# Homework Help: Potential energy

1. Apr 15, 2012

### Jalo

1. The problem statement, all variables and given/known data

Consider the force F=(y2z3 − 6xz2)i + 2xyz3j + (3xy2z2 − 6x2z)k.

I've solved the first part of the problem that asked if the force was conservative (it was) and what was the potential energy of the force(U)

U=-y2z3+3x2z2+c , c E ℝ

Find the balance points.
2. Relevant equations

3. The attempt at a solution

I know the balance points are gotten trough derivation of U and equalating it to 0. However I don't know what should i use to derivate it with. ∂U/∂x + ∂U/∂y = 0 ? Doesn't help me much... Help would be appreciated.
Thanks

2. Apr 15, 2012

### billVancouver

Hi Jalo,

I find it a bit unclear what 'balance points' refer to here - my only guess is potential minima, which will have to be in all three dimensions at once (not just x and y like you guessed). Consider the gradient of the potential function and see if that leads you anywhere,

Hope this helps,
Bill Mills

Last edited by a moderator: Apr 16, 2012