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Raising a yacht by attaching filled air bags to it

A large yacht has a mass of 305 tonnes. The yacht sinks and is lying on the sea bed at a depth of 40m. It is estimated that the volume of teh yacht is such that it displaces 0.8m3 of water when it is totally submerged under water.

A salvage team decides to raise the yacht to the surface by fixing large bags to the yacht and filling the bags with air. The total mass of the empty bags is 100kg.

Determine

A) The volume that the air filled bags will need to be so that the yacht and bags system is exactly balanced, (it doesn't rise to the surface, but doesn't sink back to the sea bed)

b) The number of moles of air needed to fill the bags to the required volume.

Data: temperature of sea water is 10 degrees celcius
Density of sea water is 1030 kg/m3
Universal gas constant = 8.31 j/mol K

ATMOSPHERIC PRESSURE AT THE SURFACE OF THE SEA = 1.013 X 10 to the power of 5 N/m2

(assume the mass of air is negligible. also assume that teh volume of the empty bags with no air in is negligible.)

Solution Preview

A.)
mass o f yacht = 305 tonnes = 305000 kg
volume of yacht = 0.8 m^3
let the volume of bags = V m^3
therefore,
volume of the water displaced by bags+yacht = V + 0.8 m^3
mass of the water displaced by bags + yacht ...

Solution Summary

The solution provides good explanations, formulas and calculations to arrive at the answers.

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