Conservative force

Conservative forces are those that possess certain properties:

• The work it does on a particle is independent of its trajectory.
• 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 force can be written as the negative of the gradient of a potential energy function, i.e. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec F = - \nabla U } .
• The curl of the force, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{F}} is zero, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \nabla \times \vec{F} = 0}

When the only forces present in a system are conservative, energy is conserved.

Examples of conservative forces include:

• Gravitational force
• Force performed by a spring

Friction is an example of a non-conservative force: