Edexcel M1 2016 June — Question 4

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2016
SessionJune
TopicMoments

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{55024b00-68f0-4f8b-9b08-58479bb291fd-06_244_1168_264_388} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} 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.
  1. Find
    1. the magnitude of the force acting on the plank at \(A\),
    2. 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 .
  2. Find, in kg, the greatest integer mass of a diver who can stand on the board at \(B\) without breaking the support at \(A\).
  3. Explain how you have used the fact that the diver is modelled as a particle.