Edexcel M1 2015 June — Question 5

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2015
SessionJune
TopicMoments

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{de3245a7-cf6e-423e-8689-9a074bdbc23b-08_582_1230_271_374} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A beam \(A B\) has length 5 m and mass 25 kg . The beam is suspended in equilibrium in a horizontal position by two vertical ropes. One rope is attached to the beam at \(A\) and the other rope is attached to the point \(C\) on the beam where \(C B = 0.5 \mathrm {~m}\), as shown in Figure 3. A particle \(P\) of mass 60 kg is attached to the beam at \(B\) and the beam remains in equilibrium in a horizontal position. The beam is modelled as a uniform rod and the ropes are modelled as light strings.
  1. Find
    1. the tension in the rope attached to the beam at \(A\),
    2. the tension in the rope attached to the beam at \(C\). Particle \(P\) is removed and replaced by a particle \(Q\) of mass \(M \mathrm {~kg}\) at \(B\). Given that the beam remains in equilibrium in a horizontal position,
  2. find
    1. the greatest possible value of \(M\),
    2. the greatest possible tension in the rope attached to the beam at \(C\).