Find the x and y coordinate of such a point.?

Question

Consider the following mass distribution:
3.1 kg at (5 m, -9 m), 1.5 kg at (0 m, 6:2 m),
and 5 kg at (4.9 m, 0 m). We need to place
a fourth mass of 4.3 kg so that the center of
gravity of the four-mass arrangement will be
at (0, 0).

Find the x coordinate of such a point. Answer in units of m.

Find the y coordinate of such a point. Answer in units of m.

Answer 1

OK. All you have to do is balance the torques about the x and y axis so that they're 0.

3.1*5+1.5*0+5*4.9 = 24.5 mKg and
4.3*x=-24.5 so x=-21.198 m

3.1*(-9) + 1.5*6.2+5*0 = 9.3 mKg and
4.3y=-9.3 so y = -25.737 m

HTH

Doug