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A salvage operation is underway to raise a sunken frigate of mass M from a depth H on theocean floor. This is to be accomplished by attaching a floatation device (an inflatable balloon in this case) to the frigate and filling it with air pumped down from the surface. The density of the ocean water can be assumed constant and equal to ?w and the average density of the materials of which the frigate is composed is ?f (>?w). The air in the balloon can be treated as an ideal gas(gas constant R) and is in good thermal contact with the ocean water at temperature T. The mass of the balloon is Mb and the volume of the materials from which it is made is Vmb. You may assume that even when fully inflated, the vertical dimension of the balloon is small compared to H, and that the air pressure equals the water pressure at the same depth. a) What is the volume of the balloon, Vb at the instant the frigate begins to rise from the ocean floor? You may neglect the gravitational forces on the gas in the balloon. b) Find an expression for the mass of air, Mair, that has been pumped into the balloon for the conditions in part a). (Hint: Ideal gas law is PV = mRT where m is the mass of an ideal gas) c) Will it be necessary to add air to the balloon as it rises, in order to bring the frigate to thesurface? Why or why not? Page
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