Separate apparent weight, mass and support contact
A scale measures contact force and may display that force divided by an assumed gravitational acceleration. It does not directly replace an object’s inertial mass when the support accelerates. Use upward as positive, with gravity10 m/s² downward and a selected object mass m.
Learning outcome: Compare support accelerations+2,−4,−10,−12 m/s² at one mass. Retain the conditional required normal and actual normal, then explain why the object cannot share the last prescribed acceleration.
Starting recap
Draw recipient-specific interactions, resolve signed components and identify the domain of each force/contact model before substituting.
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For m=6 kg and a=+2 m/s², N=72 N and the display reads7.2 kg. For a=−12 m/s², actual N is 0, mass is 6 kg and the object’s acceleration is−10 m/s².
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A zero scale reading during ideal free fall establishes:
Experiment
Compare support accelerations+2,−4,−10,−12 m/s² at one mass. Retain the conditional required normal and actual normal, then explain why the object cannot share the last prescribed acceleration.
Separate scale reading from mass and contact
Worked teaching model · synthetic values · Point and support begin touching, at rest. Uniform gravity 10 m/s² downward, no air resistance. Support motion is prescribed for 1 s and cannot pull the object. Scale displays N/(10 m/s²), not a new inertial mass.
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Scale readout versus prescribed acceleration
Unlike graph quantities rescale independently; read units and values, not screen angles. 1: admissible normal (solid). Joined curves show the supplied model, not additional observations.
Equivalent numerical coordinates for Scale readout versus prescribed acceleration
admissible normal
| support upward acceleration (m/s²) | normal force (N) |
|---|---|
| -12 | 0 |
| -11.6 | 0 |
| -11.2 | 0 |
| -10.8 | 0 |
| -10.4 | 0 |
| -10 | 0 |
| -9.6 | 1.6 |
| -9.2 | 3.2 |
| -8.8 | 4.8 |
| -8.4 | 6.4 |
| -8 | 8 |
| -7.6 | 9.6 |
| -7.2 | 11.2 |
| -6.8 | 12.8 |
| -6.4 | 14.4 |
| -6 | 16 |
| -5.6 | 17.6 |
| -5.2 | 19.2 |
| -4.8 | 20.8 |
| -4.4 | 22.4 |
| -4 | 24 |
| -3.6 | 25.6 |
| -3.2 | 27.2 |
| -2.8 | 28.8 |
| -2.4 | 30.4 |
| -2 | 32 |
| -1.6 | 33.6 |
| -1.2 | 35.2 |
| -0.8 | 36.8 |
| -0.4 | 38.4 |
| 0 | 40 |
| 0.4 | 41.6 |
| 0.8 | 43.2 |
| 1.2 | 44.8 |
| 1.6 | 46.4 |
| 2 | 48 |
| 2.4 | 49.6 |
| 2.8 | 51.2 |
| 3.2 | 52.8 |
| 3.6 | 54.4 |
| 4 | 56 |
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 |
|---|---|---|
| Required contact normal | 24 | N |
| Actual scale normal | 24 | N |
| Displayed mass-equivalent reading | 2.4 | kg |
| Unchanged inertial mass | 4 | kg |
| Actual object upward acceleration | -4 | m/s² |
| Gap above support after 1 s | 0 | m |
| Prescribed support motion can be shared | 1 | flag |
A scale senses support force; zero support force does not mean zero mass or zero gravity.
In maintained contact, N−mg=ma. At a=−g both object and support free-fall together with zero normal in the ideal initial state. If the support accelerates downward faster than g, it separates: the object falls at −g and no tensile normal keeps it attached. The stated gap uses equal initial position and velocity over one second.
Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.
A scale senses support force; zero support force does not mean zero mass or zero gravity.
In maintained contact, N−mg=ma. At a=−g both object and support free-fall together with zero normal in the ideal initial state. If the support accelerates downward faster than g, it separates: the object falls at −g and no tensile normal keeps it attached. The stated gap uses equal initial position and velocity over one second.
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Why does weightlessness describe a support-force condition rather than the absence of gravitational interaction?
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