| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Moments |
| Type | Beam suspended by vertical ropes |
| Difficulty | Moderate -0.3 This is a standard M2 moments question requiring equilibrium conditions (sum of forces = 0, sum of moments = 0) with straightforward calculations. Part (a) involves taking moments about a point to find two tensions, and part (b) requires finding an additional mass. The uniform beam assumption simplifies the problem to treating weight as acting at the center. While it requires multiple steps and understanding of moments, it follows a well-practiced textbook method with no novel insight needed, making it slightly easier than average. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force6.04e Rigid body equilibrium: coplanar forces |
4 A uniform plank $A B$, of length 6 m , has mass 25 kg . It is supported in equilibrium in a horizontal position by two vertical inextensible ropes. One of the ropes is attached to the plank at the point $P$ and the other rope is attached to the plank at the point $Q$, where $A P = 1 \mathrm {~m}$ and $Q B = 0.8 \mathrm {~m}$, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{5b1c9e8d-459a-474c-bd29-6dadff40de14-2_227_1187_2252_424}
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Find the tension in each rope.
\item State how you have used the fact that the plank is uniform in your solution. (1 mark)
\end{enumerate}\item A particle of mass $m \mathrm {~kg}$ is attached to the plank at point $B$, and the tension in each rope is now the same.
Find $m$.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2013 Q4 [12]}}