Conservation of Energy: Bungie Jumping

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SUMMARY

The discussion centers on calculating the appropriate length of a bungee cord for a jumper starting from a height of 65 meters and wanting to end their fall 10 meters above the ground. The jumper's weight and the cord's behavior under Hooke's law are critical to the calculations. The initial gravitational potential energy is calculated as mg*65, and the final energy state combines gravitational and elastic potential energy. The derived cord length of 42.15 meters contradicts the book's answer of 25.8 meters, suggesting a potential error in the provided solution.

PREREQUISITES
  • Understanding of gravitational potential energy (GPE) and elastic potential energy (EPE)
  • Familiarity with Hooke's law and its application in elastic materials
  • Basic algebra for solving equations involving energy conservation
  • Knowledge of the relationship between mass, gravity, and spring constant (k)
NEXT STEPS
  • Review the principles of energy conservation in mechanical systems
  • Study Hooke's law and its implications for elastic materials
  • Learn how to set up and solve energy equations in physics problems
  • Examine potential sources of error in textbook solutions and problem statements
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and energy conservation, as well as educators looking for examples of practical applications of these concepts.

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Homework Statement


Bungie Jumper starts 65 meters from ground.
Wants to end fall 10m from ground (55 meters from the top).
Cord follows Hookes law.

We know that when his body weight hangs at rest from a 5 meter section of cord, he stretches the cord 1.5 meters.

How long should his cord be?

Homework Equations


Gravitational Potential Energy = mgh
Elastic potential energy = .5kx^2

The Attempt at a Solution



Well, we know that mg=k(1.5) in reference to the last part of the question, because he would be hanging from the cord at rest [no net force]. We'll use this later.

All of his initial energy before the actual jump is gravitational potential energy so ENERGY = mg*65.

When, he is 10m from the ground (at the end of the jump), he has some Gravitational and some elastic potential energy, so ENERGY = mg*10 + .5kx^2.

Setting the two ENERGIES equal, I get a final equation of:
mg*65 = mg*10 + .5kx^2.

and using m=1.5k/g (from first part) I get:
(1.5k)*65 = (1.5k)*10 +.5kx^2

all k's cancel, and I can solve for x.

I get x=12.85. Subtracting this from the total jump distance of 55m, gives me a cord length of 42.15m.

The correct answer is supposedly 25.8m.

Can someone point out what I am doing wrong?
 
Last edited:
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Are you sure that is the correct answer? I got the same answer as you did.
 
IBY said:
Are you sure that is the correct answer? I got the same answer as you did.

Well, it's the answer given in the book, it may be a typo. I wanted to make sure I wasn't doing anything stupid. Thanks.
 

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