Changes

'''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]].

# 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_i = d_f) = 0) is zero.

# The work done on a particle that moves along a closed trajectory (where the initial and final positions are the same, or d_i = d_f) = 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>.

# 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.

# The [[curl]] of the force, <math>\vec{F}</math> is zero, <math>\nabla \times \vec{F} = 0</math>

Examples of conservative forces:

 

Examples of conservative forces include:

* [[Gravitational force]]

* [[Gravitational force]]

* [[Hooke's Law|force performed by a spring]]

* [[Hooke's Law|Force performed by a spring]]

 

*[[friction]]

[[Friction]] is an example of a non-conservative force:

== References ==

== References ==