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24 April, 16:54

On an ice rink, two skaters of equal mass grab hands and spin in a mutual circle once every 2.3 s. if we assume their arms are each 0.85 m long and their individual masses are 65.0 kg, how hard are they pulling on one another

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  1. 24 April, 17:11
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    We have to

    m = 65 kg

    r = 0.85 m

    t = 2.3 s

    The perimeter of the circle is given by:

    P = 2 * pi * r

    P = 2 * pi * (0.85 m)

    P = 5.34 m

    Then, by definition, the distance equals the speed by time:

    d = v * t

    v = d / t

    v = (5.34 m) / (2.3 s)

    v = 2.32 m / s

    Then, to find the radial acceleration, we must use the speed found and the radius of the circle:

    a = v ^ 2 / r

    a = (2.32 m / s) ^ 2 / (0.85 m)

    a = (5.38 m ^ 2 / s ^ 2) / (0.85 m)

    a = 6.32 m / s ^ 2

    Finally, we have that by definition the force is equal to the mass by acceleration:

    F = m * a

    F = (65 kg) * (6.32 m / s ^ 2)

    F = 410.8 N

    answer

    F = 410.8 N
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