Source: https://guthlabs.ai/docs/instruments/inclined-plane-solver/mechanism/

instrument mechanism / verified-clean

# Inclined Plane Solver mechanism

The inspectable method record for Inclined Plane Solver, kept separate from implementation and qualification.

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

## Model scope

The formulas can be verified only for the restricted case of a block already sliding down a plane, with no applied force and with theta, mu, and g explicitly defined. The advertised with/without-applied-force capability, friction output, and minimum-angle output require additional formulas and a precise static/kinetic friction model. The exact ambiguity requiring review is the magnitude and direction of the optional applied force, plus whether mu denotes static or kinetic friction.

- The acceleration formula is valid only for kinetic sliding down an incline with no applied force component along the plane; it does not support the advertised applied-force mode.

- The normal-force formula N=mg cos(theta) is valid only when there is no applied-force component perpendicular to the plane.

- The friction-force output has no formula. Under a kinetic-friction assumption it would be f=mu N, but static versus kinetic friction is unspecified.

- The minimum angle to slide is not provided. For impending motion from rest with static-friction coefficient mu_s, the standard result is theta_min=arctan(mu_s), not necessarily arctan(mu) if mu denotes kinetic friction.

- The sliding-down condition is missing: for the stated no-applied-force model, sliding down requires tan(theta)>mu for positive acceleration; otherwise the object may remain at rest under static friction.

- The angle unit and gravitational acceleration are unspecified in the instrument spec.

## Units and conventions

- Mass is in kilograms.

- Angle theta is supplied in degrees and converted to radians before evaluating sine, cosine, or arctangent.

- The test vectors use g=9.81 m/s^2.

- The coefficient mu is dimensionless and is treated as a kinetic-friction coefficient for the acceleration and friction calculations.

- Applied force is measured in newtons and is zero in all test vectors because its direction and force-component formulas are unspecified.

- Acceleration is positive down the incline; normal force and friction force are reported in newtons.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "mass_kg": 5,
    "angle_deg": 30,
    "mu": 0.2,
    "applied_force_along_plane_N": 0,
    "g_m_per_s2": 9.81
  },
  "expected_outputs": {
    "acceleration_m_per_s2": 3.205858,
    "normal_force_N": 42.478546,
    "friction_force_N": 8.495709,
    "min_angle_deg": 11.309932
  },
  "working": "sin(30°)=0.5; cos(30°)=0.8660254. a=9.81(0.5−0.2×0.8660254)=9.81(0.3267949)=3.205858 m/s². N=5×9.81×0.8660254=42.478546 N. f=muN=0.2×42.478546=8.495709 N. theta_min=arctan(0.2)=11.309932°."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The extreme coefficient input produces floating-point overflow to positive and negative Infinity. The specification also does not define static friction, the applied-force direction, or the effect of a force with a normal component, so those cases require explicit rejection or additional conventions.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/inclined-plane-solver/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/inclined-plane-solver/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/inclined-plane-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`