Calculate Force Constant for Bungee Jumping

In summary, the problem involves a bungee jumper starting at 36m above a river and wanting to stop safely 4m above the river. The unstretched length of the cord is 25m and the student weighs 700N. The required force constant of the cord can be calculated using the conservation of mechanical energy at the top of the balloon to 32 meters below the balloon. The cord needs to stretch 7 meters in order for the student to stop. At the point where the bungee cord is fully extended but unstretched, the student will have some kinetic energy that needs to be dissipated in a certain distance. Assuming the bungee cord behaves like a spring, the potential energy of a stretched spring can
  • #1
blader324
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Homework Statement



so i have a bungee jumper starting 36m above the surface of a river from a hot air ballon. the elastic cord is attached to his waist. the unstretched length of the cord is 25m, and the student weighs 700N. calculate the required force constant of the cord if the student is to stop safely 4m above the river.


Homework Equations






The Attempt at a Solution



i tried using the conservation of mechanical energy at the top of the balloon to 32 meters below the balloon because that's where the guy wants to stop. also i know that the cord has to stretch 7 meters in order for him to stop 4 meters above the river.
 
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  • #2
Its a lot like spring constants and stretching of springs. Once the guy reacheas 25m below the balloon his bungee cord will be fully extended but unstretched. At this point he will have some kinetic energy which needs dissipating in a certain distance. Do you know the potential energy of a stretched spring?

[Of course assuming the bungee cord behaves like a spring.]
 
Last edited:
  • #3
thanks so much, i figured it out as soon as i got to class! :smile:
 

FAQ: Calculate Force Constant for Bungee Jumping

How do you calculate the force constant for bungee jumping?

To calculate the force constant for bungee jumping, you will need to measure the length of the bungee cord, the mass of the jumper, and the height at which the jumper will be jumping from. You will then use the formula F = kx, where F is the force, k is the force constant, and x is the displacement of the bungee cord. By plugging in the known values and solving for k, you can calculate the force constant for bungee jumping.

Is the force constant the same for all bungee cords?

No, the force constant will vary depending on the material and thickness of the bungee cord. Thicker and stronger cords will have a higher force constant, while thinner and weaker cords will have a lower force constant.

Why is the force constant important for bungee jumping?

The force constant is important because it determines the amount of force that will be exerted on the jumper during the bungee jump. A higher force constant means a greater force will be exerted on the jumper, while a lower force constant means less force will be exerted. This information is crucial for ensuring the safety and success of the bungee jump.

Can the force constant be changed?

Yes, the force constant can be changed by altering the length, material, or thickness of the bungee cord. However, it is important to carefully calculate and test the new force constant before using it for bungee jumping, as it can greatly affect the safety and outcome of the jump.

How can the force constant be used to improve bungee jumping?

Knowing the force constant can help bungee jumping companies and engineers design safer and more thrilling bungee jumping experiences. By carefully calculating and adjusting the force constant, they can create jumps that provide the perfect amount of tension and excitement for the jumper while also ensuring their safety.

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