If 5.4 J of work are needed to stretch a spring from 17 to 23 cm and 9 J are needed to stretch it from 23 to 29 cm, what is the natural length of the spring? I know the answer is 11cm but I'm not sure how to get that.

Question

If 5.4 J of work are needed to stretch a spring from 17 to 23 cm and 9 J are needed to stretch it from 23 to 29 cm, what is the natural length of the spring?  I know the answer is 11cm but I'm not sure how to get that.

dumbcow · Answer

Let "u" be natural length of spring
then (x-u) is distance spring is stretched
Force = k(x-u)
Work = Force*dx

$$k \int\limits_{17}^{23} (x-u) dx = 5.4$$
$$k \int\limits_{23}^{29} (x-u) dx = 9$$
integrate and solve system for "u"

P.S. i just happened to notice i was wrong with other post, i misread the units i thought it was talking about just Force not Work last time