Edexcel M1 2024 June — Question 4

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2024
SessionJune
TopicMoments

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7a65555e-1bb2-4947-8e70-50f267017bfd-08_417_1745_378_258} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A non-uniform rod \(A B\) has length 6.5 m and mass 1.2 kg . The centre of mass of the rod is 3 m from \(A\). The rod rests on a horizontal step and overhangs the end of the step \(C\) by 1.5 m , as shown in Figure 2. The rod is perpendicular to the edge of the step.
A particle of mass 4 kg is placed on the rod at \(B\) and another particle, whose mass is \(M \mathrm {~kg}\), is placed on the rod at \(D\), where \(A D = 0.5 \mathrm {~m}\). The rod remains in equilibrium in a horizontal position.
  1. Find the smallest possible value of \(M\). The particle at \(B\) and the particle at \(D\) are now removed.
    A new particle is placed on the rod at the point \(E\), where \(E B = 0.9 \mathrm {~m}\).
    The rod remains in equilibrium in a horizontal position but is on the point of tilting about \(C\).
  2. Find the magnitude of the force acting on the rod at \(C\).