Find the center of mass of the system $m _ { 1 } = 5 , P _ { 1 } ( - 3,1 ) , m _ { 2 } = 9$ $P _ { 2 } = ( - 1 , - 1 ) , m _ { 3 } = 6$ $P _ { 3 } = ( 1,1 ) , m _ { 4 } = 8 , P _ { 4 } ( 3 , - 2 )$
A) $\left( \frac { 3 } { 14 } , - \frac { 1 } { 2 } \right)$
B) $\left( - \frac { 1 } { 2 } , \frac { 3 } { 14 } \right)$
C) $\left( \frac { 3 } { 14 } , \frac { 1 } { 2 } \right)$
D) $\left( - \frac { 3 } { 14 } , \frac { 1 } { 2 } \right)$
E) $( 6 , - 14 )$
F) $( - 14,6 )$
G) $( 14 , - 6 )$
H) $( - 14 , - 6 )$

Question

Find the center of mass of the system $m _ { 1 } = 5 , P _ { 1 } ( - 3,1 ) , m _ { 2 } = 9$ $P _ { 2 } = ( - 1 , - 1 ) , m _ { 3 } = 6$ $P _ { 3 } = ( 1,1 ) , m _ { 4 } = 8 , P _ { 4 } ( 3 , - 2 )$ 
A) $\left( \frac { 3 } { 14 } , - \frac { 1 } { 2 } \right)$ 
B) $\left( - \frac { 1 } { 2 } , \frac { 3 } { 14 } \right)$ 
C) $\left( \frac { 3 } { 14 } , \frac { 1 } { 2 } \right)$ 
D) $\left( - \frac { 3 } { 14 } , \frac { 1 } { 2 } \right)$ 
E) $( 6 , - 14 )$ 
F) $( - 14,6 )$ 
G) $( 14 , - 6 )$ 
H) $( - 14 , - 6 )$

Quizplus · Accepted Answer

The center of mass (COM) of a system of particles is given by the formula $\left( \frac{\sum m_i x_i}{\sum m_i}, \frac{\sum m_i y_i}{\sum m_i} \right)$. For the given system, the x-coordinate of the COM is $\frac{5(-3) + 9(-1) + 6(1) + 8(3)}{5 + 9 + 6 + 8} = \frac{-15 - 9 + 6 + 24}{28} = \frac{6}{28} = \frac{3}{14}$, and the y-coordinate is $\frac{5(1) + 9(-1) + 6(1) + 8(-2)}{28} = \frac{5 - 9 + 6 - 16}{28} = \frac{-14}{28} = -\frac{1}{2}$. Therefore, the center of mass is $\left( \frac{3}{14}, -\frac{1}{2} \right)$.

Find the Center of Mass of the System m1=5,P1(−3,1),m2=9m _ { 1 } = 5 , P _ { 1 } ( - 3,1 ) , m _ { 2 } = 9m1​=5,P1​(−3,1),m2​=9

Find the Center of Mass of the System $m _ { 1 } = 5 , P _ { 1 } ( - 3,1 ) , m _ { 2 } = 9$