| Exam Board | AQA |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2012 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Oblique and successive collisions |
| Type | Sphere rebounds off fixed wall obliquely |
| Difficulty | Standard +0.3 This is a standard M3 collision problem requiring resolution of velocities, coefficient of restitution, and impulse calculations. While it involves multiple parts and geometric reasoning with the snooker table setup, the techniques are routine for this module: resolving components parallel/perpendicular to the cushion, applying e = (separation speed)/(approach speed), and using impulse-momentum. The geometry is straightforward (right-angled triangles with given dimensions). Slightly above average due to the multi-step nature and need to coordinate geometry with mechanics, but all methods are standard textbook applications. |
| Spec | 6.03e Impulse: by a force6.03f Impulse-momentum: relation6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
**Question 4 (worked solutions):**
**(a)** The cushion is the top edge. Ball hits at 60° to cushion.
- Component **along** cushion: $u\cos60° = \frac{u}{2}$ (unchanged, smooth cushion)
- Component **perpendicular** to cushion: $u\sin60° = \frac{u\sqrt{3}}{2}$ (before)
- After rebound, ball must travel to pocket $P$: using geometry (AC = 1.20 m, width = 1.69 m), find rebound angle, then apply Newton's law of restitution to find $e$.
Would you like me to work through the full solutions for all parts?4 The diagram shows part of a horizontal snooker table of width 1.69 m .
A player strikes the ball $B$ directly, and it moves in a straight line. The ball hits the cushion of the table at $C$ before rebounding and moving to the pocket at $P$ at the corner of the table, as shown in the diagram. The point $C$ is 1.20 m from the corner $A$ of the table. The ball has mass 0.15 kg and, immediately before the collision with the cushion, it has velocity $u$ in a direction inclined at $60 ^ { \circ }$ to the cushion. The table and the cushion are modelled as smooth.\\
\includegraphics[max width=\textwidth, alt={}, center]{a90a2de3-5cc0-4e87-b29a-2562f86eee17-08_517_963_719_511}
\begin{enumerate}[label=(\alph*)]
\item Find the coefficient of restitution between the ball and the cushion.
\item Show that the magnitude of the impulse on the cushion at $C$ is approximately $0.236 u$.
\item Find, in terms of $u$, the time taken between the ball hitting the cushion at $C$ and entering the pocket at $P$.
\item Explain how you have used the assumption that the cushion is smooth in your answers.
\end{enumerate}
\hfill \mbox{\textit{AQA M3 2012 Q4 [13]}}