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Physics of the Catenary Cable
In this modern society, cables are pretty much everywhere. It’s not just the stuff that connects your computer and monitor, but data and power cables need to be run all over the place. Often these cables are suspended between poles to keep them out of the way of cars and pedestrians.
Some of these overhead lines might look like they are straight from one pole to the next, but they aren’t. There is always some bit of sag. You can really notice this when the cable mounting points are quite a distance away.
But now we get to the physics of this. What shape does a cable make as it is supported between two points? The answer is a catenary curve. No, it’s not a parabola — even though it sort of looks like one.
The exact shape of the hanging cable depends on the linear mass density, the tension, and the location of the two mounting points.
OK, let’s derive this curve. It’s going to be fun.
I’ll be honest. This is one of those problems that at first seems too hard, then it seems straight forward, then you get stuck in some maths. We are going to work through it together.
