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Work done to move a spring

  1. Dec 15, 2013 #1
    A spiral spring exerts a restoring torque on an axis proportional to the angle through which the axis is turned. If it provides a torque of 10-5 Nmrad-1, find the energy required to turn it through 180degrees from its relaxed state?

    My solution was simple

    Work done = torque* the angle theta but I seemed to get the wrong answer!
     
  2. jcsd
  3. Dec 15, 2013 #2

    tiny-tim

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    Hi KiNGGeexD! :smile:

    (try using the X2 button just above the Reply box :wink:)

    I think you're misunderstanding the question …

    the torque isn't constant, it's 10-5*θ Nm, depending on the instantaneous angle θ. :wink:
     
  4. Dec 15, 2013 #3
    So how would I go about solving the problem?:(
     
  5. Dec 15, 2013 #4

    tiny-tim

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    linear work done = ∫ F·ds

    circular work done = ∫ τ dθ :wink:
     
  6. Dec 15, 2013 #5
    Ah so I need to integrate τ dθ for 0-180 degrees?:)
     
  7. Dec 15, 2013 #6

    tiny-tim

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  8. Dec 15, 2013 #7
    Haha cheers friend!
     
  9. Dec 15, 2013 #8
    Maybe I'm getting confused but would the answer not just be the same?:)
     
  10. Dec 15, 2013 #9

    tiny-tim

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    no

    show us your integral​
     
  11. Dec 15, 2013 #10
    I'm clearly integrating wrong haha

    I had

    W= τ dθ

    From 0-180 ok I'm not 100% lol
     
  12. Dec 15, 2013 #11

    tiny-tim

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    show us your integral!! :rolleyes:
     
  13. Dec 15, 2013 #12
    W=τ dθ

    So

    W= τ*180 + c
     
  14. Dec 15, 2013 #13

    tiny-tim

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    an integral should have an ∫ in it :confused:

    (and limits)

    and what is τ ?​
     
  15. Dec 15, 2013 #14
    τ= Iα ?

    And yea I know about the imetrgral sign and limits I just can't do it on my phone:(!
     
  16. Dec 15, 2013 #15

    tiny-tim

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    try typing two #, then \int, then two more # :wink:

     
  17. Dec 15, 2013 #16
    For a non constant torque


    W= ταθ
     
  18. Dec 15, 2013 #17
    That tau was supposed to be I, moment of inertia
     
  19. Dec 15, 2013 #18
    I am integrating

    τ from 0-180

    Or τθ from 0-180?
     
  20. Dec 15, 2013 #19
    If so


    W= τ*θ^2 all divided by 2?
     
  21. Dec 15, 2013 #20

    tiny-tim

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    hmm :redface: … what you mean is correct, but that's certainly not the correct way to write it
     
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