| Exam Board | AQA |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2015 |
| Session | June |
| Marks | 2 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Oblique and successive collisions |
| Type | Successive collisions, three particles in line |
| Difficulty | Standard +0.3 This is a standard M3 collision problem involving successive collisions with given coefficients of restitution. Part (a) uses routine momentum conservation and Newton's law of restitution with straightforward algebra. Part (b) requires tracking velocities through a second collision and finding the condition for a third collision, which is methodical but not conceptually demanding. The 'show that' format and clear structure make this slightly easier than average for M3 material. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03c Momentum in 2D: vector form6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
I'm ready to help clean up the mark scheme content, but I don't see the actual mark scheme text for Question 4 in your message. You've provided the question number and a "4" but no extracted content to process.
Please provide the mark scheme content you'd like me to clean up, and I'll convert the unicode symbols to LaTeX notation, preserve all marking annotations (M1, A1, B1, etc.), and format it clearly with one marking point per line.4 Three uniform smooth spheres, $A , B$ and $C$, have equal radii and masses $m , 2 m$ and $6 m$ respectively. The spheres lie at rest in a straight line on a smooth horizontal surface with $B$ between $A$ and $C$. The sphere $A$ is projected with speed $u$ directly towards $B$ and collides with it.\\
\includegraphics[max width=\textwidth, alt={}, center]{bcd20c69-cace-408c-8961-169c19ff0231-10_218_1164_500_438}
The coefficient of restitution between $A$ and $B$ is $\frac { 2 } { 3 }$.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Show that the speed of $B$ immediately after the collision is $\frac { 5 } { 9 } u$.
\item Find, in terms of $u$, the speed of $A$ immediately after the collision.
\end{enumerate}\item Subsequently, $B$ collides with $C$. The coefficient of restitution between $B$ and $C$ is $e$.
Show that $B$ will collide with $A$ again if $e > k$, where $k$ is a constant to be determined.
\item Explain why it is not necessary to model the spheres as particles in this question.\\[0pt]
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA M3 2015 Q4 [2]}}