| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2002 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Particle-barrier collision with angle |
| Difficulty | Challenging +1.2 This is a standard M4 impulse-restitution problem requiring resolution of velocities normal and parallel to an inclined plane, application of Newton's experimental law (e = separation speed / approach speed), and impulse-momentum in 2D. The constraint that P moves horizontally after impact provides the key relationship. While it requires careful vector resolution and algebraic manipulation across multiple steps, the techniques are well-practiced in M4 and the 'show that' format guides students to the answer. It's moderately harder than average due to the 2D nature and algebraic complexity, but remains a standard bookwork-style question for this module. |
| Spec | 6.03f Impulse-momentum: relation6.03l Newton's law: oblique impacts |
A smooth uniform sphere $P$ of mass $m$ is falling vertically and strikes a fixed smooth inclined plane with speed $u$. The plane is inclined at an angle $\theta$, $\theta < 45°$, to the horizontal. The coefficient of restitution between $P$ and the inclined plane is $e$. Immediately after $P$ strikes the plane, $P$ moves horizontally.
\begin{enumerate}[label=(\alph*)]
\item Show that $e = \tan^2 \theta$. [6]
\item Show that the magnitude of the impulse exerted by $P$ on the plane is $mu \sec \theta$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2002 Q3 [10]}}