Problem $3$

Water $)=(1000\frac{kg}{m^3}$ is held in the rectangular container shown below by a triangular trapdoor $($i$.$e$.,$ a gate$),$ shown in green below. The gate is hinged along the right side. The hinge is shown in red below. Panel a shows the gate being held closed by a force, $F,$ applied to the bottom of the gate, perpendicular to the gate, at the corner farthest from the hinge. Panel $b$ shows the gate in an

a

b

open position. The box has a square crosssection in the horizontal plane with dimensions $a=b=2m.$ The water depth in the box is $c=3m.$ Determine the force, $F,$ required to hold the gate shut as shown in panel a$.$