Standard +0.3 This is a standard M2 ladder equilibrium problem requiring resolution of forces, friction inequality (F ≤ μR), and taking moments about a suitable point. While it involves multiple steps and careful angle work, it follows a well-established method taught explicitly in M2 with no novel insight required. The 9 marks reflect routine application of mechanics principles rather than conceptual difficulty.
A uniform ladder \(AB\), of mass \(m\) and length \(2a\), has one end \(A\) on rough horizontal ground. The coefficient of friction between the ladder and the ground is 0.5. The other end \(B\) of the ladder rests against a smooth vertical wall. The ladder rests in equilibrium in a vertical plane perpendicular to the wall, and makes an angle of 30° with the wall. A man of mass \(5m\) stands on the ladder which remains in equilibrium. The ladder is modelled as a uniform rod and the man as a particle. The greatest possible distance of the man from \(A\) is \(ka\).
Find the value of \(k\).
[9]
A uniform ladder $AB$, of mass $m$ and length $2a$, has one end $A$ on rough horizontal ground. The coefficient of friction between the ladder and the ground is 0.5. The other end $B$ of the ladder rests against a smooth vertical wall. The ladder rests in equilibrium in a vertical plane perpendicular to the wall, and makes an angle of 30° with the wall. A man of mass $5m$ stands on the ladder which remains in equilibrium. The ladder is modelled as a uniform rod and the man as a particle. The greatest possible distance of the man from $A$ is $ka$.
Find the value of $k$.
[9]
\hfill \mbox{\textit{Edexcel M2 2001 Q3 [9]}}