Calculating Bungee Cord Length and Spring Constant: Realistic or Unrealistic?

[Somoan]

As part of a fundraiser, the Chancellor has agreed to bungee jump from a crane 45 m above a pool filled with Jello. The plan is for the bungee cord to stop the Chancellor just before his head enters the Jello. Your task is to select a bungee cord that will safely stop the Chancellor's descent in time. To estimate the feasibility of the plan, assume for now that a bungee cord is massless and behaves like an ideal spring. Also neglect air resistance. What length and spring constant should the bungee cord have? Are those values realistic?

Things that I considered-

• Realistically, how much can a bungee cord stretch?
• Does the bungee cord begin to stretch as soon as the Chancellor is dropped from the crane?
• When is the Chancellor subject to the maximum force? How much force is safe?

Can someone please explain, I am at an absolute loss. I don't even know where to begin

 

[Sarlacc]

Well gravity will accelerate all objects at the same speed regardless of mass. I'm not entirely sure I'm going the right way with this but you have the initial velocity (0), the final velocity (also zero because at max extension he'll pause for a second), the distance and an acceleration.

So x=ut+(1/2)at^2
45=(0)t+(1/2)(9.8)t^2
Which gives him about three seconds of flight time. That may or may not be helpful.

I'm fairly sure you can also do the two spring equations. Hooke's law:

Hooke's Law F=-kx
and
Elastic potential energy: E=(1/2)kx^2

Just have a think about that and have a go. Technically the forum rules say you need to show an attempt at solving it before anyone helps you.

No wait you need the length of the extension for the spring equations...

 

[PeroK]

As part of a fundraiser, the Chancellor has agreed to bungee jump from a crane 45 m above a pool filled with Jello. The plan is for the bungee cord to stop the Chancellor just before his head enters the Jello. Your task is to select a bungee cord that will safely stop the Chancellor's descent in time. To estimate the feasibility of the plan, assume for now that a bungee cord is massless and behaves like an ideal spring. Also neglect air resistance. What length and spring constant should the bungee cord have? Are those values realistic?

Things that I considered-

• Realistically, how much can a bungee cord stretch?
• Does the bungee cord begin to stretch as soon as the Chancellor is dropped from the crane?
• When is the Chancellor subject to the maximum force? How much force is safe?

Can someone please explain, I am at an absolute loss. I don't even know where to begin

It seems you are struggling on two fronts:

1) The characteristics of an ideal spring.

2) How to model a bungee jump as motion under an ideal spring.

What do you know about 1)?

 

[DEvens]

Well, you need to make some effort to solve the problem first.

Supposing the bungee cord does begin to pull on the Chancellor right away, what will be the equation of motion for him? What will be the forces affecting him? How will you work out that he stops just at the surface of the pool?

Supposing the cord does not begin to pull on him until he gets some distance below his release point? What equation of motion will he have then?

 

[Somoan]

I should also add I have been in the hospital for three weeks and am playing catch-up in class, So I apologize if I don't understand some of these replies...

What I know is... the force is proportional to the displacement and (F=-kx)

 

[PeroK]

I should also add I have been in the hospital for three weeks and am playing catch-up in class, So I apologize if I don't understand some of these replies...

What I know is... the force is proportional to the displacement and (F=-kx)

Displacement from where?

 

[Somoan]

and an ideal spring will compress and stretch without bounds where as a real spring will break evaentually

 

[Sarlacc]

and an ideal spring will compress and stretch without bounds where as a real spring will break evaentually

Well that's pretty much your first "consideration" answered. In reality a bungee cord can only stretch as far as its tensile strength allows.

Since it asks you to estimate you might have to assume the Chancellor weighs the average human weight (I think it's 70kg) which means you can get the spring constant (70*9.8)=-k(22.5)
k=-686.

Although it may be +686 since maybe you have to make the F negative because it's acting down. I need to remember these things...

 

[Somoan]

Ok, this is unrelated to the problem but I just want to make sure my understanding of some of the chapters concepts are correct...so please tell me if this is right

-A swinging pendulums greatest potential energy is at its highest point (A classmate said it was constant but that just doesn't make sense to me)

-1)As you throw the snowball straight up, is the mechanical energy of the snowball-Earth system is not conserved 2)but during the free flight of the snowball, the mechanical energy of the snowball-Earth system is conserved.

-And when there is friction an objects mechanical energy decreases