Finding the unstretched length of a bungee cable

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SUMMARY

The discussion focuses on calculating the unstretched length of a bungee cord used by two men weighing 150 lb each, with a cord stiffness of k=80 lb/ft. The unstretched length is determined to be 90 ft based on the potential energy equation mgh. Additionally, the conversation suggests using conservation of energy principles to analyze the kinematics of the attached man after the release of the unconnected man, specifically regarding maximum acceleration and height above the water.

PREREQUISITES
  • Understanding of potential energy (mgh)
  • Familiarity with Hooke's Law and spring constants (k=80 lb/ft)
  • Knowledge of conservation of energy principles
  • Basic kinematics and dynamics of motion
NEXT STEPS
  • Study the application of Hooke's Law in bungee jumping scenarios
  • Learn about energy conservation in mechanical systems
  • Explore kinematic equations for motion under gravity
  • Investigate the dynamics of oscillatory motion in bungee systems
USEFUL FOR

Physics students, engineers, and anyone interested in the mechanics of bungee jumping and energy conservation principles.

jbrizown
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Two men both weighing 150lb jump off a bridge using a bungee cord with stiffness k=80lb/ft. One of the men is attached to the cable and plans to release the other man when they reach the water 120ft below the bridge. Once there the connected man will let go of the unconnected man when they touch the water. Determine the unstretched length of the cord. Also determine the maximum acceleration of the attached man and the maximum height he reaches above the water when he springs back up.



Homework Equations


T1 + ƩU = T2

Us = 1/2 k (s)^2


The Attempt at a Solution



I used mgh for U and got an unstretched length of 90ft, but I'm not sure if it's correct and I don't know how to approach the kinematics of the second portion.
 
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It helps if you show us your reasoning and not just your answer.
For the second part - why not just use conservation of energy again?
 

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