# Conservation of Energy

### Contents

#### Terms

Conservative force  -  Any force which conserves mechanical energy, as opposed to a nonconservative force. See statement of conservation of mechanical energy.
Conservative System  -  A system in which energy is conserved.
Nonconservative Force  -  Any force which does not conserve mechanical energy, as opposed to a conservative force.
Path independence  -  Property of conservative forces which states that the work done on any path between two given points is the same.
Potential energy  -  The energy of configuration of a conservative system. For formulae, see Definition of potential energy, gravitational potential energy, and Definition of potential energy given a position-dependent force.
Kinetic Energy  -  The energy of motion.
Total mechanical energy  -  The sum of the kinetic and potential energy of a conservative system. See definition of total mechanical energy.

#### Formulae

 Definition of potential energy. ΔU = - W

 Gravitational potential energy. UG = mgh

 Statement of conservation of mechanical energy. Δ(U+K) = 0

 Definition of total mechanical energy. U + K = E

 Definition of potential energy given a position-dependent force. ΔU = - F(x)dx