You apply a force on an object for a certain distance. Since $$ F=-\frac{dU}{dx} $$ , does there exist a potential energy graph as a function of distance along the route for your erratic path?

Question

experimentx · Answer

$$ F = -\nabla U$$
probably you mean 
$$ F= - {dU \over dx}$$ for conservtive force in 1D

anonymous · Answer

Yes, of course, sorry, I wasn't thinking

anonymous · Answer

So for my obviously nonconservative force, the equation wouldn't hold and the answer is no?

anonymous · Answer

Although, surely, loosely speaking, potential energy is the possibility of getting a free meal by means of being accelerated, by merit of your position (x), so my force must have some sort of potential energy. Or will the potential energy here|dw:1348686047732:dw|be infinite?