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What is the conservative force

  1. Jul 24, 2014 #1

    A force is conservative (the following definitions are all equivalent):

    if it complies with the work-energy theorem: work done equals change in mechanical energy

    if the work done is path-independent

    if the work done on a closed path is zero: [itex]\oint_C \mathbf{F} \cdot d\mathbf{s} =0[/itex]

    if the overall gain or loss of mechanical energy is path-independent

    if the overall gain or loss of mechanical energy on a closed path is zero

    if the force is a field with a potential (in which case it can be written as minus the gradient of the potential: [itex]\mathbf{F}\ =\ -\mathbf{\nabla}\Phi[/itex], and so [itex]\mathbf{\nabla}\times\mathbf{F}\ =\ \mathbf{\nabla}\times \mathbf{\nabla}\Phi\ =\ 0[/itex])

    if the force is a field whose curl is zero: [itex]\mathbf{\nabla}\times\mathbf{F}\ =\ 0[/itex]


    [tex]\oint_C \vec F d \vec s =0[/tex]

    Extended explanation

    A conservative force is a force such that [tex]\oint_C \vec F d \vec s =0[/tex].
    Examples of conservative forces : Gravitational force, static friction force and elastic forces.

    * This entry is from our old Library feature. If you know who wrote it, please let us know so we can attribute a writer. Thanks!
  2. jcsd
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