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Homework Help: How to find the maximal mechanical power output of a stearin engine?

  1. Aug 28, 2013 #1
    1. The problem statement, all variables and given/known data
    "How does the placement of the puncture hole of a stearin engine affect the power output of the system?"

    By a stearin engine, it just means an oscillating candle around a fixed point; a video can be viewed at .

    I have done all of the data collection by testing different puncture hole placements and videotaping the process with a protractor in the background.

    To measure the mechanical power output, I was planning on using the equation for rotational kinetic energy, KE=.5 I w^2, where "w" is the rotational velocity of the object.

    I'm having trouble determining the rotational velocity of the candle. My teacher said I could use data logger pro to analyze my videos for me, but I can't find a way to do it on the program. I have read about data logger pro, and I heard that it is not possible for it to determine the rotatinoal displacement or velocity of an object.

    I do have another program, however. It is called "Tracker", but I am once again having the same problem.

    I CAN slow down the video and pause it every fraction of a second and manually record the angular displacement at a certain time. I could do this for several seconds and then manually calculate the angular velocity, but since the experiments go on for several minutes, I would need to find where in the experiment angular velocity is greatest.

    I'm sorry if I'm not making any sense or if this isn't a very good question.

    I would really appreciate it if someone could point me in the right direction.

    Thank you so much in advance.
    Last edited by a moderator: Sep 25, 2014
  2. jcsd
  3. Aug 29, 2013 #2
    The instantaneous power, P, developed by the force (weight in this case) is given by the product of the torque, [itex]\tau[/itex], exerted and the (changing) angular velocity, [itex]\omega[/itex], of the candle

    P = [itex]\tau\omega[/itex]

    In your case you would then need to determine the maximum angular velocity of the candle during the oscillations. The torque is the product of the moment of inertia, I, of the candle and its angular acceleration, [itex]\alpha[/itex]

    [itex]\tau[/itex] = I [itex]\alpha[/itex]

    You can evaluate the angular motion of the candle in Tracker by dragging the origin of the coordinate system to the axis of rotation. You can then measure angles by rotating the coordinate system. This can be done by dragging one of the axes. The program indicates through what angle the system was rotated. Step through the frames and measure the rotation angles. You can also get info on the frame rate of the video by clicking on the Clip Settings icon.
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