Bungee jumping with elastic cord and rigid rope

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SUMMARY

The discussion focuses on calculating the appropriate length of a rigid rope (L) for a bungee jump scenario involving a 15-meter elastic cord with an elasticity of 150 N/m and a mass (M) under the influence of gravity (10 m/s²). The key equations used include the energy conservation principle, where gravitational potential energy (mgh) is equal to the elastic potential energy (1/2 kx²). The relationship between the total height (H), rope length (L), and cord stretch (X) is established as L + X = H. Participants emphasize the importance of including the unstretched length of the cord in calculations.

PREREQUISITES
  • Understanding of basic physics concepts such as gravitational potential energy and elastic potential energy.
  • Familiarity with Hooke's Law and its application in elastic materials.
  • Knowledge of kinematic equations, particularly those involving acceleration and displacement.
  • Basic algebra skills for solving equations involving multiple variables.
NEXT STEPS
  • Study the principles of energy conservation in mechanical systems.
  • Learn about Hooke's Law and its implications for elastic materials.
  • Explore kinematic equations in-depth, focusing on their applications in real-world scenarios.
  • Investigate the dynamics of bungee jumping and the physics behind elastic cord behavior.
USEFUL FOR

Physics students, engineers, and adventure sports enthusiasts interested in the mechanics of bungee jumping and the calculations involved in ensuring safety and performance during jumps.

Giff
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Happy new year everyone, if I were to bungee jump off a building height H using a cord with an elasticity of 150 N/m 15 m long when it isn't stretched that is tied to a rope of length L (does not stretch), and I have a mass of M and the cord stretches X meters. Gravity is pulling at 10 m/s^2. I want to go as close to the ground as possible when I step off the building. What should the length of rope be?

I know that at the bottom, mgh=1/2kx^2. I also know that the cord + rope is slightly less than the height of the building (L + X = H). The force on the cord must also decrease as the length of rope gets smaller because there is less time for gravity to accelerate me. I also tried Velocity = 2aΔy.

Once again,
mass = M
building height = H
Cord length = 15m
Cord elasticity = K = 150N/m
Rope length = L
Gravity = 10 m/s^2

We need to know the rope length L. Am I missing something or doing something wrong? Any and all help is much appreciated!
 
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Not sure what problem you are having. You get x from your equation 2mgh = kx2 and from that deduce L. One thing, you missed out the unstretched length of the cord in L+X=H.
 

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