| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2023 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Direct collision with given impulse |
| Difficulty | Standard +0.3 This is a standard M2 collision problem requiring systematic application of impulse-momentum theorem, conservation of momentum, and coefficient of restitution formula. All steps follow routine procedures with clear signposting, making it slightly easier than average despite being multi-part. |
| Spec | 6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
\begin{enumerate}
\item A particle $P$ of mass $3 m$ and a particle $Q$ of mass $5 m$ are moving towards each other along the same straight line on a smooth horizontal surface. The particles collide directly.
\end{enumerate}
Immediately before the collision, the speed of $P$ is $u$ and the speed of $Q$ is $k u$.\\
Immediately after the collision, the speed of $P$ is $2 v$ and the speed of $Q$ is $v$.\\
The direction of motion of each particle is reversed by the collision.\\
In the collision, $P$ receives an impulse of magnitude $15 m v$.\\
(a) Show that $u = 3 v$.\\
(b) Find the value of $k$.
The coefficient of restitution between $P$ and $Q$ is $e$.\\
(c) Find the value of $e$.
The total kinetic energy lost in the collision is $\lambda m v ^ { 2 }$\\
(d) Find the value of $\lambda$.
\hfill \mbox{\textit{Edexcel M2 2023 Q4 [12]}}