What Is Potential Energy?
Potential energy is stored energy that an object has because of its position, arrangement, or state. A book on a shelf, a stretched rubber band, and the chemical bonds in food all contain potential energy waiting to be released and converted into motion, heat, or other forms.
Potential energy (PE) is the energy stored in an object due to its position or configuration. The most common form is gravitational potential energy: PE = mgh, where m is mass (kg), g is gravitational acceleration (9.81 m/s²), and h is height (m) above a reference point. When the object falls, PE converts to kinetic energy. Other types include elastic PE (springs), chemical PE (fuels), and electrical PE (charges).
Types of Potential Energy
Gravitational PE
Energy due to height in a gravitational field. PE = mgh. A 70 kg person on a 10 m diving board has 6,867 J of gravitational PE.
Elastic PE
Energy stored in a deformed elastic object. PE = ½kx². Springs, rubber bands, and bows all store elastic PE when stretched or compressed.
Chemical PE
Energy stored in chemical bonds. Released when bonds break (combustion, digestion, battery discharge). Gasoline: ~46 MJ/kg.
Electrical PE
Energy of charges in an electric field. PE = kq&sub1;q&sub2;/r. Capacitors and batteries store electrical PE.
Nuclear PE
Energy in atomic nuclei, bound by the strong force. Released in fission (splitting) or fusion (combining). E = mc² governs the conversion.
Gravitational (General)
For large distances: PE = −GMm/r. Negative because zero PE is at infinity. Used for orbits and escape velocity.
Worked Examples
Example 1 — Lifting a box
A 15 kg box is lifted 3 m onto a shelf:
PE = mgh = 15 × 9.81 × 3 = 441.5 J
Example 2 — Roller coaster
A 500 kg roller coaster car at the top of a 40 m hill:
PE = 500 × 9.81 × 40 = 196,200 J = 196.2 kJ
At the bottom (ignoring friction), all this converts to KE: v = √(2gh) = √(2 × 9.81 × 40) = 28 m/s (101 km/h).
Example 3 — How high can you throw?
A ball thrown upward at 20 m/s. At max height, all KE converts to PE:
½mv² = mgh → h = v²/(2g) = 400/19.62 = 20.4 m
🧮 Try It Yourself
Calculate PE with your own values — interactive and instant.
🚀 Gravitational PE 🚀 Elastic PEConservation of Energy
The total mechanical energy (KE + PE) of a system is conserved when only conservative forces (like gravity) act. This means:
- A pendulum swings: PE ↔ KE continuously, with total energy constant.
- A ball dropped from height h hits the ground at v = √(2gh).
- A roller coaster converts PE at the top to KE at the bottom and back.
Friction and air resistance are non-conservative — they convert mechanical energy to heat, so total mechanical energy decreases. But total energy (including heat) is always conserved.
Common Misconceptions
- "PE is always mgh." Only near Earth's surface where g is roughly constant. For satellites and planets, use PE = −GMm/r.
- "PE is stored in the object." PE is actually stored in the field or system. Gravitational PE belongs to the Earth-object system, not the object alone.
- "The reference point matters." Only changes in PE matter physically. You can set h = 0 wherever is convenient. The physics is the same.
The Hoover Dam stores about 2.5 billion kilowatt-hours of potential energy in Lake Mead. When water flows through the turbines, gravitational PE converts to electrical energy powering 1.3 million homes.
People Also Ask
Can potential energy be negative?
Yes, in the general gravitational formula PE = −GMm/r, potential energy is always negative (with zero at infinity). This reflects the fact that you need to add energy to escape the gravitational field. Near Earth's surface, PE = mgh can be negative if h is below your chosen reference point.
What is the relationship between force and potential energy?
Force is the negative gradient of potential energy: F = −dPE/dx. This means force points in the direction of decreasing PE. Gravity pulls objects downhill because that's the direction PE decreases.
What has more potential energy: a rock on a cliff or a rock on the ground?
The rock on the cliff has more gravitational PE (relative to the ground). When it falls, that PE converts to kinetic energy. The higher the cliff, the more PE and the faster the impact.
References and further reading
- Taylor, J. R. Classical Mechanics. University Science Books, 2005.
- Goldstein, H., Poole, C. & Safko, J. Classical Mechanics, 3rd ed. Addison-Wesley, 2002.