| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Collision with unchanged direction |
| Difficulty | Standard +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. |
| Spec | 6.03b 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,
\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]}}