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Uniform circular motion with constant upward velocity.

  1. Feb 16, 2013 #1
    1. The problem statement, all variables and given/known data
    It is common to see birds of prey rising upward on thermals. The paths they take may be spiral-like. You can model the spiral motion as uniform circular motion combined with a constant upward velocity. Assume a bird completes a circle of radius 6.00m every 5.00s and rises vertically at a rate of 3.00m/s


    1. Find the speed of the bird relative to the ground.
    2. Find the magnitude of the bird's acceleration.
    3. Find the direction of the bird's acceleration.
    4. Find the angle between the bird's velocity vector and the horizontal.


    2. Relevant equations

    Velocity tanget=(2*∏*R)/T

    Acceleration radial= (4*∏^(2)*R)/T^(2)

    3. The attempt at a solution

    1:

    Velocity tanget=(2*∏*R)/T

    V tan. = (2*pi*6m)/5s = 7.53m/s
    V= sqrt[ (3m/s)^(2) + (7.53m/s)^(2) ] = 8.11m/s

    2:

    Acceleration radial= (4*∏^(2)*R)/T^(2)

    A rad= (4*pi^(2)*6m)/25s^(2)=9.47m/s^(2)

    Atan is zero because of uniform circular motion. The bird is going up at a constant veloctiy so acceleration going up is zero right. Does gravity still have an effect?

    3: I am stuck in the direction part.

    4: tan(θ) = 3m/s over 7.53m/s= 22 degress from the horizontal.

    Is my work right so far and what about part 3? Thanks!
     
  2. jcsd
  3. Feb 16, 2013 #2

    haruspex

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    You don't need to consider gravity here. It's a question about the actual movement of the bird, regardless of the forces that lead to it.
    You computed a radial acceleration, and decided, correctly, that there was no other acceleration. So haven't you determined the direction?
    Everything else looks right.
     
  4. Feb 16, 2013 #3
    Well I know that it would be inward. Since the other component atan is 0 then the direction would be 0 degrees?
     
  5. Feb 16, 2013 #4
    I had another question. Where would you put you axis at? I did this problem using 2 dimensions.
     
  6. Feb 16, 2013 #5

    haruspex

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    Sorry, which axis?
     
  7. Feb 16, 2013 #6
    Where would you make your origin for this problem? This problem can be done by using 3 dimensions or 2 dimensions right?
     
  8. Feb 16, 2013 #7

    haruspex

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    It's very much a 3D question. A natural choice would be cylindrical polar, with the z axis vertical. But you could also use Cartesian, centred on where the bird is at the instant being considered, with x as the radius and y as the horizontal projection of the tangent, say.
     
  9. Feb 17, 2013 #8
    [url=http://www.freeimagehosting.net/oewmb][PLAIN]http://www.freeimagehosting.net/t/oewmb.jpg[/url][/PLAIN]

    is this picture good?
     
  10. Feb 18, 2013 #9

    haruspex

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    The path is a helix (not, as the OP stated, a spiral).
     
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