# Homework Help: Work, Springs

1. Feb 7, 2010

### n00neimp0rtnt

1. The problem statement, all variables and given/known data
If 6 J of work is needed to stretch a spring from 10 cm to 12 cm and another 10 J is needed to stretch it from 12 cm to 14 cm, what is the natural length of the spring?

2. Relevant equations
Spring constant - f(x) = kx
$$\int$$ab f(x)dx where a,b are initial and ending positions of the particle and f(x) is the work done in moving from a to b.

3. The attempt at a solution
I first tried a non-calculus solution by turning both statements into algebra problems...
6 = (10-x) + (12-x)
6 = 22 - 2x
-2x = 16
x = -8

10 = (10-x) + (14-x)
10 = 26-2x
-2x = 16
x = -8

Obviously this didn't get me anywhere..

2. Feb 8, 2010

### tiny-tim

Welcome to PF!

Hi n00neimp0rtnt! Welcome to PF!

(have an integral: ∫ )
uhh?

You mean f(x) = kx is the force,

and the work done in moving from a to b is ∫ab f(x)dx where a,b are initial and ending positions of the particle.