Energy · 03 / 05

Potential Energy

Potential energy is stored in the configuration of an interacting system. Its zero is a reference choice; changes in potential energy are what connect physical states.

The learner question

If the zero level is arbitrary, what part of gravitational potential energy is physically meaningful?

Changing the reference shifts every potential-energy value by the same amount. The difference between two states stays unchanged.

Near Earth's surface

U_g = mgh

\Delta U_g = mg\Delta h

Reference-level lab

initial · 2.0 m

final · 6.0 m

chosen U = 0 at 0.0 m

initial U

39.2 J

final U

117.6 J

change ΔU

78.4 J

Mass2.0 kg

Initial height2.0 m

Final height6.0 m

Zero reference0.0 m

System, not object

Gravitational potential energy belongs to the Earth-object system. Elastic potential energy belongs to the spring-object system. The configuration of interacting parts is what matters.

Invariant difference

Move the zero reference. Both absolute values shift, but $\Delta U$ stays the same because the same reference offset appears in both states and cancels.

Other stores

Potential energy is broader than height. Springs, electric charges, chemical bonds, and many other interactions can store energy in configuration.

Transfer check

You raise the zero reference by 3 m without moving the object. What happens?

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