Question

Four particles are located at points (1,3), (2,2), (3,3), (4,3).

Find the moments M_x and M_y and the center of mass of the system, assuming that the particles have equal mass m. Find the center of mass of the system, assuming the particles have mass 3, 2, 5, and 7, respectively.

Answer 1

1) Same mass:
a) calculate M-x = my₁+my₂+my₃+m4₄ = m(3+2+3+3) = 11m
b) calculate M-y = mx₁+mx₂+mx₃+mx₄ = m(1+2+3+4) = 10m
The center of mass (or center of gravity: POINT(X,Y) is given by:
X = 10m/∑(m) = 10m/4m, so X= 5/2
Y = 11m/∑(m) = 11m/4m ,so Y =11/4

2) Different masses: m₁ = 3; m₂ = 2 ; m₃ = 5 ; m₄ = 7
a) calculate M-x = m₁y₁+m₂y₂+m₃y₃+m₄y₄
M-x= 3.(3)+2(2)+5(3)+7(3) = 50
b) calculate M-y =m₁x₁+m₂x₂+m₃x₃+m₄x₄
M-y=3(1)+2(2)+5(3)+7(4) = 50
The center of mass (or center of gravity: POINT(X,Y) is given by
X= 50/17
Y= 50/17

Hope that I understood the given of the problem & I didn't make mistakes in calculation