Question

The masses mi are located at the points Pi. Find the moments Mx and My and the center of mass of the system. m1=4, m2=2, m3=4; P1(2, -3), P2(-3, 1), P3(3, 5)

Answer 1

The center of mass of the system is in
`P(1.4,1)`

The moments are
`M_{x_(cm)}= 14 M_{y_(cm)}=10`

Explanation:

Relevant data:

`m_(1)=4\\ m_(1)=2\\m_(1)=4\\P1(2, -3)\\P2(-3, 1)\\P3(3, 5)\\`

1. Calculate the Center of Mass:

The center of mass could be calculated using the equations:

`x_(cm)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3) )/(m_(1)+m_(2)+m_(3)) \\y_(cm)=(m_(1)y_(1)+m_(2)y_(2)+m_(3)y_(3) )/(m_(1)+m_(2)+m_(3))`

Then,

`x_(cm)=((4)(2)+(2)(-3)+(4)(3))/(4+2+4)=(14)/(10) \\y_(cm)=((4)(-3)+(2)(1)+(4)(5))/(4+2+4)}=1`

The center of mass of the system is in
`P(1.4,1)`

2. Calculate the Moments

`M_{x_(cm)}=m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3) \\M_{y_(cm)}=m_(1)y_(1)+m_(2)y_(2)+m_(3)y_(3)`

Then:

`M_{x_(cm)}=(4)(2)+(2)(-3)+(4)(3)=14 \\M_{y_(cm)}=(4)(-3)+(2)(1)+(4)(5)=10`

The moments are
`M_{x_(cm)}= 14 M_{y_(cm)}=10`