Finding Min. Potential Energy: Variation Calculus Method

[Gayle]

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.

 

[DEvens]

What direction does gravity point in?

 

[Gayle]

along negative y direction

 

[DEvens]

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.

 

[nasu]

That shape will be a thin layer spread on the surface. Unless you consider some material going in holes under the surface.

 

[Gayle]

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

 

[Gayle]

i am sorry i understood what u meant i will workout the problem and let u know the answer.
thanks for u help