Find the center of mass of the three massed in the figure If

Find the center of mass of the three massed in the figure If the 8-kg mass starts moving at 0.5 m/s to the right, And the 2-kg ball remains stationary, how fast, and in what direction must the 1-kg ball move, such that the center of mass of the system does not move?

Solution

Masses m1 = 1kg

             m2 = 2 kg

            m3 = 8 kg

Positions of m1,m2,m3 are x1= 1 m

                                        x2 = 2 m

                                        x3 = 4 m

Center of mass Xcm = (m1x1+m2x2+m3x3)/(m1+m2+m3)

                              =[(1x1)+(2x2)+(8x4)]/(1+2+8)

                              = (1+4+32)/11

                              = 37/11

                              = 3.3636 m

(b). v1 = v1

     v2 = 0

    v3 = 0.5 m/s

Vcm = [m1v1+m2v2+m3v3 ]/[m1+m2+m3]

        = [(1xv1)+(2x0)+(8x0.5)]/[1+2+8]

        = [v1+4]/11

Given Vcm = 0

So, v1+4 = 0

         v1 = -4 m/s

i.e., mass of 1 kg is moving with velocity 4 m/s along left direction.