Problem: A gate in a small dam on a farm pond is opened periodically to clean out sediment. The gate is 1.1 x 1.4 m, and its upper edge is 2.3 m below the water level. A hinge (piano hinge) extends along the entire top edge of the gate. Find the
Solution: a) Taking the origin at the top of the gate, and considering a differential element at a constant depth y on the gate (see the drawing of the gate below),
the force acting on the element of area is
b) To find the torque, we cannot simply take this force and multiply by a moment arm, since the force varies across the face of the gate. Rather, I must take the differential torque caused by each differential force; each dF has as its moment arm the distance y:
