| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Impulse and momentum (advanced) |
| Type | Projectile with plane collision |
| Difficulty | Challenging +1.8 This is a challenging M4 mechanics problem requiring resolution of velocities parallel and perpendicular to an inclined plane, application of Newton's experimental law (coefficient of restitution), and algebraic manipulation to derive a specific relationship. The constraint that the sphere moves horizontally after impact requires insight to set up the correct geometric condition, making this significantly harder than routine collision problems but still within standard M4 scope. |
| Spec | 6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
3. 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 $\theta , \theta < 45 ^ { \circ }$, to the horizontal. The coefficient of restitution between $P$ and the inclined plane is $e$. Immediately after $P$ strikes the plane, $P$ moves horizontally.\\
(a) Show that $e = \tan ^ { 2 } \theta$.\\
\hfill \mbox{\textit{Edexcel M4 Q3 [8]}}