Elastic Collision (KE conserved): (1/2)m_1u_1^2 + (1/2)m_2u_2^2 = (1/2)m_1v_1^2 + (1/2)m_2v_2^2

Results (1D, m_2 initially at rest): v_1 = u_1*(m_1-m_2)/(m_1+m_2) v_2 = 2m_1u_1/(m_1+m_2)

Perfectly Inelastic (stick together): v = m_1u_1/(m_1+m_2) (momentum conservation) KE lost = (1/2)muu_rel^2 where mu = m_1m_2/(m_1+m_2) (reduced mass)

Coefficient of Restitution: e = (v_2 - v_1)/(u_1 - u_2) = relative speed of separation / relative speed of approach

• e = 1: perfectly elastic
• e = 0: perfectly inelastic
• 0 < e < 1: partially inelastic