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"What is the least amount work you must issue onto a silver ingot with a mass of 38 kg at 26 meters depth to bring it to the surface?"

I'm not sure how to do this one. Surely it depends on the volume of the ingot, right? Archimedes' principle says that the buoyancy of an object is its volume times the density of the fluid times the gravitational constant. We only have two of those, so I can't find the lifting force. This is how my formula looks like (Since the force is constant across all depths):

$F_L = $Lifting force

Force required $= mg - F_L$

Force required $= 38kg * g - (1000kg/m^3 * g * V)$

Work $=$ Force required * distance

Work $= 38kg * g - (1000kg/m^3 * g * V) * 26m$

Volume is still unknown, so how do I solve this one?

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They've told you what the ingot is made of. If the reason this matters is not obvious there is a hint in the Archimedes and bath story. – dmckee Apr 22 '13 at 19:54
I think you are correct, and you need to know the density of the silver. Either Google it or leave the density as a parameter in your answer. – John Rennie Apr 23 '13 at 10:34
up vote 0 down vote accepted

The problem states that it's silver. Therefore I can find the volume by multiplying the density of silver (look up) with the mass of the ingot.

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