Question

Consider the following distribution of objects: a 3.00-kg object with its center of gravity at (0, 0) m, a 4.20-kg object at (0, 3.00) m, and a 1.40-kg object at (2.00, 0) m. Where should a fourth object of mass 7.00 kg be placed so that the center of gravity of the four-object arrangement will be at (0, 0)?

Answer 1

Center of gravity of the arrangement of objects is (Xcg,Ycg) = (0,0)

given that m1 = 3 kg and (x1,y1) = (0,0)

and m2 = 4.2 kg and (x2,y2) = (0,3)

m3 = 1.4 Kg and (x3,y3) = (2,0)

m4 = 7 kg and (x4,y4) = (?,?)

Xcg = ((m1*x1)+(m2*x2)+(m3*x3)+(m4*x4))/(m1+m2+m3+m4)

0 = [(m1*0) + (m2*0) + (1.4*2) + (7*x4)]/(3+4.2+1.4+7)

1.4*2 = -7*x4

x4 = -0.4 m

Ycg = ((m1*y1)+(m2*y2)+(m3*y3)+(m4*y4))/(m1+m2+m3+m4)

0 = ((m1*0)+(4.2*3)+(1.4*0)+(7*y4))/(3+4.2+1.4+7)

4.2*3 = -7y4

y4 = -1.8 m

So coordinates of 7 kg mass is (-0.4m , -1.8m)