Answer:
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
