Answer to Question #344328 in Calculus for Jane

Question

4. A spring has a natural length of 18 inches and a force of 201 lbs is required to stretch and hold the spring to a length of 24 inches. What is the work required to stretch the spring from a length of 21 inches to a length of 26 inches?

Answer 1

$$F=k\Delta x$$

$$k=\dfrac{201\ lb}{24\ in-18\ in}=33.5\ lb/in$$

$$W=\dfrac{33.5\ lb/in(26\ in-21\ in)^2}{2}=418.75 \ lb\cdot in$$