Momentum & Collisions

Applying conservation of momentum to elastic and inelastic collisions

Golden Rule: Total momentum is conserved in all collisions (no external forces). Kinetic energy is conserved only in elastic collisions. Set up p_before = p_after for each direction.

• Step 1: Define positive direction and list knowns — Choose right/up as positive. List all masses and initial velocities. Assign negative velocities to leftward/downward motion. Identify what type of collision it is.
• Step 2: Apply conservation of momentum — Sum of momenta before = sum of momenta after. For perfectly inelastic collisions, the objects stick together: v₁f = v₂f = vf. Write the equation and identify which final velocities are unknown.
• Step 3: Add kinetic energy equation (elastic only) — Elastic collisions conserve KE. This gives a second equation for two unknowns. Use the combined result: v₁f = ((m₁−m₂)v₁ᵢ + 2m₂v₂ᵢ)/(m₁+m₂) and similarly for v₂f.
• Step 4: Check with energy or sign — For inelastic: KE after < KE before (energy is lost to heat/deformation). For elastic: KE is conserved — verify numerically. Check that the center of mass velocity is unchanged.