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Two ice skaters have masses m1 and m2 and are initially stationary. Their skates are identical. They push against one another, as shown below, and move in opposite directions with different speeds. While they are pushing against each other, any kinetic frictional forces acting on their skates can be ignored. However, once the skaters separate, kinetic frictional forces eventually bring them to a halt. As they glide to a halt, the magnitudes of their accelerations are equal, and skater 1 glides 3 times as far as skater 2. What is the ratio m1 / m2 of their masses?

  • Physics -

    Their initial velocities are in a ratio V1/V2 = m2/m1

    Their kinetic friction forces are in a ratio
    F1/F2 = M1/M2

    Gliding time t is proportional to
    V/a = V m/F

    Gliding distance D is proportional to
    V*t = V^2*m/F

    D1/D2 = 3 = [V1^2*m1/F1)][m2/(F2*V2^2)]
    = (V1/V2)^2*(m1/m2)*F2/F1
    = (m2/m1)^2

    m2/m1 = 3^1/2 = 1.732
    m1/m2 = 0.577

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