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Coupled motions

  1. Feb 3, 2014 #1
    Hello there,

    A weather ballon is released, and its acceleration in the z-x-plane, a is governed by a buoyancy force, B, which is constant in the k-direction. gravitational acceleration, 9.81 m/s^2, in the k-direction, and FD, which is is like this:

    [tex]F_D = -D|\vec{v}|\vec{v}[/tex]

    where D is some constant. Furthermore, the balloon is experiencing some wind in the i-direction:

    [tex]\vec{w} = w\vec{i}[/tex]


    1. Does the following look reasonable:

    [tex]F_D = D(|\vec{w}|\vec{w} - |\vec{v}|\vec{v})[/tex]

    And if the above is correct, 2., I fail to see how this can be a coupled motion:

    [tex]\vec{a} = {D \over m}(|\vec{w}|\,\vec{w} - |\vec{v}|\,\vec{v}) + ({F_B \over m} - g)\vec{k}[/tex]

    Will you kindly explain how it is coupled?

    Thank you for your time.

    Kind regards,
  2. jcsd
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