| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2018 |
| Session | June |
| Marks | 5 |
| Topic | Momentum and Collisions 1 |
| Type | Direct collision with direction reversal |
| Difficulty | Moderate -0.8 This is a straightforward two-part momentum and restitution problem requiring direct application of conservation of momentum and the Newton's restitution formula. All velocities are given, making it a routine algebraic exercise with no conceptual challenges or problem-solving insight required—easier than the average A-level question. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03i Coefficient of restitution: e |
**Question 9(i)**
Attempt to use conservation of linear momentum **M1** Allow sign errors, all terms present.
$2m = -0.5m + 0.4 \times 0.5$ **A1**
Get $m = 0.08$ **A1**
**Question 9(ii)**
Attempt to use formula for $e$ **M1** $e =$ separation/approach; allow sign errors
Get $e = 0.45$ **A1**9 A particle $P$ of mass $m \mathrm {~kg}$ is moving with speed $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in a straight line on a smooth horizontal table. $P$ collides directly with a stationary particle $Q$ of mass 0.5 kg . This collision reverses the direction of motion of $P$. Immediately after the collision the speed of $P$ is $0.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and the speed of $Q$ is $0.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Find\\
(i) the value of $m$,\\
(ii) the coefficient of restitution between the two particles.
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2018 Q9 [5]}}