M1 June 2013 (R) Q1
1. Two particles \(A\) and \(B\), of mass 2 kg and 3 kg respectively, are moving towards each other in opposite directions along the same straight line on a smooth horizontal surface. The particles collide directly. Immediately before the collision the speed of \(A\) is 5 m s\(^{-1}\) and the speed of \(B\) is 6 m s\(^{-1}\). The magnitude of the impulse exerted on \(B\) by \(A\) is 14 N s. Find
| Scheme | Marks |
|---|---|
| \(2v + 10 = 14\) | M1A1 |
| \(v = 2\) m s\(^{-1}\) | A1 |
| (3) |
Notes
M1 for attempt at Impulse = difference in momenta for particle \(A\), (must be considering one particle) (M0 if g is included or if mass omitted).
First A1 for \(-14 = 2(\pm v - 5)\)
Second A1 for 2 (Must be positive). Allow change of sign at end to obtain speed.
| Scheme | Marks |
|---|---|
| \(3w + 18 = 14\) | M1A1 |
| \(w = \dfrac{4}{3}\) m s\(^{-1}\) | A1 |
| (3) | |
| (6 marks) |
Notes
EITHER
M1 for attempt at Impulse = difference in momenta for particle \(B\), (must be considering one particle) (M0 if g is included or if mass omitted).
First A1 \(14 = 3(\pm w - {-6})\)
Second A1 for 4/3, 1.3 or better (Must be positive). Allow change of sign at end to obtain speed.
OR
M1 for attempt at CLM equation, with correct no. of terms, dimensionally correct. Allow consistent extra g’s and sign errors.
First A1 (Not f.t.) for a correct equation e.g.
\(2 \times 5 - 3 \times 6 = -2 \times 2 + 3w\)
Second A1 for speed is 4/3; 1.3 or better
N.B. They may find the speed of \(B\) first and then use CLM to find the speed of \(A\).
It must be clear which speed is which, in order to gain the A marks for the answers