If 9 J of work are needed to stretch a spring from 9 cm to 10 cm and 15 J are needed to stretch it from 10 cm to 11 cm, what is the natural length L of the spring?

Answer 1

The average force over the 9-10 cm interval is 900 N. Since force is linear with length (x), that means the force is 900 N at x = 9.5 cm.

Similarly, the force is 1500 N at x = 10.5 cm.

Those two points in an F = mx + b curve can be fit with

F = 600 (x - 8 cm) N

F = 0 when x = 8 cm, so that is the natural length of the spring.

The spring constant is 600 N/cm

Answer 2

how did you get the 8cm?