A 200-lb homogeneous gate \(10 \mathrm{ft}\) wide and \(5 \mathrm{ft}\) long is hinged at point \(A\) and held in place by a 12 -ft-long brace as shown in Fig. P2.105. As the bottom of the brace is moved to the right, the water level remains at the top of the gate. The line of action of the force that the brace exerts on the gate is along the brace.

(a) Plot the magnitude of the force exerted on the gate by the brace as a function of the angle of the gate, \(\theta\), for \(0 \leq \theta \leq 90^{\circ}\).

(b) Repeat the calculations for the case in which the weight of the gate is negligible. Comment on the result as \(\theta \rightarrow 0\).

Figure P2.105

12 ft Moveable stop 5 ft Gate Water Brace A