A cube with the side length 1.53 meters of solid styrofoam is completely submerg

Question

A cube with the side length 1.53 meters of solid styrofoam is completely submerged in fresh water such that the top of the styrofoam block is parallel to the water surface and is 2.55 meters beneath the surface. The density of styrofoam varies but youhave determined that this block has density of 105 kg/m^3 and also know the density of freshwater is 1000kg/m^3.

1. what is the buoyant force acting upon the styrofoam block?

2. what is the total pressure on the top of the block due to water pressure?

3. what is the total pressure on the bottom of the block due to water pressure?

4. what is the total force acting on top of the block due to water pressure?

5.what is the total force acting on bottom of the block due to water pressure?

6. what is the total force acting on the block due to the water pressure only?

Explain, show steps and answer all questions correctly to recieve full points

Explanation / Answer

a)volume of water displaced by block = volume of cube = 1.53^3 = 3.581 m^3

buoyant force = rho*v*g = 3,581*1000*9.8 = 35099.45 N

b)on top water pressure = rho*g*h = 2.55*9.8*1000 = 24990 pa

c)total pressure on bottom due to water pressure = rho*g*h = 1000*9.8*(2.55+1.53) = 39984 Pa

d)total force acting on the top of the block (due to water pressure) = pressure*area = 24990*1.53^2 = 58499.09 N

e) total force acting on the bottom of the block (due to water pressure) = pressure*area = 39984*1.53^2 = 93598.54 N

f)total force acting on the block (due to water pressure) = pressure difference*area =

(39984-24990)*1.53^2 = 35099.45 N

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