Potential energy is stored energy — energy that a system has because of the arrangement or configuration of its parts, not because anything is currently moving. It's energy that's available to become kinetic the moment that configuration changes.
The word "potential" is doing real work here. A stretched spring potentially can accelerate something. A ball held high potentially can gain speed as it falls. The energy is real and present — it's just stored rather than expressed as motion.
Potential energy is a system property, not a property of a single object. This is one of the most important conceptual points in the unit and one students consistently miss.
Why does this matter? Because when you define your system in an energy problem, what you include determines what counts as internal PE and what counts as external work. Include Earth in your system → gravity is an internal conservative force → use PE. Exclude Earth → gravity is an external force → use work done by gravity.
Near Earth's surface, where g is approximately constant at 10 m/s², gravitational PE depends only on mass and height above a reference point:
Three quantities — mass m in kg, gravitational field strength g = 10 m/s² near Earth's surface, and height h in meters above whatever reference point you chose. The result is in Joules.
Note what's not in the formula: no velocity, no force, no time. Gravitational PE depends only on position — specifically on how high the object is. An object at the same height has the same U_g regardless of how it got there. This path-independence is exactly what makes gravity a conservative force.
Set mass and height above your reference point. Watch U_g = mgh update live.
A 4 kg book sits on a shelf 1.5 m above the floor. What is the gravitational PE of the book-Earth system? Then the book falls to a table 0.6 m above the floor. What is ΔU_g?
A compressed or stretched spring stores energy in its deformation. This elastic potential energy depends on the spring constant k and the displacement x from the spring's natural (equilibrium) length:
Because x is squared, U_s is always ≥ 0. A spring stretched 0.1 m stores exactly the same energy as one compressed 0.1 m. The energy is zero only at equilibrium (x = 0) and grows parabolically in both directions — exactly matching the K vs. v parabola from Lesson 3.1, just for stored energy instead of kinetic energy.
A spring with k = 400 N/m is compressed 0.12 m from its natural length. How much elastic PE is stored? If it's then compressed an additional 0.12 m (total 0.24 m), how does the stored PE compare?
The absolute value of gravitational PE depends on where you set your zero. But ΔU_g is always the same regardless of reference — because the reference cancels out in the subtraction.
This means you can always choose the reference that makes your calculation easiest. Common choices: the ground, the lowest point of motion, the initial position of the object, or any other convenient height. The physics doesn't care.
A 5 kg object moves from h = 2 m to h = 8 m (above actual ground). Drag the reference point — watch the absolute PE values change, but ΔU stays the same.
The individual U values shift as you move the reference — but ΔU is always 300 J. Physics only uses ΔU, so the reference choice never affects the answer.