3 A triangular frame \(A B C\) consists of two uniform rigid rods each of length 0.8 m and weight 3 N , and a longer uniform rod of weight 4 N . The triangular frame has \(A B = B C\), and angle \(B A C =\) angle \(B C A = 30 ^ { \circ }\).
- Calculate the distance of the centre of mass of the frame from \(A C\).
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The vertex \(A\) of the frame is attached to a smooth hinge at a fixed point. The frame is held in equilibrium with \(A C\) vertical by a vertical force of magnitude \(F \mathrm {~N}\) applied to the frame at \(B\) (see diagram). - Calculate \(F\), and state the magnitude and direction of the force acting on the frame at the hinge.