Question

Find the coordinates for the center of mass for the system shown below

Answer 1

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.

Step-by-step explanation:

The x-coordinate of the center of mass can be calculated as

`\begin{gathered} x\text{ coordinate = }(m1x1+m2x2+m3x3)/(m1+m2+m3) \\ =((3*1)+(1*5)+(4*7))/(3+1+4) \\ =4.5\text{ } \end{gathered}`
`\begin{gathered} x\text{ coordinate = }(m1x1+m2x2+m3x3)/(m1+m2+m3) \\ =((3*1)+(1*5)+(4*7))/(3+1+4) \\ =4.5\text{ } \end{gathered}`

The y-coordinate of the center of mass can be calculated as

`\begin{gathered} \text{y-coordinate = }(m1y1+m2y2+m3y3)/(m1+m2+m3) \\ =((3*2)+(1*3)+(4*1))/(3+1+4) \\ =1.625 \end{gathered}`

Thus, the coordinates of the center of mass is (4.5,1.625)