Potential Energy Formula
The gravitational potential energy formula PE = mgh calculates stored energy based on height.
Essential for energy conservation problems.
The Formula
Gravitational potential energy is the energy stored in an object due to its height above a reference point. The higher the object, the more potential energy it has.
Variables
| Symbol | Meaning |
|---|---|
| PE | Potential energy (measured in joules, J) |
| m | Mass of the object (measured in kilograms, kg) |
| g | Acceleration due to gravity (9.81 m/s² on Earth) |
| h | Height above the reference point (measured in meters, m) |
Example 1
A 5 kg book sits on a shelf 2.5 m above the floor. What is its potential energy?
Identify the values: m = 5 kg, g = 9.81 m/s², h = 2.5 m
Apply the formula: PE = mgh = 5 × 9.81 × 2.5
PE = 122.625 J (approximately 122.6 J)
Example 2
A roller coaster car has 294,300 J of potential energy at the top of a 30 m hill. What is the mass of the car?
Rearrange: m = PE / (gh)
m = 294,300 / (9.81 × 30) = 294,300 / 294.3
m = 1,000 kg
When to Use It
Use the potential energy formula when dealing with objects at height.
- Calculating stored energy before an object falls
- Energy conservation problems (PE converting to KE)
- Determining the height needed to achieve a certain energy
- Roller coasters, waterfalls, falling objects, and lifting problems