| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2007 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Beam suspended by vertical ropes |
| Difficulty | Moderate -0.8 This is a straightforward moments problem requiring a force diagram, taking moments about one point to find tensions, and vertical equilibrium. It's a standard M2 textbook exercise with clear setup, routine application of ΣM=0 and ΣF=0, and no geometric complexity or novel insight required—easier than average A-level. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Diagram showing arrows + labels, \(w\) in centre | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Res ↑ or M(B) giving \(T_A = \frac{W}{3}\) | M1, A1, M1, A1 | Moments equation; Accept 2 dp for each A1 |
| (c) Lamina is uniform \(\Rightarrow\) weight acts at centre | B1 |
**(a)** Diagram showing arrows + labels, $w$ in centre | B1 | | **Total: 1 mark**
**(b)** $M(A) \quad 0.4W = 0.67T_B$ giving $T_B = \frac{2W}{3}$
Res ↑ or M(B) giving $T_A = \frac{W}{3}$ | M1, A1, M1, A1 | Moments equation; Accept 2 dp for each A1 | **Total: 4 marks**
**(c)** Lamina is uniform $\Rightarrow$ weight acts at centre | B1 | | **Total: 1 mark**
**Question 2 Total: 6 marks**
---2 A hotel sign consists of a uniform rectangular lamina of weight $W$. The sign is suspended in equilibrium in a vertical plane by two vertical light chains attached to the sign at the points $A$ and $B$, as shown in the diagram. The edge containing $A$ and $B$ is horizontal.\\
\includegraphics[max width=\textwidth, alt={}, center]{480a817d-074f-440d-829e-c8f8a9746151-2_289_529_1859_726}
The tensions in the chains attached at $A$ and $B$ are $T _ { A }$ and $T _ { B }$ respectively.
\begin{enumerate}[label=(\alph*)]
\item Draw a diagram to show the forces acting on the sign.
\item Find $T _ { A }$ and $T _ { B }$ in terms of $W$.
\item Explain how you have used the fact that the lamina is uniform in answering part (b).
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2007 Q2 [6]}}