Gravitational potential energy is energy stored because an object has position in a gravitational field. Near Earth’s surface, lifting an object higher increases the energy it can release if it falls. This idea matters in roller coasters, hydroelectric dams, sports, construction, and everyday lifting.
The amount of stored energy depends on the object’s mass, the strength of gravity, and the height measured from a chosen reference level.
For small height changes near Earth, gravitational potential energy is calculated with U = mgh. For large distances, such as planets, moons, or satellites, the more general formula is U = -GMm/r, where r is the distance from the center of the massive body. Potential energy can be converted into kinetic energy as an object falls, so a falling object speeds up while its gravitational potential energy decreases.
The zero level for potential energy is chosen for convenience, but changes in potential energy are what determine motion and energy transfer.
Key Facts
- Near Earth’s surface: U = mgh, where U is gravitational potential energy, m is mass, g is gravitational field strength, and h is height.
- The change in gravitational potential energy is ΔU = mgΔh for motion near Earth’s surface.
- The general gravitational potential energy formula is U = -GMm/r for two masses separated by distance r.
- Energy conservation during falling can be written as mgh = 1/2 mv^2 if air resistance is ignored and the object starts from rest.
- Gravitational field strength near Earth is approximately g = 9.8 m/s^2.
- The unit of gravitational potential energy is the joule, with 1 J = 1 kg m^2/s^2.
Vocabulary
- Gravitational potential energy
- Energy stored by an object because of its position in a gravitational field.
- Reference level
- The chosen height where gravitational potential energy is assigned a value of zero.
- Gravitational field strength
- The force of gravity per unit mass at a location, usually measured in newtons per kilogram.
- Kinetic energy
- Energy an object has because of its motion, calculated as K = 1/2 mv^2.
- Conservation of mechanical energy
- The principle that the total kinetic energy plus potential energy stays constant when only conservative forces do work.
Common Mistakes to Avoid
- Using height without choosing a reference level is wrong because h must be measured from the zero level you selected.
- Treating gravitational potential energy as always positive is wrong because the general formula U = -GMm/r uses zero energy at infinite separation.
- Forgetting units is wrong because mass must be in kilograms, height in meters, and energy in joules for U = mgh.
- Assuming all lost potential energy becomes kinetic energy is wrong when air resistance, friction, or other nonconservative forces remove mechanical energy.
Practice Questions
- 1 A 12 kg crate is lifted 3.5 m above the floor. Using g = 9.8 m/s^2 and the floor as the reference level, calculate its gravitational potential energy.
- 2 A 0.50 kg ball is dropped from rest from a height of 20 m. Ignoring air resistance, use mgh = 1/2 mv^2 to find its speed just before it reaches the ground.
- 3 Two shelves are 1 m and 3 m above the floor. A book sits on the higher shelf, but the reference level is changed from the floor to the lower shelf. Explain what happens to the book’s gravitational potential energy value and what does not change physically.