Expression for energy stored in string
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Hooke’s Law, F = -kx, where F is the force and x is the elongation.The work done = energy stored in stretched string = F.dxThe 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)