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Propeller Problem

  1. Apr 17, 2006 #1
    An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 117 kg. When the airplane's engine is first started, it applies a constant torque of 1590Nm to the propeller, which starts from rest.

    Question I:
    What is the average power output of the engine during the first 5.00 rev?

    Question II:
    What is the instantaneous power output of the motor at the instant that the propeller has turned through 5.00 rev?

    I've already solved for the angular accelleration (after 5 revolutions) which is alpha, angular speed omega (after 5 revolutions), and work after 5 revolutions W, moment of inertia 42.18kg*m^2.

    For the last two parts I've tried to solve using P=torque+angular velocity .... that turned out to be wrong. Then I tried using P=Change in work/change in time but that failed. So now I'm a little at a loss. Is there any suggestions where to try next?:cool:

    I figured it out, my methods were correct...... my ending units were wrong! @_@
    Last edited: Apr 17, 2006
  2. jcsd
  3. Apr 18, 2006 #2

    Andrew Mason

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    Energy is torque x angle (force x distance).

    [tex]\tau\Delta\theta = \text{Work}[/tex]

    So [tex]P_{avg} = \Delta E/\Delta t = \tau\Delta\theta/\Delta t[/tex]

    All you have to do is figure out how long it takes to move the propeller 5 revolutions with that torque: Use [itex]\theta = \frac{1}{2}\alpha t^2[/itex] and [itex]\alpha = \tau/I[/itex] to find the time in terms of angle and torque (and I).

    To find instantaneous power, use:

    [tex]P = \tau\omega = \tau\alpha\Delta t[/tex]

    You have to assume that in the first 5 revolutions, the resistance to motion is only the moment of inertia of the propeller, not the propulsion of air by the propeller.

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