Solving for Spring Constant and Length

[n00neimp0rtnt]

Homework Statement

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?

Homework Equations

Spring constant - f(x) = kx
\int_a^b 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.

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..

 

[tiny-tim]

Welcome to PF!

Hi n00neimp0rtnt! Welcome to PF!

(have an integral: ∫ )

Spring constant - f(x) = kx
\int_a^b 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.

uhh?

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

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