Consider the following mass distribution, where x- and y- coordinates are given in meters: 7.0 kg at (0.0, 0.0) m, 3.0 kg at (0.0, 5.0) m, and 7.0 kg at (4.0, 0.0) m. Where should a fourth object of 5.0 kg be placed so that the center of gravity of the four- object arrangement will be at (0.0, 0.0) m? What is the the x-coordinate? What is the y-coordinate?
x=(m1•x1+m2•x2+m3•x3+m4•x4)/(m1+m2+m3+m4) = 0+0+3•4+5•x4/ 22 = 0
y=( m1•y1+m2•y2+m3•y3+m4•y4)/(m1+m2+m3+m4) = 0+3•5+0+5•y4/22 =0
12+5•x4 = 0 => x4 = - 2.4 m
15+5•y4 =0 => y4= - 3 m