Test a collision with measurements
You will be able to: Design a momentum and kinetic-energy comparison using measured masses and velocities.
What evidence supports a claim that a collision is elastic?
A video of two carts bouncing can look convincing, but appearance alone does not establish an elastic collision. Measure both carts before and after, calculate totals, and compare the differences with measurement uncertainty.
A useful starting point: When objects stick: find the shared velocity →
Words and symbols before equations
- Measured velocity
- Signed displacement divided by a short time interval near the event.
- Uncertainty
- A reasonable range reflecting limits of measurement, not just arithmetic rounding.
- Residual
- A difference such as P_f−P_i or K_f−K_i.
- Controlled condition
- A feature kept consistent, such as track slope or camera placement.
What this picture assumes
Ideal data: m_A=1 kg, m_B=3 kg, v_Ai=+4, v_Bi=0, v_Af=−2, v_Bf=+2 m/s. Only the reported v_Bf is offset. This is synthetic error sensitivity, not real measured evidence or an uncertainty estimate.
Connect the picture to the physics
Use a level low-friction track, known cart masses and a fixed camera with a distance scale in the plane of motion. Define a positive direction. Use frame timing and positions immediately before and after contact to estimate each signed velocity; avoid frames during the impact itself.
Calculate P_i, P_f, K_i and K_f using the same masses and frame. Compare momentum residual with the expected external impulse and uncertainty. A small nonzero residual is not automatically a violation; investigate friction, slope, timing and calibration.
If momentum is consistent with conservation and K_f agrees with K_i within justified uncertainty, the data support an approximately elastic collision. A significant decrease supports inelastic behavior. Repeat trials and estimate uncertainty rather than calling exact conservation from rounded numbers.
The investigation below shows ideal reference data plus one deliberately biased velocity reading. It is an error-sensitivity example, not actual student measurements or a complete uncertainty calculation.
A worked example, step by step
For a 1 kg cart and a 3 kg cart, velocities before are (+4,0) m/s and after are (−2,+2) m/s. Calculate totals and propose a way to test the conclusion experimentally.
- P_i=1(4)+3(0)=4 kg·m/s; P_f=1(−2)+3(2)=4 kg·m/s.
- K_i=½(1)(4²)=8 J; K_f=½(1)(2²)+½(3)(2²)=8 J.
- The ideal data describe an elastic collision with conserved momentum.
- For real data, repeat measurements, use a calibrated distance scale and timing, estimate velocity uncertainty, and check whether both residuals are consistent with it. Equal rounded totals alone are insufficient.
A bounce is not automatically elastic, and a small measured mismatch does not by itself refute a conservation law.
Is a 1% momentum mismatch always acceptable?
Compare with an explanation
No universal cutoff applies. Judge it against the experiment’s measurement uncertainty and possible external impulse.
Predict. Change one thing. Explain.
Keep the ideal incoming and first outgoing velocities fixed. Introduce an offset into the second outgoing velocity measurement. Observe how both residuals change, especially the squared-speed energy result.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Reported v_Bf=2 m/s. Momentum residual=0 kg·m/s; energy residual=0 J. Ideal reference data agree exactly. A real conclusion needs an uncertainty estimate.
Ideal data: m_A=1 kg, m_B=3 kg, v_Ai=+4, v_Bi=0, v_Af=−2, v_Bf=+2 m/s. Only the reported v_Bf is offset. This is synthetic error sensitivity, not real measured evidence or an uncertainty estimate.
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 questionDesign a test of an elastic-collision claim for two unequal carts. (a) Identify measurements. (b) State what you calculate. (c) Describe one uncertainty check. (d) Explain how to interpret a significant K decrease when P is consistent with conservation.
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Compare with the answer and four-point rubric
- 1 point: Measure both masses and signed velocities immediately before/after; define the axis and calibrate distance/time.
- 1 point: Calculate total P_i, P_f, K_i and K_f, then compare residuals.
- 1 point: Repeat trials or repeat position/timing measurements to estimate uncertainty; check camera alignment and track slope.
- 1 point: The data support an inelastic collision; translational K changed to other forms while external impulse was negligible.
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 1Which quantities must be measured?
Both masses and both initial/final signed velocities.
RECALL 2What does a small residual mean?
Interpret it using uncertainty and external impulse; not a universal percentage rule.
RECALL 3Why use repeated trials?
To reveal variability and strengthen an uncertainty estimate.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Test a collision with measurements
- P=Σmv; K=Σ½mv², calculated before and after.
- Compare residuals with uncertainty and external impulse.
- Use signed velocities and unrounded intermediate calculations.
Remember: A bounce is not automatically elastic, and a small measured mismatch does not by itself refute a conservation law.
Conditions: Ideal data: m_A=1 kg, m_B=3 kg, v_Ai=+4, v_Bi=0, v_Af=−2, v_Bf=+2 m/s. Only the reported v_Bf is offset. This is synthetic error sensitivity, not real measured evidence or an uncertainty estimate.
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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