Edexcel M1 2023 January — Question 4

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2023
SessionJanuary
TopicMoments

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{84c0eead-0a87-4d87-b33d-794a94bb466c-10_419_1445_283_312} \captionsetup{labelformat=empty} \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
  1. the value of \(W\)
  2. the value of \(x\)