Conservative force - Wikipedia, the free encyclopedia
... the work done by a conservative force is equal to the negative ... Conservative force fields are curl-less as a direct consequence of Helmholtz decomposition. ...
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Conservative force
Conservative force tansfers energy between kinetic energy of ... Total work done by conservative force in a closed path ... one such non-conservative force. ...
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Conservative and non-conservative force-fields
... what physicists term a conservative force-field, whereas the second possibility ... example of a non-conservative force, because it dissipates energy ...
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CHAPTER 9 CONSERVATIVE FORCES
That a conservative force must be derivable from the gradient ... a force to be conservative. ... place, how can you tell if a force is conservative or not? ...
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Potential Energy and Conservative Forces
Each type of Conservative Force has an associated with it an Potential ... The work done by a conservative force, Wcf , can be transformed into a change in ...
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Conservative vector field - Wikipedia, the free encyclopedia
The most prominent example of a conservative force is the force of gravity. ... For conservative forces, path independence can be interpreted to mean that the ...
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Conservative force - Conservapedia
(Redirected from Conservative Force) Jump to: navigation, search ... When the only forces present in a system are conservative, mechanical energy is conserved. ...
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Potential Energy
... a function of position only, it is said to be a conservative force, and it can ... If the force is known, and is a conservative force, then the potential energy ...
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Potential energy
... Conservation of energy Previous: Conservative and non-conservative force-fields ... Consider a body moving in a conservative force-field. ...
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A conservative force is defined as a force that does not depend on the path taken to increase in potential energy. Informal definition Informally, a conservative force can be thought of as a force that conserves mechanical energy. Suppose a particle starts at point A, and there is a constant force F acting on it. Then the particle is moved around by other forces, and eventually ends up at A again. Though the particle may still be moving, at that instant when it passes point A again, it has traveled a closed path. If the net work done by F at this point is 0, then F passes the closed path test. Any force that passes the closed path test is classified as a conservative force.

The gravitational force, Hooke's law, magnetic force and electric force (at least in a time-independent magnetic field, see Faraday's law of induction for details) are examples of conservative forces, while friction and air drag are classical examples of non-conservative forces (the energy is transferred to the air as heat and cannot be retrieved).

Path independence is conservative.

A direct consequence of the closed path test is that the work done by a conservative force on a particle moving between any two points does not depend on the path taken by the particle. For a proof of that, let's imagine two paths 1 and 2, both going from point A to point B. The variation of energy for the particle taking the path 1 from A to B then the path 2 backwards from B to A is 0, so the work is the same in path 1 and 2 : the work is independent of the path followed, as long as it goes from A to B.

For example, if a child slides down a frictionless slide, the work done by the gravitational force on the child from the top of the slide to the bottom will be the same no matter what the shape of the slide; it can be straight or it can be a spiral. The amount of work done only depends on the vertical displacement of the child.

Mathematical description A force F is called conservative if it meets any of these (equivalent - Conservative force/Proofs) conditions:

*The curl of F is zero: :\nabla \times \vec{F} = 0. \,

*The work, W, is zero for any simple closed path: :W = \oint_C \vec{F} \cdot \mathrm{d}\vec r = 0.\,

*The force can be written as the gradient of a potential, \Phi: :\vec{F} = -\nabla \Phi. \,

Conservative force fields are curl-less as a direct consequence of Helmholtz decomposition. The term conservative force comes from the fact that when a conservative force exists, it conserves mechanical energy. The most familiar conservative forces are gravity, the electric force, and spring force.

Nonconservative forces Nonconservative forces arise due to neglected degrees of freedom (physics and chemistry). For instance, friction may be treated without resorting to the use of nonconservative forces by considering the motion of individual molecules; however that means every molecule's motion must be considered rather than handling it through statistical methods. For macroscopic systems the nonconservative approximation is far easier to deal with than millions of degrees of freedom. Examples of nonconservative forces are friction and non-elastic material stress (physics).

See also

• Conservative vector field

Conservative force - Wikipedia, the free encyclopedia
A conservative force is defined as a force that does not depend on the path taken to increase in potential energy.

Conservative Forces
Conservative Forces A Force Is Conservative If The Curl(*) Is Zero (*) The curl is the commutator of the differential operator and the force.

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