It takes 2.58 J of work to stretch a Hooke's-law spring 15.6 cm from its unstressed length. How much the extra work is required to stretch it an additional 9.39 cm? Answer in units of J.

Extra work required = 4.04 J

Explanation:

Hooks Law: Hooks law states that provided the elastic limit is not exceeded, the force applied to an elastic material is directly proportional to the extension.

E₁ = 1/2ke² ... Equation 1

Where E = Energy required to stretch or compress the spring, k = force constant of the spring, e = extension.

making k the subject of the equation in equation 1

k = 2E/e² ... Equation 2

Given: E = 2.58 J, e = 15.6 cm = 15.6/100 = 0.156 m.

Substituting these values into equation 2

k = 2*2.58 / (0.156) ²

k = 212.03 N/m

k = 5.75 N/m.

With an additional extension of 9.39 m, therefore e₂ = 15.6 + 9.39 = 24.99 cm

= 0.2499 m

using,

E₂ = 1/2k (e₂) ²

E₂ = 1/2 (212.03) (0.2499) ²

E = 6.62 J

E ≈ 6.62 J

Extra work required = E₂ - E₁

Extra work = 6.62 - 2.58

Extra work = 4.04 J