| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2014 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Range of coefficient of restitution |
| Difficulty | Standard +0.3 This is a standard M2 collision problem requiring conservation of momentum and Newton's restitution law. Part (a) involves routine application of these principles to find post-collision velocities in terms of e. Part (b) requires setting up inequalities based on physical constraints, which is slightly more demanding but still a typical M2 exercise with clear methodology. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03k Newton's experimental law: direct impact |
Three particles $A$, $B$ and $C$, each of mass $m$, lie at rest in a straight line $L$ on a smooth horizontal surface, with $B$ between $A$ and $C$. Particles $A$ and $B$ are projected directly towards each other with speeds $5u$ and $4u$ respectively. Particle $C$ is projected directly away from $B$ with speed $3u$. In the subsequent motion, $A$, $B$ and $C$ move along $L$. Particles $A$ and $B$ collide directly. The coefficient of restitution between $A$ and $B$ is $e$.
\begin{enumerate}[label=(\alph*)]
\item Find \begin{enumerate}[label=(\roman*)]
\item the speed of $A$ immediately after the collision,
\item the speed of $B$ immediately after the collision. [7]
\end{enumerate}
\end{enumerate}
Given that the direction of motion of $A$ is reversed in the collision between $A$ and $B$, and that there is no collision between $B$ and $C$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the set of possible values of $e$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2014 Q7 [11]}}