A system of two or more objects has potential energy only if those objects interact exclusively through conservative forces. Potential energy is a scalar quantity associated with the position of objects within a system. Where U = 0 is defined is a decision made by the observer to simplify the analysis — it never affects a physical prediction.
A 1 kg block is attached to a horizontal spring (k = 100 N/m) and oscillates back and forth on a frictionless table. A second, identical 1 kg block instead slides across a rough tabletop and gradually slows down due to friction. (a) Does the block–spring system have potential energy? (b) Does the block–and–rough–table system have potential energy? (c) What's the key difference between the two?
Try it on paper first, then reveal each step to check your work.