Gravitational Potential Energy
Gravitational potential energy (GPE) is the energy stored in an object due to its height above a chosen reference level in a gravitational field. It increases with both the mass of the object and its height above the reference, and is fully convertible to kinetic energy as the object falls. GPE is fundamental to the analysis of projectiles, hydroelectric power generation, and the orbital mechanics of satellites.
Key Formula
U_g = m × g × h
LaTeX: U_g = mgh
| Symbol | Meaning | Unit |
|---|---|---|
| U_g | Gravitational potential energy | J (Joule) |
| m | Mass of the object | kg |
| g | Acceleration due to gravity (≈ 9.8 m/s² near Earth's surface) | m/s² |
| h | Height above the reference level | m |
Worked Example
Problem
A 2 kg book is placed on a shelf 1.5 m above the floor. Calculate its gravitational potential energy relative to the floor. (g = 9.8 m/s²)
Solution
Step 1 — Identify values: m = 2 kg, g = 9.8 m/s², h = 1.5 m. Step 2 — Apply the formula: U_g = mgh = 2 × 9.8 × 1.5 = 29.4 J.
Answer
The gravitational potential energy of the book is 29.4 J.
Gravitational potential energy for a 2 kg object at different heights (g = 9.8 m/s²)
| Height h (m) | GPE U_g (J) | Context | If Released — Speed at Ground (m/s) |
|---|---|---|---|
| 0 | 0.00 | Reference level (floor) | 0.0 |
| 1.0 | 19.60 | Typical shelf height | 4.4 |
| 1.5 | 29.40 | Shoulder height | 5.4 |
| 3.0 | 58.80 | Roof of a single storey | 7.7 |
| 10.0 | 196.00 | Three-storey building | 14.0 |
| 100.0 | 1960.00 | Cliff edge | 44.3 |
Interactive Tools
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Related Terms
Kinetic Energy
Kinetic energy is the energy possessed by an object due to its state of motion. It depends on both the mass of the object and the square of its speed, meaning that doubling the speed quadruples the kinetic energy. Kinetic energy is transferred to objects through work and is a key quantity in collision analysis, transport safety, and the work-energy theorem.
Conservation of Energy
The law of conservation of energy states that the total energy of an isolated system remains constant over time: energy can neither be created nor destroyed, only transformed from one form to another. In mechanical systems, this means the sum of kinetic energy and potential energy remains constant in the absence of non-conservative forces such as friction. This principle, one of the most fundamental in all of science, is derived mathematically from Noether's theorem as a consequence of the time-translation symmetry of physical laws.
"Gravitational" from Latin "gravitatio" (gravity), from "gravitas" (weight, heaviness), rooted in "gravis" (heavy). The modern quantitative treatment of GPE as mgh near Earth's surface follows from Newton's law of gravitation (1687) and the work-energy theorem formalised in the 19th century by James Prescott Joule and William Rankine.