \(A\). Find
(a) the speed of \(A\) immediately after the collision, (5)
(b) the magnitude of the impulse exerted on \(B\) in the collision. (3)
| Scheme | Marks |
|---|---|
| CLM: \(0.6 \times 8 - 0.2 \times 2 = 0.6 \times v + 0.2 \times w\) | M1 A1 |
| Using \(w = 2v\) to form equn in \(v/w\) only | M1 |
| Solve to get \(v = 4.4\) m s\(^{-1}\) | M1 A1 |
| (5) |
| Scheme | Marks |
|---|---|
| Impulse on \(B = 0.2(2 + 8.8)\) | M1 A1ft |
| \(= 2.16\) Ns | A1 |
| (3) | |
| (8 marks) |