If the spring is stretched with a force of 10 N, its length is 80 cm, but if it is stretched with a force

If the spring is stretched with a force of 10 N, its length is 80 cm, but if it is stretched with a force of 20 N, its length is 100 cm. What is the length of an undeformed spring?

Let the initial length of the undeformed spring be x meters. The elastic force arising in the deformed spring Fcont = – k ∙ Δx, where k is the spring stiffness, Δx is the spring elongation (change in its length), we express the coefficient k = (F control): | Δx |. It is known that if the spring is stretched with a force F = 10 N, its length is 80 cm = 0.8 m, then the resulting elastic force Fel = 10 N and the elongation of the spring will be (0.8 – x) m, the coefficient k = 10: ( 0.8 – x). And if you stretch with a force of 20 N, its length is 100 cm = 1 m, then the resulting elastic force Fel = 20 N, the elongation of the spring will be (1 – x) m, the coefficient k = 20: (1 – x). Since the stiffness of the spring does not change in this case, we make the equation: 10: (0.8 – x) = 20: (1 – x); x = 0.6 m.
Answer: The original length of the undeformed spring was 0.6 meters.