M1 June 2012 Q1
1. Two particles \(A\) and \(B\), of mass \(5m\) kg and \(2m\) kg respectively, are moving in opposite directions along the same straight horizontal line. The particles collide directly. Immediately before the collision, the speeds of \(A\) and \(B\) are 3 m s\(^{-1}\) and 4 m s\(^{-1}\) respectively. The direction of motion of \(A\) is unchanged by the collision. Immediately after the collision, the speed of \(A\) is 0.8 m s\(^{-1}\).
In the collision, the magnitude of the impulse exerted on \(A\) by \(B\) is 3.3 N s.
| Scheme | Marks |
|---|---|
| CLM \(5m \times 3 - 2m \times 4 = 5m \times 0.8 + 2mv\) | M1 A1 |
| Leading to \(v = 1.5\) (Speed is 1.5 m s\(^{-1}\)) | A1 |
| (3) |
Notes
M1 for attempt at CLM equation, with correct no.of terms, correct masses and dimensionally consistent. Allow consistent extra g’s, consistent missing \(m\)’s and sign errors. However, M0 if masses are not paired with the correct speeds.
First A1 for a correct equation.
Second A1 for \(v = 1.5\). (\(-1.5\) A0)
N.B. Allow M1 for an attempt to equate the impulses on the particles but must have \(5m(0.8 - 3)\) or \(5m(3 - 0.8)\) on one side of the equation and \(2m(\pm v \pm 4)\) on the other.
| Scheme | Marks |
|---|---|
| Impulse for \(A\) \(5m(0.8 - 3) = -3.3\) | M1 A1 |
| Leading to \(m = 0.3\) | A1 |
| (3) | |
| (6 marks) |
Notes
M1 for attempt at impulse = difference in momenta, for either particle, (must be considering one particle) (M0 if g’s are included or if mass omitted or if just \(m\) used)
Allow Initial Momentum – Final Momentum.
A1 cao (i.e. no ft on their \(v\)) for a correct equation in \(m\) only.
A1 for \(m = 0.3\)
Alternative for (b)
| Impulse for \(B\) \(2m(1.5 - {-4}) = 3.3\) | M1 A1 |
| Leading to \(m = 0.3\) | A1 |
| (3) |