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March 26, 2017

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A brother (mass 20 kg) and his big sister (mass 32 kg) want to play on a teeter-totter. The beam is 7 m long and has a mass of 41 kg. Suppose the brother sits at the end of his side, 3.5 m away from the pivot point. How far away from the pivot point does the sister need to sit for the system to be in rotational equilibrium?

  • physics - ,

    Use the center of mass fomula:
    Xcm = (M1X1 + M2X2 + ... + MnXn)/(M1 + M2 + ... + Mn)
    Don't forget the mass of the teeter-totter and its location at its geometric center (M1 = 41 kg, X1 = 3.5 since the fulcrum is in the middle of the beam).
    Set the location of the sister at the origin (X = 0) and the brother at the opposite end of the beam (X = 7m).
    Xcm = (20 x 7 + 32 x 0 + 41 x 3.5)/(20 + 32 + 41) = 283.5/93 = 3.05
    The sister is 3.05 m from the pivot point.

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