Question

Consider the following distribution of objects: a 1.00-kg object with its center of gravity at (0, 0) m, a 2.20-kg object at (0, 3.00) m, and a 4.40-kg object at (4.00, 0) m. Where should a fourth object of mass9.00 kg be placed so that the center of gravity of the four-object arrangement will be at (0, 0)?

Answer 1

m1 = 1 kg           (x1 , y1 ) = (0,0)

m2 = 2.2 kg           (x2 , y2 ) = (0,3)

m3 = 4.4 kg           (x3 , y3 ) = (4,0)

m4 = 9 kg           (x4 , y4 ) = ?

xcm , ycm = 0 , 0

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

0 = ((1*0)+(2.2*0)+(4.4*4)+(9*x4))/(1+2.2+4.4+9)

x4 = -1.96 m

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

0 = ((1*0)+(2.2*3)+(4.4*0)+(9*y4))/(1+2.2+4.4+9)

x4 = -0.73 m

(x4 , y4 ) = (-1.96 , -0.73 )m