The masses $m_{i}$ are located at the point $P_{i}$ . Find the moments $M_{x}$ and $M_{y}$ and the center of mass of the system. $m_{1}=3, m_{2}=7, m_{3}=113$ ; $p_{1}(1,5), P_{2}(3,-2), p_{3}(-2,-1)$
A) $M_{x}=22, M_{y}=50,\left(\frac{50}{23}, \frac{22}{23}\right)$
B) $M_{x}=50, M_{y}=22,\left(\frac{50}{23}, \frac{22}{23}\right)$
C) $M_{x}=-50, M_{y}=22,\left(\frac{50}{23},-\frac{22}{23}\right)$
D) $M_{x}=22, M_{y}=50,\left(\frac{22}{23}, \frac{50}{23}\right)$
E) $M_{x}=50, M_{y}=-22,\left(-\frac{50}{23}, \frac{22}{23}\right)$

Question

Quizplus · Accepted Answer

The moments are calculated as $M_{x} = \sum m_{i}y_{i}$ and $M_{y} = \sum m_{i}x_{i}$. For the given points and masses, $M_{x} = 3(5) + 7(-2) + 113(-1) = 50$ and $M_{y} = 3(1) + 7(3) + 113(-2) = 22$. The center of mass is $\left(\frac{M_{y}}{\sum m_{i}}, \frac{M_{x}}{\sum m_{i}}\right) = \left(\frac{50}{123}, \frac{22}{123}\right)$.

The Masses mim_{i}mi​ Are Located at the Point PiP_{i}Pi​ Find the Moments

The Masses $m_{i}$ Are Located at the Point $P_{i}$ Find the Moments