4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{414946db-64d7-44b8-801d-2c7805ee9cc6-12_716_1191_246_438}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
A uniform rod \(A B\) has mass \(M\) and length \(2 a\)
A particle of mass \(2 M\) is attached to the rod at the point \(C\), where \(A C = 1.5 a\)
The rod rests with its end \(A\) on rough horizontal ground.
The rod is held in equilibrium at an angle \(\theta\) to the ground by a light string that is attached to the end \(B\) of the rod.
The string is perpendicular to the rod, as shown in Figure 2.
- Explain why the frictional force acting on the rod at \(A\) acts horizontally to the right on the diagram.
The tension in the string is \(T\)
- Show that \(T = 2 M g \cos \theta\)
Given that \(\cos \theta = \frac { 3 } { 5 }\)
- show that the magnitude of the vertical force exerted by the ground on the rod at \(A\) is \(\frac { 57 M g } { 25 }\)
The coefficient of friction between the rod and the ground is \(\mu\)
Given that the rod is in limiting equilibrium, - show that \(\mu = \frac { 8 } { 19 }\)