| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | String through hole – hanging particle in equilibrium below table |
| Difficulty | Standard +0.3 This is a standard M2 conical pendulum problem with equilibrium and circular motion. Part (a) is immediate from Q's equilibrium (T=8g). Part (b) requires resolving forces on P vertically and using circular motion horizontally—straightforward application of F=ma and F=mv²/r. Part (c) follows directly from trigonometry. All steps are routine M2 techniques with no novel insight required, making it slightly easier than average. |
| Spec | 3.03k Connected particles: pulleys and equilibrium6.05c Horizontal circles: conical pendulum, banked tracks |
A particle $P$, of mass $6$ kg, is attached to one end of a light inextensible string. The string passes through a small smooth ring, fixed at a point $O$. A second particle $Q$, of mass $8$ kg, is attached to the other end of the string.
The particle $Q$ hangs at rest vertically below the ring, and the particle $P$ moves with speed $5 \text{ m s}^{-1}$ in a horizontal circle, as shown in the diagram.
The angle between $OP$ and the vertical is $\theta$.
\includegraphics{figure_4}
\begin{enumerate}[label=(\alph*)]
\item Find the tension in the string.
[1 mark]
\item Find $\theta$.
[3 marks]
\item Find the radius of the horizontal circle.
[4 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2016 Q4 [8]}}