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Homework Help: Pendulum involving conservative energy

  1. Apr 11, 2005 #1
    Hey! I need help with this question:
    A ball having mass m is connected by a strong string of length L to a pivot point and held in place in a vertical position. A wind exerting constant force of magnitude F is blowing from left to right. If the ball is released from rest, show that the maximum height H reached by the ball, as measured from its initial height, is H= (2L)/(1+(mg/F)^2) Check that the above result is valid both for cases when 0<H,L and for L<H<2L.
    So far, I know that I'm supposed to use FLsin(theta)=mgH
    and integrate it -> W=(integral)FLcos(theta)d(theta)
    But I have no idea at all where to go from here!! Please, i really need help now!! I don't have much time left for this!! :cry:
     
  2. jcsd
  3. Apr 12, 2005 #2

    Andrew Mason

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    The solution to the pendulum motion without the wind is:

    [tex]\theta = \theta_0,sin(\omega t)[/tex] where [itex]\omega = \sqrt{g/L}[/itex]

    When you add the wind, the energy added on the forward cycle is lost on the reverse cycle so this is equivalent to a new vibration about a different equilibrium position in which the new g' is determined from the vector sum of mg and F.

    [tex]g' = \sqrt{g^2 +(F/m)^2}[/tex] and

    [tex]\theta_0' [/itex] is the angle that the vector sum of F and mg makes to the vertical. Try working out H from that.

    AM
     
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