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

instrument implementation / implementation-contract

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

A source-bound implementation contract for Newton's Second Law / Free-Body Force Solver; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t4-119

**Effect**: Computation or source lookup only

## Input and validation requirements

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.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "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."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/newton-s-second-law-free-body-force-solver/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/newton-s-second-law-free-body-force-solver/mechanism/>)[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`