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# Potential energy

Potential energy is in a sense, the storage system for energy. For example when a ball is lifted above the ground, the potential energy of the ball will increase when the ball is lifted higher. If the ball is released the potential energy changes to kinetic energy. So work done to the ball will increase the ball's potential energy and when that ball is released it transfers that work to kinetic energy and work is done on the ground by the ball when it falls and hits the ground.

[math] Wc= Ui -Uf = -(Uf - Ui) = -\Delta U [/math]

- Where

- W
_{c}= Work Conservative - U
_{i}= Potential Energy initial - U
_{f}= Potential Energy Final - -ΔU = Change in Potential Energy

When applying potential energy with the force of gravity on Earth a standard equation can be used to express the total potential energy of a system.

[math] U = mgh [/math]

- Where

- U= Potential Energy
- m= mass
- g= force of gravity (9.81 m/s
^{2} - h= difference in height

When applying Potential energy to a spring, the spring stores the energy when compressed. When the spring is released the Potential energy is converted into kinetic energy. When the spring is at equilibrium the Potential energy is 0

[math] U= 1/2 {kx}^2 [/math]

- Where

- U= Potential energy in spring system
- k= spring constant
- x= distance the spring is compressed from equilibrium