Question

19. A mass of 4 kg is located at x1 = 0 m ; y1 = 0 m and a mass of 6 kg is located at x2= 5 m, y2 = 4 m.
Where should one place a third mass of 8 kg so that the coordinates of the centre of mass of the
system is at x = 2 m, y = 2 m ?

Answer 1

Answer:

Assuming D as the origin. DC as x-axis and DA as y-axis we have

m1=1kg,(x1,y1)=(0,1m)

m2=2kg,(x2,y2)=(1m,1m)

m3=3kg,(x3,y3)=(1m,0)

m4=4kg,(x4,y4)=(0,0)

Coordination of their CM are calculated as follows.

xCM=m1+m2+m3+m4m1x1+m2x2+m3x3+m4x4

=1+2+3+4(1)(0)+2(1)+3(1)+4(0)