Given:
The mass m1 = 3 kg whose coordinates are (1,2)
The mass m2 = 1 kg whose coordinates are (5,3)
The mass m3= 4 kg whose coordinates are (7,1)
To find the coordinates of the center of mass.
Explanation:
The x-coordinate of the center of mass can be calculated as
[tex]\begin{gathered} x\text{ coordinate = }\frac{m1x1+m2x2+m3x3}{m1+m2+m3} \\ =\frac{(3\times1)+(1\times5)+(4\times7)}{3+1+4} \\ =4.5\text{ } \end{gathered}[/tex][tex]\begin{gathered} x\text{ coordinate = }\frac{m1x1+m2x2+m3x3}{m1+m2+m3} \\ =\frac{(3\times1)+(1\times5)+(4\times7)}{3+1+4} \\ =4.5\text{ } \end{gathered}[/tex]
The y-coordinate of the center of mass can be calculated as
[tex]\begin{gathered} \text{y-coordinate = }\frac{m1y1+m2y2+m3y3}{m1+m2+m3} \\ =\frac{(3\times2)+(1\times3)+(4\times1)}{3+1+4} \\ =1.625 \end{gathered}[/tex]
Thus, the coordinates of the center of mass is (4.5,1.625)
