| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2006 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Loss of energy in collision |
| Difficulty | Challenging +1.2 This M4 question involves projectile motion with a constraint (string), energy conservation, and coefficient of restitution. Part (a) is a standard energy conservation calculation (4 marks). Part (b) requires resolving the velocity into components, applying Newton's experimental law, and using the given energy loss—more involved but still follows standard M4 procedures. The geometry setup and multi-step nature elevate it slightly above average A-level difficulty, but it remains a recognizable exam pattern without requiring novel insight. |
| Spec | 6.02d Mechanical energy: KE and PE concepts6.02e Calculate KE and PE: using formulae6.03i 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 sphere $S$ of mass $m$ is attached to one end of a light inextensible string of length $2a$. The other end of the string is attached to a fixed point $A$ which is at a distance $a\sqrt{3}$ from a smooth vertical wall. The sphere $S$ hangs at rest in equilibrium. It is then projected horizontally towards the wall with a speed $\sqrt{\left(\frac{37ga}{5}\right)}$.
\begin{enumerate}[label=(\alph*)]
\item Show that $S$ strikes the wall with speed $\sqrt{\left(\frac{27ga}{5}\right)}$.
[4]
Given that the loss in kinetic energy due to the impact with the wall is $\frac{3mga}{5}$,
\item find the coefficient of restitution between $S$ and the wall.
[7]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2006 Q2 [11]}}