5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e59a66b8-c2ad-41fd-9959-9d21e9455c37-12_412_1529_242_267}
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\caption{Figure 4}
\end{figure}
A beam \(A B\) has mass 30 kg and length 3 m .
The beam rests on supports at \(C\) and \(D\) where \(A C = 0.4 \mathrm {~m}\) and \(D B = 0.4 \mathrm {~m}\), as shown in Figure 4.
A person of mass 55 kg stands on the beam between \(C\) and \(D\).
The person is modelled as a particle at the point \(P\), where \(C P = x\) metres and \(0 < x < 2.2\)
The beam is modelled as a uniform rod resting in equilibrium in a horizontal position.
Using the model,
- show that the magnitude of the reaction at \(C\) is \(( 686 - 245 x ) \mathrm { N }\).
The magnitude of the reaction at \(C\) is four times the magnitude of the reaction at \(D\).
Using the model, - find the value of \(x\)
The person steps off the beam and places a package of mass \(M \mathrm {~kg}\) at \(A\).
The package is modelled as a particle at the point \(A\).
The beam is now on the point of tilting about \(C\).
Using the model, - find the value of \(M\)