## Conservative Forces

The basic

definitionof aconservative forceis that

A force is conservative if the work it does on a particle moving between any two points is idepedent of the path ae by the particle.

Furthermore, the work done by a conservative force exerted on a particle moveing through any closted path is zero.That means the work done by a conservative force as an object moves

fromAtoB is just the negative or opposite of the work done as an object movesfromBtoA.For a conservative force, we can always write a potential energy U. Then the work done by the conservative force is

W

_{c}= U_{i}- U_{f}or

W

_{c}= - U = - ( U_{f}- U_{i })We have already seen this with the force of gravity.

In talking about work done by a varying force, we also saw this for the elastic force of a spring. The force exerted

by a springis given byF = - k x

We found that the work done by a spring as it acts on an object that moves from initial position xi to final position xf is

W

_{s}= (^{1}/_{2}) k x_{i}^{2}- (^{1}/_{2}) k x_{f}^{2}If we define the

spring potential energybyU

_{s}= (^{1}/_{2}) k x^{2}then we can write

W

_{s}= U_{si}- U_{sf}W

_{s}= - U_{s}= - (U_{sf}- U_{si})The force of gravity and the force exerted by a spring are examples of

conservative forces.For any conservative force, we can write a Potential Energy and the work done by that conservative force is equal toW

_{g}= - U = - (U_{f}- U_{i})

(c) Doug Davis, 2001; all rights reserved