A small barge with a draft D = 0.5 m and a wetted beam of b = 2m and a length L = 10 m (into the page) needs bracing in the deck (BC) to keep the hull from being crushed when loaded. The profile of the right side of the hull between A and B follows the curve y = D*(x/b)^3 with the origin taken to be at the bottom of the hull centerline at point A, as shown in the gure. For the purpose of the a conservative estimate, assume the halves of the hull have no bending resistance about centerline, that is it is free to pivot about the point A. Assume the hull has no mass, and the load of the cargo acts only through point A. Take the density of water to be 1030 kg/m3.

a) Calculate the total vertical component of the hydrostatics force on the hull due to the water (this is equivalent to the displacement of the barge).

b) Calculate the total horizontal component of the hydrostatic force acting on the right half of the hull.

c) Locate the point of action of the total hydrostatic force acting on the right half of the hull (or equivalently, the location of the vertical and horizontal components of the hydrostatic force).