Question

Find the center of the mass of the four particles having the masses of 2, 3, 3 and 4 kg and located at the points (-1, -2), (1, 3), (0, 5), and (2, 1), respectively.

Answer 1

The coordinates $\overrightarrow{R}$  of the center of mass can be found using the formula

$\displaystyle \overrightarrow{R}=\frac1M\sum_{i=0}^{n} m_i\overrightarrow{r_i}$ , where $\displaystyle M=\sum_{i=0}^n m_i$ is the total mass of all of the particles.

$\displaystyle M=2+3+3+4=12$ (kg)

$\displaystyle \overrightarrow{R}=\frac{1}{12}(2\cdot(-1,-2)$$+3\cdot(1,3)+3\cdot(0,5)+4\cdot(2,1))$ $=\frac{1}{12}(9,24)=(\frac34,2)$ .

Answer: Coordinates of the center of the mass are $(\frac34,2)$ .