State of matter: Potential Energy - seperation graph

[Kurokari]

The graph should look something like this http://en.wikipedia.org/wiki/File:12-6-Lennard-Jones-Potential.svg (the other information has nothing to do with what I ask though, only the shape of the graph for clarity sake)

My question is, does resultant force = 0, or when potential energy is minimum occur during absolute zero only, if so then what is the kinetic energy? Is kinetic energy maximum, or simply zero since it is absolute zero.

If I'm wrong about U = 0 occurring at absolute zero only please correct me.

My second question is, why is it that potential energy is minimum when at equilibrium seperation? Why not kinetic energy is minimum since at equilibrium, attractive force = repulsive force and the 2 particle is not moving?

 

[technician]

At the equilibrium separation the resultant force on an atom = zero.
To INCREASE the separation work must be done against the attraction force between atoms... this means an increase in potential energy
To DECREASE the separation work must be done against the force of repulsion between atoms... this also means an increase in potential energy.
So the minimum of potential energy is when the resultant force between atoms = zero.
At temperatures above absolute zero atoms are vibrating... they have vibrational KE.
They are not moving around like molecules in a gs which have TRANSLATIONAL KE