What Length of Bungee Cord is Needed to Stop a 70 kg Person from Plunging 226m?

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SUMMARY

The discussion focuses on calculating the required length of a bungee cord for a 70 kg person jumping from a height of 226 meters, intending to stop 10 meters above the ground. The force constant of the bungee cord is specified as 4900 N/m. The key equation involves equating the gravitational potential energy at the starting height to the elastic potential energy of the bungee cord when the jumper is 10 meters above the sidewalk. The gravitational potential energy is calculated using the height of 216 meters, while the spring potential energy is derived from the length of the cord.

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  • Understanding of gravitational potential energy and its formula (PE = mgh)
  • Knowledge of elastic potential energy and the spring constant (PE = 1/2 kx²)
  • Basic algebra for solving equations involving energy
  • Familiarity with the concept of energy conservation in physics
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  • Study the principles of energy conservation in mechanical systems
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  • Explore real-world applications of bungee jumping physics
  • Investigate the effects of varying spring constants on bungee cord performance
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Physics students, engineers, and anyone interested in the mechanics of bungee jumping and energy conservation principles.

raindropecho
Hi I'm having trouble with a certain question. Could someone please guide me to the right answer? Thanks
"Consider a 70 kg person leaping off a 226m building. He plans to use a rope with force constant 4900 N/m. What length of rope does he need to stop his plunge 10m above the sidewalk? What max force will the rope exert on him?"
Any help is greatly appreciated
 
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Construct an equation with those 3 peices of information using length as your variable and solve it. Each side will be an energy equation. There are two important things to consider: the gravitational potential energy at the beginning (when on the roof) is exactly equal to the potential energy in the spring (bungee cord) when the person is 10m off the sidewalk (make that the zero point to make the calculations easier and make the building 216m). And second, remember that for the first part of the plunge, the bungee cord isn't stretching.
 
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