| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2010 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Collision followed by wall impact |
| Difficulty | Standard +0.3 This is a standard M2 collision problem requiring conservation of momentum and Newton's restitution law, followed by straightforward kinematics. The multi-part structure and 'show that' element add some length, but all techniques are routine textbook applications with no novel insight required—slightly easier than average. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03i Coefficient of restitution: e6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
A small ball $A$ of mass $3m$ is moving with speed $u$ in a straight line on a smooth horizontal table. The ball collides directly with another small ball $B$ of mass $m$ moving with speed $u$ towards $A$ along the same straight line. The coefficient of restitution between $A$ and $B$ is $\frac{1}{2}$. The balls have the same radius and can be modelled as particles.
\begin{enumerate}[label=(\alph*)]
\item Find
\begin{enumerate}[label=(\roman*)]
\item the speed of $A$ immediately after the collision,
\item the speed of $B$ immediately after the collision.
\end{enumerate}
(7)
\end{enumerate}
After the collision $B$ hits a smooth vertical wall which is perpendicular to the direction of motion of $B$. The coefficient of restitution between $B$ and the wall is $\frac{2}{3}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the speed of $B$ immediately after hitting the wall.
(2)
\end{enumerate}
The first collision between $A$ and $B$ occurred at a distance $4a$ from the wall. The balls collide again $T$ seconds after the first collision.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Show that $T = \frac{112a}{15u}$.
(6)
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2010 Q8}}