| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2014 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Oblique and successive collisions |
| Type | Oblique collision, direction deflected given angle |
| Difficulty | Challenging +1.8 This M4 oblique collision problem requires resolving velocities along/perpendicular to the line of centres, applying Newton's experimental law and momentum conservation, then finding post-collision velocities and directions. Part (b) requires calculus to maximize the deflection angle. While systematic, it demands careful vector resolution, algebraic manipulation with parameters, and optimization—significantly above average difficulty but standard for M4 collision questions. |
| Spec | 6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
A smooth uniform sphere $S$ is moving on a smooth horizontal plane when it collides obliquely with an identical sphere $T$ which is at rest on the plane. Immediately before the collision $S$ is moving with speed $U$ in a direction which makes an angle of $60°$ with the line joining the centres of the spheres. The coefficient of restitution between the spheres is $e$.
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $e$ and $U$ where necessary,
\begin{enumerate}[label=(\roman*)]
\item the speed and direction of motion of $S$ immediately after the collision,
\item the speed and direction of motion of $T$ immediately after the collision.
\end{enumerate}
(12)
\end{enumerate}
The angle through which the direction of motion of $S$ is deflected is $\delta°$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find
\begin{enumerate}[label=(\roman*)]
\item the value of $e$ for which $\delta$ takes the largest possible value,
\item the value of $\delta$ in this case.
\end{enumerate}
(3)
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2014 Q4}}