Keep calibration ambiguity in an energy fit
A height-to-speed experiment can compare released gravitational energy with final kinetic energy, but only if both height and speed are calibrated. In this synthetic packet, an object starts at rest and descends heights1,2,3 m under g=10. The true fraction entering final kinetic energy is η, so true v²=2ηgh.
Learning outcome: Compare an η=0.8,s=1.1 packet with η=1,s=1 where available, then choose a state with apparent fraction above unity. Retain the product relationship and propose an independent measurement capable of separating its factors.
Starting recap
Choose the system, interval and reference frame before using a conservation statement. Keep vector momentum, scalar energy and transferred power distinct.
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At η=0.8,s=1.1 and h=2 m, true speed is√32≈5.65685 m/s and indicated speed≈6.22254 m/s. The indicated squared-speed slope is 19.36 m/s², compared with 20 for an ideal lossless calibrated packet.
Open the experimentPredict
A speed-readout scale factor 1.2 changes an inferred kinetic energy by a factor:
Experiment
Compare an η=0.8,s=1.1 packet with η=1,s=1 where available, then choose a state with apparent fraction above unity. Retain the product relationship and propose an independent measurement capable of separating its factors.
Distinguish energy loss from speed-scale error
Worked teaching model · synthetic values · Synthetic point starts at rest and descends heights 1,2,3 m with g=10. True final v²=2 eta g h; indicated speed is s times true speed. Loss fraction and speed scale are disclosed generator parameters, not independently inferred from the same packet.
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Speed-squared packet and its calibration ambiguity
Unlike graph quantities rescale independently; read units and values, not screen angles. 1: indicated packet (open markers).2: ideal lossless comparison (dashed). Joined curves show the supplied model, not additional observations.
Equivalent numerical coordinates for Speed-squared packet and its calibration ambiguity
indicated packet
| descent height (m) | indicated speed squared (m²/s²) |
|---|---|
| 1 | 19.36 |
| 2 | 38.72 |
| 3 | 58.08 |
At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.
ideal lossless comparison
| descent height (m) | indicated speed squared (m²/s²) |
|---|---|
| 0 | 0 |
| 3 | 60 |
At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.
| Quantity | Value | Unit |
|---|---|---|
| True kinetic fraction | 0.8 | ratio |
| Inferred fraction from indicated speeds | 0.968 | ratio |
| Apparent fraction exceeds unity | 0 | flag |
| True speed at height 2 m | 5.65685 | m/s |
| Indicated speed at height 2 m | 6.22254 | m/s |
| Indicated speed-squared slope | 19.36 | m/s² |
A linear energy-pattern fit can identify a product of parameters rather than loss and calibration separately.
The indicated v²/(2gh) is eta times speedScale². The same three height points cannot uniquely separate these two factors. An apparent fraction greater than one signals a failed calibration/model premise, not proof of energy creation. Independently calibrating speed or measuring another energy channel can distinguish hypotheses; a changed potential-energy zero cannot change a height difference.
Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.
A linear energy-pattern fit can identify a product of parameters rather than loss and calibration separately.
The indicated v²/(2gh) is eta times speedScale². The same three height points cannot uniquely separate these two factors. An apparent fraction greater than one signals a failed calibration/model premise, not proof of energy creation. Independently calibrating speed or measuring another energy channel can distinguish hypotheses; a changed potential-energy zero cannot change a height difference.
Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.
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Public practice checks a specific claim. It does not establish independent mastery.
Why does a small residual from a straight-line fit not establish an accurate speed scale?
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