Gravitational Potential Energy

Definition: Gravitational Potential Energy ( PE_g ) is given by:

PE_g = mgy, (3)

where m is the mass of an object, g is the acceleration due to gravity, and y is the distance the object is above some reference level.

The term ``energy'' is motivated by the fact that potential energy and kinetic energy are different aspects of the same thing (mechanical energy).

For Example: When an object is dropped from rest at some height above the earth's surface, it starts with some PE_g but no KE. As the object falls towards the Earth, it loses PE_g and gains KE. Just before the object hits the ground, it has lost all of its initial PE_g but gained an equal amount of KE.

Proof: Find the work done by the force of gravity when an object falls from rest at position y_i to y_f = 0 . We have W = Fs , F = |m$\vec{a}$| = mg and s = (y_i - y_f) = y_i . This gives, W = mgy_i .

Combining with Eq.(5.2) gives 1/2m(v_f² - 0) = mgy_i or PE_i = KE_f .