projected-force-factor-cross-scan - Surface Tension and Capillarity Step by Step

Projected contact force is scanned across bounded projection factors. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Projection starts after the line force is already checked

The projected pull does not choose its own source. It cites the two-surface line force and then applies a bounded rational factor.

F_{\parallel}=pF=\frac{1}{2}\cdot24\ \text{N}=12\ \text{N}

The projection factor gates how much pull remains

The line force is fixed in all three rows. The projected column changes only because the bounded factor changes.

\begin{array}{c|c|c}p&F&F_{\parallel}\\0&24\ \text{N}&0\ \text{N}\\\frac{1}{2}&24\ \text{N}&12\ \text{N}\\1&24\ \text{N}&24\ \text{N}\\\end{array}

The projected force cannot exceed its line-force source

The final diagram keeps the half projection tied to the line source. The table supplies the zero and full endpoints.

0\le F_{\parallel}\le F\qquad12\ \text{N}\le24\ \text{N}