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Work done by springs in a series

  1. Feb 17, 2008 #1
    1. The problem statement, all variables and given/known data
    Two springs, with force constants k1 and k2, are connected in series, as shown in the figure

    How much work is required to stretch this system a distance x from the equilibrium position?
    2. Relevant equations


    3. The attempt at a solution

    I have no idea how to derive this. I mean I've looked on the wikipedia article on hooke's law and figured that I just change the equation to W=1/2 (1/k1 + 1/k2)x^2

    I'm guessing the problem with this is that the distances that the two stretch are not equal because of the different spring constants but I don't know how to go about showing this in an equation.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Feb 17, 2008 #2
    is that 1/(2kx^2) or (1/2k)x^2
  4. Feb 17, 2008 #3
    it is (1/2k)x^2
  5. Feb 17, 2008 #4
    using 1/kt=1/k1+1/k2. Substitute into elastic potential energy equation.

    Edit: forget that... Misunderstood your question I think.
    Last edited: Feb 17, 2008
  6. Feb 17, 2008 #5
    i did that
    W=1/2 (1/k1 + 1/k2)x^2

    and this was wrong
  7. Feb 17, 2008 #6
    I know. That'd why I edited and said forget it, Lol.
  8. Feb 17, 2008 #7
    ah i see. so any other takers.
  9. Feb 18, 2008 #8
    still need help. is my theory about distances being different right?
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