Boundary Depth Scans

surface-energy-floor-three-row-scan

Surface area is scanned below, at, and above an energy floor. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Surface area is scanned against an energy floor

The gamma source is fixed at 3 N/m while checked area moves to 4 square meters. The energy ledger reads 12 J which is below boundary relative to the 24 J floor.

E=γA=3 N/m×4 m2=12 JEmin⁡=24 JE=\gamma A=3\ \text{N/m}\times4\ \text{m}^{2}=12\ \text{J}\qquad E_{\min}=24\ \text{J}
Surface-energy boundary rowThe energy row cites the same checked gamma source.lengthforceareabelow boundary

Surface area is scanned against an energy floor

The gamma source is fixed at 3 N/m while checked area moves to 8 square meters. The energy ledger reads 24 J which is on boundary relative to the 24 J floor.

E=γA=3 N/m×8 m2=24 JEmin⁡=24 JE=\gamma A=3\ \text{N/m}\times8\ \text{m}^{2}=24\ \text{J}\qquad E_{\min}=24\ \text{J}
Surface-energy boundary rowThe energy row cites the same checked gamma source.lengthforceareaon boundary

Surface area is scanned against an energy floor

The gamma source is fixed at 3 N/m while checked area moves to 12 square meters. The energy ledger reads 36 J which is above boundary relative to the 24 J floor.

E=γA=3 N/m×12 m2=36 JEmin⁡=24 JE=\gamma A=3\ \text{N/m}\times12\ \text{m}^{2}=36\ \text{J}\qquad E_{\min}=24\ \text{J}
Surface-energy boundary rowThe energy row cites the same checked gamma source.lengthforceareaabove boundary