Three small masses are positioned as follows: 2.0 kg at (0.0 m, 0.0 m), 2.0 kg at (2.0 m, 0.0 m), and 4.0 kg at (2.0 m, 1.0 m). determine the coordinates of the center of mass (or center of gravity) of this system.

Refer to the diagram shown below.

The given data is

mass, kg   Coordinates. m
-------------   -----------------
   2               (0, 0)
   2               (2, 0)
   4               (2, 1)

Total mass, M = 2+2+4 = 8kg
Let (x,y) be the coordinates of M.

Then, taking moments about the origin, we obtain
8x = 2*0 + 2*2 + 4*2 = 12
x = 1.5 m

8y = 2*0 + 2*0 + 4*1 = 4
y = 0.5 m

  (1.5, 0.5) m

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