A spring has natural length 16 cm. A force of 3 N is required to holdthe spring compressed compressed to 11 cm. Find the amount ofwork instretching the spring from 17 cm to 19 cm.

W = 0.012 J

Explanation:

For this exercise let's use Hooke's law to find the spring constant

         F = K Δx

         K = F / Δx

         K = 3 / (0.16 - 0.11)

         K = 60 N / m

Work is defined by

         W = F. x = F x cos θ

in this case the force and the displacement go in the same direction therefore the angle is zero and the cosine is equal to 1

         W = ∫ F dx        

         W = k ∫ x dx

we integrate

         W = k x² / 2

          W = ½ k x²

let's calculate

         W = ½ 60 (0.19 -0.17)²

         W = 0.012 J