AS October 2020 Q1
1. Two particles \(P\) and \(Q\) have masses \(m\) and \(4m\) respectively. The particles are at rest on a smooth horizontal plane. Particle \(P\) is given a horizontal impulse, of magnitude \(I\), in the direction \(PQ\). Particle \(P\) then collides directly with \(Q\). Immediately after this collision, \(P\) is at rest and \(Q\) has speed \(w\). The coefficient of restitution between the particles is \(e\).
| Scheme | Marks | AO |
|---|---|---|
 | ||
| Use of CLM: \(m \times \dfrac{I}{m} = 4mw\) | M1 | 3.1a |
| \(I = 4mw\) | A1 | 1.1b |
| (2) |
Notes
M1: Correct no. of terms, condone extra \(g\) s, sign errors (must be equation in \(I\), \(m\) and \(w\) only)
A1: Correct equation
Answer not given, so a correct answer with no clear error seen will score M1A1
An answer that relies on an impulse-momentum equation using \(4m\) will score M0
| Scheme | Marks | AO |
|---|---|---|
| \(e = \dfrac{w}{4w} = \dfrac{1}{4}\) * | B1* | 3.4 |
| (1) |
Notes
B1*: Use of NLR to obtain given answer
| Scheme | Marks | AO |
|---|---|---|
| KE Loss \(= \dfrac{1}{2}m(4w)^2 - \dfrac{1}{2}4mw^2\) | M1 | 3.4 |
| \(= 6mw^2\) | A1 | 1.1b |
| (2) | ||
| (5 marks) |
Notes
M1: Allow negative loss
A1: cao