4.
\begin{figure}[h]
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\caption{Figure 1}
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A diving board \(A B\) consists of a wooden plank of length 4 m and mass 30 kg . The plank is held at rest in a horizontal position by two supports at the points \(A\) and \(C\), where \(A C = 0.6 \mathrm {~m}\), as shown in Figure 1. The force on the plank at \(A\) acts vertically downwards and the force on the plank at \(C\) acts vertically upwards.
A diver of mass 50 kg is standing on the board at the end \(B\). The diver is modelled as a particle and the plank is modelled as a uniform rod. The plank is in equilibrium.
- Find
- the magnitude of the force acting on the plank at \(A\),
- the magnitude of the force acting on the plank at \(C\).
The support at \(A\) will break if subjected to a force whose magnitude is greater than 5000 N .
- Find, in kg, the greatest integer mass of a diver who can stand on the board at \(B\) without breaking the support at \(A\).
- Explain how you have used the fact that the diver is modelled as a particle.