What Is the Potential Energy in Bungee Jumping?

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SUMMARY

The discussion focuses on calculating the potential energy involved in bungee jumping, specifically for a 64.0 kg jumper descending from a height of 65.0 m. The elastic potential energy of the bungee cord is expressed as a function of the vertical position y below 37.9 m, where the cord begins to stretch. The total potential energy of the jumper-cord-Earth system is also derived for points below this height. Additionally, the minimum height of the jumper above the ground during the plunge is determined, alongside an analysis of equilibrium points in the potential energy graph and the jumper's maximum speed.

PREREQUISITES
  • Understanding of gravitational potential energy calculations
  • Familiarity with elastic potential energy concepts
  • Knowledge of basic physics principles, including forces and motion
  • Ability to manipulate equations involving variables such as mass (m), gravitational acceleration (g), and spring constant (k)
NEXT STEPS
  • Study the derivation of elastic potential energy equations in physics
  • Learn about the conservation of energy principles in mechanical systems
  • Explore the effects of air resistance on falling objects
  • Investigate the dynamics of oscillatory motion in bungee jumping scenarios
USEFUL FOR

Physics students, engineers, and anyone interested in the mechanics of bungee jumping and energy transformations in dynamic systems.

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Starting from rest, a 64.0 kg person bungee jumps from a tethered balloon h = 65.0 m above the ground. The bungee cord has negligible mass and unstretched length L = 27.1 m. One end is tied to the basket of the balloon and the other end to a harness around the person's body.

.(a) Express the elastic potential energy of the cord, Us, as a function of y for points below y = h - L = 37.9 m. (Use m, g, h, L, k, and y as necessary.)

(b) Express the total potential energy of the person-cord-Earth system as a function of y for points below y = 37.9 m. (Use m, g, h, L, k, and y as necessary.)

(c) Assume that air resistance is negligible. Determine the minimum height of the person above the ground during his plunge.

(d) Does the potential energy graph show any equilibrium points or positions? If so, at what elevations? Are they stable or unstable?
what is equilibrium at Y?

(e) Determine the jumper's maximum speed.
 
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