Separate pulse area from a force-reading baseline
Impulse is the signed area under net force versus time, equal to the change in momentum. For a triangle, area is half base times height, so no calculus is needed to compare pulse shapes in this packet. Peak force, average force and impulse are different quantities with different units or roles.
Learning outcome: Compare two durations at zero baseline, then introduce one nonzero baseline. Retain true and indicated areas separately and propose a pre-/post-pulse baseline check without pretending those observations were already supplied.
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 T=0.5 s the peak is 24 N; at T=2 s it is 6 N. Both true areas are6 N s. A baseline of 1 N contributes errors0.5 and 2 N s respectively over those windows.
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For the same mass and initial velocity, equal true net impulse guarantees equal:
Experiment
Compare two durations at zero baseline, then introduce one nonzero baseline. Retain true and indicated areas separately and propose a pre-/post-pulse baseline check without pretending those observations were already supplied.
Integrate a triangular force pulse with a baseline fault
Worked teaching model · synthetic values · True net force is a symmetric triangular pulse of impulse 6 N s over selected duration. A 2 kg point begins at −1 m/s. The additive baseline affects the indicated record, not the actual force. Integrate exactly the declared full-pulse window.
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Full triangular force record and baseline fault
Unlike graph quantities rescale independently; read units and values, not screen angles. 1: true triangular force (solid).2: indicated force (dashed). Joined curves show the supplied model, not additional observations.
Equivalent numerical coordinates for Full triangular force record and baseline fault
true triangular force
| time (s) | net force readout (N) |
|---|---|
| 0 | 0 |
| 0.5 | 12 |
| 1 | 0 |
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.
indicated force
| time (s) | net force readout (N) |
|---|---|
| 0 | 0.5 |
| 0.5 | 12.5 |
| 1 | 0.5 |
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 pulse peak | 12 | N |
| True net impulse | 6 | N s |
| Indicated impulse including baseline | 6.5 | N s |
| Baseline impulse error | 0.5 | N s |
| True final velocity | 2 | m/s |
| Velocity inferred from biased impulse | 2.25 | m/s |
| True average force | 6 | N |
The area under the true pulse is fixed while peak and average force depend on duration.
Triangle area is half duration times peak, here 6 N s. For initial momentum −2 kg m/s, final momentum is 4 and velocity 2 m/s. An additive baseline contributes offset times window length to the inferred impulse. Equal true net impulse from the same initial state gives the same final velocity and kinetic-energy change; different force histories alone do not change that endpoint result.
Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.
The area under the true pulse is fixed while peak and average force depend on duration.
Triangle area is half duration times peak, here 6 N s. For initial momentum −2 kg m/s, final momentum is 4 and velocity 2 m/s. An additive baseline contributes offset times window length to the inferred impulse. Equal true net impulse from the same initial state gives the same final velocity and kinetic-energy change; different force histories alone do not change that endpoint result.
Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.
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Why can increasing the recording window increase a baseline bias even when it captures the whole pulse?
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