Bungee Jumping potential energy

In summary, a 64.0 kg person bungee jumps from a tethered balloon h = 65.0 m above the ground. The bungee cord has negligible mass and unstretched length L = 27.1 m. The elastic potential energy of the cord, Us, is expressed as a function of y for points below y = h - L = 37.9 m. The total potential energy of the person-cord-Earth system is also expressed as a function of y for points below y = 37.9 m. Assuming air resistance is negligible, the minimum height of the person above the ground during the plunge is determined. The potential energy graph does not show any equilibrium points or positions. The equilibrium
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puspita
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Starting from rest, a 64.0 kg person bungee jumps from a tethered balloon h = 65.0 m above the ground. The bungee cord has negligible mass and unstretched length L = 27.1 m. One end is tied to the basket of the balloon and the other end to a harness around the person's body.

.(a) Express the elastic potential energy of the cord, Us, as a function of y for points below y = h - L = 37.9 m. (Use m, g, h, L, k, and y as necessary.)

(b) Express the total potential energy of the person-cord-Earth system as a function of y for points below y = 37.9 m. (Use m, g, h, L, k, and y as necessary.)

(c) Assume that air resistance is negligible. Determine the minimum height of the person above the ground during his plunge.

(d) Does the potential energy graph show any equilibrium points or positions? If so, at what elevations? Are they stable or unstable?
what is equilibrium at Y?

(e) Determine the jumper's maximum speed.
 
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ideas? the idea is to attempt some work & get some help through it
 

1. What is potential energy in the context of bungee jumping?

Potential energy is the stored energy that an object possesses due to its position or state. In the case of bungee jumping, potential energy refers to the energy stored in the bungee cord when it is stretched to its maximum length.

2. How does potential energy affect bungee jumping?

Potential energy plays a crucial role in bungee jumping. As the jumper falls, the potential energy stored in the bungee cord is converted into kinetic energy, causing the jumper to accelerate towards the ground. The stretching and releasing of the bungee cord also helps to slow down the jumper's descent and prevent them from hitting the ground too hard.

3. How is potential energy calculated in bungee jumping?

The potential energy of a bungee cord can be calculated using the equation PE = mgh, where m is the mass of the jumper, g is the acceleration due to gravity, and h is the height at which the bungee cord is stretched. This calculation gives an idea of the amount of potential energy that will be converted into kinetic energy during the jump.

4. Can potential energy be increased in bungee jumping?

Yes, potential energy in bungee jumping can be increased by either increasing the height from which the jumper jumps or by using a longer bungee cord. However, it is essential to ensure that the increase in potential energy does not exceed the maximum safe limit for a successful bungee jump.

5. How does potential energy affect the safety of bungee jumping?

Potential energy plays a crucial role in ensuring the safety of bungee jumping. Too much potential energy can lead to a dangerously fast descent and increase the risk of injury. On the other hand, too little potential energy can result in the jumper not reaching the desired height and hitting the ground. Therefore, proper calculations and measurements of potential energy are necessary for a safe and successful bungee jump.

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