Edexcel M2 2022 June — Question 6 12 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2022
SessionJune
Marks12
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMomentum and Collisions 1
TypeDirect collision with given impulse
DifficultyStandard +0.3 This is a standard M2 collision problem requiring systematic application of conservation of momentum, coefficient of restitution, and impulse-momentum theorem. While it involves multiple parts and algebraic manipulation with parameters, it follows a well-established template with no novel insight required—slightly easier than average due to its routine nature.
Spec6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact

6. Two particles, \(P\) and \(Q\), are moving in opposite directions along the same straight line on a smooth horizontal surface so that the particles collide directly.
The mass of \(P\) is \(k m\) and the mass of \(Q\) is \(m\).
Immediately before the collision, the speed of \(P\) is \(x\) and the speed of \(Q\) is \(y\). Immediately after the collision, \(P\) and \(Q\) are moving in the same direction, the speed of \(P\) is \(v\) and the speed of \(Q\) is \(2 v\). The coefficient of restitution between \(P\) and \(Q\) is \(\frac { 1 } { 5 }\) The magnitude of the impulse received by \(Q\) in the collision is \(5 m v\)
  1. Find (i) \(y\) in terms of \(v\) (ii) \(x\) in terms of \(v\) (iii) the value of \(k\)
  2. Find, in terms of \(m\) and \(v\), the total kinetic energy lost in the collision between \(P\) and \(Q\).

6. Two particles, $P$ and $Q$, are moving in opposite directions along the same straight line on a smooth horizontal surface so that the particles collide directly.\\
The mass of $P$ is $k m$ and the mass of $Q$ is $m$.\\
Immediately before the collision, the speed of $P$ is $x$ and the speed of $Q$ is $y$. Immediately after the collision, $P$ and $Q$ are moving in the same direction, the speed of $P$ is $v$ and the speed of $Q$ is $2 v$.

The coefficient of restitution between $P$ and $Q$ is $\frac { 1 } { 5 }$\\
The magnitude of the impulse received by $Q$ in the collision is $5 m v$
\begin{enumerate}[label=(\alph*)]
\item Find (i) $y$ in terms of $v$\\
(ii) $x$ in terms of $v$\\
(iii) the value of $k$
\item Find, in terms of $m$ and $v$, the total kinetic energy lost in the collision between $P$ and $Q$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2022 Q6 [12]}}