| Exam Board | SPS |
|---|---|
| Module | SPS FM Mechanics (SPS FM Mechanics) |
| Year | 2026 |
| Session | January |
| Marks | 8 |
| Topic | Oblique and successive collisions |
| Type | Ball between two walls, successive rebounds |
| Difficulty | Challenging +1.2 This is a two-part mechanics problem involving oblique collisions with barriers and coefficient of restitution. Part (a) requires resolving velocities, applying the restitution formula, and using the kinetic energy condition to find e—straightforward but multi-step. Part (b) requires geometric reasoning to track the particle through two collisions with the 60° angle constraint. While it involves several steps and careful angle work, the techniques are standard A-level Further Maths mechanics with no novel insights required. |
| Spec | 6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
\includegraphics{figure_5}
$AB$ and $BC$ are two fixed smooth vertical barriers on a smooth horizontal surface, with angle $ABC = 60°$. A particle of mass $m$ is moving with speed $u$ on the surface. The particle strikes $AB$ at an angle $\theta$ with $AB$. It then strikes $BC$ and rebounds at an angle $\beta$ with $BC$ (see diagram). The coefficient of restitution between the particle and each barrier is $e$ and $\tan \theta = 2$.
The kinetic energy of the particle after the first collision is 40% of its kinetic energy before the first collision.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $e$. [4]
\item Find the size of angle $\beta$. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Mechanics 2026 Q5 [8]}}