To solve this problem we will apply the concepts related to Hooke's law for which the force exerted on a spring is described as the product between the spring constant and its displacement, that is
[tex]F = kx[/tex]
Where k is the spring's constant and x is the elongation,
Rearranging to find the elongation we have
[tex]x = \frac{F}{k}[/tex]
Replacing,
[tex]x = \frac{100}{500}[/tex]
[tex]x = 0.2in[/tex]
[tex]x = 5.08mm[/tex]
Therefore the elongation produced in the rope from its original length is 0.2in or 5.08mm
