$(35$ pts $)$ The tank shown below is open to the atmosphere. The tank has a $\frac{1}{4}-$ circular $($curved$)$ gate with pivot $($or hinge$)$ as shown. The gate is $1$ meter in width into the page. When the depth of the water in the tank is $4$ meters deep as shown, the gate is just about to open, thus the force of the ground on the gate is zero