Source: https://guthlabs.ai/docs/instruments/newton-s-second-law-free-body-force-solver/mechanism/

instrument mechanism / verified-clean

# Newton's Second Law / Free-Body Force Solver mechanism

The inspectable method record for Newton's Second Law / Free-Body Force Solver, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The Newton's Second Law formula is valid. The instrument needs explicit 2-D or 3-D vector scope, angle convention, unit validation/conversion rules, and a precise missing-force input contract before it can receive an unqualified PASS.

- ΣF=ma is the correct Newtonian relation, but the specification does not state whether forces and acceleration are treated as scalar quantities or vectors resolved into components.

- A missing force is not uniquely determined unless the target acceleration vector and every other known force vector are supplied; the spec does not define this constraint.

- The force-angle convention is unspecified, so vector results are ambiguous without a stated reference axis and positive rotation direction.

## Units and conventions

- All calculations use SI units: force in newtons (N), mass in kilograms (kg), and acceleration in meters per second squared (m/s²).

- Angles are assumed to be in degrees, measured counterclockwise from the positive x-axis.

- Force components use Fx=F cos(theta) and Fy=F sin(theta).

- For a missing force, F_missing=m*a_target-ΣF_known.

- A zero-magnitude vector has magnitude zero but no defined direction angle.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "forces": [
      {
        "magnitude": 10,
        "angle_deg": 0
      },
      {
        "magnitude": 6,
        "angle_deg": 90
      }
    ],
    "mass_kg": 2
  },
  "expected_outputs": {
    "net_force_N": {
      "x": 10,
      "y": 6,
      "magnitude": 11.6619,
      "angle_deg": 30.9638
    },
    "acceleration_m_s2": {
      "x": 5,
      "y": 3,
      "magnitude": 5.831,
      "angle_deg": 30.9638
    }
  },
  "working": "F1=(10 cos 0°,10 sin 0°)=(10,0) N. F2=(6 cos 90°,6 sin 90°)=(0,6) N. ΣF=(10+0,0+6)=(10,6) N. |ΣF|=sqrt(10²+6²)=sqrt(136)=11.6619 N. angle=atan2(6,10)=30.9638°. a=ΣF/m=(10,6)/2=(5,3) m/s². |a|=sqrt(5²+3²)=sqrt(34)=5.831 m/s²."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

A zero-mass input produces undefined acceleration through division by zero and must be rejected. The directional-output branch also exposes a potential angle-wrapping discrepancy, and the force-angle orientation convention can reverse the result.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/newton-s-second-law-free-body-force-solver/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/newton-s-second-law-free-body-force-solver/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/newton-s-second-law-free-body-force-solver/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`