| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2008 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Beam suspended by vertical ropes |
| Difficulty | Moderate -0.8 This is a straightforward M2 equilibrium problem requiring standard moment and force resolution techniques. Parts (a)-(c) involve routine application of taking moments about a point and resolving vertically, with the uniform beam simplifying calculations. Part (d) tests conceptual understanding but requires minimal additional work. The problem is easier than average A-level maths due to its predictable structure and lack of complicating factors. |
| Spec | 3.04b Equilibrium: zero resultant moment and force6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| Diagram with tensions \(T_A\) and \(T_B\) and 40g force shown | B1 | 1 mark |
| Answer | Marks | Guidance |
|---|---|---|
| Taking moments about A: \(2.1 \times 40g = T_B \times 4\), \(T_B = 21g\) | M1 B1 A1 | 3 marks |
| Answer | Marks | Guidance |
|---|---|---|
| Resolve vertically: \(T_A + T_B = 40g\), \(T_A = 19g\) or 186 N | M1 A1 | 2 marks |
| Answer | Marks | Guidance |
|---|---|---|
| Gravitational force acts through mid point of the rod | E1 | 1 mark |
**Part (a)**
Diagram with tensions $T_A$ and $T_B$ and 40g force shown | B1 | 1 mark
**Part (b)**
Taking moments about A: $2.1 \times 40g = T_B \times 4$, $T_B = 21g$ | M1 B1 A1 | 3 marks | B1 for 2.1
**Part (c)**
Resolve vertically: $T_A + T_B = 40g$, $T_A = 19g$ or 186 N | M1 A1 | 2 marks
**Part (d)**
Gravitational force acts through mid point of the rod | E1 | 1 mark
**Total: 7 marks**
---2 A uniform plank, of length 6 metres, has mass 40 kg . The plank is held in equilibrium in a horizontal position by two vertical ropes attached to the plank at $A$ and $B$, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{03994596-21ad-4201-8d64-ba2d7b7e0a77-2_323_1162_1464_440}
\begin{enumerate}[label=(\alph*)]
\item Draw a diagram to show the forces acting on the plank.
\item Show that the tension in the rope attached to the plank at $B$ is $21 g \mathrm {~N}$.
\item Find the tension in the rope that is attached to the plank at $A$.
\item State where in your solution you have used the fact that the plank is uniform.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2008 Q2 [7]}}