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>
  
1. The [[work]] it does on a particle is independent of its [[trajectory]].
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# The [[work]] it does on a particle is independent of its [[trajectory]].
  
2. 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.
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# 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.
  
3.  The force can be written as the negative of the gradient of a potential energy function, i.e. <math>\vec F = - \nabla U </math>.
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# The force can be written as the negative of the gradient of a potential energy function, i.e. <math>\vec F = - \nabla U </math>.
  
When the only forces present in a system are conservative, [[mechanical energy]] is conserved.
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# The [[curl]] of the force, <math>\vec{F}</math> is zero, <math>\nabla \times \vec{F} = 0</math>
  
Examples of conservative forces:
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When the only forces present in a system are conservative, [[energy]] is conserved.
  
* [[Gravitational force]]
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Examples of conservative forces include:
* [[Hooke's Law|force performed by a spring]]
+
  
Example of a non-conservative force:
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* [[Gravitational force]]
 +
* [[Hooke's Law|Force performed by a spring]]
  
*[[friction]]
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[[Friction]] is an example of a non-conservative force:
  
 
== References ==
 
== References ==

Revision as of 16:00, 13 December 2016

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

  1. The work it does on a particle is independent of its trajectory.
  1. 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.
  1. The force can be written as the negative of the gradient of a potential energy function, i.e. .
  1. 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

  1. Serway and Beichner, Physics for Scientists and Engineers, Fifth Edition