### Potential Energy

Potential energy is energy that a system has because of how its parts are arranged, or energy that an object has because of where it is located. There are numerous types of potential energy, corresponding to various types of forces:

• Gravitational potential energy is the energy that an object or system has due to the force of gravity.

A system has gravitational potential energy if parts of the system have mass and are separated by a distance. The force of gravity enables parts of the system to do work on each other—that is, to exert forces that move each other for a distance.

The solar system has gravitational potential energy, because it consists of many parts with mass (the sun, planets, comets, asteroids, etc.) that are separated from each other by various distances. These parts have the potential to do work on each other, and work is in fact done whenever any two of them get closer together. (No work is done when the distance between the objects remains constant. For instance, the gravitational force between the earth and the moon isn’t doing any work, because the earth and moon aren’t getting closer together.)

An individual object with mass has gravitational potential energy relative to any other object with mass, provided the two objects are separated by a distance.

An apple hanging from a tree branch has gravitational potential energy relative to the earth, because it has mass and is located at a distance from the earth’s surface.

Suppose the apple has a mass of 0.2 kg, and is hanging 3 meters above the ground. What is its gravitational potential energy relative to the earth? First, we must determine the earth’s gravitational force on the apple—i.e., the apple’s weight. Gravitational acceleration near the earth’s surface is 9.8 m/s2, so we can calculate the weight of the apple using Newton’s second law:
force = mass × acceleration
force = 0.2 kg × 9.8 m/s2
force = 1.96 kg m/s2
force = 1.96 N
If the apple falls 3 meters to the ground, 1.96 newtons of force will be exerted for that distance. The earth’s gravity has the potential to do work on the apple:
work = force × distance
work = 1.96 N × 3 m
work = 5.88 N m
work = 5.88 J
Thus, the earth-and-apple system has the potential to do 5.88 joules of work. In other words, the gravitational potential energy of the apple (relative to the surface of the earth) is 5.88 J.

• Electromagnetic potential energy is the energy that an object or system has due to electromagnetic forces.

A system has electromagnetic potential energy if parts of the system have charge or are magnetized (and therefore exert forces that could do work on each other).

Individual objects have electromagnetic potential energy if they have charge and are located in an electric field, or if they are magnetized and are located in a magnetic field.

• Chemical potential energy is the energy that a system has because of its chemical composition. Chemical potential energy is really just a special type of electromagnetic potential energy, since the energy released in chemical reactions comes from electromagnetic forces, as we’ll see in chapter 4.
• Elastic potential energy is the energy that elastic (“stretchy”) objects have when they are stretched or compressed. For example, a stretched rubber band has the ability to exert force for a distance. The forces exerted by stretched rubber bands, compressed springs, etc., are due to the electromagnetic forces acting between atoms or molecules; so elastic potential energy is just another type of electromagnetic potential energy.
• Nuclear potential energy is the energy that a system has due to the nuclear strong force (a fundamental force which will be introduced in chapter 5).