Calculating Closest Bungee Jump Distance

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SUMMARY

The discussion focuses on calculating the closest distance a bungee jumper reaches to the ground, given specific parameters: an 80 kg jumper, a 50 m jump height, a 25 m relaxed bungee cord, an elastic modulus (E) of 8 MPa, and a cross-sectional area of 400 mm². The key equation for solving this problem involves energy conservation, specifically mgh = (1/2)k(h-L)². To determine the spring constant (k), the jumper's weight and the bungee cord's properties are utilized, with the suggestion to calculate k using the formula k = E*A/L, where L is the relaxed length of the bungee cord.

PREREQUISITES
  • Understanding of energy conservation principles in physics
  • Knowledge of elastic potential energy and spring constants
  • Familiarity with material properties, specifically Young's modulus
  • Basic algebra for solving equations
NEXT STEPS
  • Calculate the spring constant (k) using the formula k = E*A/L
  • Explore the concept of elastic potential energy in bungee jumping scenarios
  • Research the effects of different bungee cord materials on jump dynamics
  • Learn about energy conservation in mechanical systems
USEFUL FOR

Students studying physics, engineers working on bungee jump designs, and anyone interested in the mechanics of elastic materials and energy conservation principles.

snoitcelfer
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Homework Statement



an 80Kg bungee jumper steps off the jump platform which is 50m above the ground.
the bungee cord is 25m long when relaxed and has an E value of 8 MPa and a cross sectional area of 400mm^2.
Calculate the closest the jumper gets to the ground. Consider the center of gravity of the jumper to be at the end of the bungee cord.

Homework Equations



Energy conservation / strain energy

The Attempt at a Solution



i am stuck here because facing this problem i can find solutions using energy conservation such as mgh = (1/2)k(h-L)^2. however I have no idea how to get k from this as k = fx and i am not given a length with the jumper attached. so is it possible to find k from this information or do i need to go in a different direction?
 
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snoitcelfer: Perhaps they want you to use the relaxed (initial) length L and assume k = E*A/L. But maybe someone will give a second opinion.
 

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