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So I'm able to do the spring problems when they ask you to find the work, but I'm having trouble with its inverse where they give you the work and ask you to find its length.

Problem:

It takes 6J to stretch a spring from 10cm to 12cm and a work of 10J to stretch it from 12cm to 14 cm, what is it's length in it's resting position.

edit : I have a feeling I'm suppose to apply Hooke's law, but not quite sure how.

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    Possible duplicate of [Work on Springs using Hooke's Law](http://math.stackexchange.com/questions/930061/work-on-springs-using-hookes-law) – 2017-01-27

1 Answers 1

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Hooke's Law: The force needed to compress/extend a (ideal) spring is given in magnitude by $F=kX$, where $X$ is the distance from natural length and $k$ is constant.

Let $x_0$ be the natural length of the spring. Then,

$$|.10-x_0|$$

Is the distance required to stretch or compress, to go from $x_0$ to $.10$. Then,

$$|.12-x_0|$$

Is the distance required to go from $x_0$ to $.12$.

So the energy required to go from $.10$ to $.12$ is by Hooke's law, and work:

$$6=\int \vec F \cdot d \vec r=\int_{|.10-x_0|}^{|.12-x_0|} k x dx$$

Now set up a similar integral for the other given information and you shall have a system of equations.

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    S. Attalla Ty! I would of never though to put an equation in the bounds of an integral to create a system of equations. – 2017-01-27
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    Happy to help! ${}{}{}{}$ – 2017-01-27