AS June 2024 Q1
1. A particle \(A\) has mass \(2m\) and a particle \(B\) has mass \(3m\). The particles are moving in opposite directions along the same straight line and collide directly.
Immediately before the collision, the speed of \(A\) is \(2u\) and the speed of \(B\) is \(u\).
Immediately after the collision, the speed of \(A\) is \(0.5u\) and the speed of \(B\) is \(w\).
Given that the direction of motion of each particle is reversed by the collision,
| Scheme | Marks | AO |
|---|---|---|
| Use of CLM: | M1 | 3.1a |
| \(2m \times 2u - 3mu = -2m \times 0.5u + 3mw\) OR: \((I =)\ \ 2m(0.5u - -2u) = 3m(w - -u)\) | A1 | 1.1b |
| \(w = \dfrac{2u}{3}\) accept \(0.67u\) or better | A1 | 1.1b |
| (3) |
Notes
M1: Use of CLM, with correct no. of terms, condone consistent extra \(g\)’s, sign errors, cancelled \(m\)’s, to produce an equation in (\(m\)), \(u\) and \(w\) only.
OR:
Use of two imp-mom equations, with \(I\) then eliminated, to produce an equation in (\(m\)), \(u\) and \(w\) only, condone consistent extra \(g\)’s, sign errors, cancelled \(m\)’s.
N.B. Allow the use of another letter for \(w\) in the working.
A1: Correct equation in (\(m\)), \(u\) and their \(w\) only.
A1: Cao. Must see \(w = ku\)
| Scheme | Marks | AO |
|---|---|---|
| Use of NEL | M1 | 3.4 |
| \(e = \dfrac{0.5u + \dfrac{2u}{3}}{2u + u}\) | A1ft | 1.1b |
| \(\dfrac{7}{18}\) accept 0.39 or better | A1 | 1.1b |
| (3) |
Notes
M1: Use of NEL, must be the right way up with the ‘correct’ terms but condone sign errors.
Allow without the \(u\)’s
A1ft: Correct unsimplified expression, ft on their \(w\)
A1: cao
| Scheme | Marks | AO |
|---|---|---|
| Use of impulse-momentum principle for \(A\) or \(B\) | M1 | 3.1a |
| \(\pm 2m(0.5u - -2u)\) OR \(\pm 3m\left(\dfrac{2u}{3} - -u\right)\) | A1 | 1.1b |
| \(5mu\) | A1 | 1.1b |
| (3) | ||
| (9 marks) |
Notes
M1: Correct structure but condone sign errors (M0 if \(g\) included or \(m\)’s missing)
Can score this mark if they use \(m\) for the mass with a ‘correct’ pair of velocities.
A1: Correct equation
A1: cao