Suppose that a large cylindrical steel barrel (filled with something very heavy)

Question

Suppose that a large cylindrical steel barrel (filled with something very heavy) falls off the deck of a ship and sinks to the bottom of the ocean at a location where its depth is 805 km (one-half mile). Assume that seawater is incompressible, so that its density at the bottom of the ocean is the same as at the surface: 1030 kg/m^3. If the absolute pressure inside the barrel is 1.00 atm (it was sealed at sea level), and the total surface area of the barrel is 3.20 m^2, find the net inward force acting on the surface of the barrel when it reaches the bottom of the ocean. Show your work. Assume that the barrel's inner and outer surface areas are equal. (thought question: What do you think will happen to the barrel?)

Explanation / Answer

given that

Psurface = 1 atm = 101325 Pa

h = 0.805*10^3 m

density rho = 1030 kg/m^3

area A = 3.20 m^2

we know that

Ptotal = Psurface + rho*g*h

Ptot = 101325 + 1030*9.8*0.805*10^3

Ptot = 8226995 Pa

we also know that

Ptotal = Fnet / A

Fnet = Ptot * A = 8226995*3.20

Fnet = 26326384 N

Fnet = 26.32*10^6 N

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