Question

calculate the workdone to stretch an elastic string by 40cm if a force of 10N produces an extension of 4cm in it

Answer 1

The force of F=10 N produces an extension of
$x=4 cm=0.04 m$
on the string, so the spring constant is equal to
$k= \frac{F}{x}= \frac{10 N}{0.04 m}=250 N/m$

Then the string is stretched by $\Delta x=40 cm=0.40 m$. The work done to stretch the string by this distance is equal to the variation of elastic potential energy of the string with respect to its equilibrium position:
$W= \Delta U= \frac{1}{2}k(\Delta x)^2 = \frac{1}{2}(250 N/m)(0.40 m)^2=20 J$