What do I need to know for AP Physics 1 Topic 4.4?
Topic 4.4 Elastic and Inelastic Collisions: A collision is elastic if both total momentum and total kinetic energy are conserved; it is inelastic if momentum is conserved for an isolated system but kinetic energy decreases, with a perfectly inelastic collision ending with objects stuck together.
- Classify collisions from before/after information, use momentum conservation correctly, and distinguish momentum conservation from kinetic-energy conservation.
- Practice target: 42 original MCQs and 4 original FRQs for this exact topic.
- Course alignment: current AP Physics 1 framework for the 2026–27 school year and May 2027 exam.
Elastic and Inelastic Collisions
A collision is elastic if both total momentum and total kinetic energy are conserved; it is inelastic if momentum is conserved for an isolated system but kinetic energy decreases, with a perfectly inelastic collision ending with objects stuck together.
A collision is elastic if both total momentum and total kinetic energy are conserved; it is inelastic if momentum is conserved for an isolated system but kinetic energy decreases, with a perfectly inelastic collision ending with objects stuck together.
What you need to understand before calculating
Classify collisions from before/after information, use momentum conservation correctly, and distinguish momentum conservation from kinetic-energy conservation.
This page explains the key vocabulary where it is used. Internal links are for deeper study, not a requirement for understanding the sentence you are reading.
Key terms explained on this page
These terms are defined here before they are used in the calculations. A deeper internal link is optional where one exists; the reader does not need to leave this page to understand the current explanation.
Collision
A collision is a short interaction in which objects exert large forces on one another, often making external impulse negligible over the collision interval.
Real example: Two carts striking and separating can conserve total momentum even though each cart’s momentum changes.
Deeper lesson: CollisionKinetic energy
Kinetic energy is a scalar measure of motion energy; it is conserved only in elastic collisions, not in every momentum-conserving collision.
Real example: Putty that sticks to a cart can conserve total momentum while losing kinetic energy to internal energy.
Deeper lesson: Kinetic energyTranslate the physics into a representation
AP Physics 1 frequently asks you to move between words, diagrams, graphs and equations. Use this representation as a reasoning anchor, then explain what each labeled quantity means in this topic.
Core concepts with real physical examples
| Concept | Meaning | Real example 1 | Real example 2 |
|---|---|---|---|
| Elastic collision | Both system momentum and kinetic energy are conserved. | Idealized air-track carts can collide nearly elastically. | Two hard spheres may rebound with little energy transformed internally. |
| Inelastic collision | Momentum can be conserved while some kinetic energy becomes thermal, sound, deformation, or internal energy. | Cars crumple in a collision. | A lump of clay hits a cart and deforms. |
| Perfectly inelastic collision | Objects stick and share one final velocity. | A bullet embeds in a block. | Two Velcro carts collide and move together. |
| Explosion/recoil | An interaction can convert internal energy to kinetic energy while conserving momentum. | A spring between carts releases and sends them apart. | A firework explodes from rest. |
| Kinetic-energy test | Comparing total K before and after distinguishes elastic from inelastic when momentum is conserved. | Equal total K before and after supports an elastic model. | Smaller final K indicates an inelastic interaction. |
Equations and relationships: variables, units, conditions, examples
| Relationship | Variables & SI units | When to use it | Real example |
|---|---|---|---|
| m1v1i+m2v2i = m1v1f+m2v2f | kg·m/s termsAll symbols used here: m₁,m₂ = masses (kg); v₁i,v₂i,v₁f,v₂f = initial/final velocities (m/s); p = momentum (kg·m/s); K = kinetic energy (J). | One-dimensional isolated collision momentum. | Use signed velocities. |
| v_f = (m1v1i+m2v2i)/(m1+m2) | v_f: m/sAll symbols used here: m₁,m₂ = masses (kg); v₁i,v₂i,v₁f,v₂f = initial/final velocities (m/s); p = momentum (kg·m/s); K = kinetic energy (J). | Perfectly inelastic two-object collision. | Objects stick and share v_f. |
| K_total = Σ½mv² | K: JAll symbols used here: m₁,m₂ = masses (kg); v₁i,v₂i,v₁f,v₂f = initial/final velocities (m/s); p = momentum (kg·m/s); K = kinetic energy (J). | Compare kinetic energy before/after. | Equal K totals indicate elastic behavior if isolated momentum is also conserved. |
Worked physical reasoning
Velcro carts
Situation: A moving cart sticks to a stationary cart.
Physics: Use momentum to find shared v_f; final K is lower, so the collision is perfectly inelastic.
Elastic rebound
Situation: Two carts bounce and measured total K is unchanged within uncertainty.
Physics: If momentum also matches, the collision is consistent with elastic.
Car crash
Situation: Cars deform and may stick or separate.
Physics: Momentum of an isolated car system can be conserved while significant K becomes deformation/thermal energy.
AP scope and boundary
AP questions often ask for classification plus evidence, not just a numerical final velocity.
