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# Archimede's principle, buoyancy and pressure

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A hollow metal cube made of aluminum has an outer-length of 12cm and an inner length of 8cm (each "side" of the outside of the cube is 12cm long, each "side" of the inside of the cube is 8cm long). The density of Al is 2,700 kg per cubic meter. The density of water is 1,000 kg per cubic meter.

If this empty, sealed cube is submerged under water, what is the buoyant force on the cube?

Explain and prove with calculations why this cube sinks or why this cube floats in water.

If this cube is filled with gold and thrown overboard in the Atlantic Ocean and it sinks to a depth of 160 meters, what gauge pressure would a diver have to withstand to recover the gold? Give your answer in multiples of the atmospheric pressure.

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This solution is provided in 576 words. It provides step-by-step solutions to each problem to calculate the buoyancy force and pressure.

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SOLUTION
known constants: Density of water DH20 = 1000 kg/m^3
Density of aluminum Dal = 2700 kg/m^3
Density of sea water Dsea = 1025 kg/m^3
Volume of whole cube Vcube = (.12 m)^3
Volume of inner space Vspace = (.08 m)^3
g = 9.8 m/sec^2 = 9.8 nt/kg
pressure: Po = 1 atm = 101000 nt/m^2
Part 1.
Step 1. In general, ...

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