A cube with 20-cm-long sides is sitting on the bottom of an aquarium in which the water is one meter deep. Find the hydrostatic force on (a) the top of the cube and (b) one of the sides of the cube.

a) 313.6N

b) 78.4 N

Step-by-step explanation:

The pressure in a fluid varies with depth.

a) Hydrostatic force on the top surface of the cube = Pressure on the top surface × Area of the top surface.

Pressure at that depth = ρgh

ρ = density of the fluid = 1000 kg/m³

g = acceleration due to gravity = 9.8 m/s²

h = depth of water at that top surface = (1 - edge length of the cube) = 1 - 0.2 = 0.8 m

Pressure at the depth = 1000 × 9.8 × 0.8 = 7840 Pa

Area of the top surface = (edge length)² = (0.2)² = 0.04 m²

Hydrostatic force on the top surface = 7840 × 0.04 = 313.6 N

b) Hydrostatic force on the side = (sum of pressure on the side × Area of the side)

Sum of pressure on the side = sum of pressure at each depth level of the side and is given by

P = ∫ ρg dh

Integrating from the depth at the top of the cube to its bottom, that is, from 0.8 to 1.0m

P = ρg (1 - 0.8) = 1000 × 9.8 × 0.2 = 1960 N

A = 0.04 m²

Hydrostatic force on the side = 1960 × 0.04 = 78.4 N

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