Elastic energy

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The elastic energy is the energy which causes or is released by the Elastic distortion of a solid or a fluid.

[edit] Thermodynamics

The elastic energy is internal energy (U) that can be converted into mechanical energy (work) under adiabatic conditions by virtue of spontaneous changes in volume or shape of a body. Elastic distortion is characterised by reversibility. As the process is adiabatic, heat=0 and using the first law of thermodynamics, for a gas the elastic energy can be defined in differential form as

dU = dW = − PdV

where P is the external pressure, equal to the internal pressure as the process is quasi-estatic (reversible), and V is the volume of the gas. The minus sign appears as the external pressure exerts a force contrary to the expansion. In Thermodynamics the work that is carried out by a gas (in general by a system) is negative, whilst the work exerted over a system is positive.

[edit] Mechanics

For a spring the elastic energy is

where k is the elastic constant of the spring (see Hooke's law) and x is the elongation of the spring. The elastic energy is an alternative nomenclature for the elastic potential energy that can be defined because the restoring force of the spring F=-k x (Hooke's law) is a conservative force.