A submarine uses tanks that can be filled with air so that the submarine can hav

Question

A submarine uses tanks that can be filled with air so that the submarine can have “neutral buoyancy.” This means that its average density is equal to the density of the water, so that it will stay (i.e., float) at a desired level underwater. The density of water changes a small amount with depth in the ocean, due to the changes in pressure and temperature. How much additional mass must a submarine take on to sit at the ocean bottom at a depth of 560 m?

At this depth the density of water is about 0.32% larger than at atmospheric pressure. Assume that the volume of the submarine is 3.4 x104 m3 and that it is initially floating at the surface.

Explanation / Answer

Volume of the submarine V = 3.4*104 m3 Density of water = 1000 kg/m3 Density at a depth ' = 1000 kg/m3 + 1000 kg/m3 (0.0032)                                  = 1003.2 kg/m3 ---------------------------------------------------------------------------------- By applying Newton's laws                mg + m'g = V'g Therefore the extra mass is                m'g = V'g - mg                       = V'g - Vg                   m'= V ('-)                       = (3.4*104 m3 )[1003.2 kg/m3 - 1000kg/m3 ]                       = 1.088*105 kg ---------------------------------------------------------------------------------- By applying Newton's laws                mg + m'g = V'g Therefore the extra mass is                m'g = V'g - mg                       = V'g - Vg                   m'= V ('-)                       = (3.4*104 m3 )[1003.2 kg/m3 - 1000kg/m3 ]                       = 1.088*105 kg

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