8.1: Gravitational Potential Energy
Potential energy is not just a property of each object, but also a property of the interactions between objects in a chosen system. For each type of interaction present in a system, there is a corresponding type of potential energy. The total potential energy of the system is the sum of the potential energies of all the objects. Potential energy can be classified into two major categories: gravitational potential energy and elastic potential energy. The potential energy associated with a body's weight and height above the ground is called gravitational potential energy.
The gravitational force on each particle (or body) is simply its weight (mg) near the surface of Earth, acting towards the center of the earth. According to Newton's third law, each particle exerts a force of equal magnitude and opposite direction on Earth. In addition, Newton's second law tells us that the magnitude of the acceleration produced by each of these forces on Earth is (mg) divided by the Earth's mass. Since the ratio of any ordinary object's mass to the Earth's mass is vanishingly small, the motion of Earth can be completely neglected. Therefore, we consider this system to be a group of single-particle systems, subject to the uniform gravitational force of Earth. The work done on a body by Earth's uniform gravitational force near its surface depends on the mass of the body, the acceleration due to gravity, and the difference in height that the body traversed. This work is the negative of the difference in the gravitational potential energy.
This text is adapted from Openstax, University Physics Volume 1, Section 8.1: Potential Energy of a System.