Elastic potential energy in a heavy wire due to its own weight derivation
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The following schematic for this analysis shows a simplified representation of a bungee jumper and bungee cord, at the initial position (1), before he jumps. The jumper is represented as a point object of mass M. The bungee cord is represented by two lengths of rope, each with length L/2, with a bend at the bottom of radius R. The left side of the bungee cord is attached to a fixed support. The mass of the bungee cord is m. The acceleration due to gravity is g (equal to 9.8 m/s2 on earth). The sign convention is "up" as positive and "down" as negative.
Additional assumptions in this analysis are:
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