Question

Need Help please.
Consider the following mass distribution where the x and y coordinates are given in meters: 5.0 kg at (0.0, 0.0) m, 3.0 kg at (0.0, 4.3) m, and 4.0 kg at (2.8, 0.0) m. Where should a fourth object of 8.2 kg be placed so the center of gravity of the four-object arrangement will be at (0.0, 0.0) m?
x___m
Y___m
okay this is what I did but, it not right any idea please.
m1x1+m2x2+m3x3+m4x4/m1+m2+m3+m4
-(5.0)(0)+(3.0)(0)+(4.0)(2.8)+8.2(0)
19.4/20.2=-0.960 for x-axis
and for y-axis I did the same thing.

Answer 1

You want to solve for x4 and y4, so that the CM location is (0,0)

Require that the numerator in your expression for the x centroid be zero. If it is, the denomiator doesn't matter.

m1x1 + m2x2 + m3x3 + m4x4 = 0
(5.0)(0)+(3.0)(0)+(4.0)(2.8)+ 8.2*x4 = 0
x4 = -1.366 (meters)

Solve for y4 similarly