Relation Cross Scans

Stress Equivalent Pairs Three-Row Scan

Stress is a quotient, so scaled force-area pairs can land on the same value. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A different force-area pair can give the same stress

Force 6 N over area 2 square meters gives stress 3 Pa.

σ=FA=6 N2 m2=3 Pa\sigma=\frac{F}{A}=\frac{6\ \text{N}}{2\ \text{m}^{2}}=3\ \text{Pa}
Stress quotient scanForce and area can scale together while stress stays fixed.forceareaforce=6 Narea=2 m^2stress=3 Pa

A different force-area pair can give the same stress

Force 9 N over area 3 square meters gives stress 3 Pa.

σ=FA=9 N3 m2=3 Pa\sigma=\frac{F}{A}=\frac{9\ \text{N}}{3\ \text{m}^{2}}=3\ \text{Pa}
Stress quotient scanForce and area can scale together while stress stays fixed.forceareaforce=9 Narea=3 m^2stress=3 Pa

A different force-area pair can give the same stress

Force 12 N over area 4 square meters gives stress 3 Pa.

σ=FA=12 N4 m2=3 Pa\sigma=\frac{F}{A}=\frac{12\ \text{N}}{4\ \text{m}^{2}}=3\ \text{Pa}
Stress quotient scanForce and area can scale together while stress stays fixed.forceareaforce=12 Narea=4 m^2stress=3 Pa