What is its total length?

Question

A spring, whose equilibrium length is 5 ft, extends to a length of 8 ft when a force of 2 lb is applied. If 8 ft-lb of work is required to extend this spring from its equilibrium position, what is its total length?

Answer 1

F_spring = kx

2 = k(8-5)

k = 2/3

Work, W = ∫₀^x kt dt = kx²/2 = (2/3)x²/2 = x²/3

When W = 8

8 = x²/3

x = √24 = 2√6

Total length = 5 + 2√6 ≈ 9.9 feet