- #1
- 19,907
- 10,912
Definition/Summary
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: \oint_C \mathbf{F} \cdot d\mathbf{s} =0
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: \mathbf{F}\ =\ -\mathbf{\nabla}\Phi, and so \mathbf{\nabla}\times\mathbf{F}\ =\ \mathbf{\nabla}\times \mathbf{\nabla}\Phi\ =\ 0)
if the force is a field whose curl is zero: \mathbf{\nabla}\times\mathbf{F}\ =\ 0
Equations
\oint_C \vec F d \vec s =0
Extended explanation
A conservative force is a force such that \oint_C \vec F d \vec s =0.
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!
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: \oint_C \mathbf{F} \cdot d\mathbf{s} =0
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: \mathbf{F}\ =\ -\mathbf{\nabla}\Phi, and so \mathbf{\nabla}\times\mathbf{F}\ =\ \mathbf{\nabla}\times \mathbf{\nabla}\Phi\ =\ 0)
if the force is a field whose curl is zero: \mathbf{\nabla}\times\mathbf{F}\ =\ 0
Equations
\oint_C \vec F d \vec s =0
Extended explanation
A conservative force is a force such that \oint_C \vec F d \vec s =0.
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!