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    "scope": [
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      "sources",
      "tests"
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  "limitations": [
    "The surface is level and the force is horizontal",
    "The weight acts through the center of a base of width b",
    "mode is slip, tip, or either",
    "Not an incline, a wedge, a screw, or a belt"
  ],
  "boundary_conditions": [
    "missing W, μ, b, or d → MISSING_REQUIRED_INPUT",
    "W ≤ 0, b ≤ 0, or d ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "μ < 0 → VALUE_OUT_OF_RANGE"
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  "sources": [
    {
      "title": "Hibbeler, Engineering Mechanics: Statics",
      "section": "Dry friction — tipping or slipping",
      "supports": "On a level surface the horizontal force to slip is μW, and the force to tip is the weight times the half-width divided by the height of the force",
      "kind": "reference"
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  "methods": [],
  "fingerprint": "sha256:dc42fbe4b796b5ff53f2a28767251849b8f1db6c2b324139a1f2f0f775075e51",
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      "ok": true,
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        "mu": 0.25,
        "b": 2,
        "d": 2
      },
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        "P": 25,
        "P_slip": 25,
        "P_tip": 50,
        "N": 100,
        "model": "slip_or_tip"
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      "actual": {
        "model": "slip_or_tip",
        "W": 100,
        "mu": 0.25,
        "b": 2,
        "d": 2,
        "N": 100,
        "P_slip": 25,
        "P_tip": 50,
        "P": 25,
        "mode": "slip",
        "solver": "friction + moment about the leading edge",
        "convention": "The surface is level. P is horizontal at height d. The weight acts through the center of a base of width b. Slip uses F = μN with N = W. Tip is the moment of W about the leading edge."
      },
      "tol": 1e-12
    },
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      "ok": true,
      "kind": "golden",
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        "mu": 0.5,
        "b": 1,
        "d": 4
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      "expect": {
        "mode": "tip",
        "P": 12.5,
        "P_slip": 50,
        "P_tip": 12.5
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      "actual": {
        "model": "slip_or_tip",
        "W": 100,
        "mu": 0.5,
        "b": 1,
        "d": 4,
        "N": 100,
        "P_slip": 50,
        "P_tip": 12.5,
        "P": 12.5,
        "mode": "tip",
        "solver": "friction + moment about the leading edge",
        "convention": "The surface is level. P is horizontal at height d. The weight acts through the center of a base of width b. Slip uses F = μN with N = W. Tip is the moment of W about the leading edge."
      },
      "tol": 1e-12
    },
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      "ok": true,
      "kind": "golden",
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        "mu": 0.25,
        "b": 2,
        "d": 4
      },
      "expect": {
        "mode": "either",
        "P": 20,
        "P_slip": 20,
        "P_tip": 20
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        "model": "slip_or_tip",
        "W": 80,
        "mu": 0.25,
        "b": 2,
        "d": 4,
        "N": 80,
        "P_slip": 20,
        "P_tip": 20,
        "P": 20,
        "mode": "either",
        "solver": "friction + moment about the leading edge",
        "convention": "The surface is level. P is horizontal at height d. The weight acts through the center of a base of width b. Slip uses F = μN with N = W. Tip is the moment of W about the leading edge."
      },
      "tol": 1e-12
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      "ok": true,
      "kind": "boundary",
      "inputs": {
        "W": 0,
        "mu": 0.25,
        "b": 2,
        "d": 2
      },
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      "error": "Weight W must be positive."
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        "mu": 0.25,
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        "d": 0
      },
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      "inputs": {
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        "mu": -0.1,
        "b": 2,
        "d": 2
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      "error": "mu must be non-negative."
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      "inputs": {
        "W": 100,
        "mu": 0.25,
        "d": 2
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "b is required."
    }
  ],
  "tier": "engine_tested",
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