A glass cube is immersed in water; its lower edge is 15 cm from the water surface. a) determine the force

A glass cube is immersed in water; its lower edge is 15 cm from the water surface. a) determine the force of water pressure on the lower and upper edges of the cube. b) calculate the resultant of these forces, i.e. buoyancy c) make sure that the Archimedes force is equal to the weight of the displaced liquid

We denote by a – the edge of the cube, then:
1) The pressure on the lower surface is: p1 = ρ * g * h, where ρ is the density of the liquid, g is the acceleration of gravity, h is the depth.
Upper pressure: p2 = ρ * g (h-a)
2) p1-p2 = ρ * g * h-ρ * g (h-a) = ρ * g * a
3) The volume of the cube is v = a ^ 3, then the Archimedes force: Fa = ρ * a ^ 3 * g.
On the other hand, F = S * p = a ^ 2 * ρ * g * a = ρ * a ^ 3 * g.