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{excerpt}An interaction which produces a change in the energy of a system.{excerpt}

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h2. Motivation for Concept

It requires effort to alter the energy of an object, as can clearly be seen by attempting to impart [kinetic energy] by pushing a car which has stalled or to impart [gravitational potential energy|gravity] by lifting a heavy barbell.  We would like to quantify what we mean by "effort".  It is clear that force alone is not enough to impart energy.  Suppose that the car or the barbell is just too heavy to move.  Then, for all the pushing or pulling that is done (a considerable _force_), no _energy_ is imparted.  For the energy of a system to change, the system must alter its position or its configuration.  In effect, the force must impart or reduce motion of the object to which it is applied.  

h2. Mathematical Definition

h4.  Work-Kinetic Energy Theorem as Postulate

Suppose that we postulate the Work-Kinetic Energy Theorem for a [point particle] as the _defining_ relationship of work.  Doing so will allow us to find a mathematical definition of work in terms of [force].

{include:Work-Kinetic Energy Theorem}

h4. Definition of Work

By comparing the derivation of the theorem to its statement, we see that in order for the theorem to be satisfied, we must make the definition:

{latex}\begin{large}\[ W_{net} = \int_{path} \vec{F}_{net}\cdot d\vec{r}\]\end{large}{latex}

which leads us to define the work done by an individual force as:

{latex}\begin{large}\[ W = \int_{path}\vec{F}\cdot d\vec{r}\]\end{large}{latex}

h2. Importance of Path

h4. Conservative Forces

The form of our definition of work involves a path integral.  For some forces, however, the value of the path integral is determined solely by its endpoints.  These forces are, by definition, [conservative forces].  This path-independence is the property which allows us to define a [potential energy] to associate with the force.  Thus, the work done by conservative forces will usually be ignored, since their interaction is instead expressed as a contribution to the [mechanical energy] of the system.  The two commonly considered conservative forces in introductory mechanics are:

* [gravity]
* spring forces

h4. Non-Conservative Forces

Common forces in introductory physics whose effects are usually path _dependent_ are:

* [contact force] 
* [normal force]
* [friction] 
* [tension]

For these forces, the path of the system must be understood in order to compute the work.

h4. Example of Friction

To see the dependence of non-conservative work on path, consider a box moving along a rough, level surface.  Suppose the box is subject only to horizontal applied forces, gravity, normal force and kinetic friction as it moves.