4 Fig. 4.1 shows a uniform beam, CE, of weight 2200 N and length 4.5 m . The beam is freely pivoted on a fixed support at D and is supported at C . The distance CD is 2.75 m . \begin{figure}[h] \end{figure} \begin{figure}[h] \end{figure} The beam is horizontal and in equilibrium.

1. Show that the anticlockwise moment of the weight of the beam about D is 1100 Nm . Find the value of the normal reaction on the beam of the support at C . The support at C is removed and spheres at P and Q are suspended from the beam by light strings attached to the points C and R . The sphere at P has weight 440 N and the sphere at Q has weight \(W \mathrm {~N}\). The point R of the beam is 1.5 m from D . This situation is shown in Fig. 4.2.
2. The beam is horizontal and in equilibrium. Show that \(W = 1540\). The sphere at P is changed for a lighter one with weight 400 N . The sphere at Q is unchanged. The beam is now held in equilibrium at an angle of \(20 ^ { \circ }\) to the horizontal by means of a light rope attached to the beam at E. This situation (but without the rope at E) is shown in Fig. 4.3. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{b2962c91-4739-4d1e-98f3-62d420f6dddf-5_451_611_1635_767} \captionsetup{labelformat=empty} \caption{Fig. 4.3}
   \end{figure}
3. Calculate the tension in the rope when it is
   (A) at \(90 ^ { \circ }\) to the beam,
   \(( B )\) horizontal.