Any help would be appreciated thank you! A circular gate of diameter 2m is hinge

Question

Any help would be appreciated thank you!

A circular gate of diameter 2m is hinged along its horizontal diameter. The gate weighs 20kN. A force F is applied to keep the gate at equilibrium. The figure is not drawn to scale. Determine F. Determine the magnitude and direction of the force on the hinge. The circular gate is replaced by a square gate with a length 2m and width 2m (into the page). The cross-section is shown by the same figure, but the hinge is moved to another position such that F = 0. Determine where the gate should be installed if the gate is weightless? if the gate weighs 30kN?

Explanation / Answer

buoyancy force =ghA

where h =depth of center of mass

hence buoyancy force=B =g[0.3+(0.5+1)sin40]A

hence action of buoyancy force is 1/2-1/3 =0.167 from hinge

hence B*0.167 =F*1

hence F =0.167B

B is as calculated above

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