1D/2D Inelastic Collision Solver (coefficient of restitution) mechanism

Model scope

The scalar formula and momentum conservation are valid for 1D collisions, but the instrument name claims 1D/2D while the specification provides only scalar velocities and no collision geometry. The exact ambiguity is whether the product is intended to support genuine 2D collisions or only 1D collisions. The honest label should state 1D unless vector inputs, collision-normal handling, and 2D formulas are added.

• The restitution formula e=(v2'−v1')/(v1−v2) is correct for a 1D collision under the sign convention that v1>v2 means approach; it is not sufficient for a general 2D collision.
• The stated scalar inputs v1 and v2 and scalar formula do not define 2D collision behavior. A 2D solver requires velocity vectors and a collision normal/contact direction, with restitution applied to the normal components.
• The formulas for v1', v2', and energy lost are not explicitly supplied. With M=m1+m2, the required 1D results are v1'=(m1v1+m2v2−m2e(v1−v2))/M and v2'=(m1v1+m2v2+m1e(v1−v2))/M.
• Energy lost must be defined as initial kinetic energy minus final kinetic energy: ΔK=0.5m1v1²+0.5m2v2²−0.5m1(v1')²−0.5m2(v2')². For a valid 1D collision this equals 0.5(m1m2/(m1+m2))(1−e²)(v1−v2)².

Units and conventions

• m1 and m2 must use the same mass unit, and both must be strictly positive.
• v1, v2, v1', and v2' must use the same signed velocity unit; positive direction must be defined consistently.
• Energy lost is in mass·velocity² units; it is in joules only when masses are in kilograms and velocities are in metres per second.
• For ordinary passive collisions, e must satisfy 0≤e≤1. The stated interpretation of e=0 and e=1 assumes this range.
• The supplied restitution sign convention assumes v1−v2 is the approach relative velocity and v2'−v1' is the separation relative velocity.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "m1": 2,
    "m2": 3,
    "v1": 5,
    "v2": -1,
    "e": 0.5,
    "mass_units": "kg",
    "velocity_units": "m/s"
  },
  "expected_outputs": {
    "v1_prime": -0.4,
    "v2_prime": 2.6,
    "energy_lost": 16.2
  },
  "working": "M=m1+m2=2+3=5. Initial momentum p=2(5)+3(-1)=10−3=7. Initial relative velocity v1−v2=5−(−1)=6. Final relative velocity v2'−v1'=e(v1−v2)=0.5(6)=3. Solve v1'=(p−m2·3)/M=(7−3·3)/5=(7−9)/5=−0.4. Solve v2'=v1'+3=−0.4+3=2.6. Initial KE=0.5(2)(5²)+0.5(3)((−1)²)=25+1.5=26.5 J. Final KE=0.5(2)((−0.4)²)+0.5(3)(2.6²)=0.16+10.14=10.3 J. Energy lost=26.5−10.3=16.2 J."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

Zero total mass causes division by zero and an underdetermined collision, so the solver must reject that input. The e>1 branch is also outside the stated physical domain and must be rejected rather than silently treated as an ordinary inelastic collision.

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