In the process of loading a ship, a shipping container gets dropped into the wat

Question

In the process of loading a ship, a shipping container gets dropped into the water and sinks to the bottom of the harbor. Salvage experts plan to recover the container by attaching a spherical balloon to the container and inflating it with air pumped down from the surface. The dimensions of the container are 5.00 m long, 2.35 m wide, and 3.60 m high. As the crew pumps air into the balloon, its spherical shape increases and when the radius is 1.20 m, the shipping container just begins to rise toward the surface. Determine the mass of the container. You may ignore the weight of the balloon and the air in the balloon. The density of seawater is 1027 kg/m3.

Explanation / Answer

Let the mass of the container be m.

When the container just begins to rise, the combined buoyant force on the container and balloon balances the weight of the container.

mg = (Vc + Vb)wg

=> m = (Vc + 4R3/3)w

=> m = [(5.20 * 2.35 * 3) + (4 * 1.33 / 3)] * 1027

=> m = 47101 kg

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