Question

A particle of mass 3kg moving along a track at 8ms/1 towards another particle of mass 5kg travelling 5ms/1 impact, find their common velocity, if they were traveling .

Find ;

a. Same direction

b. Opposite direction

Answer 1

a) From the law of conservation of linear momentum, we have:

$$m_1v_1+m_2v_2=(m_1+m_2)v_c,$$ $$v_c=\dfrac{m_1v_1+m_2v_2}{m_1+m_2},$$ $$v_c=\dfrac{3\ kg\cdot8\ \dfrac{m}{s}+5\ kg\cdot5\ \dfrac{m}{s}}{3\ kg+5\ kg}=6.125\ \dfrac{m}{s}.$$

b) From the law of conservation of linear momentum, we have:

$$m_1v_1-m_2v_2=(m_1+m_2)v_c,$$ $$v_c=\dfrac{m_1v_1-m_2v_2}{m_1+m_2},$$ $$v_c=\dfrac{3\ kg\cdot8\ \dfrac{m}{s}-5\ kg\cdot5\ \dfrac{m}{s}}{3\ kg+5\ kg}=-0.125\ \dfrac{m}{s}.$$