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Math Help - Fly, little birdie!!

  1. #1
    Member Chokfull's Avatar
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    Fly, little birdie!!

    OK, I may just be stupid, having just taken a long break from physics, but I'm having trouble with a problem about--you'll never guess--a bird.

    It's flying--sorry, soaring--in a horizontal circular path. It's bank angle (relative to the horizontal) is estimated to be 25^o and the bird takes 13 s to complete one circle. How fast is the bird flying and what is the radius of the circle?

    I would start by taking the normal force exerted on the bird by the air, at an angle of [MATH65^o[/tex] to the horizontal (90-25), and then finding the percentage of that force pushing the bird toward the center of the circle, but I don't know what to do after that.
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  2. #2
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    skeeter's Avatar
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    let L = lift force, m = bird mass

    three equations ... three unknowns v, r, and L

    \displaystyle v = \frac{2\pi r}{t}

    \displaystyle L\sin(25) = F_c = \frac{mv^2}{r}

    L\cos(25) = mg

    solve the system
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  3. #3
    Member Chokfull's Avatar
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    OK, I did this:

    v=\frac{2\pi R}{t}

    L\sin(25)=\frac{mv^2}{R}

    L\cos(25)=mg

    L=\frac{mv^2}{R\sin(25)}=\frac{mg}{\cos(25)}

    R=\frac{\sin(25)g}{v^2\cos(25)}=\frac{4.57}{v^2}

    v=\frac{2\pi4.57}{tv^2}

    So, solving this, I get about 1.3 m/s for V. My book gives a different answer, though. What am i doing wrong?
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  4. #4
    MHF Contributor ebaines's Avatar
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    The problem is in your equation for R - check your units and you'll see that you got a couple of terms upside down. It should be:

    R=\frac{\cos(25)v^2}{g \sin(25)}=\frac{v^2}{14.67 m /s^2}

    v=\frac {2 \pi R} t = \frac{2\pi v^2}{14.67 t}

    Solve for v, and I get 30.3 m/s
    Last edited by ebaines; September 16th 2010 at 10:03 AM.
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