Edexcel M2 2014 June — Question 6 14 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2014
SessionJune
Marks14
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMomentum and Collisions 1
TypeParticle brought to rest by collision
DifficultyStandard +0.3 This is a standard M2 momentum-collision question requiring systematic application of conservation of momentum and Newton's restitution law across two collisions. Part (a) is routine algebraic manipulation, part (b) requires interpreting a physical condition (reversed motion means v < 0), and part (c) involves straightforward kinetic energy calculation. While multi-part with several steps, it follows predictable M2 patterns without requiring novel insight or particularly complex algebra.
Spec6.03b Conservation of momentum: 1D two particles6.03c Momentum in 2D: vector form6.03d Conservation in 2D: vector momentum6.03i Coefficient of restitution: e6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts

6. Three particles \(P , Q\) and \(R\) have masses \(3 m , k m\) and 7.5m respectively. The three particles lie at rest in a straight line on a smooth horizontal table with \(Q\) between \(P\) and \(R\). Particle \(P\) is projected towards \(Q\) with speed \(u\) and collides directly with \(Q\). The coefficient of restitution between \(P\) and \(Q\) is \(\frac { 1 } { 9 }\).
  1. Show that the speed of \(Q\) immediately after the collision is \(\frac { 10 u } { 3 ( 3 + k ) }\).
  2. Find the range of values of \(k\) for which the direction of motion of \(P\) is reversed as a result of the collision. Following the collision between \(P\) and \(Q\) there is a collision between \(Q\) and \(R\). Given that \(k = 7\) and that \(Q\) is brought to rest by the collision with \(R\),
  3. find the total kinetic energy lost in the collision between \(Q\) and \(R\).

6. Three particles $P , Q$ and $R$ have masses $3 m , k m$ and 7.5m respectively. The three particles lie at rest in a straight line on a smooth horizontal table with $Q$ between $P$ and $R$. Particle $P$ is projected towards $Q$ with speed $u$ and collides directly with $Q$. The coefficient of restitution between $P$ and $Q$ is $\frac { 1 } { 9 }$.
\begin{enumerate}[label=(\alph*)]
\item Show that the speed of $Q$ immediately after the collision is $\frac { 10 u } { 3 ( 3 + k ) }$.
\item Find the range of values of $k$ for which the direction of motion of $P$ is reversed as a result of the collision.

Following the collision between $P$ and $Q$ there is a collision between $Q$ and $R$. Given that $k = 7$ and that $Q$ is brought to rest by the collision with $R$,
\item find the total kinetic energy lost in the collision between $Q$ and $R$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2014 Q6 [14]}}