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Circular motion. Uniform and accelerating. (Bridge)

  1. Mar 19, 2012 #1
    1. The problem statement, all variables and given/known data

    A bridge takes 2 minutes to open up fully from 0 to 80 degrees. The first 20 degrees it is accelerating, and the last 60 degrees it is traveling with even velocity.

    I will have to find acceleration for the first 20 degrees and angular velocity for the last 60 degrees.

    http://peecee.dk/upload/view/357409 Illustration.



    3. The attempt at a solution

    I have tried setting up three equations with three unknowns:

    http://peecee.dk/upload/view/357410

    I have tried isolating a in the first two equations, and then put 1=2. Then isolating ω in this new equation, and replacing this with the ω in the third equation. Then i isolate t, and get 48 second. This gives the correct answer to the acelleration, but i don't know why. Can you help?

    Is there other way to do it maybe?

    Thank you in advance.
     
    Last edited: Mar 19, 2012
  2. jcsd
  3. Mar 19, 2012 #2

    tiny-tim

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    Hi EVriderDK! :smile:

    That looks ok … you eliminated α, then you solved for t, that is the way to do it.
    I don't understand. If it solves the equations, isn't that enough justification? :confused:
     
  4. Mar 19, 2012 #3
    Why is it correct to use these three equations. I didn't come up with them my self.
    I was just told that this i s the correct way to do it, but i lack the understanding.
     
  5. Mar 19, 2012 #4

    tiny-tim

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    ah!!! :rolleyes:

    ok, first, are you familiar with the standard constant acceleration equations for ordinary (linear) motion?
     
  6. Mar 20, 2012 #5
    Yes i'm familiar with all the formulas, i just cannot see, how the person who put them together, knew, that this was the way to do it.
     
  7. Mar 20, 2012 #6

    tiny-tim

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    if a is constant …

    then dv/dt = a, so ∆v = at

    d2x/dt2 = a, so ∆x = vot + 1/2 at2

    a = dv/dt = dv/dx dx/dt = vdv/dx = 1/2 d(v2)/dx, so ∆(v2) = 2as :wink:
     
  8. Mar 20, 2012 #7
    But how did he know, that I had to use these three equations, in that order etc. ?
     
  9. Mar 20, 2012 #8

    tiny-tim

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  10. Mar 20, 2012 #9
    Argh! :D

    Let me rephrase.

    How to find out how many equations you are going to work with, and what these equations have to contain?
     
  11. Mar 20, 2012 #10

    tiny-tim

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    it's always obvious which one to use …

    it's the one that has the variables you're given, and the variable you want

    one has s u a and t

    one has u v a and s

    one has u v a and t​
     
  12. Mar 20, 2012 #11
    So because i don't have ω in the first equation, i have to have an equation with ω in it? Because the third equation needs this ω ?
     
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