# Center of gravity

The mass points are distributed in space as follows - specify by coordinates and weight. Find the center of gravity of the mass points system:

A1 [14; -2; 5] m1 = 10.2 kg
A2 [-2; -16; 7] m2 = 13.6 kg
A3 [14; 6; 20] m3 = 16.5 kg
A4 [2; 20; 19] m4 = 15.8 kg
A5 [9; -5; 16] m5 = 1.6 kg
A6 [-3; 6; -4] m6 = 3.6 kg
A7 [-20; 12; 19] m7 = 12.5 kg
A8 [-5; -11; -16] m8 = 5.2 kg

Result

x =  1.339
y =  3.587
z =  11.923
=:  0

#### Solution:

$x = \dfrac{ 10.2\cdot 14 + 13.6\cdot (-2) + 16.5\cdot 14 + 15.8\cdot 2 + 1.6\cdot 9 + 3.6\cdot (-3) + 12.5\cdot (-20) + 5.2\cdot (-5) }{ 10.2 + 13.6 + 16.5 + 15.8 + 1.6 + 3.6 + 12.5 + 5.2} \ \\ x= 1.339$
$y = \dfrac{ 10.2\cdot (-2) + 13.6\cdot (-16) + 16.5\cdot 6 + 15.8\cdot 20 + 1.6\cdot (-5) + 3.6\cdot 6 + 12.5\cdot 12 + 5.2\cdot (-11) }{ 10.2 + 13.6 + 16.5 + 15.8 + 1.6 + 3.6 + 12.5 + 5.2} \ \\ y = 3.587$
$z = \dfrac{ 10.2\cdot 5 + 13.6\cdot 7 + 16.5\cdot 20 + 15.8\cdot 19 + 1.6\cdot 16 + 3.6\cdot (-4) + 12.5\cdot 19 + 5.2\cdot (-16) }{ 10.2 + 13.6 + 16.5 + 15.8 + 1.6 + 3.6 + 12.5 + 5.2} \ \\ z = 11.923$

= 0

Calculated by our linear equations calculator.

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