Types of Potential Energy
Potential energy is stored energy due to position or configuration. The most common forms are gravitational (height) and elastic (stretched/compressed spring).
Gravitational PE
GPE = m × g × h
m = mass (kg)
g = 9.81 m/s² (Earth surface)
h = height above reference (m)
Example: 70 kg person on 10 m diving board:
GPE = 70 × 9.81 × 10 = 6,867 J ≈ 6.87 kJElastic PE
EPE = ½ × k × x²
k = spring constant (N/m)
x = compression/extension (m)
Spring: k=2000 N/m, compressed 0.1 m:
EPE = 0.5 × 2000 × 0.01 = 10 JEnergy Conservation
At top of fall (h=10m, v=0):
GPE = mgh, KE = 0
At bottom (h=0, v=?):
KE = ½mv² = GPE → v = √(2gh) = √(2×9.81×10) = 14 m/s
Energy conserved: GPE → KE (ignoring friction)Real-World Applications
- Hydroelectric dam: GPE of water → electrical energy
- Roller coaster: height converts to speed
- Bow and arrow: elastic PE → kinetic
- Pumped storage: electricity → GPE (water pumped uphill)
Calculate potential energy: Free Potential Energy Calculator
Gravitational Potential Energy Quick-Reference Table
| Object | Mass (kg) | Height (m) | GPE (J) |
|---|---|---|---|
| Book on desk | 1 | 0.75 | 7.36 |
| Person (70 kg) climbing stairs | 70 | 3 | 2,058 |
| Car lifted 1 m on jack | 1,500 | 1 | 14,715 |
| Water in dam (1,000 L) | 1,000 | 50 | 490,500 |
| Skydiver at 4,000 m | 80 | 4,000 | 3,136,000 |
How Gravitational Potential Energy Works
Gravitational potential energy (GPE = mgh) is stored energy due to an object's position in a gravitational field. On Earth, g ≈ 9.81 m/s². GPE is always measured relative to a chosen reference height — usually the ground or the lowest point of a system. The choice is arbitrary; only changes in GPE matter for energy calculations.
Hydroelectric dams convert GPE of elevated water into electrical energy. Pile drivers store GPE in a raised hammer and release it on impact. Counterweights in elevators use GPE to reduce the net energy needed to lift a cab. Understanding GPE is fundamental to any system where objects move vertically against gravity.
Common Mistakes
- Wrong reference level: Make sure the height h is measured from your chosen zero reference — usually the lowest point the object can reach.
- Using g = 10 instead of 9.81: Fine for rough estimates, but use 9.81 m/s² for accurate engineering or physics answers.
- Ignoring elastic potential energy: Stretched springs and compressed gas also store potential energy; GPE = mgh applies only to gravitational fields.
Frequently Asked Questions
As the object descends, GPE converts to kinetic energy (assuming negligible air resistance). At any point during free fall, the total mechanical energy (KE + GPE) remains constant — a direct consequence of conservation of energy.
Yes, in the sense that it can be converted to kinetic energy, heat, or work. GPE is a convenient accounting tool: it represents the work the gravitational force would do if the object were released and fell to the reference level.
Engineers ensure that the initial GPE (highest point) exceeds the sum of KE needed at the fastest sections plus energy lost to friction and air resistance. Every dip, loop, and hill is a precisely engineered exchange between GPE and KE.