What is Potential Energy?
Potential energy is stored energy an object possesses due to its position, configuration, or state. Unlike kinetic energy, which is the energy of motion, potential energy is the energy of *position* or *potential*.
There are several types of potential energy (like elastic, chemical, and nuclear), but the most common in introductory physics is Gravitational Potential Energy (PE). This is the energy stored in an object based on its vertical position (height) within a gravitational field. The higher you lift an object, the more gravitational potential energy it gains.
The Potential Energy Formula (PE = mgh)
The formula for calculating gravitational potential energy is:
- PE: Potential Energy, measured in Joules (J).
- m: Mass of the object, measured in kilograms (kg).
- g: Acceleration due to gravity (on Earth, this is approximately 9.8 m/s²).
- h: Height of the object, measured in meters (m).
How PE Relates to Work and Force
Potential energy is directly related to the concept of work. The work done *against* gravity to lift an object is stored as potential energy.
Recall that `Work = Force × Distance`. The force required to lift an object is equal to its weight (Force of gravity, $F_g$), which is calculated as `Mass × Gravity` ($F_g = mg$). The distance you lift it is its change in height ($h$).
Therefore:
Work to lift = $Force_g \times height = (mg) \times h = mgh$
This shows that the work done on the object is exactly equal to the potential energy it gains. If you lift a 10 kg object 5 meters high, the work you do is `10 kg × 9.8 m/s² × 5 m = 490 J`, and the potential energy stored in the object is 490 J.
The Law of Conservation of Energy
The Law of Conservation of Energy is a fundamental principle stating that in an isolated system, energy cannot be created or destroyed, only transformed from one form to another. The relationship between potential and kinetic energy is the classic example.
Imagine a roller coaster car at the very top of its highest hill. It is moving slowly, so it has maximum potential energy (high $h$) and minimum kinetic energy. As it races down the hill, its height ($h$) decreases, causing its potential energy to be converted into kinetic energy. Its speed ($v$) increases, and at the bottom of the hill, it has minimum potential energy and maximum kinetic energy.
- Top of Hill: $Total Energy = PE_{max} + KE_{min}$
- Bottom of Hill: $Total Energy = PE_{min} + KE_{max}$
In a perfect system (with no friction or air resistance), the total energy remains constant. This principle allows engineers and scientists to predict the motion of objects, from satellites in orbit to pendulums. For more, the Wikipedia article on Potential Energy is a great resource.