| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Oblique and successive collisions |
| Type | Successive collisions, three particles in line |
| Difficulty | Standard +0.3 This is a standard M2 collision problem involving conservation of momentum and Newton's law of restitution applied twice in succession. Part (a) is a routine 'show that' requiring two equations and simple algebra. Parts (b) and (c) follow the same method with given numerical coefficient. While multi-step, it requires only direct application of standard formulae with no novel insight or geometric reasoning. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
7. Three particles $P , Q$ and $R$ lie at rest in a straight line on a smooth horizontal table with $Q$ between $P$ and $R$. The particles $P , Q$ and $R$ have masses $2 m , 3 m$ and $4 m$ respectively. Particle $P$ is projected towards $Q$ with speed $u$ and collides directly with it. The coefficient of restitution between each pair of particles is $e$.
\begin{enumerate}[label=(\alph*)]
\item Show that the speed of $Q$ immediately after the collision with $P$ is $\frac { 2 } { 5 } ( 1 + e ) u$.
After the collision between $P$ and $Q$ there is a direct collision between $Q$ and $R$.\\
Given that $e = \frac { 3 } { 4 }$, find
\item \begin{enumerate}[label=(\roman*)]
\item the speed of $Q$ after this collision,
\item the speed of $R$ after this collision.
Immediately after the collision between $Q$ and $R$, the rate of increase of the distance between $P$ and $R$ is $V$.
\end{enumerate}\item Find $V$ in terms of $u$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2013 Q7 [15]}}