Edexcel M2 2014 January — Question 7 11 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2014
SessionJanuary
Marks11
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMomentum and Collisions 1
TypeRange of coefficient of restitution
DifficultyStandard +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.
Spec6.03b 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 \(e\).
  1. Find
    1. the speed of \(A\) immediately after the collision,
    2. the speed of \(B\) immediately after the collision. [7]
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 \(C\),
  1. find the set of possible values of \(e\). [4]

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]}}