| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2010 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Direct collision with direction reversal |
| Difficulty | Moderate -0.3 This is a standard two-particle collision problem requiring application of conservation of momentum and Newton's restitution formula. While it involves algebraic manipulation with two equations and two unknowns, it follows a completely routine template that M2 students practice extensively. The setup is straightforward with no geometric complications or novel insights required. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03k Newton's experimental law: direct impact |
| Answer | Marks |
|---|---|
| \(\text{CLM: } 4mu - mu = 2mv_1 + mv_2\) | M1 A1 |
| \(\text{i.e. } 3u = 2v_1 + v_2\) | M1 A1 |
| \(\text{NIL: } 3eu = -v_1 + v_2\) | M1 A1 |
| \(v_1 = u(1-e)\) | DM1 A1 |
| \(v_2 = u(1 + 2e)\) | A1 |
$\text{CLM: } 4mu - mu = 2mv_1 + mv_2$ | M1 A1 |
$\text{i.e. } 3u = 2v_1 + v_2$ | M1 A1 |
$\text{NIL: } 3eu = -v_1 + v_2$ | M1 A1 |
$v_1 = u(1-e)$ | DM1 A1 |
$v_2 = u(1 + 2e)$ | A1 |
**Total: [7]**
---Two particles, $P$, of mass $2m$, and $Q$, of mass $m$, are moving along the same straight line on a smooth horizontal plane. They are moving in opposite directions towards each other and collide. Immediately before the collision the speed of $P$ is $2u$ and the speed of $Q$ is $u$. The coefficient of restitution between the particles is $e$, where $e < 1$. Find, in terms of $u$ and $e$,
\begin{enumerate}[label=(\roman*)]
\item the speed of $P$ immediately after the collision,
\item the speed of $Q$ immediately after the collision.
\end{enumerate}
[7]
\hfill \mbox{\textit{Edexcel M2 2010 Q2 [7]}}