Source: https://guthlabs.ai/docs/instruments/work-energy-impulse-momentum-calculator/

instrument / verified-clean

# Work-Energy & Impulse-Momentum Calculator

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

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

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/work-energy-impulse-momentum-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/work-energy-impulse-momentum-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/work-energy-impulse-momentum-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/work-energy-impulse-momentum-calculator/qualification/>)

## Ledger state

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

**Area**: Mechanical, Civil & Structural Engineering — Statics/Dynamics, Strength of Materials, Machine Design, Civil, HVAC, Vibration

**Tranche**: tranche-4

**Evidence ID**: t4-214

**Ledger rows**: 1

No ledger note is attached.

## Review findings

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.

### Formula and scope findings

- 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.

### Unit assumptions

- 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.

## Boundary hardening

**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.

## 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": 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."
}
````

## 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-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`