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Homework Help: Work, Springs

  1. Feb 7, 2010 #1
    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
    [tex]\int[/tex]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. jcsd
  3. Feb 8, 2010 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi n00neimp0rtnt! Welcome to PF! :smile:

    (have an integral: ∫ :wink:)
    uhh? :confused:

    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.
     
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