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Work done by spring

  1. Oct 10, 2011 #1
    1. The problem statement, all variables and given/known data

    The torsion spring at A applies the counterclockwise couple C(θ)= − 10θ N · m to the uniform bar.The angle θ (in radians) is measured counterclockwise
    from position 1, where the spring is undeformed.

    Calculate the work done by the spring on the bar as it rotates from position 2 to position 3.

    http://img849.imageshack.us/img849/1696/182z.jpg [Broken]


    2. Relevant equations

    U1-2 = ∫C dθ

    U1-2 = C(θ2 − θ1)= C Δθ

    3. The attempt at a solution

    U1-2 = ∫− 10θ dθ = -10∫θ dθ

    = -10 (1/2) θ2

    50° = 5π/18 rad

    U1-2 = -3.8

    I am not sure if that is the correct way of solving it, any guidance would be helpful
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Oct 10, 2011 #2
    Looks right to me.
     
  4. Oct 10, 2011 #3
    I just checked the book. The answer says it is −8.38 N·m
    I can't figure out what I am doing wrong
     
  5. Oct 10, 2011 #4
    Oh, here's the issue. Sorry I didn't check more closely before. I think your limits of integration were off. It should be

    [itex]W = \int^{\theta = 4\pi/9}_{\theta = \pi/6} -10\theta d\theta[/itex]

    because the equilibrium position of the system is at position 1, where [itex]\theta = 0[/itex]. You want to find the work done by the spring moving from position 2 ([itex]\theta = \frac{\pi}{6}[/itex], relative to position 1) to position 3 ([itex]\theta = \frac{4\pi}{9}[/itex], with respect to position 1).
     
  6. Oct 10, 2011 #5
    So the moral of the story is that it's highly important to take into account your equilibrium conditions and how the interactions occur relative to the equilibrium conditions. It's also important for people who answer questions on PF not to get ahead of themselves and forget (like I did here) to check that the approach the OP takes is duly considerate of the equilibrium conditions and their relation to the conditions stated as the bounds of the problem.
     
  7. Oct 10, 2011 #6
    That helped me a lot. Thank you very much
     
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