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November 15th, 2017, 05:56 PM   #1
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Elastic PE

There are a couple questions I am trying to solve. I can't seem to figure out the process, and I would like some more elaboration on potential energy and kinetic energy.





THE PERSON'S MASS IS 75 kg


Using that image, I need to figure out:

Speed at Point A

Speed at Point B (When cord is at maximum length)

And finally the spring constant of the cord.

If you could not spoon feed me the answer, just walk me through it. Thank you!

Last edited by skipjack; November 17th, 2017 at 04:21 AM.
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November 16th, 2017, 03:45 AM   #2
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I don't mind helping, but I don't wish to go off site to find out what your question is.
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November 17th, 2017, 03:49 AM   #3
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Sorry about that. I have no other way to display the picture in the thread.
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November 17th, 2017, 04:54 AM   #4
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Assume a (constant) particular value for the acceleration due to gravity. Choose variable(s) for the person's speed. Assume that air resistance is negligible. Assume that the cord's initial length is 9.00m, so that it has stretched by 22m at point B. Assume that the cord has negligible kinetic energy. Assume that the person drops vertically from rest, and that their kinetic energy is half their mass times the square of their speed. That's not quite all the assumptions needed, but you get the idea.

When a cord is stretched by a distance x, its restoring force has magnitude kx, and its potential energy is ½kx², where k is the cord's spring constant.
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November 23rd, 2017, 03:58 AM   #5
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This is one of those multi-stage energy transfer problems. Consider the problem step-by-step and calculate stuff as you go. I'll give hints as to what to calculate.

Remember the following:

Total energy = kinetic energy + gravitational potential energy + elastic potential energy
(energy is conserved)

$\displaystyle GPE = mgh$

$\displaystyle KE = \frac{1}{2} mv^2$

Okay...


Initial state: person is at the top just about to perform the bungee jump. The person no kinetic energy (KE) and lots of gravitational potential energy (GPE). Can you calculate the GPE?

Stage 1: person is falling and the cord is slack. The person loses GPE and gains KE.

State at A: person has reached the point where the cord is just about to start stretching. Can you calculate the GPE at this new point? What is the KE of the person at this point?
Hint: energy is conserved...

Stage 2: person is falling, but the cord is stretching. The person loses GPE and KE and the cord gains elastic potential energy (EPE).

State at B: person has stopped falling (speed = 0 m/s) because of the bungee cord and is just about to start rising. Can you calculate the GPE at this point? What is the KE? Therefore, what is the total energy converted to EPE during stage 2?

Once you know the EPE of the cord, you can use the formulae from SkipJack's post to calculate properties of the cord.
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