How Do You Calculate the Speed of a Bungee Jumper 19m Below the Launch Point?

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Homework Help Overview

The problem involves calculating the speed of a bungee jumper who falls 19 meters below a launch point, considering the dynamics of gravitational potential energy and elastic potential energy in the context of a bungee cord. The subject area includes mechanics and energy conservation principles.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculation of the distance the bungee cord stretches and the application of energy conservation equations. There is a focus on the correct height to use in the potential energy calculations, with some questioning the assumptions about total height versus the height fallen.

Discussion Status

Participants are actively engaging with the problem, with some providing guidance on the correct interpretation of height in the energy equations. There is an ongoing exploration of different interpretations regarding the potential energy calculations, but no consensus has been reached.

Contextual Notes

There is a noted confusion regarding the height used in energy calculations, specifically whether to use the total height of the cliff or the height fallen. This reflects a common challenge in understanding energy conservation in dynamic systems.

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Homework Statement


A bungee jumper of mass 75 kg is standing on a platform 53m above the river. The length of the unstretched bungee cord is 11m. The spring constant of the cord is 65.5N/m. Calculate the jumpers speed at 19m below the bridge on the first fall.


Homework Equations


Em1=Em2 Ek=1/2mv^2 Es=1/2kx^2 GPE=mgh


The Attempt at a Solution



Find x by subtracting 11m from 19m which is 8m, this is how far the bungee cord is stretched. Use x in formula gpe=Ek+Es. Problem arises when I sub values in answer is off.
 
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Show us what you did.
 
x=19m-11m
mgh=1/2mv^2+1/2kx^2
subbed values in but didnt get right answer :S
 
What did you use for h?
 
Height of the cliff or bridge which is 53m
 
That's your problem. He hasn't fallen the whole distance yet. He has only fallen h = 19 m.
 
wait but total energy at top of the cliff is mgh where height is 53 m though
 
Try 19 m in your equations and see what you get. The equation should be mgΔh. It is the change in potential energy that matters, not the total potential energy relative to some arbitrary reference.
 

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