Edexcel M2 2015 June — Question 5 13 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2015
SessionJune
Marks13
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMomentum and Collisions 1
TypeThree-particle sequential collisions
DifficultyStandard +0.3 This is a standard two-collision momentum problem requiring systematic application of conservation of momentum and Newton's restitution law. Part (a) involves routine calculations with given coefficient of restitution, while part (b) requires working backwards from kinetic energy to find an unknown coefficient. The multi-step nature and algebraic manipulation place it slightly above average, but the techniques are all standard M2 material with no novel insights required.
Spec6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation6.03k Newton's experimental law: direct impact

Three particles \(A\), \(B\) and \(C\) lie at rest in a straight line on a smooth horizontal table with \(B\) between \(A\) and \(C\). The masses of \(A\), \(B\) and \(C\) are \(3m\), \(4m\), and \(5m\) respectively. Particle \(A\) is projected with speed \(u\) towards particle \(B\) and collides directly with \(B\). The coefficient of restitution between \(A\) and \(B\) is \(\frac{1}{3}\).
  1. Show that the impulse exerted by \(A\) on \(B\) in this collision has magnitude \(\frac{16}{7}mu\) [7]
After the collision between \(A\) and \(B\) there is a direct collision between \(B\) and \(C\). After this collision between \(B\) and \(C\), the kinetic energy of \(C\) is \(\frac{72}{245}mu^2\)
  1. Find the coefficient of restitution between \(B\) and \(C\). [6]

Three particles $A$, $B$ and $C$ lie at rest in a straight line on a smooth horizontal table with $B$ between $A$ and $C$. The masses of $A$, $B$ and $C$ are $3m$, $4m$, and $5m$ respectively. Particle $A$ is projected with speed $u$ towards particle $B$ and collides directly with $B$. The coefficient of restitution between $A$ and $B$ is $\frac{1}{3}$.

\begin{enumerate}[label=(\alph*)]
\item Show that the impulse exerted by $A$ on $B$ in this collision has magnitude $\frac{16}{7}mu$ [7]
\end{enumerate}

After the collision between $A$ and $B$ there is a direct collision between $B$ and $C$.

After this collision between $B$ and $C$, the kinetic energy of $C$ is $\frac{72}{245}mu^2$

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the coefficient of restitution between $B$ and $C$. [6]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2015 Q5 [13]}}