| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2022 |
| 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 conservation of momentum, coefficient of restitution, and impulse-momentum theorem. While it involves multiple parts and algebraic manipulation with parameters, it follows a well-established template with no novel insight required—slightly easier than average due to its routine nature. |
| 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 |
6. Two particles, $P$ and $Q$, are moving in opposite directions along the same straight line on a smooth horizontal surface so that the particles collide directly.\\
The mass of $P$ is $k m$ and the mass of $Q$ is $m$.\\
Immediately before the collision, the speed of $P$ is $x$ and the speed of $Q$ is $y$. Immediately after the collision, $P$ and $Q$ are moving in the same direction, the speed of $P$ is $v$ and the speed of $Q$ is $2 v$.
The coefficient of restitution between $P$ and $Q$ is $\frac { 1 } { 5 }$\\
The magnitude of the impulse received by $Q$ in the collision is $5 m v$
\begin{enumerate}[label=(\alph*)]
\item Find (i) $y$ in terms of $v$\\
(ii) $x$ in terms of $v$\\
(iii) the value of $k$
\item Find, in terms of $m$ and $v$, the total kinetic energy lost in the collision between $P$ and $Q$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2022 Q6 [12]}}