Bungee Jumping and Conservation of Energy

In summary, a bored college student goes bungee jumping off a tall bridge with an elastic bungee cord attached to his ankles. The equation mgy = 0.5KX^{2} is used to find the student's mass m in terms of variables given in the problem introduction and any appropriate constants. The student's mass can be expressed as m = (0.5KX^{2})/gy, where y_e represents the length of the relaxed cord and y_0 is the distance between the bridge and the water. With this information, the amount of stretch in the cord at the lowest point can be calculated.
  • #1
cse63146
452
0
[SOLVED] Bungee Jumping and Conservation of Energy

Homework Statement



A bored college student decides to try bungee jumping. He attaches an elastic bungee cord to his ankles and happily jumps off a tall bridge across a river. He ends up barely touching the water before the cord jerks him back up.

Find the mass of the student m.
Express the student's mass in terms of variables given in the problem introduction and any appropriate constants.

98693A.jpg

98693B.jpg


Homework Equations



mgy = 0.5K[tex]X^{2}[/tex]

The Attempt at a Solution



so I get m = (0.5K[tex]X^{2}[/tex])/gy

but this doesn't seem right. Any ideas?
 
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  • #2
What doesn't seem right about it? Looks OK to me. (Not a good model for a real bungee cord, but that's OK.)
 
  • #3
would I use [tex]y_{e}[/tex] instead of y and X?
 
  • #4
cse63146 said:
would I use [tex]y_{e}[/tex] instead of y?
What is [itex]y_{e}[/itex]? If that's how much the cord stretches, then you should use that instead of X.
 
  • #5
It's there on the picture, but it looks like it only goes half way (y_e) of the bungee cord

I tried inputing this:[tex]o.5k(y_e)^2/gy_0[/tex] and it says it's wrong. Any suggestions?
 
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  • #6
cse63146 said:
It's there on the picture, but it looks like it only goes half way (y_e) of the bungee cord
Without a clear definition, we can only guess. It's not clear from the diagram, but I presume y_e is either the unstretched length of the bungee cord, or the amount that it stretches. There's no additional information? (What text is this?)
 
  • #7
It's masteringphysics (online assignment). It's says that y_e is the length the of relaxed cord y_o is the distance between the bridge and the water and y_o>y_e, so once the cord stretches, would it have a length of y_o?
 
  • #8
Yes. Now that you know what y_e and y_0 mean, you can find the amount of stretch in the cord at the lowest point. (Of course, the cord is attached to his ankles, so it doesn't stretch the full distance to y_0. Lacking any data, I would ignore that issue.)
 
  • #9
Got it, thanks again.
 

FAQ: Bungee Jumping and Conservation of Energy

1. What is bungee jumping and how does it relate to conservation of energy?

Bungee jumping is an extreme sport in which a person jumps from a high platform or structure while attached to a long elastic cord. The conservation of energy refers to the principle that energy cannot be created or destroyed, but rather transformed from one form to another. In bungee jumping, the potential energy of the person at the top of the platform is converted to kinetic energy as they fall, and then back to potential energy as the cord stretches and recoils. This demonstrates the conservation of energy in action.

2. How does the length and elasticity of the bungee cord affect the conservation of energy in bungee jumping?

The length and elasticity of the bungee cord play a crucial role in the conservation of energy in bungee jumping. A longer cord allows for a greater distance for the person to fall, increasing their potential energy and resulting in a higher bounce. The elasticity of the cord also affects the amount of potential energy that can be converted into kinetic energy and back, ultimately determining the height of the bounce and the overall experience for the jumper.

3. Is bungee jumping a safe activity in terms of conservation of energy?

Yes, bungee jumping is a safe activity in terms of conservation of energy. The principle of conservation of energy ensures that the potential energy of the jumper is not lost, but rather transformed back and forth between potential and kinetic energy. As long as the bungee cord is properly designed and maintained, the energy will be safely conserved throughout the entire jump.

4. Can conservation of energy be applied to other activities or sports?

Yes, conservation of energy can be applied to many other activities and sports. Any time an object or person is in motion, conservation of energy is at play. For example, a roller coaster uses potential and kinetic energy to propel riders along the track, while a skateboarder converts their potential energy at the top of a ramp into kinetic energy as they move down it. Understanding conservation of energy can help explain the science behind many different actions and movements.

5. How does the conservation of energy impact the environment and conservation efforts?

The conservation of energy is a fundamental principle in understanding and preserving the environment. It reminds us that energy cannot be created or destroyed, but rather transferred and transformed. This is crucial in sustainable energy practices, where renewable sources such as solar and wind power are used to convert energy from one form to another without depleting non-renewable resources. In conservation efforts, understanding the conservation of energy can help us make more informed decisions about resource usage and management to ensure a sustainable future for our planet.

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