Chapter 3, Problem 19P

The center of mass, ( $\bar{x}$ , $\bar{y}$, $\bar{z}$). of n particles can be calculated by:

$\bar{x}=\frac{{\displaystyle \underset{i=1}{\overset{i=n}{\sum }}{m}_i{x}_i}}{{\displaystyle \underset{i=1}{\overset{i=n}{\sum }}{m}_i}}$ , $\bar{y}=\frac{{\displaystyle \underset{i=1}{\overset{i=n}{\sum }}{m}_i{y}_i}}{{\displaystyle \underset{i=1}{\overset{i=n}{\sum }}{m}_i}}$ , $\bar{z}=\frac{{\displaystyle \underset{i=1}{\overset{i=n}{\sum }}{m}_i{z}_i}}{{\displaystyle \underset{i=1}{\overset{i=n}{\sum }}{m}_i}}$

where x_i,y_i, and z_iand m_iare the coordinates and the mass of particle i, respectively. The coordinates and mass of six particles are listed in the following table. Calculate the center of mass of the particles.

Particle	Mass(kg)	Coordinate x (mm)	Coordinate y (mm)	Coordinate z (mm)
A	0.5	-10	8	32
B	0.8	-18	6	19
C	0.2	-7	11	2
D	1.1	5	12	-9
E	0.4	0	-8	-6
F	0.9	25	-20	8