Question

The masses mi are located at the points Pi. Find the moments Mx and My and the center of mass of the system. m1 = 4, m2 = 3, m3 = 3; P1(2, −3), P2(−3, 1), P3(3, 5)

Answer 1

Answer:

$M_x$= 8

$M_y$ = 6

Therefore the co-ordinate of the center of mass is = $(\frac{4}{5},\frac{3}{5})$

Step-by-step explanation:

Center of mass: Center of mass of an object is a point on the object. Center of mass is the average position of the system.

Center of mass of a triangle is the centriod of a triangle.

Given that m₁= 4, m₂=3, m₃=3 and the points are P₁(2,-3), P₂(-3,1) and P₃(3,5)

$M_x$ = ∑(mass × x-co-ordinate)

$M_y$ = ∑(mass × y-co-ordinate)

Therefore  

$M_x$ = (4×2)+{3×(-3)}+(3×3)

     =8

$M_y$ = {4×(-3)}+{3×1}+(3×5)

    =6

The x co-ordinate of the center of mass is the ratio of $M_x$ to the total mass.

The y co-ordinate of the center of mass is the ratio of $M_y$ to the total mass.

Total mass (m) = m₁+ m₂+ m₃

                        = 4+3+3

                        =10

The x co-ordinate of the center of mass is $\frac {8}{10} = \frac {4}{5}$

The y co-ordinate of the center of mass is $\frac{6}{10}=\frac{3}{5}$

Therefore the co-ordinate of the center of mass is = $(\frac{4}{5},\frac{3}{5})$