2 A uniform beam, AB , is 6 m long and has a weight of 240 N .
Initially, the beam is in equilibrium on two supports at C and D, as shown in Fig. 2.1. The beam is horizontal. \begin{figure}[h] \end{figure}

1. Calculate the forces acting on the beam from the supports at C and D . A workman tries to move the beam by applying a force \(T \mathrm {~N}\) at A at \(40 ^ { \circ }\) to the beam, as shown in Fig. 2.2. The beam remains in horizontal equilibrium but the reaction of support C on the beam is zero. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{c1785fde-a6ce-4f8b-9948-4b4dd973ce84-3_318_691_1119_687} \captionsetup{labelformat=empty} \caption{Fig. 2.2}
   \end{figure}
2. (A) Calculate the value of \(T\).
   (B) Explain why the support at D cannot be smooth. The beam is now supported by a light rope attached to the beam at A , with B on rough, horizontal ground. The rope is at \(90 ^ { \circ }\) to the beam and the beam is at \(30 ^ { \circ }\) to the horizontal, as shown in Fig. 2.3. The tension in the rope is \(P \mathrm {~N}\). The beam is in equilibrium on the point of sliding. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{c1785fde-a6ce-4f8b-9948-4b4dd973ce84-3_438_633_1909_708} \captionsetup{labelformat=empty} \caption{Fig. 2.3}
   \end{figure}
3. (A) Show that \(P = 60 \sqrt { 3 }\) and hence, or otherwise, find the frictional force between the beam and the ground.
   (B) Calculate the coefficient of friction between the beam and the ground.