Respuesta :
Answer:
[tex]M_x[/tex]= 8
[tex]M_y[/tex] = 6
Therefore the co-ordinate of the center of mass is = [tex](\frac{4}{5},\frac{3}{5})[/tex]
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)
[tex]M_x[/tex] = ∑(mass × x-co-ordinate)
[tex]M_y[/tex] = ∑(mass × y-co-ordinate)
Therefore
[tex]M_x[/tex] = (4×2)+{3×(-3)}+(3×3)
=8
[tex]M_y[/tex] = {4×(-3)}+{3×1}+(3×5)
=6
The x co-ordinate of the center of mass is the ratio of [tex]M_x[/tex] to the total mass.
The y co-ordinate of the center of mass is the ratio of [tex]M_y[/tex] to the total mass.
Total mass (m) = m₁+ m₂+ m₃
= 4+3+3
=10
The x co-ordinate of the center of mass is [tex]\frac {8}{10} = \frac {4}{5}[/tex]
The y co-ordinate of the center of mass is [tex]\frac{6}{10}=\frac{3}{5}[/tex]
Therefore the co-ordinate of the center of mass is = [tex](\frac{4}{5},\frac{3}{5})[/tex]
