| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Ladder against wall |
| Difficulty | Standard +0.8 This is a challenging M2 statics problem requiring students to set up and solve three equilibrium equations (horizontal/vertical forces and moments) with friction at two surfaces simultaneously at limiting equilibrium. The algebraic manipulation to eliminate variables and arrive at tan θ in terms of μ is non-trivial, and students must correctly apply F=μR at both contact points. While it follows standard ladder problem methodology, the dual friction coefficients and final algebraic simplification make it harder than typical textbook exercises. |
| Spec | 3.03u Static equilibrium: on rough surfaces3.04b Equilibrium: zero resultant moment and force3.04c Use moments: beams, ladders, static problems |
A uniform ladder, of weight $W$, rests with its top against a rough vertical wall and its base on rough horizontal ground.
The coefficient of friction between the wall and the ladder is $\mu$ and the coefficient of friction between the ground and the ladder is $2\mu$.
When the ladder is on the point of slipping, the ladder is inclined at an angle of $\theta$ to the horizontal.
\begin{enumerate}[label=(\alph*)]
\item Draw a diagram to show the forces acting on the ladder.
[2 marks]
\item Find $\tan \theta$ in terms of $\mu$.
[7 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2016 Q7 [9]}}