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The design and setup of bungee jumping ropes is a matter of "life or death." When done wrong, we read about it in the newspapers. The rail of the New River Gorge Bridge passes 785 feet above the surface of the slow, trickling stream, the New River.
Our jumper, a 120 pound "living-dangerous" lady, wants the ropes set so at the bottom of her jump she can scarf a fistful of water from the river. The jump sketch (right) shows three stages of her proposed event. The elastic constant of the bungee cord is two pounds force per foot of extension.
Calculate the length of bungee cord required.
♦ We take the woman and the cord as our system. There will be no heat. Since the cord is part of the system; there will be no work. The energy equation is:
The internal energy of the woman does not change and her kinetic energy is initially and finally equal to zero. The change of kinetic energy of the cord is zero. We assume the change of potential energy of the cord to be negligibly small. This leaves two terms:
Obviously we need to know more about the bungee cord. Here we assume it is adequate to the task. The cord will act like a spring. The energy equation for a spring was derived previously. We substitute for ΔU as shown:
Initially, the cord is unstretched; its length, L1 equals its free length, L therefore L1 - L = 0. At the bottom of the fall, the cord length is: L2 = 775 ft. We enter these numbers with the mass and change of elevation of the woman.
Certainly none of us would take the leap based upon this calculation. Multiple cords are used and some factor, maximum load per cord must be taken into consideration. Our equation, however, addresses the energy change of the event.