Question

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise The masses m/ are located at the points Pi. Find the moments Mx and My and the center of mass of the system. m1 = 3, m2 = 4, m3 = 3; P1 = (2,-6), P2 = (-3,2), P3 = (3, 4) Step 1 The total mass of the system is the sum of the individual masses. m = m + m2 + m3

Answer 1

Answer:

$M_x = 2, M_y = 3$

Center of mass at $(\frac{3}{10},\frac{2}{10})$

Step-by-step explanation:

Given a set of objects $m_1, \dots, m_k$ located at the points $P_1(x_1, y_1), \dots, P_k(x_k,y_k)$ The moments Mx and My are calculated as follows.

$M_x = \sum_{n=1}^k m_n\cdot y_n, M_y = \sum_{n=1}^k m_n\cdot x_n$

and the Center of mass is given at the coordinates $(\frac{My}{M}, \frac{Mx}{M})$ where M is the total mass of the system.

We have that m1=3, m2=4 and m3=3, so M = 3+4+3 = 10.

We have that m1 is at point P1(2,-6), m2 at point P2(-3,2) and m3 at point P3 (3,4), then

$M_x = \sum_{n=1}^k m_n\cdot y_n = 3\cdot(-6)+4\cdot(2)+3\cdot(4)=2$

$M_y = \sum_{n=1}^k m_n\cdot x_n = 3\cdot(2)+4\cdot(-3)+3\cdot(3)= 3$

Then, the center of Mass is at $(\frac{3}{10},\frac{2}{10})$