Edexcel Paper 3 2024 June — Question 6

Exam BoardEdexcel
ModulePaper 3 (Paper 3)
Year2024
SessionJune
TopicMoments

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{184043b7-1222-44fb-bc9f-3f484f72147b-16_458_798_258_630} \captionsetup{labelformat=empty} \caption{Figure 5}
\end{figure} Figure 5 shows a uniform rod \(A B\) of mass \(M\) and length \(2 a\).
  • the rod has its end \(A\) on rough horizontal ground
  • the rod rests in equilibrium against a small smooth fixed horizontal peg \(P\)
  • the point \(C\) on the rod, where \(A C = 1.5 a\), is the point of contact between the rod and the peg
  • the rod is at an angle \(\theta\) to the ground, where \(\tan \theta = \frac { 4 } { 3 }\)
The rod lies in a vertical plane perpendicular to the peg.
The magnitude of the normal reaction of the peg on the rod at \(C\) is \(S\).
  1. Show that \(S = \frac { 2 } { 5 } M g\) The coefficient of friction between the rod and the ground is \(\mu\).
    Given that the rod is in limiting equilibrium,
  2. find the value of \(\mu\).