Edexcel M2 — Question 6 14 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Marks14
PaperDownload PDF ↗
TopicMomentum and Collisions 1
TypeCollision with unchanged direction
DifficultyStandard +0.3 This is a standard M2 collision problem requiring conservation of momentum and Newton's restitution law. Part (a) is routine algebraic manipulation, part (b) requires recognizing that P must slow down (giving e ≤ 1/2), part (c) is straightforward KE calculation, and part (d) is trivial recall. The multi-part structure and 14 marks indicate moderate length, but all techniques are textbook-standard with no novel insight required.
Spec6.03b Conservation of momentum: 1D two particles6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts

A smooth sphere \(P\) of mass \(m\) is moving in a straight line with speed \(u\) on a smooth horizontal table. Another smooth sphere \(Q\) of mass \(2m\) is at rest on the table. The sphere \(P\) collides directly with \(Q\). After the collision the direction of motion of \(P\) is unchanged. The spheres have the same radii and the coefficient of restitution between \(P\) and \(Q\) is \(e\). By modelling the spheres as particles,
  1. show that the speed of \(Q\) immediately after the collision is \(\frac{1}{3}(1 + e)u\), [5]
  1. find the range of possible values of \(e\). [4]
Given that \(e = \frac{1}{4}\),
  1. find the loss of kinetic energy in the collision. [4]
  1. Give one possible form of energy into which the lost kinetic energy has been transformed. [1]
TURN OVER FOR QUESTION 7

A smooth sphere $P$ of mass $m$ is moving in a straight line with speed $u$ on a smooth horizontal table. Another smooth sphere $Q$ of mass $2m$ is at rest on the table. The sphere $P$ collides directly with $Q$. After the collision the direction of motion of $P$ is unchanged. The spheres have the same radii and the coefficient of restitution between $P$ and $Q$ is $e$. By modelling the spheres as particles,

\begin{enumerate}[label=(\alph*)]
\item show that the speed of $Q$ immediately after the collision is $\frac{1}{3}(1 + e)u$,
[5]
\end{enumerate}

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the range of possible values of $e$.
[4]
\end{enumerate}

Given that $e = \frac{1}{4}$,

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item find the loss of kinetic energy in the collision.
[4]
\end{enumerate}

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Give one possible form of energy into which the lost kinetic energy has been transformed.
[1]
\end{enumerate}

TURN OVER FOR QUESTION 7

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