| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2010 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Uniform beam on two supports |
| Difficulty | Moderate -0.8 This is a straightforward M2 statics problem requiring a force diagram, taking moments about one point to find a reaction force (with the answer given), then using vertical equilibrium to find the other reaction. The uniform beam assumption (weight acts at center) is standard bookwork, and all steps follow routine procedures with no problem-solving insight required. |
| Spec | 3.04b Equilibrium: zero resultant moment and force6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Diagram showing \(R_A\), \(R_B\), \(20g\), \(B\), \(30g\) | B2 | B1 for four forces; B2 for two different reactions and \(30g\) and \(20g\) marked. Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Taking moments about \(A\): \(3.2\times30g = R_B \times 5\) | M1B1 | B1 for 3.2 |
| \(R_B = 19.2g\) | A1 | AG. Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Resolve vertically: \(R_A + R_B = 50g\) | M1 | Can be awarded in (b) |
| \(R_A = 30.8g\) or \(302\) N | A1 | Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Gravitational force acts through mid-point of the rod | E1 | Total: 1 |
## Question 3:
### Part (a):
| Working | Marks | Guidance |
|---------|-------|----------|
| Diagram showing $R_A$, $R_B$, $20g$, $B$, $30g$ | B2 | B1 for four forces; B2 for two different reactions and $30g$ and $20g$ marked. **Total: 2** |
### Part (b):
| Working | Marks | Guidance |
|---------|-------|----------|
| Taking moments about $A$: $3.2\times30g = R_B \times 5$ | M1B1 | B1 for 3.2 |
| $R_B = 19.2g$ | A1 | AG. **Total: 3** |
### Part (c):
| Working | Marks | Guidance |
|---------|-------|----------|
| Resolve vertically: $R_A + R_B = 50g$ | M1 | Can be awarded in (b) |
| $R_A = 30.8g$ or $302$ N | A1 | **Total: 2** |
### Part (d):
| Working | Marks | Guidance |
|---------|-------|----------|
| Gravitational force acts through mid-point of the rod | E1 | **Total: 1** |
---3 A uniform plank, of length 8 metres, has mass 30 kg . The plank is supported in equilibrium in a horizontal position by two smooth supports at the points $A$ and $B$, as shown in the diagram. A block, of mass 20 kg , is placed on the plank at point $A$.\\
\includegraphics[max width=\textwidth, alt={}, center]{06b431ca-d3a8-46d6-b9f8-bac08d3fd51e-3_193_1216_477_404}
\begin{enumerate}[label=(\alph*)]
\item Draw a diagram to show the forces acting on the plank.
\item Show that the magnitude of the force exerted on the plank by the support at $B$ is $19.2 g$ newtons.
\item Find the magnitude of the force exerted on the plank by the support at $A$.
\item Explain how you have used the fact that the plank is uniform in your solution.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2010 Q3 [8]}}