Question

A spring has a natural length of 20 cm. If a 26-N force is required to keep it stretched to a length of 38 cm, how much work W is required to stretch it from 20cm to 29 cm? (Round your answer to two decimal places.)
W = ______ J

Answer 1

Given

F = forece requred to stretch 38cm = 26N

x = stretched length from original length = 18 cm = 0.18m

find 1^st spring constant (K)

K * x = F

K = F/x = 26/0.18 = 144.44 N/m

Then find work required to stretch the spring from 20cm to 29 cm

$Work = \frac{1}{2}k x^{2}$

x = Change in length of spring = stretched length - origunal length = 29 - 20 = 9 cm

x = 9 cm = 0.09m

then

$Work = \frac{1}{2} * 144.44*0.09^{2} = 0.585 J$

Work = 0.585 J