An elastic string of unstretched length L and | vedclass

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(B) The elastic force is a conservative force. The work done by an external agent to stretch a spring is equal to the change in its potential energy.T

Vedclass · Accepted Answer

$\frac{1}{2} ky(2x+y)$

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(B) The elastic force is a conservative force. The work done by an external agent to stretch a spring is equal to the change in its potential energy.The potential energy of a spring stretched by a length $x$ is given by $U = \frac{1}{2} kx^2$.Initially,the string is stretched by length $x$. The initial potential energy is $U_i = \frac{1}{2} kx^2$.After stretching it further by length $y$,the total extension becomes $(x+y)$. The final potential energy is $U_f = \frac{1}{2} k(x+y)^2$.The work done by the external agent in the second stretching is the change in potential energy:$W = U_f - U_i$$W = \frac{1}{2} k(x+y)^2 - \frac{1}{2} kx^2$$W = \frac{1}{2} k(x^2 + y^2 + 2xy) - \frac{1}{2} kx^2$$W = \frac{1}{2} kx^2 + \frac{1}{2} ky^2 + kxy - \frac{1}{2} kx^2$$W = \frac{1}{2} ky^2 + kxy$$W = \frac{1}{2} ky(y + 2x)$Thus,the work done is $\frac{1}{2} ky(2x+y)$.

An elastic string of unstretched length $L$ and force constant $k$ is stretched by a small length $x$. It is further stretched by another small length $y$. The work done in the second stretching is

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