derive an expression for the elastic potential energy of a streched spring.
Answers
expression for the elastic potential
▶energy of a streched spring
The characteristic of a spring is that the force needed to stretch or compress a spring by an amount x is equal to k x and is in the direction opposite to the extension or compression. Here k is called the spring constant.
Restoration Force of the spring (compression or tensile) Fs = - k x = - external force F
Work done by the external force in compressing the spring from x = 0 to x = L can be obtained by:
is the energy given by the external force to the spring with an extension x.
This energy is stored as potential energy in the spring.
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HERE IS UR ANSWER
Hooke's Law, F = -kx, where F is the force and x is the elongation.
The work done = energy stored in stretched string = F.dx
The energy stored can be found from integrating by substituting for force,
and we find,
The energy stored = kx2/2, where x is the final elongation.
The energy density = energy/volume
= (kx2/2)/(AL)
=1/2(kx/A)(x/L) = 1/2(F/A)(x/L) = 1/2(stress)(strain)
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