A flat rectangular plate is submerged horizontally in water to a depth of 3.6 ft. If the top surface of the plate has an area of 30 ft², and the liquid in which it is submerged is water, find the force on the top of the plate. Neglect the effect of the atmosphere above the liquid. (The density of water is 62.2 lb/ft³.) A) 108 lb B) 22,392 lb C) 1,866 lb D) 6,717.6 lb E) 671.76 lb

Question

Quizplus · Accepted Answer

The force on the top of the plate is the weight of the water above it. The volume of water displaced is the same as the volume of the plate submerged, which is given by

Volume = (depth submerged) x (area of plate)

Volume = 3.6 ft x 30 ft² = 108 ft³

The weight of this volume of water is given by

Weight = (density of water) x (volume of water) 
Weight = 62.2 lb/ft³ x 108 ft³ = 6717.6 lb

Therefore, the force on the top of the plate is 6,717.6 pounds.

A Flat Rectangular Plate Is Submerged Horizontally in Water to a Depth