Archemides principle/ Center of buoyancy

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Homework Statement


One way of moving a large undersea rock or mooring is to fasten a closed, empty oil drum to the rock while at low tide. As the tide comes in the drum is drawn down into the water increasing the buoyant foce acting on the system of the rock and drum. Suppose a cylindrical drum of radius 25 cm, length 100cm, and mass 20kg is used. What is the maximum mass of a rock (of density 5.0 x10^3) that the drum can lift from the bottom? Assume the density of sea water is the same as that of pure water.

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Homework Equations



PfVs=PoVo

The Attempt at a Solution


So to solve this I am trying to use archimedes principle which is the density of a fluid times the volume submerged=the density of the system times the volume of the system (PfVs=PoVo). I know That Pf=1000kg/m^3 because its pure water and I know that the Po is approx 102.4 because i can use m=PV to find the density of the drum and add it to the density of the rock. I also know that the volume of the system is Vdrum+Vrock.

I end up with the formula 1000kg/m^3*Vsubmerged=102.04(0.196+(Mrock/5.0x10^3) where 0.196 is the volume of the drum and 5.0x10^3 is the density of the rock.

Rearranged I get that Mrock=(1000kg/m^3-20.04/102.04)*5.0x10^3

What do i need to do to find the volume of the submerged?
 
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Discussion

First find the max lift from the drum = volume of drum x density... minus weight of drum

This is the weight of the rock (WHEN IN WATER) that can be lifted ...from this calculate weight of rock in AIr... and from this mass of rock
 
Whoops, it looks like I calculated the volume of the drum wrong. It's actually 19.63
 
oz93666 said:
First find the max lift from the drum = volume of drum x density... minus weight of drum

This is the weight of the rock (WHEN IN WATER) that can be lifted ...from this calculate weight of rock in AIr... and from this mass of rock
When i take the volume of drum x density... minus weight of drum i end up getting -176.2, would that be right? I don't see how it would be a negative number