The bathyscaphe Trieste is a diving vessel operated by the US Navy that took sci
ID: 1524019 • Letter: T
Question
The bathyscaphe Trieste is a diving vessel operated by the US Navy that took scientists to the deepest part of the ocean. It consists of a cylindrical steel hull with outer dimensions of 15.2 m long and 3.66 m in diameter. The walls of the hull are 13 cm thick. The hull is filled with gasoline (density 880 kg/m^3) to make the craft buoyant. When it is completely submerged in sea water (density 1025 kg/m^3) the craft is exactly balanced in the waterm, neither floating nor sinking.
a) What is the buoyant force on the craft?
b) What is the weight of the craft when the hull is empty and it is outside of the water?
Explanation / Answer
a)
volume hull, V = pi*r^2*h
= pi*(3.66/2)^2*15.2
= 160 m^3
buoynat force = weight of the water dispalced by the hull
= rho_water*V*g
= 1025*160*9.8
= 1.607*10^6 N <<<<<<<<<<-------------------Answer
b)
volume of gasoline = pi*(3.66/2 - 0.13)^2*15.2
= 138 m^3
mass of gasoline, m = density*volume
= 880*138
= 1.214*10^5 kg
weight of the gasoline = m*g
= 1.214*10^5*9.8
= 1.189*10^6 N
so, weight of the hull = Buoynat force - weight of gasoline
= 1.607*10^6 - 1.189*10^6
= 4.18*10^5 N <<<<<<<<<<-------------------Answer
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