Difference between revisions of "Conservative force"

Revision as of 14:10, April 5, 2017

Conservative forces are those that possess certain properties:^[1]

The work it does on a particle is independent of its trajectory.
The work done on a particle that moves along a closed trajectory (where the initial and final positions are the same, or d_i = d_f) = 0) is zero.
The force can be written as the negative of the gradient of a potential energy function, i.e. $\text{[math]}$ .
The curl of the force, $\text{[math]}$ is zero, $\text{[math]}$

When the only forces present in a system are conservative, energy is conserved.

Examples of conservative forces include:

Friction is an example of a non-conservative force:

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 '''Conservative [[force]]s''' are those that possess certain properties:<ref>Serway and Beichner, ''Physics for Scientists and Engineers'', Fifth Edition</ref>
-# The [[work]] it does on a particle is independent of its [[trajectory]].
+* The [[work]] it does on a particle is independent of its [[trajectory]].
+* The work done on a particle that moves along a closed trajectory (where the initial and final positions are the same, or d<sub>i</sub> = d<sub>f</sub>) = 0) is zero.
-# The work done on a particle that moves along a closed trajectory (where the initial and final positions are the same, or d<sub>i</sub> = d<sub>f</sub>) = 0) is zero.
+* The force can be written as the negative of the gradient of a potential energy function, i.e. <math>\vec F = - \nabla U </math>.
+* The [[curl]] of the force, <math>\vec{F}</math> is zero, <math>\nabla \times \vec{F} = 0</math>
-# The force can be written as the negative of the gradient of a potential energy function, i.e. <math>\vec F = - \nabla U </math>.
-# The [[curl]] of the force, <math>\vec{F}</math> is zero, <math>\nabla \times \vec{F} = 0</math>
 When the only forces present in a system are conservative, [[energy]] is conserved.