Bungee jump | simple harmonic motion

[DarkEnergy890]

Homework Statement:

Bungee jump | simple harmonic motion

Relevant Equations:

No maths involved

As you all know, a bungee jump is where a person is tied to a cord and the person jumps off and bounces up again.

The natural length of a cord is 75 metres. Then when a person is attached onto the cord, the length becomes 83 metres when the person is at rest. I am sure that the person is not executing simple harmonic motion because the cord goes slack at some point. My question is that does the cord go slack when the length of the cord is < 75 metres, or when the length of the cord is < 83 metres?

In the solutions it said that it goes slack when the cord is < 75 metres. However, it makes more sense to me that the cord goes slack < 83 metres because 83 metres was its natural length when the man is attached on to the cord (due to the man's weight). Any help with understanding this is appreciated!

 

[Lnewqban]

Welcome, @DarkEnergy890 !

Why the difference between 83 and 75 meters?
Why not more or less than that value?
What would it be for a heavier or lighter person?

 

[Frabjous]

Think about tension in the cord and how it relates to slack.

 

[DarkEnergy890]

Welcome, @DarkEnergy890 !

Why the difference between 83 and 75 meters?
Why not more or less than that value?
What would it be for a heavier or lighter person?

Hi, thanks for the reply. Sorry if my question was unclear. The length is 75m if nobody is on it. Then when a "certain human" is attached the length increases to 83m.

Edit: Ah, I see what you mean. When the person is attached to the cord the cord has already been stretched. So no matter what the weight of the person is as long as the length is > 75m then the cord will not go slack, but rather it will "decompress".

 

[PeroK]

Edit: Ah, I see what you mean. When the person is attached to the cord the cord has already been stretched. So no matter what the weight of the person is as long as the length is > 75m then the cord will not go slack, but rather it will "decompress".

Precisely!

 

[Lnewqban]

Hi, thanks for the reply. Sorry if my question was unclear. The length is 75m if nobody is on it. Then when a "certain human" is attached the length increases to 83m.

Edit: Ah, I see what you mean. When the person is attached to the cord the cord has already been stretched. So no matter what the weight of the person is as long as the length is > 75m then the cord will not go slack, but rather it will "decompress".

Exactly!
At 76 meters, there is still some fraction of the weight force acting on the cord and stretching it a little.
At 74 meters, the cord does not “feel” anything attached to any of its ends.