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 5.6 m long, 2.4 m wide, and 2.3 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 1.2 m, the shipping container just begins to rise towards 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

The mass of the container must be the mass of the water displaced by the container itself *plus* the mass of the water displaced by the balloon

Just determine the total volume of water being displaced by the two objects, determine the mass of the water, and that gives you the mass of the container.

V (container) = 5.6 x 2.4 x 2.3 = 30.912 m^3
V(balloon) = (4/3)* pi*(1.2)^3 = 7.238 m^3

Total Vol = 38.15 m^3

Mass = 38.15 m^3 * (1025 kg/m^3) = 39103.98 kg.

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