8.1:
Gravitational Potential Energy
The gravitational potential energy is the energy stored in an object due to its position in the gravitational field.
Mathematically, it is defined as the product of an object’s weight and height above the ground.
Thus, the gravitational potential energy of a ball of mass m hanging at a height y from the ground is mgy.
For example, in ice hockey, if a puck of mass m takes a parabolic path after the shot, then the gravitational potential energy at point B is mgy, where y is the height of the puck from the ground.
When the puck moves from point A to B, the change in gravitational potential energy is positive as the gravitational potential energy increases and is equal to the negative of the work done.
Similarly, when the puck moves from point B to C, the gravitational potential energy decreases, and the work done by the gravitational force is positive.
Thus, when a body moves upwards, the gravitational potential energy increases and decreases when the body moves downwards.
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.