Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A triangular frame $ABC$ is formed by two uniform rigid rods, each of length $0.8\,\text{m}$ and weight $3\,\text{N}$, together with a longer uniform rod of weight $4\,\text{N}$. In the frame, $AB = BC$, and $\angle BAC = \angle BCA = 30\degree$.
(i)[3]
Calculate how far the centre of mass of the frame is from $AC$.
(ii)[3]
The vertex $A$ of the frame is connected to a smooth hinge at a fixed point. The frame is kept in equilibrium with $AC$ vertical by a vertical force of magnitude $F\,\text{N}$ 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.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Taking moments about AC gives: $d(3+3+4) = 3 \times 0.4\sin30 \times 2$” …