Elastic Collision (KE conserved): \frac{1}{2}$$m_1$u_1^2$ + \frac{1}{2}$$m_2$u_2^2$ = \frac{1}{2}$$m_1$v_1^2$ + \frac{1}{2}$$m_2$v_2^2$

Results (1D, $m_2$ initially at rest): $v_1$ = $u_1$$\frac{m_1-m_2}{(m_1+m_2)}$ $v_2$ = 2$m_1$*$\frac{u_1}{m_1+m_2}$

Perfectly Inelastic (stick together): v = $m_1$$\frac{u_1}{m_1+m_2}$ (momentum conservation) KE lost = $\frac{1}{2}$mu$u_{rel}^2$ where mu = $m_1$$\frac{m_2}{m_1+m_2}$ (reduced mass)

Coefficient of Restitution: e = $\frac{v_2 - v_1}{(u_1 - u_2)}$ = relative speed of separation / relative speed of approach

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