Work needed to flip cone upside down.

[bbhill]

Given the cone, z^2=x^2+y^2 z<= 1 filled with water, find the work needed to flip the cone upside down.



W = Fd



Well, I figured I could integrate the force along the distance (0,1) by multiplying the distance from 0 times the cross section circle area times the density. That would give me the force of the cone, but then I would need to find the distance each infinitesimally small cross section would have to be displaced to flip the cone and I've gotten lost there.

 

[Dick]

You'll find it a lot easier to use potential energy for this problem. Can you find the potential energy of the original cone and then the potential energy of the flipped cone?