8.3. Work-Energy Principle http://www.ck12.org
∆h=vf^2 −vi^2
2 gmultiplying both sides by $mg$, we find:
mg∆h=mg
vf^2 −vi^2(^2) g
=∆Ke[8]
In other words, the work performed on the object by gravity in this case ismg∆h. We refer to this quantity as
gravitational potential energy; here, we have derived it as a function of height. For most forces (exceptions are
friction, air resistance, and other forces that convert energy into heat), potential energy can be understood as the
ability to perform work.
Spring Force
A spring with spring constantka distance∆xfrom equilibrium experiences a restorative force equal to:
Fs=−k∆x[9]
This is a force that can change an object’s kinetic energy, and therefore do work. So, it has a potential energy
associated with it as well. This quantity is given by:
Es p=^12 k∆x^2 [10] Spring Potential Energy
The derivation of [10] is left to the reader. Hint: find the average force an object experiences while moving from
x=0 tox=∆xwhile attached to a spring. The net work is then this force times the displacement. Since this quantity
(work) must equal to the change in the object’s kinetic energy, it is also equal to the potential energy of the spring.
This derivation is very similar to the derivation of the kinematics equations — look those up.