CAIE M2 2005 June — Question 3

Exam BoardCAIE
ModuleM2 (Mechanics 2)
Year2005
SessionJune
TopicCentre of Mass 1

3 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6fe2c5e0-0496-4fb4-95d2-354b90607b5b-3_426_429_264_858} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} \(A B C D E F\) is the L -shaped cross-section of a uniform solid. This cross-section passes through the centre of mass of the solid and has dimensions as shown in Fig. 1.
  1. Find the distance of the centre of mass of the solid from the edge \(A B\) of the cross-section. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{6fe2c5e0-0496-4fb4-95d2-354b90607b5b-3_588_1020_1087_561} \captionsetup{labelformat=empty} \caption{Fig. 2}
    \end{figure} The solid rests in equilibrium with the face containing the edge \(A F\) of the cross-section in contact with a horizontal table. The weight of the solid is \(W\) N. A horizontal force of magnitude \(P\) N is applied to the solid at the point \(B\), in the direction of \(B C\) (see Fig. 2). The table is sufficiently rough to prevent sliding.
  2. Find \(P\) in terms of \(W\), given that the equilibrium of the solid is about to be broken.