3
\includegraphics[max width=\textwidth, alt={}, center]{dd23f4a8-f7e7-4f80-bad6-7e9ec21565fc-2_828_476_1338_836} A door is modelled as a lamina \(A B C D E\) consisting of a uniform rectangular section \(A B D E\) of weight 60 N and a uniform semicircular section \(B C D\) of weight 10 N and radius \(40 \mathrm {~cm} . A B\) is 200 cm and \(A E\) is 80 cm . The door is freely hinged at \(F\) and \(G\), where \(G\) is 30 cm below \(B\) and \(F\) is 30 cm above \(A\) (see diagram).

1. Find the magnitudes and directions of the horizontal components of the forces on the door at each of \(F\) and \(G\).
2. Calculate the distance from \(A E\) to the centre of mass of the door.