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

instrument / verified-clean

# Work-Energy Theorem 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-theorem-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/work-energy-theorem-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/work-energy-theorem-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/work-energy-theorem-calculator/qualification/>)

## 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-4

**Evidence ID**: t4-131

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The formulas are standard under the stated assumptions, but the specification needs explicit definitions for net force, constant force, theta's reference direction, and theta's unit. The exact unresolved ambiguity is whether theta is entered in degrees or radians, and whether F denotes net force or an individual force; therefore the instrument is not ready for an unconditional PASS.

### Formula and scope findings

- W=Fd cos(theta) is correct for a constant force, where theta is the angle between the force vector and displacement vector; the specification does not state the required constant-force assumption.

- The stated computation is for net work and resulting change in kinetic energy, so F must be the net force. The input label F does not explicitly require that it be the net force.

- The work-energy equality W=Delta KE applies to net work; work by one individual force is not generally equal to the total kinetic-energy change unless all other work is included or zero.

### Unit assumptions

- F is in newtons, d is in meters, m is in kilograms, u and v are in meters per second, and W and Delta KE are in joules.

- theta must be explicitly defined as the angle between the force and displacement vectors.

- The specification does not state whether theta is entered in degrees or radians; this must be made explicit because plain-JS trigonometric functions use radians.

- For the F,d,theta pathway, F is assumed to be the constant net force over the displacement.

- For the m,u,v pathway, u and v are initial and final speeds or velocity magnitudes in a fixed inertial frame.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The extreme-magnitude case overflows ordinary JavaScript numeric arithmetic: the mathematically valid work value 1e616 J becomes Infinity. If the calculator does not reject or flag non-finite results, this is a robustness failure.

## 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": {
    "F": 50,
    "d": 12,
    "theta": 0,
    "theta_unit": "degrees"
  },
  "expected_outputs": {
    "W_J": 600,
    "DeltaKE_J": 600
  },
  "working": "cos(0 degrees)=1. W=F*d*cos(theta)=50 N*12 m*1=600 J. By the work-energy theorem, DeltaKE=W=600 J."
}
````

## Related workflows

[Kinematics & Collisions Tutorenergy bridge](<https://guthlabs.ai/docs/instrument-workflows/kinematics-tutor/>)

## 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`