Answer to Question #161955 in Physics for Ayamdor Emmanuel

Question

If a particle of mass 3kg moving along a track at 8ms towards another particle of mass 5kg traveling 5ms on the same track.if the particles move together after impact, find their common velocity if they were traveling

(I) same direction

(II) opposite direction

Answer 1

Apply conservation of momentum.

(I) Same direction

$$p_i=p_f,\\ m_1v_1+m_2v_2=(m_1+m_2)u,\\\space\\ u=\frac{m_1v_1+m_2v_2}{m_1+m_2}=6.1\text{ m/s}$$

in the initial direction of both particles,

(II) Opposite direction

$$p_i=p_f,\\ m_1v_1-m_2v_2=(m_1+m_2)u,\\\space\\ u=\frac{m_1v_1-m_2v_2}{m_1+m_2}=-0.1\text{ m/s}$$

in the initial direction of the particle with greater momentum (5 kg at 5 m/s).