Inclined Plane Solver mechanism

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

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