Elastic/Spring Potential Energy Calculator mechanism

Model scope

The spring-energy formula is valid, but the instrument's advertised combined spring+gravity capability is unsupported by the listed formula and inputs. Clarify whether x is measured from the unstretched or equilibrium position, and either remove the combined-gravity claim or specify U_total = ½kx² + mgh together with m, h, g, units, and a height reference.

• U=½kx² is correct for elastic potential energy in an ideal linear spring, with x measured from the spring's unstretched/equilibrium reference position.
• The stated computation includes combined spring+gravity potential-energy problems, but the specification provides no gravity formula, mass, height, or gravitational-field input. The listed formula computes spring energy only.
• The reference position for x is not explicitly defined; using total length instead of displacement from the unstretched position would be incorrect.

Units and conventions

• k must be in N/m and x must be in meters for U to be returned in joules.
• x may be positive for extension or negative for compression; squaring makes the spring energy nonnegative.
• If combined gravity energy is added later, mass must be in kilograms, height in meters, and g in m/s²; gravitational potential energy would require a defined reference and sign convention.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "k": 200,
    "k_unit": "N/m",
    "x": 0.15,
    "x_unit": "m"
  },
  "expected_outputs": {
    "U": 2.25,
    "U_unit": "J"
  },
  "working": "U = ½kx² = ½(200)(0.15²) = 100(0.0225) = 2.25 J"
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The extreme finite inputs k=10^308 N/m and x=10^154 m produce a mathematically finite value of 5×10^615 J but overflow ordinary JavaScript numeric arithmetic to Infinity.

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