# Potential energy from force?

In my physics class, my teacher has been referring to Potential Energy in a 1D force field as the negative integral of the force with respect to position.

AKA:
$U(x)=-\int{F(x)dx}$
where U is the potential energy at x and F is the force at x.

Can someone please explain this to me in conceptual terms?

Last edited:

Simon Bridge
Homework Helper
Sure - look at the relationship between gravitational potential energy and gravitational force.
Note: the rule only applies to conservative forces.

Objects like to go from high potential energy to low potential energy ...
In Newtonian mechanics, we describe this by saying the object experiences a force.
By thinking about how the change in potential relates to the instantanious acceleration you shoud be able to spot the connection.

You can also think of it in terms of the work energy relation ... where the force changes with position.

UltrafastPED