Overhead power transmission lines rely on cables to carry electricity across large distances. To ensure the stability and functionality of these lines, it is crucial to understand the shape and tension experienced by the cables under the influence of their weight.
A generalized loading function is employed to analyze a cable subjected to its own weight. This function considers the force acting along the cable's arc length rather than its projected length, providing a more accurate...

A tracheostomy is a surgical procedure that creates an artificial opening into the trachea, typically at the second or third cartilaginous ring level. This opening allows the insertion of a tracheostomy tube, which can replace an endotracheal tube, provide mechanical ventilation, bypass an upper airway obstruction, or remove accumulated tracheobronchial secretions.
Tracheostomy tubes can be made of semiflexible plastic (polyurethane or silicone), rigid plastic, or metal, and they come in...

Flexible cables are commonly used in various applications for support and load transmission. Consider a cable fixed at two points and subjected to multiple vertically concentrated loads. Determine the shape of the cable and the tension in each portion of the cable, given the horizontal distances between the loads and supports.

The most common application of magnetic force on current-carrying wires is in electric motors. These consist of loops of wire, which are placed between the magnets with a magnetic field. When current flows through the loops, the magnetic field applies torque, which causes the shaft to rotate, thus converting electrical energy to mechanical energy.
Consider a rectangular current-carrying loop containing N turns of wire, placed in a uniform magnetic field. The net force on a current-carrying loop...