Intermediate · 10 min
Gravitational potential energy
Track energy when an object rises or falls near Earth's surface.
Lifting stores energy
Near Earth's surface, a rise in height changes gravitational potential energy by ΔE = m × g × Δh. This approximation treats g as constant. The height change is vertical, even if the path is sloped. You choose a reference height for zero potential energy; changes in energy do not depend on that choice. Gravitational potential energy belongs to the interacting object–Earth system.
Worked example
A 3 kg object rises vertically by 2 m with g = 10 m/s². Potential energy increase = 3 × 10 × 2 = 60 J
Follow the energy transfer
If gravity is the only force doing work, a decrease in gravitational potential energy equals an increase in kinetic energy. For an object dropped from rest, m × g × h = ½ × m × v², giving v² = 2 × g × h. Mass cancels. Air resistance or other dissipative forces transfer some energy into internal energy, reducing the final speed compared with this ideal model.
Worked example
An object falls 1.8 m from rest with g = 10 m/s² and no air resistance. v² = 2 × 10 × 1.8 = 36; speed = 6 m/s
Compare two routes
- Calculate the potential energy gained by a 2 kg object lifted through 4 m with g = 10 m/s².
- Compare a vertical lift and a frictionless ramp ending at the same height. Explain why the potential energy changes are equal.