Step-by-Step Collision Problem Checklist

Step 1: Identify Collision Type

• Is e given? (e = 1 elastic; e = 0 perfectly inelastic; 0 < e < 1 partially inelastic)
• Do bodies stick together? → Perfectly inelastic
• Is KE conserved? → Elastic

Step 2: Momentum Conservation (Always) $m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$

Step 3: Apply Type-Specific Condition

• Elastic: use elastic formulae or additionally apply KE conservation
• Perfectly inelastic: v_{1} = v_{2} = v_f (common velocity)
• Use e formula if e is given

Step 4: Calculate Required Quantities

Step 5: Verify

• Check momentum conservation: p_before = p_after (should match to 4 significant figures)
• Check KE: elastic → KE conserved; inelastic → KE decreased
• Check e: verify with formula

Verification Formula

For elastic collision: $\frac{1}{2}m_1 u_1^2 + \frac{1}{2}m_2 u_2^2 = \frac{1}{2}m_1 v_1^2 + \frac{1}{2}m_2 v_2^2$