5.

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 4}
  \includegraphics[alt={},max width=\textwidth]{218383c1-0875-46f2-9416-8e827065a7a6-5_328_993_491_483}
\end{center}
\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 $D$.
\begin{enumerate}[label=(\alph*)]
\item 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,
\item 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
\item a new estimate for the weight of the log,
\item the value of $x$.
\item State how you have used the modeling assumption that the log is a rod.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2001 Q5 [13]}}