Answer to Question #331853 in Calculus for neither

Question

An unstretched spring is 10 ft long. A pull of 40 lb stretches the

spring by ½ ft. Find the work done in stretching the spring from

10 ft to 14 ft.

Answer 1

Hooke's Law

$$F=-k x$$

$$k=\dfrac{40\ lb}{1/2\ ft}=80\ lb/ft$$

The work done in stretching the spring is

$$W=k(x_2-x_1)^2/2$$

$$W=80\ lb/ft\cdot(14\ ft-10\ ft)^2/2=640\ ft- lb$$