Answer to Question #150481 in Mechanics | Relativity for Rain

Question

Three particles are situated in 3-D space. The position of each particle is represented by the following vectors:
• A 5-kg particle at r1 = 4i + 3j + 5k
• A 3-kg particle at r2 = –3i + 5j + 3k
• A 6-kg particle at r3 = 5i – 6k
a. Find the location of the center of mass of these particles

Answer 1

$m_1=5kg \space \&\space \vec r_1=(4,3,5)\\ m_2=3kg \space \&\space \vec r_2=(-3,5,3)\\ m_3=6kg \space \&\space \vec r_3=(5,0,-6)\\ r_{cm}=\cfrac{m_1\vec r_1+m_2\vec r_2+m_3\vec r_3}{m_1+m_2+m_3}\\ r_{cm}=\cfrac{5(4\hat i+3\hat j+5\hat k)+3(-3\hat i+5\hat j+3\hat k)+6(5\hat i-6\hat k)}{14}\\ r_{cm}=\cfrac{41\hat i+30 \hat j-2\hat k}{14}$

which is location of center of mass.