5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{64b0abc9-4021-44e6-8bf7-1a5862617085-16_606_1287_260_331}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
A uniform rod \(A B\), of mass 5 kg and length 8 m , has its end \(B\) resting on rough horizontal ground. The rod is held in limiting equilibrium at an angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 3 } { 4 }\), by a rope attached to the rod at \(C\). The distance \(A C = 1 \mathrm {~m}\). The rope is in the same vertical plane as the rod. The angle between the rope and the rod is \(\beta\) and the tension in the rope is \(T\) newtons, as shown in Figure 3. The coefficient of friction between the rod and the ground is \(\frac { 2 } { 3 }\). The vertical component of the force exerted on the rod at \(B\) by the ground is \(R\) newtons.
- Find the value of \(R\).
- Find the size of angle \(\beta\).