projected-pull-is-smaller-than-line-force - Surface Tension and Capillarity Step by Step

A rational projection factor reduces a checked line force. 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 begins from a checked line force

The projected pull is allowed only because it cites the existing line-force source.

F=24\ \text{N}\qquad p=\frac{1}{2}

Allowed projection factors reduce the pull

The training surface only allows zero, one half, and one. The projected force follows that bounded factor exactly.

\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}

A projection factor can only reduce the line force

The projection is a rational multiplier on a checked line-force source, not a real contact-angle law.

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