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Circular Motion

  1. Jun 15, 2008 #1
    1. The problem statement, all variables and given/known data
    A pilot with mass m fles an airplane at a speed of v in a turn of radius r. Prove that angle of the wings of the airplane to the horizontal is tanQ=(VxV)/gr


    2. Relevant equations



    3. The attempt at a solution
    This was asked on my first exam last week.
    Since it's tangent. All we need to get is the force, result will equal to (FxcosQ)/(FxSinQ)=(VxV)/gr?

    I'm not getting anywhere with this? Can someone help me?
     
  2. jcsd
  3. Jun 15, 2008 #2

    dynamicsolo

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    The issue we are concerned with here is how we get the plane to move along a circle of radius r. Start with thinking about the plane flying with the wings level (in a horizontal plane). There are two forces acting on the plane in the vertical direction: its weight, Mg, and the "lift", L, supplied by the wings. With the plane in level flight, these vertical forces must balance.

    Now we want the plane to make a turn, so we "bank" the wings by an angle Q. So the "lifting force" will be off-vertical by an angle Q; since it must still balance the weight of the plane vertically, its magnitude will change to L' . (How is it related to Mg?)

    This altered lifting force now has a horizontal component as well. This component of L', which will equal L' sin Q , is what supplies the centripetal force to pull the plane into a circular path (for the interval of the wing-banking). So we have

    L' sin Q = M·(v^2)/r .

    Try things from there.

    BTW, a similar argument can be used to explain why a cyclist (leg- or motor-powered) must "lean into the turn" when they want to go round a corner...
     
    Last edited: Jun 15, 2008
  4. Jun 15, 2008 #3
    oh, I think i got it.

    So we got our force FnXsinQ=m.a=m.(vXv)/r, also the other component is "mg", so

    when you divide those two, you will get mvv/gr.

    thanks a lot.
     
  5. Jun 15, 2008 #4

    dynamicsolo

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    I'm presuming that what you are calling 'Fn' corresponds to the lift force; there is no normal force for an aviation problem. The lift force when the plane is banked by an angle Q will be L' = mg/cos Q .

    In your last sentence, shouldn't the mass m have divided out?
     
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