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Mechanics Formula

What is Gravitational Potential Energy?

Energy stored by an object raised in a gravitational field — the near-Earth approximation.

Formula: U = mgh

Plain-English Meaning

Lifting something gives it energy. Put a ball on a high shelf and it has more potential energy than on the floor. U = mgh: heavier things (bigger m), higher up (bigger h), in stronger gravity (bigger g) store more energy.

Mechanics questions usually become easier once you identify whether the problem is about force balance, kinematics, energy, or conservation.

Deeper Explanation

U = mgh is valid near Earth's surface where g ≈ constant. It's the first-order Taylor expansion of U = −GMm/r evaluated at r = R + h for h ≪ R. The reference height (h = 0) is arbitrary — only differences in U are physically meaningful.

Worked Example

Problem: A 2 kg book is lifted 1.5 m onto a shelf. How much gravitational PE is gained?

  • U = mgh
  • U = 2 × 9.8 × 1.5
  • U = 29.4 J

Result: ΔU = 29.4 J

At A Glance

Category: Mechanics

Levels covered: High School, College, Masters, PhD

Best use: Start with the formula meaning, then move to the worked example and quiz so the equation turns into a tool instead of a memorised line.