Answer to Question #229096 in Physics for Ella

Question

a 100 kg cart moving to the right of 5 m/s collides head-on with an 80 kg cart moving to the left at 4 m/s. if the collision is elastic calculate the speeds of two carts before and after the collision in the centre of mass of frame of reference

Answer 1

$p_1'=\frac{m_1m_2}{m_1+m_2}(v_1-v_2)\to v_1'=\frac{1}{m_1}\frac{m_1m_2}{m_1+m_2}(v_1-v_2)=$

$=\frac{1}{100}\frac{100\cdot 80}{100+80}(5-4)=0.44\ (m/s)$

$p_2'=\frac{m_1m_2}{m_1+m_2}(v_2-v_1)\to v_2'=\frac{1}{m_2}\frac{m_1m_2}{m_1+m_2}(v_1-v_2)=$

$=\frac{1}{80}\frac{100\cdot 80}{100+80}(4-5)=-0.55\ (m/s)$