Collision Solver (1D Elastic/Inelastic) mechanism

Model scope

The velocity formula for v1' is standard under the stated 1D assumptions. The specification requires review because v2' is left ambiguous and energy loss is listed as an output without a formula or explicit definition.

• The v1' formula is standard for a 1D collision with positive masses and coefficient of restitution e, but v2' is specified only as 'similarly'; its exact formula is ambiguous and must be stated explicitly: v2'=[(m2-e*m1)v2+(1+e)m1v1]/(m1+m2).
• The instrument claims to output energy loss, but no energy-loss formula is provided. It should define energy loss as ΔE=0.5*m1*v1^2+0.5*m2*v2^2-0.5*m1*(v1')^2-0.5*m2*(v2')^2.
• The valid domain for the coefficient of restitution is not stated. For ordinary passive impacts, 0<=e<=1; e=1 is elastic and e=0 is perfectly inelastic. Values outside this range require explicit handling or a different physical interpretation.

Units and conventions

• m1 and m2 are positive masses in a common unit, preferably kilograms.
• v1, v2, v1', and v2' are signed one-dimensional velocities in a common unit, preferably m/s; the positive direction must be defined.
• e is dimensionless.
• Energy loss is reported in joules when masses are in kilograms and velocities are in m/s.
• The energy-loss calculation assumes translational kinetic energy only and no rotational energy, deformation energy retained in the bodies, external work, or other energy exchanges.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "m1": 2,
    "m2": 3,
    "v1": 5,
    "v2": -1,
    "e": 1
  },
  "expected_outputs": {
    "v1_prime": -2.2,
    "v2_prime": 3.8,
    "energy_loss": 0
  },
  "working": "Denominator=m1+m2=2+3=5. v1'=[(2-1*3)*5+(1+1)*3*(-1)]/5=[(-1)*5+2*3*(-1)]/5=(-5-6)/5=-11/5=-2.2. v2'=[(3-1*2)*(-1)+(1+1)*2*5]/5=[1*(-1)+2*2*5]/5=(-1+20)/5=19/5=3.8. Initial KE=0.5*2*5^2+0.5*3*(-1)^2=25+1.5=26.5 J. Final KE=0.5*2*(-2.2)^2+0.5*3*3.8^2=4.84+21.66=26.5 J. Energy loss=26.5-26.5=0 J."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The solver formulas produce undefined results when m1+m2=0, and the tested case also has a nonphysical negative mass. The instrument should reject nonpositive masses and any zero total mass before arithmetic.

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