Three point masses lie in a plane and are connected by masses rods so that they cannot move relative to each other. The masses and their positions are:

Question

Three point masses lie in a plane and are connected by masses rods so that they cannot move relative to each other. The masses and their positions are:

m₁ = 2 kg at (0 m, 6 m)

m₂ = 5.4 kg at (6 m, -3 m)

m₃ = 4.1 kg at (10 m, -8 m)

Calculate the location of this system's center of mass.

The location of center of mass is (  m,  m)

We never went over solving a center of mass question in class so I have no idea how to do this...

Answer 1

We can solve the x and y coordinates of the center of mass separately. The general rule is

Xcm = (m1x1 + m2x2 + m3x3) / (m1+m2+m3)

We will call the center of mass a variable Xcm or Ycm

For x:

mass = 2 at 0

mass = 5.4 at 6

mass = 4.1 at 10

(2)(0)+ (5.4)(6)+ (4.1)(10) all divided by (2+5.4+4.1)

=(0+ 32.4+41)/11.5 = 73.4/11.5 = 6.38m for x

For y:

mass = 2 at 6

mass = 5.4 at -3

mass = 4.1 at -8

(2)(6) + (5.4)(-3) + (4.1)(-8) all over (2+5.4+4.1)

= (12 - 16.2 - 32.8)/11.5 = -37/11.5 = -3.22m for y

center of mass: (6.38m, -3.22m)