Edexcel M2 2011 January — Question 5

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2011
SessionJanuary
TopicCentre of Mass 1

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c5760fa5-3c7f-4e29-87a2-b3b4145b9361-10_823_908_269_513} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} The uniform L-shaped lamina \(A B C D E F\), shown in Figure 2, has sides \(A B\) and \(F E\) parallel, and sides \(B C\) and \(E D\) parallel. The pairs of parallel sides are 9 cm apart. The points \(A , F\), \(D\) and \(C\) lie on a straight line.
\(A B = B C = 36 \mathrm {~cm} , F E = E D = 18 \mathrm {~cm} . \angle A B C = \angle F E D = 90 ^ { \circ }\), and \(\angle B C D = \angle E D F = \angle E F D = \angle B A C = 45 ^ { \circ }\).
  1. Find the distance of the centre of mass of the lamina from
    1. side \(A B\),
    2. side \(B C\). The lamina is freely suspended from \(A\) and hangs in equilibrium.
  2. Find, to the nearest degree, the size of the angle between \(A B\) and the vertical.