[Mechanics] Tension in bungee jumping

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SUMMARY

The discussion focuses on calculating the spring constant of a bungee rope for a jumper with a mass of 60 kg who jumps from a height of 24 m. The correct spring constant, k, is determined to be 200 N/m, based on the energy conservation principle where gravitational potential energy (Ep) equals elastic potential energy (E). The jumper's height above the water is crucial for accurate calculations, as the extension of the rope is 12 m, leading to the equation mgh = ½kx². Misinterpretation of the height used in calculations led to an incorrect initial value of k as 100 N/m.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Familiarity with gravitational potential energy (Ep = mgh)
  • Knowledge of elastic potential energy (E = ½ kx²)
  • Basic principles of energy conservation in physics
NEXT STEPS
  • Study Hooke's Law and its applications in real-world scenarios
  • Explore energy conservation principles in mechanical systems
  • Learn about the dynamics of bungee jumping and safety considerations
  • Investigate the effects of different spring constants on bungee jump performance
USEFUL FOR

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

sushichan
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Homework Statement


A bungee jumper of mass 60kg jumps from a bridge 24 m above the surface of the water. The rope is 12 m long and is assumed to obey Hooke's law. What should the spring constant of the rope be if the woman is to just reach the water?

Homework Equations


Ep=mgh
E=1/2 kx^2

The Attempt at a Solution


Energy conservation? I'm definitely doing something wrong here and not understanding something but I don't know what.

mgh = ½kx^2
(60)(10)(12) = ½k(12)^2
[I put the length of the unstretched part of the rope as my h value and x as the extension, which is 24-12=12]

k= 100 Nm^-1
[This is the answer I got]

But the answer is k=200 Nm^-2
 
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sushichan said:
I put the length of the unstretched part of the rope as my h
To calculate the initial gravitational PE, use the height above the water.
 
Doc Al said:
To calculate the initial gravitational PE, use the height above the water.
okay thanks!
 
This is the key statement : The woman jumps from a bridge 24 m above the surface of water.
 

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