A collision can lose kinetic energy without sticking
You will be able to: Check total momentum and kinetic energy, then inspect whether outgoing velocities match.
How do you tell elastic, inelastic and sticking outcomes apart?
A 1 kg cart moving at 4 m/s strikes an identical cart at rest. If they leave at 1 and 3 m/s, total momentum is still 4 kg·m/s, but K drops from 8 J to 5 J. They separate, so the collision is inelastic but not perfectly inelastic.
A useful starting point: An elastic collision conserves momentum and kinetic energy →
Words and symbols before equations
- Inelastic
- Total kinetic energy decreases during the collision.
- Perfectly inelastic
- Objects stick and share a final velocity; a special inelastic case.
- Separation-speed ratio e
- Optional model parameter: outgoing relative speed divided by incoming approach speed.
- Passive collision
- No stored energy is released to increase the pair’s kinetic energy.
What this picture assumes
Passive isolated one-dimensional collision. The optional ratio e selects a family of outcomes: 1 elastic, between 0 and 1 partially inelastic, 0 modeled as sticking. The parameter is a teaching aid, not a new official curriculum requirement.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Final velocities: left 1 m/s, right 3 m/s. Total P = 4 kg·m/s before and after; K_i = 8 J, K_f = 5 J; converted 3 J. Partially inelastic: the objects separate with reduced K.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
First check whether total momentum is conserved for the selected system. Then calculate K_i and K_f independently. Equal K defines elasticity; smaller final K means an inelastic collision. Different outgoing velocities do not rule out energy loss.
For one-dimensional approaching objects, an optional model parameter e = (v₂ − v₁)/(u₁ − u₂) varies from 0 for the common-velocity limit to 1 for elastic separation. Intermediate values describe partially inelastic outcomes. This parameter is a modeling aid here, not an additional official AP topic or a required vocabulary item.
Momentum conservation and the chosen separation ratio determine the final velocities. For fixed masses and initial velocities, reducing relative separation reduces final K while preserving center-of-mass translation. A computed K increase would require an internal energy release or external input, so it cannot be silently labeled an ordinary passive collision.
| Property | Elastic | Inelastic |
|---|---|---|
| Total momentum | Conserved | Conserved |
| Total kinetic energy | Conserved | Decreases |
| Must objects stick? | No | Only in the perfectly inelastic case |
A worked example, step by step
Two 1 kg carts start with velocities +6 and 0 m/s and leave at +2 and +4 m/s. Classify the collision and calculate the converted kinetic energy.
- Initial momentum is 6 kg·m/s; final momentum is 2 + 4 = 6 kg·m/s.
- Initial K = ½(1)(6²) = 18 J.
- Final K = ½(1)(2²) + ½(1)(4²) = 10 J; converted amount is 8 J.
- The collision is inelastic but not perfectly inelastic because outgoing velocities differ. The optional separation ratio is (4−2)/(6−0) = 1/3.
“Inelastic” does not necessarily mean sticking. “Bounces apart” does not necessarily mean elastic.
Can a larger mass have the same final velocity as a smaller mass after sticking?
Compare with an explanation
Yes. The common velocity is shared, but their momenta and kinetic energies differ in proportion to their masses.
Predict. Change one thing. Explain.
Hold masses and approach speed fixed. Vary the relative separation ratio from 1 toward 0. Watch total momentum stay constant while kinetic-energy conversion grows.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Final velocities: left 1 m/s, right 3 m/s. Total P = 4 kg·m/s before and after; K_i = 8 J, K_f = 5 J; converted 3 J. Partially inelastic: the objects separate with reduced K.
Passive isolated one-dimensional collision. The optional ratio e selects a family of outcomes: 1 elastic, between 0 and 1 partially inelastic, 0 modeled as sticking. The parameter is a teaching aid, not a new official curriculum requirement.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant impulse, system boundary, momentum or calculus 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 equal 2 kg carts start at +3 and −1 m/s and finish at 0 and +2 m/s. Compare total momentum and K and classify the outcome.
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Compare with the answer and four-point rubric
- 1 point: Initial P = 2(3) + 2(−1) = 4 kg·m/s.
- 1 point: Final P = 2(0) + 2(2) = 4 kg·m/s.
- 1 point: Initial K = 10 J and final K = 4 J, giving 6 J converted.
- 1 point: Final velocities differ, so this is inelastic but not perfectly inelastic.
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 1Must objects stick to lose kinetic energy?
No. Partially inelastic collisions can have separating objects.
RECALL 2Does conserved momentum imply conserved K?
No. They are different quantities with different conservation conditions.
RECALL 3What does a kinetic-energy increase require?
An energy source such as released internal energy or external work; momentum conservation alone cannot supply energy.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
A collision can lose kinetic energy without sticking
- Compare total P and total K separately.
- Elastic: K_f = K_i; inelastic: K_f < K_i.
- Perfectly inelastic: shared final velocity. Optional model e = relative separation / relative approach.
Remember: “Inelastic” does not necessarily mean sticking. “Bounces apart” does not necessarily mean elastic.
Conditions: Passive isolated one-dimensional collision. The optional ratio e selects a family of outcomes: 1 elastic, between 0 and 1 partially inelastic, 0 modeled as sticking. The parameter is a teaching aid, not a new official curriculum requirement.
Refresh Kid · AP Physics C: Mechanics Unit 4 (official 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 alongside the Fall 2026 clarifications. This is Mechanics Unit 4: Linear Momentum. The unit covers Topics 4.1–4.4. Calculus connects force to momentum derivatives and impulse integrals. Collision calculations use one or two dimensions; the optional spatial fragment diagram is qualitative. Changing-mass examples explicitly account for momentum carried across a boundary, so dp/dt is not used blindly for an open system. 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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