(Force on plane surface) The rectangular gate CD of the figure below is 1.7 m wide and 2.0 m long. Assuming the material of the gate to be homogeneous and neglecting friction at the hinge C, determine the weight of the gate necessary to keep it shut until the water level rises to 2.2 m above the hinge. Water 2.2 m 2.0 m Hinge W = i kN

. A buoy is a solid cylinder 0.30 m in diameter and 1.20 m long. It is made of material with a specific weight of 7.90 kN/m³. If it floats upright, how much of its length is above the water. Answer: H = Water y = 9806.6 N/m³ H d = 0.3m L = 1.2 m

Rectangle Gate AB has length L and width b into the paper is hinged at B and has negligible weight. The liquid level, water, h does not reach the top of the gate for an angle theta. Find an equation for the force P, required to keep the gate in equilibrium. Solve for width, b. In the figure. (hint: draw a free-body diagram for the left and right side of the gate separately)

Determine the force P necessary to just keep the 2 m-wide gate closed. Ignore the weight of the gate. Specific weight of water = 9.81 kN/m³