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 5.80 m long, 2.60 m wide, and 2.80 m high. As the crew pumps air into the balloon, its spherical shape increases and when the radius is 1.50 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.

Answer 1

57.885.8 kg weight of the container

Step-by-step explanation:

The volume of the balloon * density of water = buoyant force of balloon

volume of a sphere = 4/3 pi r^3

= 4/3 pi * (1.5)^3 = 14.14 m^3 <===balloon volume

Now, find the buoyant force on the container ALONE ....

5.8 * 2.6 * 2.8 * 1027 = 43 364 kg <===== buoyant force

Now add the buoyant force of the balloon to find the weight

43 364 + 14.14 * 1027 = 57885.8 kg