Three point masses are located in the xy plane as follows: a 1-kg mass is at the origin i. e., at (0,0), a second 1-kg mass is at x = 4m on the x axis, i. e., at (4,0), and a 2-kg mass is at the point x = 2m, by = 2m, i. e., at (2,2). Find both the x and y center of mass.

r=  ( 2 , 1) m

Explanation:

The important concept of center of mass is  where all external forces can be applied,  

= 1 /M ∑  

y_{cm} = 1 /M ∑ y_{i} m_{i}

Where  x, y is the coordinate of each mass, is the mass of each point and M is the total mass of the body

Let's apply these expressions to our exercise  

    M = 1 + 1 +2  

    M = 4 kg  

    x_{cm} = 1/4 (1 0 + 1 4 +2 2)  

    x_{cm} = 2m  

    y_{cm} = 1/4 (1 0 + 1 0 + 2 2)  

y_{cm} = 1m

coordinates of the center of mass

r= ( 2 , 1) m