| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2008 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Ladder against smooth wall in limiting equilibrium |
| Difficulty | Standard +0.3 This is a standard M2 ladder equilibrium problem requiring three equations (vertical/horizontal equilibrium and moments) with straightforward substitution. The 'limiting equilibrium' setup and given coefficient of friction make it slightly easier than average, as students follow a well-practiced routine with clear numerical values throughout. |
| Spec | 3.03u Static equilibrium: on rough surfaces3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Diagram with S, C, 80g, 20g, R, F, A, 60° | B2 | 2 marks |
| Answer | Marks | Guidance |
|---|---|---|
| \(F = 0.4 \times 100g = 40g\) or 392 N | B1 m1 A1 | 3 marks |
| Answer | Marks | Guidance |
|---|---|---|
| \(x = \frac{118.56}{40} = 2.96\) m | B1 M1A1 m1 A1 | 6 marks |
**(a)** Diagram with S, C, 80g, 20g, R, F, A, 60° | B2 | 2 marks | B1 for any 4 correct
**(b)** Resolve vertically:
$R = 20g + 80g = 100g$
Using $F = \mu R$:
$F = 0.4 \times 100g = 40g$ or 392 N | B1 m1 A1 | 3 marks | Must see 20g + 80g or 100g to obtain any marks in (b); Dep on B1
**(c)** Resolve horizontally:
$S = 40g$
Moments about A:
$80g\cos 60 + 20g.2\cos 60 = 5.4\cos 30$
$40gx + 20g = 138.56g$
$x = \frac{118.56}{40} = 2.96$ m | B1 M1A1 m1 A1 | 6 marks | M1 for 3 terms, all moments; Dep on M1; Accept $2\sqrt{3} - \frac{1}{2}$
**Total: 11 marks**
---3 A uniform ladder of length 4 metres and mass 20 kg rests in equilibrium with its foot, $A$, on a rough horizontal floor and its top leaning against a smooth vertical wall. The vertical plane containing the ladder is perpendicular to the wall and the angle between the ladder and the floor is $60 ^ { \circ }$.
A man of mass 80 kg is standing at point $C$ on the ladder. With the man in this position, the ladder is on the point of slipping. The coefficient of friction between the ladder and the floor is 0.4 . The man may be modelled as a particle at $C$.\\
\includegraphics[max width=\textwidth, alt={}, center]{1bc18163-b20e-4dc6-bd35-496efec8dc73-3_567_448_708_788}
\begin{enumerate}[label=(\alph*)]
\item Draw a diagram to show the forces acting on the ladder.
\item Show that the magnitude of the frictional force between the ladder and the ground is 392 N .
\item Find the distance $A C$.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2008 Q3 [11]}}