Relativistic Momentum & Kinetic Energy Calculator

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo

Tranche

tranche-5

Evidence ID

t5-221

Ledger rows

1

No ledger note is attached.

Review findings

The core relativistic formulas are standard when v denotes physical velocity and c is in consistent units. Because the specification instead defines v as a fraction of c, and because gamma and classical KE formulas plus domain constraints are omitted, the instrument needs an explicit input convention and formula completion before passing verification.

Formula and scope findings

• The Lorentz factor formula gamma=1/sqrt(1-beta^2) is missing even though gamma is an output.
• The input is specified as v (fraction of c), so v is dimensionless beta; in that case momentum must be written p=gamma*m*beta*c, not gamma*m*v unless v is first converted to the physical velocity beta*c.
• The classical kinetic-energy comparison formula KE_classical=0.5*m*(beta*c)^2 is missing.
• The valid input domain is not stated: for a massive particle, m>=0 and |beta|<1 are required.

Unit assumptions

• m is in kilograms.
• The velocity input is beta=v/c, dimensionless; the physical velocity is u=beta*c in meters per second.
• c is the exact SI speed of light, 299792458 m/s.
• p is reported in kg*m/s.
• E_total, KE, and classical KE are reported in joules.
• Gamma is dimensionless.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

An exact input of v_fraction_c=1 makes 1-v^2/c^2 equal zero, so gamma and all relativistic outputs depending on it are undefined or divergent. The calculator should reject |v_fraction_c|>=1. Momentum also has a sign-convention ambiguity if a negative input is interpreted as a speed rather than a signed velocity.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "m_kg": 1,
    "v_fraction_of_c": 0.6,
    "c_m_per_s": 299792458
  },
  "expected_outputs": {
    "gamma": 1.25,
    "p_kg_m_per_s": 224844343.5,
    "E_total_J": 112344397342102200,
    "KE_J": 22468879468420440,
    "classical_KE_J": 16177593217262718
  },
  "working": "beta=0.6. gamma=1/sqrt(1-0.6^2)=1/sqrt(0.64)=1/0.8=1.25. Physical velocity u=beta*c=0.6*299792458=179875474. p=gamma*m*beta*c=1.25*1*0.6*299792458=224844343.5 kg*m/s. E_total=gamma*m*c^2=1.25*1*(299792458)^2=1.25*89875517873681764=112344397342102205 J. KE=(gamma-1)*m*c^2=0.25*89875517873681764=22468879468420441 J. Classical KE=0.5*m*(beta*c)^2=0.5*1*0.6^2*c^2=0.18*89875517873681764=16177593217262717.52 J."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json