5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{38f4333d-b374-4064-bf12-e1a0bbd72f56-4_395_826_360_642}
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\caption{Figure 1}
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A heavy uniform steel girder \(A B\) has length 10 m . A load of weight 150 N is attached to the girder at \(A\) and a load of weight 250 N is attached to the girder at \(B\). The loaded girder hangs in equilibrium in a horizontal position, held by two vertical steel cables attached to the girder at the points \(C\) and \(D\), where \(A C = 1 \mathrm {~m}\) and \(D B = 3 \mathrm {~m}\), as shown in Fig. 1. The girder is modelled as a uniform rod, the loads as particles and the cables as light inextensible strings. The tension in the cable at \(D\) is three times the tension in the cable at \(C\).
- Draw a diagram showing all the forces acting on the girder.
Find
- the tension in the cable at \(C\),
- the weight of the girder.
- Explain how you have used the fact that the girder is uniform.