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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You get a parabola on *suspension bridges,* not on free-hanging cables by themselves. The difference is that when you just have a cable or rope or chain, its mass is distributed evenly *along the length of the rope,* whereas in a suspension bridge, where the mass of the deck dominates the mass of the cable, the mass is distributed evenly *across the horizontal length,* no matter what angle the cable is hanging at in that section.
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