Question

Derive an expression for potential energy of a stretched string

Answer 1

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)
It may help you

Answer 2

Potential energy for stretched spring::

As we know that rate of change of kinetic energy is equal to potential energy stored in the spring.
P.E=( 1/2)KX^ 2
K is spring constant
X is anything between mean and extreme position , when spring is at extreme position X become X° ( x nod)
when spring is at mean position X = o , so P.E at mean position is 0 but is max at extreme position.