# Potential Energy: Elastic Formula

#### Potential energy is energy that is stored in a system. There is the possibility, or potential, for it to be converted to kinetic energy. Elastic potential energy is stored in a spring that has been stretched or compressed by a distance x away from its equilibrium position. Position x = 0 must always be the position where the spring is most relaxed. Springs have their own natural “spring constants” that define how stiff they are. The letter k is used for the spring constant, and it has the units N/m. Like all work and energy, the unit of potential energy is the Joule (J), where 1 J = 1 N∙m = 1 kg m^{2}/s^{2} .

*potential energy = 1/2(spring constant)(distance from equilibrium)*^{2}

^{2}

*U = 1/2kx*^{2}

^{2}

*U* = potential energy of a spring at a certain position

*k* = the spring constant, specific to the spring, with units N/m.

*x* = distance the spring is stretched or compressed away from equilibrium

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**Potential Energy: Elastic Formula Questions:**

#### 1) A spring, which has a spring constant k = 7.50 N/m, has been stretched 0.40 m from its equilibrium position. What is the potential energy now stored in the spring?

#### Answer: The spring has been stretched x = 0.40 m from equilibrium. The potential energy can be found using the formula:

*U = 1/2kx*^{2}

^{2}