Common mistakes—and the corrected physics
| Incorrect idea | Correct understanding |
|---|---|
| Inelastic means momentum is not conserved. | For an isolated system, momentum is conserved in both elastic and inelastic collisions. |
| If objects bounce, the collision must be elastic. | Bouncing alone does not guarantee K conservation. |
| Perfectly inelastic means the objects stop. | They stick together and can move with a nonzero common velocity. |
Master this topic beyond a formula list
This checkpoint combines the current AP Physics 1 content boundary with representation, experiment/data reasoning, real situations and cross-topic transfer.
2026–27 mastery checklist
- Classify elastic, inelastic and perfectly inelastic collisions by what happens to system kinetic energy while momentum conservation is considered separately.
- Apply momentum conservation for an isolated collision regardless of whether kinetic energy is conserved.
- Recognize perfectly inelastic collisions as cases where objects move together after impact.
- Distinguish collisions from explosions, where internal energy can transform into kinetic energy.
Must-not-miss relationship
Elastic: K_i = K_f (for the modeled isolated system) and momentum conserved. Inelastic: K_f < K_i while momentum can still be conserved. Perfectly inelastic: objects share a common final velocity.
Symbols & SI units used on this topic: m₁,m₂ = masses (kg); v₁i,v₂i,v₁f,v₂f = initial/final velocities (m/s); p = momentum (kg·m/s); K = kinetic energy (J).
Two anchor situations
Two ideal magnetic carts can approximate an elastic collision with nearly unchanged total kinetic energy.
A lump of clay sticking to a cart is perfectly inelastic: momentum is conserved approximately while kinetic energy decreases.
Diagram / graph / equation / claim
Use one before/after table containing v, p and K for every object; verify momentum first, then use kinetic energy to classify the event.
How to test the physics
Collect video data for bouncing and sticking cart collisions. Compare percent changes in system momentum and kinetic energy with uncertainty.
Do not use “inelastic” to mean momentum is not conserved; it describes kinetic-energy behavior, not the external-impulse condition.
Combine collision energy ideas with rotational/rolling energy partitions later in the course.
Reconnect to Topic 3.4 energy conservationGo beyond memorizing the equation
This topic now combines model selection, physical intuition, a worked transfer problem, graph/data analysis, answer verification, and the four current AP free-response reasoning modes.
Choose the model before calculating
Conserve momentum for an isolated collision, then separately decide whether kinetic energy is conserved to classify it as elastic or inelastic.
Why the physics works
Momentum conservation follows from negligible external impulse; kinetic-energy conservation is an additional condition that only elastic collisions satisfy.
Solve this before opening the solution
A 1 kg cart at 4 m/s hits an identical stationary cart. Compare the ideal one-dimensional elastic outcome with the perfectly inelastic outcome.
Reveal complete reasoning
Solution: Elastic identical-mass case: the first cart stops and the second moves at 4 m/s. Perfectly inelastic case: they stick and move at 2 m/s. Momentum is conserved in both, but kinetic energy decreases in the sticking case.
Physics check: Initial momentum is 4 kg·m/s in both models; final momenta must sum to 4 kg·m/s.
What should you plot?
For repeated trials, plot K_final versus K_initial while also checking p_final versus p_initial.
What does the graph mean?
Elastic trials approach K_f=K_i; inelastic trials fall below that line while momentum still remains near conserved.
How this exact topic can appear in each current FRQ mode
Elastic: K_i = K_f (for the modeled isolated system) and momentum conserved. Inelastic: K_f < K_i while momentum can still be conserved. Perfectly inelastic: objects share a common final velocity.
Use one before/after table containing v, p and K for every object; verify momentum first, then use kinetic energy to classify the event.
Collect video data for bouncing and sticking cart collisions. Compare percent changes in system momentum and kinetic energy with uncertainty.
Combine collision energy ideas with rotational/rolling energy partitions later in the course.
Use momentum conservation first, then compute/compare kinetic energies to justify the collision classification.
Continue with the exact topic question banks
Use the focused banks for skill practice. The five full model papers are reserved for whole-exam simulation.
Topic 4.4 quick review
What is the definition I should know first?
A collision is elastic if both total momentum and total kinetic energy are conserved; it is inelastic if momentum is conserved for an isolated system but kinetic energy decreases, with a perfectly inelastic collision ending with objects stuck together.
What should I identify before using an equation?
Classify collisions from before/after information, use momentum conservation correctly, and distinguish momentum conservation from kinetic-energy conservation.
Where do I practice this exact topic?
Use the 42-MCQ and 4-FRQ Topic 4.4 banks linked directly on this page.
Where Topic 4.4 appears in AP-style released work
These are original topic summaries and alignment notes, not reproduced College Board question text. One released FRQ can legitimately connect to several topics.
Moving cart, dropped block and collision energy
Combines momentum/collision reasoning with translational kinetic-energy accounting.
Mathematical RoutinesElastic collision, center of mass and position graph
Links collisions, momentum, center-of-mass motion and graphical reasoning.
Mathematical RoutinesCollision comparisons and momentum vectors
Useful for vectors, momentum, collisions and representation translation.
Translation Between RepresentationsRecent public FRQs are the safest format reference. Older released questions can still contain excellent physics, but the course and exam changed; use the atlas alignment notes before treating a legacy question as a current-format simulation.