Why is it that when we fix the two ends of a rope and let gravity act, the rope forms a curve that looks like a parabola?
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The entire weight of the rope is held at the two ends. If you measure a small amount in, the weight below that point is slightly less so the tension isn’t pulling it down as much but the tension is the same so in order for the system to be balanced the rope has to point the tension at a slightly less steep angle. Measure in slightly more and the cycle continues. Once you get to the center the tension is still the same but their is no weight under it so if the rope pulled at any angle other than horizontal it would be unbalanced so it has to be level.
The reason it is a parabola (some people point out this isn’t accurate but it is very close so let’s stick with it for the 5yo) has to do with how we perceived the earlier part. The balance of the tension and the weight was linear measuring along the rope which is angled, but if we measured horizontally we have to account for a constantly changing amount of weight per unit of horizontal distance. To simplify some complex math, the amount of weight below a specific point reduces by both the horizontal distance and the rope length which makes it look kinda like a square function (parabola).
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