$(30$ pts $)$ Consider the gate shown below. The black stopper prevents the gate from ever

opening to the right. Weight can be added to the top horizontal portion of the gate to open it

to the left, shown as W$.$ Determine the weight W that would alleviate all resultant forces

from the stopper while also keeping the gate closed. The gate is $2$ m wide. Consider the

cross$-$section of the gate exposed to water to be rectangle and the water at $20\backslash$deg C$.$

rsin$\backslash$theta $($I$\_($xy$))/($P$\_($cg$)$A$)$

The L$-$shaped gate is hinged at a point A$.$