Answer to Question #172541 in Physics for Kenneth

Question

Locate the center of mass of three particles m1=5kg, m2=7kg and m3=8kg located at ( -1,2,3),(2,4,6) and ( 3,-2,5) respectively coordinates in metres.

Answer 1

By definition, the radius-vector of the center of mass is given by the formula:

$$\mathbf{R} = \dfrac{\sum\mathbf{r}_im_i}{\sum m_i}$$

where

$\mathbf{r}_1m_1 = (-1,2,3)\cdot 5kg = (-5,10,15)\space (kg)$ is the product of the radius-vector and the mass of the first particle, and

$\mathbf{r}_2m_2 = (2,4,6)\cdot 7kg = (14,28,42)\space (kg)$ - the same for the second mass

$\mathbf{r}_3m_3 = (3,-2,5)\cdot 8kg = (24,-16,40)\space (kg)$ - the same for the third mass.

The summation is over all particles, thus, obtain:

$$\mathbf{R} = \dfrac{(-5,10,15) + (14,28,42) + (24,-16,40)}{5 + 7+8} = \dfrac{1}{20}(33, 22, 97) = (1.65,1.1,4.85)$$

Answer. $(1.65,1.1,4.85)$