6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3eb71ecb-fa88-4cca-a2b6-bcf11f1d689b-16_639_561_246_689}
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\caption{Figure 3}
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A ladder \(A B\) has length 6 m and mass 30 kg . The ladder rests in equilibrium at \(60 ^ { \circ }\) to the horizontal with the end \(A\) on rough horizontal ground and the end \(B\) against a smooth vertical wall, as shown in Figure 3.
A man of mass 70 kg stands on the ladder at the point \(C\), where \(A C = 2 \mathrm {~m}\), and the ladder remains in equilibrium. The ladder is modelled as a uniform rod in a vertical plane perpendicular to the wall. The man is modelled as a particle.
- Find the magnitude of the force exerted on the ladder by the ground.
The man climbs further up the ladder. When he is at the point \(D\) on the ladder, the ladder is about to slip.
Given that the coefficient of friction between the ladder and the ground is 0.4
- find the distance \(A D\).
- State how you have used the modelling assumption that the ladder is a rod.