# Elastic Potential Energy

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Elastic potential energy, abbreviated as PE, is a form of potential energy that is stored within an elastic object when it is deformed or stretched and has the potential to return to its original shape or position.  It arises due to the forces that act on the object when it is subjected to deformation and is characterized by its ability to be recovered as kinetic energy when the object returns to its undeformed state.  The concept of elastic potential energy is rooted in Hooke's Law, which states that the force required to stretch or compress an elastic object (like a spring) is directly proportional to the amount of deformation produced.

When an elastic object is stretched or compressed, work is done on it against the resisting force (provided by the spring constant).  This work is stored as potential energy within the object, and it is released when the object returns to its original shape or position.

Elastic potential energy is commonly observed in various everyday situations, such as when stretching a rubber band, compressing a spring, or bending a bow.  It's an important concept in physics and engineering, as it relates to the behavior of materials and mechanical systems under deformation and stress.

### Elastic Potential Energy formula

$$PE = (1\;/\;2) \; k_s\; x^2$$     (Elastic Potential Energy)

$$k_s = 2 \;PE \;/\; x^2$$

$$x = \sqrt{ 2 \;PE \;/\; k_s }$$

Symbol English Metric
$$PE$$ = elastic potential energy $$lbf-ft$$ $$J$$
$$k_s$$ = spring constant $$lbf\;/\;ft$$ $$N\;/\;m$$
$$x$$ = length or displacement $$ft$$ $$m$$

Tags: Energy