Bungee jump | simple harmonic motion

In summary: At 72 meters, the cord feels “pulled” at one end and is taut at the other. Finally, at 70 meters the cord feels “tugged” at both ends, and it cannot support any more weight.
  • #1
DarkEnergy890
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Homework Statement
Bungee jump | simple harmonic motion
Relevant Equations
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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!
 
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  • #2
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?
 
  • #3
Think about tension in the cord and how it relates to slack.
 
  • #4
Lnewqban said:
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".
 
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  • #5
DarkEnergy890 said:
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!
 
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  • #6
DarkEnergy890 said:
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.
 
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FAQ: Bungee jump | simple harmonic motion

What is a bungee jump?

A bungee jump is an extreme sport in which a person jumps off a tall structure, such as a bridge or a platform, while attached to an elastic cord. The person experiences a free fall before the cord stretches and pulls them back up, creating a bouncing motion.

What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object oscillates back and forth around a central equilibrium point. The motion is characterized by a constant period and amplitude, and can be described mathematically using sine or cosine functions.

How does simple harmonic motion relate to bungee jumping?

In a bungee jump, the jumper experiences simple harmonic motion as they bounce up and down on the elastic cord. The cord acts as a spring, which stretches and contracts as the jumper falls and is pulled back up, respectively. This creates a repeating pattern of motion that is similar to simple harmonic motion.

What factors affect the bungee jump's simple harmonic motion?

The main factors that affect the simple harmonic motion of a bungee jump are the length and elasticity of the cord, the weight of the jumper, and the gravitational force. The longer and more elastic the cord, the longer the period of the motion. A heavier jumper will also experience a longer period of motion. The gravitational force affects the amplitude of the motion, as it determines how far the jumper will fall before being pulled back up by the cord.

Is bungee jumping safe due to the simple harmonic motion?

Bungee jumping is generally considered safe, as long as proper safety measures are in place and the equipment is well-maintained. The simple harmonic motion of the bungee jump allows for a controlled and predictable descent and ascent, making it a relatively safe activity. However, as with any extreme sport, there is always a risk of injury or accidents, so it is important to always follow safety guidelines and instructions from trained professionals.

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