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 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.