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19 September, 20:27

Consider a system of two particles: ball A with a mass m is moving to the right a speed 2v and ball B with a mass 3m is moving to the left at a speed v. In the time interval before the two balls collide, what is the magnitude and the direction of the velocity of the center of mass of this system?

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  1. 19 September, 22:10
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    Given that,

    System of two particle

    Ball A has mass

    Ma = m

    Ball A is moving to the right (positive x axis) with velocity of

    Va = 2v •i

    Ball B has a mass

    Mb = 3m

    Ball B is moving to left (negative x axis) with a velocity of

    Vb = - v •i

    Velocity of centre of mass Vcm?

    Velocity of centre of mass can be calculated using

    Vcm = 1/M ΣMi•Vi

    Where M is sum of mass

    M = M1 + M2 + M3 + ...

    Therefore,

    Vcm=[1 / (Ma + Mb) ] * (Ma•Va + Mb•Vb

    Rearranging for better understanding

    Vcm = (Ma•Va + Mb•Vb) / (Ma + Mb)

    Vcm = (m•2v + 3m•-v) / (m + 3m)

    Vcm = (2mv - 3mv) / 4m

    Vcm = - mv / 4m

    Vcm = - v / 4

    Vcm = - ¼V •i
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