4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f2737a11-4a15-41e9-9f87-31a705a8948b-08_625_1488_246_287}
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\caption{Figure 1}
\end{figure}
Figure 1 shows a beam \(A B\), of mass \(m \mathrm {~kg}\) and length 2 m , suspended by two light vertical ropes.
The ropes are attached to the points \(C\) and \(D\) on the beam, where \(A C = 0.6 \mathrm {~m}\) and \(D B = 0.2 \mathrm {~m}\)
The beam is in equilibrium in a horizontal position.
A particle of mass pmkg is attached to the beam at \(A\) and the beam remains in equilibrium in a horizontal position.
The beam is modelled as a uniform rod.
- Given that the tension in the rope attached at \(C\) is four times the tension in the rope attached at \(D\), use the model to find the exact value of \(p\).
The particle of mass \(p m \mathrm {~kg}\) at \(A\) is removed and replaced by a particle of mass \(q m \mathrm {~kg}\) at \(A\).
The beam remains in equilibrium in a horizontal position but is now on the point of tilting. - Using the model, find the exact value of \(q\)
- State how you have used the modelling assumption that the beam is uniform.