Finding Min. Potential Energy: Variation Calculus Method

AI Thread Summary
The discussion revolves around finding a shape on Earth that minimizes potential energy using variation calculus. The initial assumption involved a function rotated around the Y-axis, but it was clarified that gravity points towards the center of mass, not strictly in the negative Y direction. Participants noted that the formula for potential energy needed reevaluation, especially considering the shape's distribution on the surface. There was also a concern about determining the center of mass without knowing the geometry of mass distribution. The conversation concluded with a commitment to revisit the problem for further clarification.
Gayle
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I was solving for a shape on Earth which has minimum potential energy. i used method of variation calculus.
I assumed a function f(x) and rotated it around Y axis. sorry for uploading the problem in word.
 

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What direction does gravity point in?
 
along negative y direction
 
Gayle said:
along negative y direction

I was hoping it would be enough of a hint for you.

Gravity points towards the centre of the mass, not in the y direction. So as you go along the surface the direction of gravity changes.

In other words, you have the wrong formula.

Also, check your formula for potential energy.
 
That shape will be a thin layer spread on the surface. Unless you consider some material going in holes under the surface.
 
Dear DEvens
i assumed a random curve so how to find the center of mass if i don't know in what geometry the mass is distributed
 
i am sorry i understood what u meant i will workout the problem and let u know the answer.
thanks for u help
 

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