Test momentum conservation with cart data
You will be able to: Plan an experiment and compare signed before/after momenta with uncertainty.
What measurements would support a claim that momentum was conserved?
A video shows two carts collide, but a picture alone cannot establish momentum conservation. Measure both masses and their velocities just before and just after the collision, then compare the two signed totals.
A useful starting point: Balance momentum separately along two axes →
Words and symbols before equations
- Measurement uncertainty
- A plausible range around a measured value due to resolution and variability.
- Residual R
- Difference P_after − P_before; an ideal isolated model predicts zero.
- Time window
- The chosen interval around the interaction over which external impulse is assessed.
- Systematic bias
- An error such as a tilted track or calibration offset that repeats in the same direction.
What this picture assumes
Five synthetic trials, not real experimental evidence. P_after = P_before + external impulse + a small fixed measurement offset. Each before/after total has the selected bound, so a conservative residual bound is twice it. These bounds are illustrative, not statistical confidence intervals.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Modeled external impulse 0 N·s; residual bound ±0.12 kg·m/s. 5 of 5 synthetic residual intervals include zero. Compatibility with zero is not proof of perfect isolation; inspect systematic trends and real uncertainty.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
Use a level low-friction track, measured total moving masses, and a calibrated video or velocity sensors. Choose one axis and retain negative velocities. Estimate velocities over short intervals immediately before and after contact, rather than long averages that include frictional slowing.
Repeat with several initial velocities or mass combinations. Plot P_after vertically against P_before horizontally with the same units. The isolated model predicts slope 1 and intercept 0. A systematic external impulse shifts the relation; uncertainty and scatter limit how closely an individual run should agree.
Record the equipment resolution and repeat variability. A residual smaller than a reasonable combined uncertainty is consistent with conservation, not proof of perfect isolation. If residuals have a consistent sign, investigate external friction, track tilt, omitted mass or a timing mismatch instead of deleting inconvenient points.
A worked example, step by step
Measured total momenta are P_before = 1.20 ± 0.04 kg·m/s and P_after = 1.16 ± 0.05 kg·m/s. Use a conservative sum-of-bounds comparison to assess the result.
- Residual is R = 1.16 − 1.20 = −0.04 kg·m/s.
- Adding the quoted bounds gives a conservative residual bound of ±0.09 kg·m/s; this is not a statistical confidence calculation.
- Zero lies within −0.04 ± 0.09, so the result is consistent with conservation at this resolution.
- It does not prove zero external impulse. Repeat trials and check timing, friction and sensor calibration.
Close agreement does not certify perfect conservation experimentally. Interpret it against uncertainty and the selected system and interval.
Why measure near the collision instead of several seconds later?
Compare with an explanation
The longer interval can include significant external impulse from friction or other forces.
Predict. Change one thing. Explain.
Keep measurement bounds fixed. Add a modeled external impulse and watch the synthetic data move away from the equality line. Then change the bound and explain why wider uncertainty reduces the strength of the conclusion.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Modeled external impulse 0 N·s; residual bound ±0.12 kg·m/s. 5 of 5 synthetic residual intervals include zero. Compatibility with zero is not proof of perfect isolation; inspect systematic trends and real uncertainty.
Five synthetic trials, not real experimental evidence. P_after = P_before + external impulse + a small fixed measurement offset. Each before/after total has the selected bound, so a conservative residual bound is twice it. These bounds are illustrative, not statistical confidence intervals.
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 questionDesign a two-cart test of momentum conservation. Specify measured quantities, an isolation check, a graph or residual comparison, and how uncertainty affects the claim.
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Compare with the answer and four-point rubric
- 1 point: Measure each cart’s total mass and signed velocity immediately before and after contact in one frame.
- 1 point: Level the track and estimate whether friction or other external impulse is small during the chosen interval.
- 1 point: Plot P_after versus P_before and compare with the equality line, or calculate residuals for repeated trials.
- 1 point: Use resolution and repeat variability to assess agreement; investigate systematic offsets and report consistency rather than proof.
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 1Why retain signs in the data table?
Opposite directions can cancel in the momentum sum.
RECALL 2What does a residual reveal?
It estimates external impulse together with measurement errors or omitted contributions.
RECALL 3What does momentum agreement not establish?
That the collision was elastic; kinetic energy must be checked separately.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Test momentum conservation with cart data
- P_before = Σmᵢvᵢ,before; P_after = Σmᵢvᵢ,after.
- Residual R = P_after − P_before = J_ext in the ideal measurement model.
- Isolated-system comparison: P_after versus P_before has slope 1, intercept 0.
Remember: Close agreement does not certify perfect conservation experimentally. Interpret it against uncertainty and the selected system and interval.
Conditions: Five synthetic trials, not real experimental evidence. P_after = P_before + external impulse + a small fixed measurement offset. Each before/after total has the selected bound, so a conservative residual bound is twice it. These bounds are illustrative, not statistical confidence intervals.
Refresh Kid · AP Physics C: Mechanics Unit 4 (official Unit 4) · Objectives 4.3.A; 4.3.B · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 4.3, objectives 4.3.A; 4.3.B. 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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