Difference between revisions of "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> | '''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 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> | |
| − | + | When the only forces present in a system are conservative, [[energy]] is conserved. | |
| − | + | Examples of conservative forces include: | |
| − | + | ||
| − | + | * [[Gravitational force]] | |
| + | * [[Hooke's Law|Force performed by a spring]] | ||
| − | + | [[Friction]] is an example of a non-conservative force: | |
== References == | == References == | ||
Revision as of 21:00, December 13, 2016
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 di = df) = 0) is zero.
- The force can be written as the negative of the gradient of a potential energy function, i.e.
.
- The curl of the force,
is zero, 
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:
References
- ↑ Serway and Beichner, Physics for Scientists and Engineers, Fifth Edition
