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

oscillating
Moving in a repeated backandforth motion.

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.
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.
Key Term Reference
 Hooke's law
 Appears in these related concepts: Hooke's Law, Sinusoidal Nature of Simple Harmonic Motion, and Springs
 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: Period of a Mass on a Spring, Energy, Intensity, Frequency, and Amplitude, and Stability, Balance, and Center of Mass
 displacement
 Appears in these related concepts: Position, Displacement, Velocity, and Acceleration as Vectors, Reference Frames and Displacement, and Introduction to Human Language
 distortion
 Appears in this related concept: Aberrations
 elastic
 Appears in these related concepts: Defining Price Elasticity of Demand, Applications of Elasticities, and Tax Incidence, Efficiency, and Fairness
 elastic potential energy
 Appears in these related concepts: What is Potential Energy?, Energy in a Simple Harmonic Oscillator, and Work Done by a Variable Force
 energy
 Appears in these related concepts: Surface Tension, Energy Transportation, and Introduction to Work and Energy
 equilibrium
 Appears in these related concepts: Homogeneous versus Heterogeneous Solution Equilibria, Diffusion, and Second Condition
 force
 Appears in these related concepts: Force of Muscle Contraction, Force, and First Condition
 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: Escape Speed, Defining Graviational Potential Energy, and Types of Energy
 static
 Appears in these related concepts: LongTerm Approach, Time and Motion, and Alternative Views
 thermal energy
 Appears in these related concepts: Heat Engines, Other Forms of Energy, and The Greenhouse Effect
 work
 Appears in these related concepts: Heat and Work, Free Energy and Work, and The First Law of Thermodynamics
Sources
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