Source: https://guthlabs.ai/docs/instruments/atwood-machine-solver/
instrument / verified-clean
# Atwood Machine Solver
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo
**Tranche**: tranche-4
**Evidence ID**: t4-272
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The acceleration formula and m1-side tension formula are standard under the stated idealized assumptions, but the specification is incomplete because g, sign convention, and the meaning of 'tension(s)' are not defined. It must add T2=m2(g-a) if both tensions are claimed, plus input validation and explicit SI-unit handling.
### Formula and scope findings
- The acceleration formula is correct for two masses connected by a massless, inextensible string that does not slip on a pulley, with m2's downward direction defined as positive: a=(m2-m1)g/(m1+m2+I/r²).
- T=m1(g+a) computes only the tension on the m1 side under that sign convention. With pulley inertia, the two string tensions differ; the m2-side tension must also be provided as T2=m2(g-a).
- The stated output is 'tension(s)', but only one tension formula is supplied. The specification must explicitly define whether it outputs T1, T2, or both.
- The gravitational acceleration g is used but is not listed as an input or fixed constant; its value and units must be stated.
### Unit assumptions
- m1 and m2 are positive masses in kilograms.
- g is assumed to be 9.81 m/s².
- Pulley inertia I is in kg·m² and pulley radius r is in meters, so I/r² has units of kilograms.
- Acceleration is reported in m/s² and tension in newtons.
- The string is massless, inextensible, and does not slip on the pulley; the pulley axle is frictionless.
- For the signed formulas, positive acceleration means m2 moves downward and m1 moves upward.
## Boundary hardening
**BREAK_CLAIMED** · SELF_FLAGGED
A nonzero pulley inertia combined with zero pulley radius makes I/r^2 undefined. Without explicit input validation, the solver can propagate undefined or nonfinite values into acceleration and tension instead of rejecting the input.
## Errata and corrections
No applied erratum is attached to this unique-name record.
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"inputs": {
"m1_kg": 2,
"m2_kg": 5,
"pulley_I_kg_m2": 0,
"pulley_radius_m": 0.2,
"g_m_s2": 9.81
},
"expected_outputs": {
"acceleration_m_s2": 4.2042857143,
"tension_m1_N": 28.0285714286,
"tension_m2_N": 28.0285714286
},
"working": "I/r²=0/0.2²=0. Denominator=2+5+0=7 kg. Numerator=(5-2)×9.81=29.43. a=29.43/7=4.2042857143 m/s². T1=2×(9.81+4.2042857143)=2×14.0142857143=28.0285714286 N. T2=5×(9.81-4.2042857143)=5×5.6057142857=28.0285714286 N; with an ideal massless pulley, both tensions are equal."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`
- `evidence-tranche4/tranche4-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`