## Potential Energy

Gravity provides a nice example of work done by a force that can be considered Potential Energy. Potential Energy is sometimes written as PE or V. Most common is the notation of the text where Potential Energy is written as U. How much work does the force of gravity do on an object of mass m as the mass moves from initial height y

_{i}to final height y_{f}?W

_{g}= (F)_{g}s= (mg)s= ( - m gj) ( y_{f}- y_{i})j= - m g y_{f}+ m g y_{i}We

couldeven get carried away with this and write a more general form of the displacements,Let

s= ( x_{f}- x_{i})i+ ( y_{f}- y_{i})jThen the work done by gravity is

W _{g}= (mg)s= ( - m gj) [( x_{f}- x_{i})i+ ( y_{f}- y_{i})j] = - m g y_{f}+ m g y_{i}The

horizontalcomponent of the displacement doesnotmake and difference!In either case, we have

W _{g}= - m g y_{f}+ m g y_{i}This means we can

definethe gravitational potential energy asU _{g}= m g yand then we can write the work done by the force of gravity as

W _{g}= - ( U_{f}- U_{i})Notice the

orderof thesesubscripts,W _{g}= - U = - (U_{f}- U_{i})U -- the change in potential energy -- is the

finalvalue minus theinitialvalue.W _{g}= - U

ToCConservative ForcesReturn to ToC, Ch8, Conservation of Energy(c) Doug Davis, 2001; all rights reserved