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Physics LibreTexts

9: Conservative Forces

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A conservative force is a force with the property that the work done in moving a particle between two points is independent of the taken path.

  • 9.1: Introduction
    In Chapter 7 we dealt with forces on a particle that depend on the speed of the particle. In Chapter 8 we dealt with forces that depend on the time. In this chapter, we deal with forces that depend only on the position of a particle. Such forces are called conservative forces. While only conservative forces act, the sum of potential and kinetic energies is conserved.
  • 9.2: The Time and Energy Equation
    Consider a one-dimensional situation in which there is a force F(x)F(x) that depends on the one coordinate only and is therefore a conservative force.
  • 9.3: Virtual Work
    In the principle of virtual work, we imagine that we act upon the system in such a manner as to increase one of the coordinates. We ask ourselves how much work we have to do on the system in order to increase this coordinate by a small amount. If the system starts from equilibrium, this work will be very small, and, in the limit of an infinitesimally small displacement, this “virtual work” will be zero.
  • 9.E: Conservative Forces (Exercises)

Thumbnail: A direct consequence of the closed path test is that the work done by a conservative force on a particle moving between any two points does not depend on the path taken by the particle. (Public Domain; CompuChip).


This page titled 9: Conservative Forces is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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