Classify collisions with an energy check
You will be able to: Distinguish elastic, inelastic and perfectly inelastic collisions by system totals.
Why can momentum stay constant while kinetic energy falls?
Two equal carts approach one another at equal speeds. They can bounce back or stick and stop. Both outcomes can have zero total momentum. Only the bounce with unchanged speeds restores all the initial kinetic energy.
A useful starting point: Translational kinetic energy →
Words and symbols before equations
- Elastic collision
- Total kinetic energy is the same before and after.
- Inelastic collision
- Total kinetic energy decreases; energy changes into other forms.
- Perfectly inelastic
- The colliding objects stick together and share a final velocity.
- Total energy
- Includes kinetic, elastic, thermal and other forms; it is broader than kinetic energy.
What this picture assumes
Two 1 kg carts initially move at +2 and −2 m/s. Outgoing velocities are −speed and +speed. Negligible external impulse. At speed=0 the model assumes sticking.
Connect the picture to the physics
First check the momentum balance for the selected system and external impulse. Next compare K_i=Σ½mv_i² with K_f=Σ½mv_f² in the same frame. Total momentum can be conserved in both elastic and inelastic collisions.
Elastic describes the system’s total kinetic energy. One object can lose kinetic energy while another gains it. During contact, some energy may temporarily be stored in deformation even if the collision ultimately returns it to motion.
In an inelastic collision, some initial kinetic energy becomes deformation, thermal energy, sound or other forms. An inelastic pair can separate afterward. Sticking is the perfectly inelastic special case. An interaction that increases K needs a source of stored energy and is not described by the ordinary inelastic-loss model here.
| Feature | Elastic collision | Inelastic collision |
|---|---|---|
| Total momentum | Constant if external impulse is negligible | Constant if external impulse is negligible |
| Total kinetic energy | Same before and after | Decreases |
| Must objects stick? | No | Only in the perfectly inelastic case |
A worked example, step by step
Two 1 kg carts initially move at +2 and −2 m/s. Compare final velocities (−2,+2), (−1,+1), and (0,0). Assume negligible external impulse.
- Initial P=2−2=0; K_i=½(1)(4)+½(1)(4)=4 J.
- Final (−2,+2): P=0 and K_f=4 J. This is elastic.
- Final (−1,+1): P=0 and K_f=1 J. This is inelastic even though the carts separate; 3 J has changed to other forms.
- Final (0,0), sticking: P=0 and K_f=0. This is perfectly inelastic; all 4 J of the initial translational K changes form.
Inelastic does not mean momentum is lost or that every collision sticks. Kinetic energy and total energy are different accounts.
Must an elastic collision preserve each cart’s kinetic energy?
Compare with an explanation
No. It preserves the system’s total kinetic energy, which can be redistributed between carts.
Predict. Change one thing. Explain.
Two 1 kg carts start at ±2 m/s. Set the outgoing speed of each from 0 to 2 m/s. They leave in opposite directions; at zero they remain together. Compare total momentum with total kinetic energy.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Inelastic; carts separate. K_i=4 J; K_f=1 J; 3 J converted from translational K. P_i=P_f=0 kg·m/s.
Two 1 kg carts initially move at +2 and −2 m/s. Outgoing velocities are −speed and +speed. Negligible external impulse. At speed=0 the model assumes sticking.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use a momentum or impulse relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionTwo 2 kg carts approach with velocities +3 and −3 m/s. They leave at −1 and +1 m/s. (a) Find P before and after. (b) Find K_i. (c) Find K_f and the decrease. (d) Classify and explain the energy account.
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Compare with the answer and four-point rubric
- 1 point: P_i=P_f=0 kg·m/s.
- 1 point: K_i=18 J.
- 1 point: K_f=2 J; 16 J has left translational kinetic energy.
- 1 point: Inelastic, not perfectly inelastic because they separate; energy is transferred into other forms.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What identifies an elastic collision?
Equal initial and final total kinetic energies.
RECALL 2What identifies perfectly inelastic?
Objects stick and move together.
RECALL 3Does inelastic mean total energy is destroyed?
No. Some kinetic energy changes form or leaves the chosen system.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Classify collisions with an energy check
- Elastic: K_f=K_i. Inelastic: K_f<K_i.
- Perfectly inelastic: shared final velocity after sticking.
- Momentum conservation requires negligible net external impulse, whatever the collision type.
Remember: Inelastic does not mean momentum is lost or that every collision sticks. Kinetic energy and total energy are different accounts.
Conditions: Two 1 kg carts initially move at +2 and −2 m/s. Outgoing velocities are −speed and +speed. Negligible external impulse. At speed=0 the model assumes sticking.
Refresh Kid · Unit 4 · Objectives 4.4.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 4.4, objectives 4.4.A. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Fall-2026 corrections also checked. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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