Potential Energy
The energy stored by lifting something up. Solve for the energy, the mass, the height or the gravity — on Earth or another planet — and see how fast it would land if you let go.
What is Potential Energy?
Gravitational potential energy is energy stored by lifting something against gravity. Let it fall and that energy turns into kinetic energy — without air resistance, every object dropped from the same height lands at the same speed, whatever its mass.
Only height differences matter: you can measure h from the floor, the table or sea level, as long as you measure it from where the object ends up. On the Moon the same lift stores only a sixth of the energy.
Live Graph
Eₚ ∝ hLifting 1 kg by 1 m
Ep = g × 1 kg × 1 m| Place | g (m/s²) | Energy | Landing speed from 1 m |
|---|---|---|---|
| Earth | 9.81 | 9.81 J | 4.43 m/s |
| Moon | 1.62 | 1.62 J | 1.80 m/s |
| Mars | 3.71 | 3.71 J | 2.72 m/s |
| Jupiter (cloud tops) | 24.79 | 24.79 J | 7.04 m/s |
Worked Techniques
All the potential energy turns into kinetic energy. The mass cancels, so a heavy and a light ball land at the same speed (ignoring air resistance).
The energy you gain going up, divided by the time it takes, is the power your legs deliver (on top of what your body wastes as heat).
Pumped-storage plants pump water uphill when power is cheap and let it run down through turbines later. 1 m³ of water has a mass of about 1000 kg.
Sources & Verification
- D. Halliday, R. Resnick & J. Walker, Fundamentals of Physics, 10th ed., Wiley, 2014 — Ch. 8 (Potential Energy and Conservation of Energy).