5.
\begin{figure}[h]
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\caption{Figure 4}
\includegraphics[alt={},max width=\textwidth]{218383c1-0875-46f2-9416-8e827065a7a6-5_328_993_491_483}
\end{figure}
A large \(\log A B\) is 6 m long. It rests in a horizontal position on two smooth supports \(C\) and \(D\), where \(A C = 1 \mathrm {~m}\) and \(B D = 1 \mathrm {~m}\), as shown in Figure 4. David needs an estimate of the weight of the log, but the log is too heavy to lift off both supports. When David applies a force of magnitude 1500 N vertically upwards to the \(\log\) at \(A\), the \(\log\) is about to tilt about \(D\).
- State the value of the reaction on the \(\log\) at \(C\) for this case.
David initially models the log as uniform rod. Using this model,
- estimate the weight of the log
The shape of the log convinces David that his initial modelling assumption is too simple. He removes the force at \(A\) and applies a force acting vertically upwards at \(B\). He finds that the log is about to tilt about \(C\) when this force has magnitude 1000 N. David now models the log as a non-uniform rod, with the distance of the centre of mass of the \(\log\) from \(C\) as \(x\) metres. Using this model, find
- a new estimate for the weight of the log,
- the value of \(x\).
- State how you have used the modeling assumption that the log is a rod.