| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2005 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Impulse and momentum (advanced) |
| Type | Projectile with plane collision |
| Difficulty | Standard +0.3 This is a standard M4 oblique impact question requiring resolution of velocity components perpendicular and parallel to an inclined plane, application of Newton's experimental law with given coefficient of restitution, and impulse calculation. While it involves multiple steps and careful component resolution, it follows a well-established procedure taught in all M4 courses with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.05a Sine, cosine, tangent: definitions for all arguments6.03e Impulse: by a force6.03f Impulse-momentum: relation6.03i Coefficient of restitution: e6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
A small smooth ball of mass $\frac{1}{2}$ kg is falling vertically. The ball strikes a smooth plane which is inclined at an angle $\alpha$ to the horizontal, where $\tan \alpha = \frac{1}{3}$. Immediately before striking the plane the ball has speed 10 m s$^{-1}$. The coefficient of restitution between ball and plane is $\frac{1}{2}$.
Find
\begin{enumerate}[label=(\alph*)]
\item the speed, to 3 significant figures, of the ball immediately after the impact, [5]
\item the magnitude of the impulse received by the ball as it strikes the plane. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2005 Q1 [7]}}