Challenging +1.2 This is a standard ladder equilibrium problem requiring resolution of forces, friction inequality, and taking moments about a point. While it involves multiple steps (drawing diagram, identifying forces, resolving horizontally/vertically, applying moment equation, using limiting friction), these are well-practiced techniques in M2. The setup is conventional and the algebra straightforward, making it slightly above average difficulty but not requiring novel insight.
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 \(0.15\) and \(B\) 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 \(6a\).
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 $0.15$ and $B$ 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 $6a$.
Find the value of $k$.
[9]
\hfill \mbox{\textit{Edexcel M2 Q3 [9]}}