If a $5.00 \mathrm{~kg}$ mass is moving EAST at $10.0 \mathrm{~m} / \mathrm{s}$ and a $15.0 \mathrm{~kg}$ mass is moving WEST at $10 \mathrm{~m} / \mathrm{s}$, what is the velocity of the center of mass of the pair?

Question

Quizplus · Accepted Answer

The velocity of the center of mass can be calculated using the formula: $v_{cm} = \frac{m_1v_1 + m_2v_2}{m_1 + m_2}$. Here, $m_1v_1 = 5 \times 10 = 50 \, \text{kg m/s EAST}$ and $m_2v_2 = 15 \times (-10) = -150 \, \text{kg m/s WEST}$ (taking east as positive and west as negative). Thus, $v_{cm} = \frac{50 - 150}{5 + 15} = \frac{-100}{20} = -5 \, \text{m/s}$, which means 5.0 m/s WEST.

If A 5.00 kg5.00 \mathrm{~kg}5.00 kg Mass Is Moving EAST At 10.0 m/s10.0 \mathrm{~m} / \mathrm{s}10.0 m/s

If A $5.00 \mathrm{~kg}$ Mass Is Moving EAST At $10.0 \mathrm{~m} / \mathrm{s}$