- A ladder \(A B\), of weight \(W\) and length \(2 l\), has one end \(A\) resting on rough horizontal ground. The other end \(B\) rests against a rough vertical wall. The coefficient of friction between the ladder and the wall is \(\frac { 1 } { 3 }\). The coefficient of friction between the ladder and the ground is \(\mu\). Friction is limiting at both \(A\) and \(B\). The ladder is at an angle \(\theta\) to the ground, where \(\tan \theta = \frac { 5 } { 3 }\). The ladder is modelled as a uniform rod which lies in a vertical plane perpendicular to the wall.
Find the value of \(\mu\).