| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Circular Motion 2 |
| Type | Maximum/minimum tension or reaction |
| Difficulty | Standard +0.3 This is a standard M2 circular motion problem requiring energy conservation (part a) and force resolution at an intermediate point (part b). The 'show that' in part (a) guides students to the answer, and part (b) involves routine application of centripetal force equations with basic trigonometry. While multi-step, it follows a well-practiced template with no novel insight required, making it slightly easier than average. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.05d Variable speed circles: energy methods6.05e Radial/tangential acceleration |
8 A bead, of mass $m$, moves on a smooth circular ring, of radius $a$ and centre $O$, which is fixed in a vertical plane. At $P$, the highest point on the ring, the speed of the bead is $2 u$; at $Q$, the lowest point on the ring, the speed of the bead is $5 u$.
\begin{enumerate}[label=(\alph*)]
\item Show that $u = \sqrt { \frac { 4 a g } { 21 } }$.\\
(4 marks)
\item $\quad S$ is a point on the ring so that angle $P O S$ is $60 ^ { \circ }$, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{5b1c9e8d-459a-474c-bd29-6dadff40de14-4_600_540_657_760}
Find, in terms of $m$ and $g$, the magnitude of the reaction of the ring on the bead when the bead is at $S$.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2013 Q8 [9]}}