When the spring is stretched by 3 cm, the elastic force is 30N. What work needs to be done to stretch this spring 9 cm.

Data: Δx0 (initial tension of the spring) = 3 cm (in SI Δx0 = 0.03 m); Fupr0 (initial elastic force) = 30 N; Δx (required spring tension) = 9 cm (in SI Δx = 0.09 m).
1) We calculate the rigidity of the spring taken (Hooke’s law): k = Fcont0 / Δx0 = 30 / 0.03 = 1000 N / m.
2) Calculate the work required to stretch the spring by 9 cm: A = ΔEp = k * Δx ^ 2/2 = 1000 * 0.09 ^ 2/2 = 4.05 J.
Answer: It is necessary to complete work at 4.05 J.