A lost shipping container is found resting on the ocean floor and completely sub

Question

A lost shipping container is found resting on the ocean floor and completely submerged. The container is 6.2 m long, 2.2 m wide, and 2.9 m high. Salvage experts attach a spherical balloon to the top of the container and inflate it with air pumped down from the surface. When the balloon's radius is 1.7 m, the shipping container just begins to rise toward the surface. What is the mass of the container? Ignore the mass of the balloon and the air within it. Do not neglect the buoyant force exerted on the shipping container by the water. The density of seawater is 1025 kg/m3.

Explanation / Answer

let buoyant force on balloon be B1

and buoyant force on container be B2

the container begins to move towards the surface when

B1 + B2 = Weight of container

let volume of ballon = V1 = (4 X 3.14 X R^3 )/3 = 20.57 m^3

Density of sea water = p = 1025 kg/m^3

B1 = volume of balloon immersed in water X p X g = V1 X p X g = 206616.5 N

volume of container = V2 = 6.2 X 2.2 X 2.9 = 42.108 m^3

B2= volume of container immersed in water X p X g = V2 X p Xg= 422974.86 N

weight of container = B1 + B2 = 206616.5 N + 422974.86 N = 629591.36

mass of cantainer X g = weight of container (g is acceleration due to gravity = 9.8 m/s^2)

mass of container = 629591.36/9.8 = 64244 kg

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