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  4. The potential energy of a certain spring when stretched through a distance S is 10 joule. The amount of work (in joule) that must be done on this spring to stretch it through additional distance S will be

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Q. The potential energy of a certain spring when stretched through a distance $S$ is $10$ joule. The amount of work (in joule) that must be done on this spring to stretch it through additional distance $S$ will be

Work, Energy and Power

Solution:

$U=\frac{1}{2} k S^{2}=10 \,J \ldots$(i)
$U^{\prime}=\frac{1}{2} k(S+S)^{2}=U\left(\frac{1}{2} k S^{2}\right)=40 \,J$ (Using (i))
$\therefore W=U' - U = 40\, J -10\, J =30\, J$