Problem $3$d$.1$

The cross$-$section of a flood gate is shown. The quarter cylinder

gate $AB$ has a horizontal width of $6$ ft $($normal to the paper$)$ and

controls the flow of fresh water over the ledge at $B.$ The gate is

hinged about its upper edge A and rests on the frictionless ledge at

B$.$ Accounting for the $6$ ft cross$-$sectional width, the gate has a

weight of $481l\frac{b}{f}t$ along it's curved length.

Determine the minimum force $P$ required to keep the gate closed.

${}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=62\mathrm{.}43l\frac{b}{f}{t}^3$

Answer: $,P=10\mathrm{.}8$ kip