college physics

two people- one twice as heavy as the other one, play tug-of-war with a 12m ideal rope while standing on a frctionless ice surface.Would any of them move and if he does, how far?explain why.

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  1. Their center of gravity would not move because there is no net force on the system comprising the two masses.
    Say they start a distance d apart
    the 2m mass is at x = 0
    the 1 m mass is at x = d
    Then the center of gravity is at
    2m Xcg = m (d-Xcg)
    2 Xcg = d - Xcg
    Xcg = d/3
    which is where it stays.

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