M1 June 2013 Q1
1. Particle \(P\) has mass 3 kg and particle \(Q\) has mass \(m\) kg. The particles are moving in opposite directions along a smooth horizontal plane when they collide directly. Immediately before the collision, the speed of \(P\) is 4 m s\(^{-1}\) and the speed of \(Q\) is 3 m s\(^{-1}\). In the collision the direction of motion of \(P\) is unchanged and the direction of motion of \(Q\) is reversed. Immediately after the collision, the speed of \(P\) is 1 m s\(^{-1}\) and the speed of \(Q\) is 1.5 m s\(^{-1}\).
| Scheme | Marks |
|---|---|
| For \(P\), \(-I = 3(1 - 4)\) | M1 A1 |
| \(I = 9\) Ns | A1 |
| (3) |
Notes
M1 for attempt at Impulse = difference in momenta for particle \(P\), (must be considering one particle i.e. have same mass in both terms) (M0 if g is included or if mass omitted).
First A1 for \(\pm 3(1 - 4)\)
Second A1 for 9 (Must be positive). Allow change of sign at end to obtain magnitude.
N.B. For M1 they may use CLM to find a value for \(m\) first and then use it when considering the change in momentum of \(Q\) to find the impulse.
| Scheme | Marks |
|---|---|
| For \(Q\), \(9 = m(1.5 - {-3})\) | M1 A1 |
| \(m = 2\) | A1 |
| (3) | |
| (6 marks) |
OR
| \(12 - 3m = 3 + 1.5m\) | M1 A1 |
| \(m = 2\) | A1 |
| (3) |
Notes
EITHER
M1 for attempt at:
their Impulse from (a) = difference in momenta for particle \(Q\), (must be considering one particle) (M0 if g is included or if mass omitted).
First A1 for \(9 = m(1.5 - {-3})\) oe.
Second A1 for \(m = 2\).
OR
M1 for attempt at CLM equation, with correct no. of terms, dimensionally correct. Allow consistent extra g’s and sign errors.
First A1 for a correct equation i.e. \(12 - 3m = 3 + 1.5m\) oe.
Second A1 for \(m = 2\).