Would a knot in a falling chain make a difference?

In summary, the conversation is about a free falling chain problem and the question of what would happen if the chain is knotted. The two questions asked are whether the knot would fall to one side or continue falling in a straight line, and if the knot's area and mass would slow the chain down when it hits the table. The expert clarifies that when the knot hits the table, it will fall to one side and the chain will retain its initial shape. The possibility of the table not stopping the chain is also mentioned. The person asking the questions admits to not being well-versed in physics and asks for more information.
  • #1
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While I was looking up about free falling chain problem(the question about a chain falling on to a table), I wondered how it would be if the chain is knotted. What I'm thinking is that if the chain has a knot, would it make much difference?

Two questions;

1) Once the knot hits the table, would it fall to one side or would it just keep falling in a straight line? (in real life)

2) Wouldn't the knot's area and mass be too big that the force from hitting the table would slow the chain down, when the knot hits the table?

I'm not that advanced in physics so it would be helpful if you can tell me everything that could change:smile:
 
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  • #2
Can you provide some more information about the problem you're looking at, and what exactly you're wondering will happen... I'm not following you so far.
 
  • #3
When the knot hits the table, it's going to fall to one side. Now it's going to fall straight down until it hits the table. In fact, the chain is going to retain the same shape it initially had when you let go of it. Do you understand what I mean? Every link in the chain will fall at the same speed, so that means no two links will hit the table at the same time.

The only way the table isn't going to stop the chain is if the force of the chain falling is greater than the resistance of the table.
 

What is the Knotted Falling Chain Problem?

The Knotted Falling Chain Problem is a mathematical problem that involves a chain or rope hanging from two points and forming a knot as it falls under its own weight. It is an example of a self-avoiding random walk, meaning that the chain cannot intersect or overlap itself as it falls.

Why is the Knotted Falling Chain Problem important?

The Knotted Falling Chain Problem has applications in various fields, including polymer physics, protein folding, and knot theory. It also has practical applications in engineering and material design, as understanding the behavior of falling chains can help improve the design and stability of structures.

What are the main challenges in solving the Knotted Falling Chain Problem?

One of the main challenges in solving the Knotted Falling Chain Problem is finding an efficient algorithm that can accurately simulate the chain's behavior as it falls. Another challenge is dealing with the complexity of the chain's motion, which can involve multiple loops and tangles.

What are some proposed solutions to the Knotted Falling Chain Problem?

Some proposed solutions to the Knotted Falling Chain Problem involve using computer simulations, physical experiments, and mathematical models to study the chain's behavior. Other approaches involve creating simplified versions of the problem or considering special cases that can provide insight into the general problem.

What are some open questions and future directions for research on the Knotted Falling Chain Problem?

There are still many open questions and potential areas for future research on the Knotted Falling Chain Problem. Some of these include studying the effects of various parameters, such as chain length and initial conditions, on the chain's behavior, and exploring the relationship between the chain's shape and its fall time. Additionally, there is ongoing research on using machine learning and artificial intelligence techniques to improve our understanding and solutions to this problem.

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