Conservation of Energy: Bungie Jumping

In summary, Bungie Jumper starts 65 meters from the ground and wants to end the fall 10 meters from the ground. The cord follows Hookes law and when his body weight hangs at rest from a 5 meter section of cord, he stretches the cord 1.5 meters. Based on this information, the length of the cord should be 42.15 meters, but the given answer in the book is 25.8 meters.
  • #1
Seda
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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?
 
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  • #2
Are you sure that is the correct answer? I got the same answer as you did.
 
  • #3
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.
 

FAQ: Conservation of Energy: Bungie Jumping

What is the concept of conservation of energy in bungee jumping?

The concept of conservation of energy in bungee jumping states that energy cannot be created or destroyed, it can only be transferred from one form to another. In bungee jumping, potential energy from the jumper's position at the top is converted into kinetic energy as they fall, and then back into potential energy as the bungee cord stretches and recoils.

How does the bungee cord help conserve energy in bungee jumping?

The bungee cord acts as a spring, storing the potential energy of the jumper as they fall and then releasing it as they bounce back up. This helps to conserve energy and allows the jumper to experience multiple jumps without the need for additional energy input.

What factors affect the conservation of energy in bungee jumping?

The conservation of energy in bungee jumping can be affected by several factors, such as the elasticity of the bungee cord, the weight and height of the jumper, and the height and surface of the jumping platform. Wind resistance and other external forces can also impact the transfer of energy.

How does the conservation of energy relate to safety in bungee jumping?

The conservation of energy is an important factor in ensuring the safety of bungee jumping. If the bungee cord is not properly elastic or the jumping platform is too high, the jumper may not have enough potential energy to rebound safely. Similarly, if the cord is too long or too short, the transfer of energy may not be sufficient for a safe jump.

Can the conservation of energy be applied to other extreme sports?

Yes, the concept of conservation of energy can be applied to other extreme sports such as zip lining, skydiving, and base jumping. In all of these sports, potential energy is converted into kinetic energy and back again, demonstrating the principle of conservation of energy.

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