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Elastic Energy calculation

  1. Aug 28, 2016 #1
    1. The problem statement, all variables and given/known data
    Given the scheme
    https://www.dropbox.com/s/nm943gleo2nc8ft/Screenshot%202016-08-28%2013.47.33.png?dl=0
    Springs' constant k=40 N\m
    mass of bulk m=6kg
    The wooden bulk is released at rest when all the springs are not stretched
    Question: What is the elastic total maximal Energy of the system?
    2. Relevant equations

    E=0.5*K*(deltaX)^2
    A=0.375m
    Maximal kinetic energy 11.25Joul
    3. The attempt at a solution
    If I substitute all the givens in the equation given in section 2 above, I get Etot=4*0.5*40*0.375^2=45/4=11.25
    Let me know if it's correct because what I saw in the book answers is 45J, which doesn't match my calculations. Maybe I'm missing something
    Thanks for your attention
     
  2. jcsd
  3. Aug 28, 2016 #2

    mfb

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    2016 Award

    Staff: Mentor

    How did you get deltaX and what is A?
    Initially the springs are at rest, at which point are they stretched maximally?

    I get the same answer as the book (assuming g=10m/s^2).
     
  4. Aug 28, 2016 #3
    Let me see if I got it right:
    A-is the point beyond the initial rest point, in which we get equilibrium. So you've got to add the 0.375 of movement towards the bottom so eventually we get 0.75 of stretch of the upper springs down and equally 0.75 shrink of the bottom ones.
    Well, you get the 0.375 from equilibrium equation on the bulk:
    mg=4k*deltaX
    is that what you meant?
    Thanks for the response
     
  5. Aug 28, 2016 #4

    mfb

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    2016 Award

    Staff: Mentor

    Right. And if you plug that in, you get 45 J.
     
  6. Aug 28, 2016 #5
    gr8! Thank you
     
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