Source: High school physics (Chinese)
Problem Sets:
Problem
Two objects, A and B, move in the same direction on the same straight line, with A in front. Object A has a mass of $m_A = 2$ kg and a speed of $v_A = 1$ m/s. Object B has a mass of $m_B = 4$ kg and a speed of $v_B = 3$ m/s. After B catches up to A for a head-on collision, both objects continue in the original direction. The speed of A becomes $v_A' = 3$ m/s, and the speed of B becomes $v_B' = 2$ m/s.
No.
An elastic collision conserves total kinetic energy. Initial kinetic energy: $K_i = \frac{1}{2}m_A v_A^2 + \frac{1}{2}m_B v_B^2 = \frac{1}{2}(2 kg)(1 m/s)^2 + \frac{1}{2}(4 kg)(3 m/s)^2 = 1 J + 18 J = 19 J$. Final kinetic energy: $K_f = \frac{1}{2}m_A (v_A')^2 + \frac{1}{2}m_B (v_B')^2 = \frac{1}{2}(2 kg)(3 m/s)^2 + \frac{1}{2}(4 kg)(2 m/s)^2 = 9 J + 8 J = 17 J$. Since $K_i eq K_f$, kinetic energy is not conserved, and the collision is inelastic.