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Elastic Potential Energy
If a force results in only deformation, with no thermal, sound, or kinetic energy, the work done is stored as elastic potential energy.
Learning Objective

Express elastic energy stored in a spring in a mathematical form
Key Points
 In order to produce a deformation, work must be done.
 The potential energy stored in a spring is given by
$PE_{el} = \frac{1}{2}k x^2$ , where k is the spring constant and x is the displacement.  Deformation can also be converted into thermal energy or cause an object to begin oscillating.
Terms

deformation
A transformation; change of shape.

kinetic energy
The energy possessed by an object because of its motion, equal to one half the mass of the body times the square of its velocity.

oscillating
Moving in a repeated backandforth motion.
Example
 A mouse trap stores elastic potential energy by twisting a piece of metal; this energy is released when the mouse steps into it.
Full Text
Elastic Potential Energy
In order to produce a deformation, work must be done. That is, a force must be exerted through a distance, whether you pluck a guitar string or compress a car spring. If the only result is deformation and no work goes into thermal, sound, or kinetic energy, then all the work is initially stored in the deformed object as some form of potential energy. Elastic energy is the potential mechanical energy stored in the configuration of a material or physical system when work is performed to distort its volume or shape. For example, the potential energy PE_{el} stored in a spring is
where k is the elastic constant and x is the displacement.
It is possible to calculate the work done in deforming a system in order to find the energy stored. This work is performed by an applied force F_{app}. The applied force is exactly opposite to the restoring force (actionreaction), and so
Applied force versus deformation
A graph of applied force versus distance for the deformation of a system that can be described by Hooke's law is displayed. The work done on the system equals the area under the graph or the area of the triangle, which is half its base multiplied by its height, or
Elastic energy of or within a substance is static energy of configuration. It corresponds to energy stored principally by changing the interatomic distances between nuclei. Thermal energy is the randomized distribution of kinetic energy within the material, resulting in statistical fluctuations of the material about the equilibrium configuration. There is some interaction, however. For example, for some solid objects, twisting, bending, and other distortions may generate thermal energy, causing the material's temperature to rise. This energy can also produce macroscopic vibrations sufficiently lacking in randomization to lead to oscillations that are merely the exchange between (elastic) potential energy within the object and the kinetic energy of motion of the object as a whole.
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Key Term Reference
 Hooke's law
 Appears in these related concepts: Sinusoidal Nature of Simple Harmonic Motion, Springs, and Hooke's Law
 Law
 Appears in these related concepts: Physics and Other Fields, Damped Harmonic Motion, and Models, Theories, and Laws
 Restoring force
 Appears in these related concepts: Energy, Intensity, Frequency, and Amplitude, Stability, Balance, and Center of Mass, and Period of a Mass on a Spring
 displacement
 Appears in these related concepts: Calculus with Parametric Curves, Position, Displacement, Velocity, and Acceleration as Vectors, and Introduction to Human Language
 distortion
 Appears in this related concept: Aberrations
 elastic
 Appears in these related concepts: Internal vs. External Forces, Taxation Impact on Economic Output, and Applications of Elasticities
 elastic potential energy
 Appears in these related concepts: What is Potential Energy?, Work Done by a Variable Force, and Energy in a Simple Harmonic Oscillator
 energy
 Appears in these related concepts: Energy Transportation, Surface Tension, and Introduction to Work and Energy
 equilibrium
 Appears in these related concepts: The Function and Nature of Markets, Demand Schedules and Demand Curves, and Supply Schedules and Supply Curves
 force
 Appears in these related concepts: Newton and His Laws, Work, and Force
 kinetic
 Appears in these related concepts: Friction: Static, The Kinetic Molecular Theory of Matter, and Postmodernist Sculpture
 motion
 Appears in these related concepts: Motion Diagrams, TwoComponent Forces, and Moving Source
 potential
 Appears in these related concepts: Maslow's Hierarchy of Needs, Conservative and Nonconservative Forces, and Linear Expansion
 potential energy
 Appears in these related concepts: Potential Energy Curves and Equipotentials, Escape Speed, and Defining Graviational Potential Energy
 static
 Appears in these related concepts: LongTerm Approach, General ProblemSolving Tricks, and Time and Motion
 thermal energy
 Appears in these related concepts: Heat Engines, Other Forms of Energy, and The Greenhouse Effect
 work
 Appears in these related concepts: Force at an Angle to Displacement, Free Energy and Work, and Potentials and Charged Conductors
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Cite This Source
Source: Boundless. “Elastic Potential Energy.” Boundless Physics. Boundless, 13 Apr. 2016. Retrieved 03 May. 2016 from https://www.boundless.com/physics/textbooks/boundlessphysicstextbook/wavesandvibrations15/hookeslaw122/elasticpotentialenergy4266067/