Natural length of a spring

[dez88]

If 27 J of work are needed to stretch a spring from 17 cm to 23 cm and 45 J are needed to stretch it from 23 cm to 29 cm, what is the natural length of the spring? ................ I need this desperately. I don't even know where to start. We've BRIEFLY solved for K with a known X in our calculus class. I haven't taken physics so this is all new to me. can someone save me?

 

[HallsofIvy]

If 27 J of work are needed to stretch a spring from 17 cm to 23 cm and 45 J are needed to stretch it from 23 cm to 29 cm, what is the natural length of the spring? ................ I need this desperately. I don't even know where to start. We've BRIEFLY solved for K with a known X in our calculus class. I haven't taken physics so this is all new to me. can someone save me?

With spring constant K and calling the natural length L, so that F= K(x- L), the work necessary to stretch the spring from length $\displaystyle x_1$ to $\displaystyle x_2$ is $\displaystyle K\int_{x_1}^{x_2}(x- L)dx$. Since this is a Calculus class I presume you know that.

The information you are given says that $\displaystyle K\int_{17}^{23} (x- L)dx= 27$ and $\displaystyle K\int_{23}^{29} (x- L)dx= 45$.

Do the integration and you will have two equations to solve for K and L.