User:Ilyaskhan451

Gravitational Potential Energy

Let's study an example of an apple to see what's gravitational potential energy. When an apple falls out of a tree, it accelerates towards the earth. In other words, it gains kinetic energy. From the law of conservation of energy, the gain in one form of energy must be accompanied with the loss of energy in another form. We say that the "Gravitational potential energy" of an apple is being converted to its kinetic energy as it falls.

The gravitational potential energy of a mass, m at a distance r from another mass M is defined as the work done by the external force in moving m from r to infinity. (I'm sure you'll have a better idea of what I'm telling by seeing the figure below.)

figure By team C007571, ThinkQuest 2000.

In the figure, the gravitational force and the external force are equal in magnitude and opposite in direction. By defining the gravitational potential energy at ground level as zero, we now derive a equation for calculating gravitational potential energy.

F_grav = -GMm/r^2

(The minus sign indicates that the force is always attractive.)

F_ext = GMm/r^2

The work done by the external force in moving the mass m from r to infinity is given by the equation:

work done by external force: GMm/r

Thus by definition,

Gravitational potential energy: GMm/r