Use an unused speed to challenge a resistance law
A force observation at one speed can fit different models. Write the synthetic resistance magnitude as Fref(v/vref)^p, where vref=1 m/s and p is1 or2. The ratio is dimensionless, so Fref always has force units. If rewritten as b v or k v², the two fitted coefficients have different dimensions.
Learning outcome: Fit at the common reference, freeze a higher-speed prediction and evaluate the withheld residual for both exponents. Preserve coefficient units.
Starting recap
Differentiate/integrate with explicit initial conditions; identify each force recipient and the inertial frame. Preserve force dimensions, geometric constraints and the distinction between model and solver error.
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Try
At Fref=1.5 N, the two laws predict3 N and6 N at2 m/s. A quadratic packet leaves a+3 N residual against the line fitted only at1 m/s.
Open the experimentPredict
If two candidate resistance laws agree at the fitted reference speed, the fit alone:
Experiment
Fit at the common reference, freeze a higher-speed prediction and evaluate the withheld residual for both exponents. Preserve coefficient units.
Distinguish resistance laws with an unused speed
Worked teaching model · synthetic values · Synthetic resistance magnitude F=Fref(v/vref)^p, vref1 m/s and p1 or2. Fit a linear law using only vref, then withhold2 m/s. Fref has force units; dimensional linear/quadratic coefficients differ. No fitted real fluid parameters.
Reset keeps your prediction, captures and practice history.
Fit once, then compare at an unused speed
Unlike graph quantities rescale independently; read units and values, not screen angles. 1: supplied true law (solid).2: linear law fitted only at1 m/s (dashed). Joined curves show the supplied model, not additional observations.
Equivalent numerical coordinates for Fit once, then compare at an unused speed
supplied true law
| speed (m/s) | resistance magnitude (N) |
|---|---|
| 0 | 0 |
| 0.5 | 0.25 |
| 1 | 1 |
| 1.5 | 2.25 |
| 2 | 4 |
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.
linear law fitted only at1 m/s
| speed (m/s) | resistance magnitude (N) |
|---|---|
| 0 | 0 |
| 2 | 2 |
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 |
|---|---|---|
| Force at fitted reference speed | 1 | N |
| Linear coefficient fitted at reference | 1 | kg/s |
| Withheld true resistance at2 m/s | 4 | N |
| Linear prediction at2 m/s | 2 | N |
| Withheld observed minus predicted | 2 | N |
One calibration speed cannot distinguish two laws that agree at that speed.
Fref(v/vref)^p keeps the power dimensionless. At vref both p1 and p2 give the same force, but at twice vref they predict2Fref and4Fref. A withheld discrepancy challenges the assumed law under the disclosed no-error observations; it does not uniquely determine a real drag mechanism. Additional speeds, error bounds and independent geometry/medium information are needed.
Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.
One calibration speed cannot distinguish two laws that agree at that speed.
Fref(v/vref)^p keeps the power dimensionless. At vref both p1 and p2 give the same force, but at twice vref they predict2Fref and4Fref. A withheld discrepancy challenges the assumed law under the disclosed no-error observations; it does not uniquely determine a real drag mechanism. Additional speeds, error bounds and independent geometry/medium information are needed.
Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.
Understand
Apply
Public practice checks a specific claim. It does not establish independent mastery.
Why is a repeat at the same speed not the same test as an unused speed?
Continue
Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.
Skipping retains experiments and awards no mastery.
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