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Help with a work problem(spring)

  1. Jul 15, 2012 #1
    1. The problem statement, all variables and given/known data
    A force of 4 lbs is needed to stretch a 10-in. spring 1 inch beyond its natural length.
    Find the work done in stretching the same spring from its natural length to a length of 15 inches.

    2. Relevant equations
    f=kd
    W=∫(kx)dx


    3. The attempt at a solution
    So I know that a force of 4lbs is required to stretch a spring 1inch.
    so 4=1K
    K=4
    I plug K into my work equation and i get
    ∫(4x)dx
    I integrate it and get 2x^2 from 0 to 15/12(converting to feet)
    I plug in my limits of integration and I get 3.125ft-lbs

    The solution says ~4.167 ft-lbs.

    I have no idea where I went wrong.
     
  2. jcsd
  3. Jul 15, 2012 #2

    Doc Al

    User Avatar

    Staff: Mentor

    15 inches is the total length of the stretched spring. Don't convert units until after you've evaluated the integral.
     
  4. Jul 15, 2012 #3
    Ah, ok. I retried the integral going from 0 to 5
    I also noticed one mistake I made. I converted my limits of integration to foot in my integral but when I was solving for K, I didn't convert it.
    So it would be 4=k/12
    k=48

    Doing this did indeed give me the correct answer. Thank you!
     
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