6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{10b4d660-3980-4204-b18d-5240dea61a45-4_250_1036_1251_422}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{figure}
Figure 2 shows a bench of length 3 m being used in a gymnasium.
The bench rests horizontally on two identical supports which are 2.2 m apart and equidistant from the middle of the bench.
- Explain why it is reasonable to model the bench as a uniform rod.
When a gymnast of mass 55 kg stands on the bench 0.1 m from one end, the bench is on the point of tilting.
- Find the mass of the bench.
The first gymnast dismounts and a second gymnast of mass 33 kg steps onto the bench at a distance of 0.4 m from its centre.
- Show that the magnitudes of the reaction forces on the two supports are in the ratio \(5 : 3\).
(6 marks)