4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{84c0eead-0a87-4d87-b33d-794a94bb466c-10_419_1445_283_312}
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\caption{Figure 1}
\end{figure}
A branch \(A B\), of length 1.5 m , rests horizontally in equilibrium on two supports.
The two supports are at the points \(C\) and \(D\), where \(A C = 0.24 \mathrm {~m}\) and \(D B = 0.36 \mathrm {~m}\), as shown in Figure 1.
When a force of 150 N is applied vertically upwards at \(B\), the branch is on the point of tilting about \(C\).
When a force of 225 N is applied vertically downwards at \(B\), the branch is on the point of tilting about \(D\).
The branch is modelled as a non-uniform rod \(A B\) of weight \(W\) newtons.
The distance from the point \(C\) to the centre of mass of the rod is \(x\) metres.
Use the model to find
- the value of \(W\)
- the value of \(x\)