# If a spring has a constant of 4 (kg)/s^2, how much work will it take to extend the spring by 87 cm ?

Feb 3, 2018

Here,work done is equals to the energy stored in the spring as elastic potential energy = $\frac{1}{2} k {x}^{2}$

Given, $k = 4 , x = \frac{87}{100}$

So,work done = $1.5138 J$

ALTERNATIVELY

Force required to stretch the spring is $F = k x$

So,work done here is $\mathrm{dW} = F . \mathrm{ds} = k x \mathrm{dx}$

So,integrating from $W = 0 \to W$ and $x = 0 \to \frac{87}{100}$

$W = \frac{1}{2} k {x}^{2} = 1.5138 J$