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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It’s not actually a parabola, but the reason it forms is that the horizontal stress is the same at all points of the rope, but the vertical component depends on how much weight is being carried at that point. At the lowest point it’s horizontal, because that part is being held up by the parts either side of it. Near the ends it will be steepest, because it’s holding up everything between that and the lowest point, in addition to the sideways force.
The angle at any particular point depends on the ratio of the horizontal force to the vertical force being carried at that part of the cable.
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