| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2014 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 2 |
| Type | Vertical circle: speed at specific point |
| Difficulty | Standard +0.3 This is a standard vertical circle problem using conservation of energy and circular motion equations. Part (a) requires straightforward application of energy conservation between lowest and highest points, and part (b) uses the standard tension equation at the top of a circle. Both are textbook exercises with well-practiced techniques, making this slightly easier than average. |
| Spec | 6.05d Variable speed circles: energy methods6.05e Radial/tangential acceleration |
A light inextensible string, of length $a$, has one end attached to a fixed point $O$. A particle, of mass $m$, is attached to the other end of the string. The particle is moving in a vertical circle with centre $O$. The point $Q$ is the highest point of the particle's path. When the particle is at $P$, vertically below $O$, the string is taut and the particle is moving with speed $7\sqrt{ag}$, as shown in the diagram.
\includegraphics{figure_5}
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $g$ and $a$, the speed of the particle at the point $Q$. [4 marks]
\item Find, in terms of $g$ and $m$, the tension in the string when the particle is at $Q$. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2014 Q5 [7]}}