Ball 1 and ball 2 are each moving in the +x direct...

Ball 1 and ball 2 are each moving in the +x direction. THe ratio of their velocities is v2/v1 =4.0. A force is then applied to ball 2, causing its velocityto triple. The velocity of ball 1 remainsunchanged. As a result, the velocity of the center of mass ofthe system doubles. Find the ratiom2/m1  of the masses of theballs.

Answers ( 1 )

  1. jacob chen
    jacob chen
    The center of mass of the system initially is
    Xcm = (m1 x1 + m2x2 )/ ( m1 + m2) or if M=(m1 + m2 )
    Xcm = (1/M)(m1 x1 +m2 x2 )
    the velocity of the cm initially is
    Vcm = (1/M)(m1 v1 +m2 v2 )
    the velocity of the cm after the force is appliedis

    Vcm (final)= (1/M)(m1 v1 +m2 3v2 )
    and according to the statement of the problem this is alsotwice the
    initial velocity of the center of mass, i.e.
    Vcm (final)= (1/M)(m1 v1 +m2 3v2 ) = 2Vcm

    or

    (1/M)(m1 v1 + m23v2 ) = 2(1/M)(m1 v1 +m2 v2 )

    but

        v2 = 4v1          
    and now you have an equation in which the v1 termdivides out and
    with a little algebra you get
    m2 / m1 = 1/4

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