5.
\begin{figure}[h]
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\caption{Figure 3}
\includegraphics[alt={},max width=\textwidth]{3a8395fd-6e44-48a1-8c97-3365a284956a-07_237_805_303_598}
\end{figure}
A steel girder \(A B\) has weight 210 N . It is held in equilibrium in a horizontal position by two vertical cables. One cable is attached to the end \(A\). The other cable is attached to the point \(C\) on the girder, where \(A C = 90 \mathrm {~cm}\), as shown in Figure 3. The girder is modelled as a uniform rod, and the cables as light inextensible strings.
Given that the tension in the cable at \(C\) is twice the tension in the cable at \(A\), find
- the tension in the cable at \(A\),
- show that \(A B = 120 \mathrm {~cm}\).
A small load of weight \(W\) newtons is attached to the girder at \(B\). The load is modelled as a particle. The girder remains in equilibrium in a horizontal position. The tension in the cable at \(C\) is now three times the tension in the cable at \(A\).
- Find the value of \(W\).