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Help using Hooke's law to find work

  1. Feb 26, 2012 #1
    1. The problem statement, all variables and given/known data
    Use Hooke's Law to determine the variable force in spring problem.

    Eighteen foot-pounds of work is required to stretch a spring 4 inches from it's natural length. Find the work required to stretch the spring an additional 3 inches.

    2. Relevant equations

    3. The attempt at a solution

    I set the work equal to 18 and the distance equal to 4.
    so 18=4K, K=18/4
    with this knowledge I set my function is (18/4)X
    ∫(18x/4)dx from 4 to 7
    I get 9x(^2)/4
    using the fundamental theorum of Calculus from 4 to 7
    I get 74 1/4 (not sure of units, is it inches-pound)
  2. jcsd
  3. Feb 26, 2012 #2


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    Gold Member

    You need to start off recognizing that

    W - W(t) = ∫0df(x) dx = ∫0d kx dx

    If you will re-work the problem with this beginning, I think you will get a totally different outcome.
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