Edexcel M2 2019 January — Question 7 13 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2019
SessionJanuary
Marks13
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMomentum and Collisions 1
TypeDirect collision with direction reversal
DifficultyStandard +0.3 This is a standard M2 collision problem requiring conservation of momentum and Newton's restitution law. Part (a) is a straightforward 'show that' requiring basic algebra, part (b) involves finding a range by solving an inequality, and part (c) is routine kinetic energy calculation. All techniques are standard textbook exercises with no novel insight required, making it slightly easier than average.
Spec6.02d Mechanical energy: KE and PE concepts6.02i Conservation of energy: mechanical energy principle6.03b Conservation of momentum: 1D two particles6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact

7. A particle \(P\) of mass \(3 m\) is moving in a straight line with speed \(u\) on a smooth horizontal table. A second particle \(Q\) of mass \(2 m\) is moving with speed \(2 u\) in the opposite direction to \(P\) along the same straight line. Particle \(P\) collides directly with \(Q\). The coefficient of restitution between \(P\) and \(Q\) is \(e\).
  1. Show that the direction of motion of \(P\) is reversed as a result of the collision with \(Q\).
  2. Find the range of values of \(e\) for which the direction of motion of \(Q\) is also reversed as a result of the collision. Given that \(e = \frac { 1 } { 2 }\)
  3. find, in terms of \(m\) and \(u\), the kinetic energy lost in the collision between \(P\) and \(Q\).

7. A particle $P$ of mass $3 m$ is moving in a straight line with speed $u$ on a smooth horizontal table. A second particle $Q$ of mass $2 m$ is moving with speed $2 u$ in the opposite direction to $P$ along the same straight line. Particle $P$ collides directly with $Q$. The coefficient of restitution between $P$ and $Q$ is $e$.
\begin{enumerate}[label=(\alph*)]
\item Show that the direction of motion of $P$ is reversed as a result of the collision with $Q$.
\item Find the range of values of $e$ for which the direction of motion of $Q$ is also reversed as a result of the collision.

Given that $e = \frac { 1 } { 2 }$
\item find, in terms of $m$ and $u$, the kinetic energy lost in the collision between $P$ and $Q$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2019 Q7 [13]}}