The gate AB below $($S$.$G$.=8\mathrm{.}0)$ is $0\mathrm{.}1$ m thick, $2$ m long $($from A to B$),$ and $10$ m wide into the

page. It is hinged at point A and has a stopper at point B that can hold back water up to a depth

of $4$m before it fails. What is the force provided by this stopper just before it fails, when water

depth is $4$m$?$ Assume that when water depth is $4$m$,$ the centroid of the gate is located $3\mathrm{.}1$ m

below the water surface. Account for the weight of the gate $($acting through the gate$$s centroid$),$

but assume the hinge is frictionless and negligibly small. Assume water density is constant and

static conditions apply