| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2009 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Oblique and successive collisions |
| Type | Particle bouncing on inclined plane |
| Difficulty | Challenging +1.2 This is a standard M4 oblique impact question requiring resolution of velocities parallel and perpendicular to the inclined plane, application of Newton's experimental law with coefficient of restitution, and calculation of kinetic energy loss. While it involves multiple steps and careful geometric reasoning with the 45° plane and 30° rebound angle, it follows a well-established method taught in M4 courses with no novel insight required. |
| Spec | 6.02d Mechanical energy: KE and PE concepts6.03k Newton's experimental law: direct impact |
| Answer | Marks |
|---|---|
| M1 A1 |
| Answer | Marks |
|---|---|
| M1 M1 A1 |
**Part (a)**
CLM along plane: $v \cos 30° = u \cos 45°$
$v = u\sqrt{\frac{2}{3}}$
| M1 A1 |
**Part (b)**
Fraction of KE Lost = $\frac{\frac{1}{2}mu^2 - \frac{1}{2}mv^2}{\frac{1}{2}mu^2} = \frac{\frac{1}{2}mu^2 - \frac{1}{4}m\left(\frac{2}{3}\right)u^2}{\frac{1}{2}mu^2} = \frac{1}{3}$
| M1 M1 A1 |
**Total: [6]**
---1.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{f4c33171-597e-4ef3-9f21-3e2271d48f30-02_460_638_230_598}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
A fixed smooth plane is inclined to the horizontal at an angle of $45 ^ { \circ }$. A particle $P$ is moving horizontally and strikes the plane. Immediately before the impact, $P$ is moving in a vertical plane containing a line of greatest slope of the inclined plane. Immediately after the impact, $P$ is moving in a direction which makes an angle of $30 ^ { \circ }$ with the inclined plane, as shown in Figure 1.
Find the fraction of the kinetic energy of $P$ which is lost in the impact.\\
\hfill \mbox{\textit{Edexcel M4 2009 Q1 [6]}}