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Plane's minimum radius

  1. Feb 27, 2013 #1
    Hi all,

    1. The problem statement, all variables and given/known data

    My problem is exactly the same as the one here: https://www.physicsforums.com/showthread.php?p=2377784

    In the solution that Vykan12 provides (which results in the correct answer according to the textbook), however, there is a normal force included in the equation. I don't understand why this is so? From what I can tell, the question is about the plane, not the pilot.

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 27, 2013 #2

    ehild

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    It is about the pilot,
    but he moves together with the plane. No need to calculate with the normal force. The pilot moves along a circular path, what is his acceleration in terms of the speed and radius of circle?

    ehild
     
  4. Feb 27, 2013 #3
    So there IS no normal force, meaning that the answer is indeed 3.8 x 10^2 m and not 3.3 x 10^2?
     
  5. Feb 27, 2013 #4

    ehild

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    No, 330 m was the correct answer.


    ehild
     
  6. Feb 28, 2013 #5
    I don't understand. This is how I solved it:

    m=82 kg
    v=150 m/s
    a=7.0g

    Fa is the 'upward force'

    Fc = Fa - Fg
    mv^2/r = ma - mg
    v^2/r = a - g
    v^2/(a-g) = r
    r=v^2/(7g-g)
    r=v^2/6g
    r = (150m/s)^2/(6x9.8m^2/s^2)
    =3.83 x 10^2 m

    How do I get 330 m without using the force of normal, as is done in the solution in the link?
     
  7. Feb 28, 2013 #6

    ehild

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    What do you call Fa? Is that not the normal force?

    The acceleration of the plane (and the pilot) flying at constant speed v along a circle of radius R is equal to the centripetal acceleration. The acceleration can not exceed 7g. Fcp<7g. What is the problem?

    ehild
     
  8. Feb 28, 2013 #7
    Sorry, I don't understand?

    Edit: Nevermind, I think I got it. Is the equation simply:

    a = v^2/r?
     
    Last edited: Feb 28, 2013
  9. Feb 28, 2013 #8

    ehild

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    Yes, it is that simple.

    ehild
     
  10. Feb 28, 2013 #9
    Okay, but I am wondering, why is it that the force of gravity does that not factor into the equation?
     
  11. Feb 28, 2013 #10

    ehild

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    "The pilot's acceleration can not exceed 7g"

    The acceleration is a=v2/R. The acceleration is 70 m/s2. It is simple logic that if a=b and b=c then a=c.


    If the question was "The pilot feels 7g, what is the radius of the circle" then gravity would come in:
    The pilot moves along a circle. The forces are gravity and normal force N (from the seat). So Fcp=N-mg. The pilot feels the normal force from the seat: N = 7mg.

    ehild
     
  12. Mar 1, 2013 #11
    Ah, okay. Thanks so much for your help!
     
  13. Mar 1, 2013 #12

    ehild

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    You are welcome.

    ehild
     
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