AP Physics 1  ·  Unit 4: Linear Momentum  ·  Lesson 4.4

Elastic and Inelastic Collisions

All collisions conserve momentum. Only one type also conserves kinetic energy. Know the difference — and how to use both  ·  Approx. 3–4 class days

StarringSp_i = Sp_f  (always)KE_i = KE_f  (elastic only)
Unit 4: Linear Momentum

Use this as a quick reference for all three collision types and the AP skills required for each.

Physics of Impact: Elastic vs. Inelastic Collisions infographic

🧭 Plot Summary

In Lesson 4.3 you established that momentum is always conserved in isolated systems. This lesson adds the crucial question: what about kinetic energy?The answer divides all collisions into three types. Momentum is conserved in every single one. Kinetic energy is only conserved in elastic collisions — which means you get to use two equations instead of one, and solve for two unknowns.

The three collision types

🔵 Elastic
p: ✓ conserved
KE: ✓ conserved
Objects bounce. No energy lost. Rare in practice — billiard balls approximate it.
🟠 Inelastic
p: ✓ conserved
KE: ✗ decreases
Most real collisions. KE converts to heat, sound, or deformation. Objects may or may not stick.
🟢 Perfectly Inelastic
p: ✓ conserved
KE: ✗ max loss
Objects stick and move together. Use v_f = Sp_i / (m1+m2). Maximum possible KE loss.

AP Skills this lesson

AP
Symbolic Derivation
Derive final velocity expressions algebraically from conservation equations.
AP
Data Visualization
Create and interpret quantitative KE and momentum graphs for collision scenarios.
AP
Comparative Analysis
Compare KE before and after — identify collision type from data, not just from labels.

What you will do in this lesson

  • Classify collisions: elastic (p and KE conserved), inelastic (p conserved, KE not), perfectly inelastic (objects stick, maximum KE loss).
  • Apply Sp_i = Sp_f to all collision types.
  • Apply KE_i = KE_f as an additional constraint for elastic collisions only.
  • Solve for final velocities in perfectly inelastic collisions using v_f = Sp_i / (m1+m2).
  • Calculate energy lost in inelastic collisions: DKE = KE_f - KE_i.
  • Derive symbolic expressions for collision outcomes from known quantities.

Why it matters

This is the season finale of Unit 4 — and it ties together momentum conservation from 4.3 with kinetic energy from Unit 3 in a single problem. Elastic collision problems are the most algebraically demanding in the unit. Master the two-equation system and you have unlocked the full toolkit for every collision the AP exam can throw at you.

✅ Self-Check Before You Roll On

Check off each item as you get there. These are not grades — they are your own signal.

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