M2 January 2013 Q3

EdexcelOld spec9 marksMomentsResolving Forces

3.

Figure 1: ladder AB of length 5 m against a vertical wall at angle alpha to the ground, point C with AC = 3 m
Figure 1

A ladder, of length 5 m and mass 18 kg, has one end \(A\) resting on rough horizontal ground and its other end \(B\) resting against a smooth vertical wall. The ladder lies in a vertical plane perpendicular to the wall and makes an angle \(\alpha\) with the horizontal ground, where \(\tan\alpha = \dfrac{4}{3}\), as shown in Figure 1. The coefficient of friction between the ladder and the ground is \(\mu\). A woman of mass 60 kg stands on the ladder at the point \(C\), where \(AC = 3\) m. The ladder is on the point of slipping. The ladder is modelled as a uniform rod and the woman as a particle.

Find the value of \(\mu\). (9)

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