4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d1989e18-1a4a-47e9-9f12-3beb8985ed87-12_803_767_239_647}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
A ladder \(A B\) has mass \(M\) and length \(6 a\).
The end \(A\) of the ladder is on rough horizontal ground.
The ladder rests against a fixed smooth horizontal rail at the point \(C\).
The point \(C\) is at a vertical height \(4 a\) above the ground.
The vertical plane containing \(A B\) is perpendicular to the rail.
The ladder is inclined to the horizontal at an angle \(\alpha\), where \(\sin \alpha = \frac { 4 } { 5 }\), as shown in Figure 1.
The coefficient of friction between the ladder and the ground is \(\mu\).
The ladder rests in limiting equilibrium.
The ladder is modelled as a uniform rod.
Using the model,
- show that the magnitude of the force exerted on the ladder by the rail at \(C\) is \(\frac { 9 M g } { 25 }\)
- Hence, or otherwise, find the value of \(\mu\).