A flexible cable is anchored at two supports A and B, which are at the same elevation and $10\text{ m}$ apart. A single concentrated load of $100\text{ kN}$ is hung exactly in the middle of the span ($x = 5\text{ m}$). The sag at the center is measured to be $2\text{ m}$. Determine the maximum tension in the cable. Neglect the weight of the cable.

A suspension bridge cable has a span of $100\text{ m}$ and a maximum sag of $10\text{ m}$. It supports a uniformly distributed deck load of $w = 20\text{ kN/m}$ (measured horizontally). Determine the equation of the cable shape and the maximum tension.

A high-voltage transmission line is strung between two towers $200\text{ m}$ apart. The cable itself weighs $10\text{ N/m}$ along its own length. If the minimum tension in the cable (at the lowest point) is $5000\text{ N}$, find the maximum sag.

The main cables of the Golden Gate Bridge are often assumed to be parabolas, while the cables of high-voltage transmission lines are modeled as catenaries. What is the fundamental physical difference in the loading that causes these two distinct mathematical shapes?

The Gateway Arch in St. Louis is designed in the shape of an inverted weighted catenary. How does the concept of a "funicular shape" relate arches to hanging cables, and why is this shape structurally ideal?