Question

The mass $100g$ and $300g$ at a given time have velocities $10\hat{i}-7\hat{j}-3\hat{k}$ and $7\hat{i}-9\hat{j}+6\hat{k}$ respectively. Determine velocity of $COM$.

Answer 1

$m_1=100g=0.1kg$, and

$v_1=(10i-7j-3k)m/s$

$m_2=300g=0.3kg$, and

$v_2=(7i-9j+6k)m/s$

Velocity of COM in x direction $V_x=\frac{10\times 0.1+7\times 0.3}{0.1+0.3}=\frac{31}{4}$

Velocity of COM in y direction $V_y=\frac{-7\times 0.1-9\times 0.3}{0.1+0.3}=\frac{-34}{4}$

Velocity of COM in z direction $V_z=\frac{-3\times 0.1+6\times 0.3}{0.1+0.3}=\frac{15}{4}$

Thus, velocity of the center of mass, $V=V_x+V_y+V_z=\frac{31-34+15}{4}=3m/s$