Work-Energy & Impulse-Momentum Calculator mechanism

Model scope

The formulas are standard under their stated physical conditions, but the specification is not complete enough for an unambiguous instrument: g, the potential-energy reference, initial/final velocities, force-versus-net-force semantics, force constancy, and angle units must be defined. The honest_label field is empty; it should honestly state that this is a constant-force/constant-g particle calculator and not a general variable-force work or impulse solver.

• KE=½mv² is correct for a particle of mass m moving at speed v, with mass in kg and speed in m/s.
• PE=mgh is correct only for gravitational potential energy near a specified constant-g field; g is missing from the declared inputs and the zero/reference height is unspecified.
• W=Fd cosθ is correct only for a constant force and a displacement with θ defined as the angle between the force vector and displacement vector. Variable-force work requires W=∫F·ds.
• J=FΔt is correct only for a constant net force. In general, impulse is J=∫F_net dt.
• J=Δ(mv) is correct for net impulse, but Δp requires clearly defined initial and final velocities. The declared single velocity input v is insufficient to compute Δp independently.
• The specification does not state whether F is the applied force or the net force; the impulse-momentum equality requires the net force and matching system boundary conditions.

Units and conventions

• Use SI units: m in kg, v in m/s, h and d in m, F in N, and Δt in s; outputs are KE and PE in J, W in J, J in N·s (equivalent to kg·m/s), and Δp in kg·m/s.
• θ is assumed to be an angle in degrees in these test vectors and must be converted to radians internally if the implementation uses standard JavaScript trigonometric functions.
• g is assumed to be 9.81 m/s²; the instrument must expose this value or document it as a fixed constant.
• h is a signed height relative to an explicitly selected zero-potential reference.
• v is treated as the final or stated instantaneous speed; separate initial and final velocities are required for Δp.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "m": 2,
    "v": 4,
    "v_i": 2,
    "v_f": 4,
    "h": 5,
    "g": 9.81,
    "F": 8,
    "d": 4,
    "theta_deg": 0,
    "delta_t": 0.5
  },
  "expected_outputs": {
    "KE_J": 16,
    "PE_J": 98.1,
    "W_J": 32,
    "J_Ns": 4,
    "delta_p_kg_m_per_s": 4
  },
  "working": "KE = 0.5×2×4² = 1×16 = 16 J. PE = 2×9.81×5 = 98.1 J. W = 8×4×cos(0°) = 32×1 = 32 J. J = 8×0.5 = 4 N·s. Δp = m(v_f−v_i) = 2×(4−2) = 4 kg·m/s; this matches J."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

Extreme finite inputs overflow the plain-arithmetic JavaScript Number representation to Infinity. The specification also leaves angle units, height reference direction, and gravitational acceleration convention implicit, producing materially different results for plausible interpretations.

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