Infer inertial mass while retaining a force-reading fault
A force-versus-acceleration plot can estimate inertial mass only under explicit force and measurement assumptions. Here independent acceleration labels are stipulated exact. The synthetic true mass is 2 kg and force readings follow ma+o, where o is a common additive readout offset. A second selected fault affects only the high-acceleration reading.
Learning outcome: Compare offsets−2,0,2 N at zero fault, then vary fault at one offset. Retain slope, intercept and held-out residual. Propose a changed acceleration that would test a curved force law rather than merely repeat one fitting point.
Starting recap
Draw recipient-specific interactions, resolve signed components and identify the domain of each force/contact model before substituting.
All lessons are open directly. Your saved experiments remain when you leave and return.
Try
For offset o=1 N and high-point faultδ=0.2 N, readings are3 and 7.2 N. Fitted mass is 2.1 kg and intercept0.9 N. The held-out5 N reading lies0.1 N below the fitted line.
Open the experimentPredict
A common additive force offset applied to both fitting readings changes:
Experiment
Compare offsets−2,0,2 N at zero fault, then vary fault at one offset. Retain slope, intercept and held-out residual. Propose a changed acceleration that would test a curved force law rather than merely repeat one fitting point.
Fit inertial mass without confusing a force offset
Worked teaching model · synthetic values · Synthetic true mass 2 kg; readings at independently known accelerations 1 and 3 m/s² are ma+offset, with extra selected fault only at the second point. A held-out 2 m/s² reading has the common offset but no extra fault. No real instrument is calibrated.
Reset keeps your prediction, captures and practice history.
Two-point fit and a held-out force reading
Unlike graph quantities rescale independently; read units and values, not screen angles. 1: fitted affine force model (solid).2: fitting readings (filled markers).3: held-out reading (filled markers). Joined curves show the supplied model, not additional observations.
Equivalent numerical coordinates for Two-point fit and a held-out force reading
fitted affine force model
| independently known acceleration (m/s²) | indicated force (N) |
|---|---|
| 0 | 0.9 |
| 3 | 7.2 |
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.
fitting readings
| independently known acceleration (m/s²) | indicated force (N) |
|---|---|
| 1 | 3 |
| 3 | 7.2 |
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.
held-out reading
| independently known acceleration (m/s²) | indicated force (N) |
|---|---|
| 2 | 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 |
|---|---|---|
| Force reading at acceleration 1 | 3 | N |
| Force reading at acceleration 3 | 7.2 | N |
| Fitted inertial mass | 2.1 | kg |
| Fitted force offset | 0.9 | N |
| Held-out force reading at acceleration 2 | 5 | N |
| Held-out residual observed minus fitted | -0.1 | N |
| Mass error bound for independent endpoint ±0.1 N | 0.1 | kg |
Slope estimates inertial mass; an additive force offset affects the intercept, but a one-point fault affects both.
Subtract force readings to cancel their common offset: fitted m=(F3−F1)/(3−1)=2+fault/2. Intercept becomes offset−fault/2 and the independent midpoint residual is −fault/2. The separate ±0.1 N endpoint-reading bound gives worst-case slope uncertainty ±0.1 kg for exact acceleration labels; it does not cover the selected systematic fault unless explicitly included. A zero residual at one midpoint cannot prove all calibrations or every possible force law.
Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.
Slope estimates inertial mass; an additive force offset affects the intercept, but a one-point fault affects both.
Subtract force readings to cancel their common offset: fitted m=(F3−F1)/(3−1)=2+fault/2. Intercept becomes offset−fault/2 and the independent midpoint residual is −fault/2. The separate ±0.1 N endpoint-reading bound gives worst-case slope uncertainty ±0.1 kg for exact acceleration labels; it does not cover the selected systematic fault unless explicitly included. A zero residual at one midpoint cannot prove all calibrations or every possible force law.
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 must an uncertainty budget say which errors it includes and which it does not?
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.
Save a science backup or import one
Science work is stored locally in this browser, separately from mathematics and AI. It does not sync automatically. Use this science-only backup; this checkout's older all-subject export does not include science.
A legacy file is available only when the complete snapshot fits the 36 MB limit. For larger snapshots, prepare a complete file set below; never discard notebooks to make a smaller file.
Matching imported notebook drafts replace their current drafts. Omitted lessons and known first attempts remain. Export your current work first if you want to retain both drafts.
Complete file sets and course backups
A file set can hold more work than one science file. Keep its manifest and every part together. Each file is limited to 36 MB. This format needs this version of LearnAI or a compatible newer version; older versions can use only the legacy single-file backup above.
The set includes every saved science course and global continuation at this moment. Later edits need a new export. A conflicting tab exports its own visible work, which may differ from saved work in another tab.
0 file(s) selected. File order and filenames do not determine identity. Missing, changed or conflicting parts block the entire restore; no good part is applied by itself.
Science storage: loading. No account or remote computation is required.