Bungee Jumping Physics: Minimum Height Needed

[harihrn]

Um this problem involves a man jumping off a bridge with a bungee chord holding him. he weighs 102 kg and the stretch constant of the chord is 167n/m. And there is a 12N air resistance. what is the minimum height needed for him to do this? thanks! (one more thing, the length of the rope when slack is 20 ft

 

[Nathanael]

Have you attempted the problem yet? Please show your work.

 

[Danger]

In my opinion, anything involving bungee jumping should be in a mental health forum...

 

[harihrn]

yes of course, i divided the problem into three parts, the initial fall till the rope starts to stretch, then the stretch
the Ke value that i came up with was mgH, and the sum of the energies is KE-W, which was mg(6.09) -12(6.09). 6.09 m is the length of the chord when it is slack (20ft). the sum of the energies came up to be 6014.484 joules. I then set that equal to 1/2kx^2 12x, which became a quadratic equation: 83.5x^2+12x-6014.484, x being the amount it should stretch, which came up to be about 8.42 meters. The minimum height that i found was 14.51 meters

 

[harihrn]

Im not sure whether my approach was right in the first place, since another method that i tried gave me a different answer.
I set mg(height of the bridge)= 0.5kx=(height-the length of chord/rope)^2 which gave me 22.3 m.

 

[Danger]

Do you have multiple personality disorder, or did you quote yourself by accident? :D

I'm sorry. I know that you are serious about the subject, and other folk like Nathanael will help you. I was just temporarily bored and couldn't resist the urge. I promise that this was my last interruption of your thread.

 

[harihrn]

my bad I'm new to this lol

 

[Nathanael]

I agree with your first approach. The reason the second method gives a different answer is because it neglects air resistance.

Danger...

 

[harihrn]

there is another way i did it and it gave me ANOTHER answer, lol i must sound annoying, but i watched a simulation which showed that when the chord is fully stretched, the kinetic energy during the fall converts to elastic potential and gravitational potential. so, i set the KE = mgx+0.5kx^2, x being the distance it is stretched, and i got 4.4 as the answer for the stretch, and the total height came out to be 10.49m. IDK which one to go with

 

[harihrn]

i really need some help

 

[Nathanael]

which showed that when the chord is fully stretched, the kinetic energy during the fall converts to elastic potential and gravitational potential.

If the rope is stretched and the person is moving upwards, then the KE will be converted to elastic PE and gravitational PE
But if the person is moving downwards (like in our situation) then the GPE and KE will be converted to elastic PE.

Imagine if there was no rope (and so no elastic PE). If the person is moving upwards, KE is converted to GPE. But if the person is moving downwards, GPE is converted to KE.

 

[harihrn]

so what would be the conceptual formula that i should use? like which method of the ones that i did is right?

 

[Nugatory]

OK, everyone... Stop it now.

Harihrn, start over again with a new post in the introductory physics homework section of this forum, and use the homework template to organize your thoughts and let us know what you've already figured out. You will get much better and more helpful answers that way.