Natural Length of a spring

  1. I'm having problems with the work section of my calc book. This is the problem:

    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 from 12 cm to 14 cm, what is the natural length of the spring?

    I set up two equations:

    6 J= Kx^2/2 evaluated at 10-L and 12-L
    10 J= Kx^2/2 evaluated at 12-L and 14-L

    I'm not sure what to do after the mess hell of algebra, I end up with a K and an L. Do I solve for K in one equation and plug it into the other?
  2. jcsd
  3. I got a length of 8
  4. HallsofIvy

    HallsofIvy 40,310
    Staff Emeritus
    Science Advisor

    If that's the easiest way to solve the two equations. Any any case, you want to eliminate K from the equations, resulting in single equation for L.
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