Velocity and momentum of the CM

Problem

CM velocity. Two masses: $m_1 = 4\;\text{kg}$ at velocity $v_1 = +2\;\text{m/s}$ and $m_2 = 6\;\text{kg}$ at velocity $v_2 = -3\;\text{m/s}$. Calculate the velocity and momentum of the centre of mass.

Solution

Total momentum: $P_\text{tot} = m_1 v_1 + m_2 v_2 = 4\cdot 2 + 6\cdot(-3) = 8 - 18 = -10\;\text{kg}\cdot\text{m/s}$

CM velocity (total mass $10\;\text{kg}$): $v_\text{cm} = \frac{P_\text{tot}}{M_\text{tot}} = \frac{-10}{10} = -1\;\text{m/s}$

$\ev{P_\text{tot} = -10\;\text{kg}\cdot\text{m/s}, \quad v_\text{cm} = -1\;\text{m/s}}$

Links

Topics: Centre of mass Concepts: Centre of mass · Momentum