Edexcel M2 — Question 5

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
TopicCentre of Mass 1

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f0e751be-f095-4a56-8ee9-8433cc4873e9-3_591_609_785_623} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} Figure 2 shows a uniform plane lamina \(A B C D E G\) in the shape of a letter ' \(L\) ' consisting of a rectangle \(A B F G\) joined to another rectangle \(C D E F\). The sides \(A B\) and \(D E\) are both 8 cm long and the sides \(E G\) and \(G A\) are of length 24 cm and 32 cm respectively.
  1. Show that the centre of mass of the lamina lies on the line \(B F\).
  2. Find the distance of the centre of mass from the line \(A B\). The uniform lamina in Figure 2 is a model of the letter ' \(L\) ' in a sign above a shop. The letter is normally suspended from a wall at \(A\) and \(B\) so that \(A B\) is horizontal but the fixing at \(B\) has broken and the letter hangs in equilibrium from the point \(A\).
  3. Find, in degrees to one decimal place, the acute angle \(A G\) makes with the vertical.