Unsolvable: The Physics of a Hanging Rod and String Dilemma Explained

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In summary, there is no way for the string and the rod in this rigid solid problem to be in the same direction all the time. This is due to the fact that the system has multiple degrees of freedom, with each component having its own direction of movement. Even if the setup is perfect, external forces such as wind can cause the rod and string to have different directions, making it impossible for them to stay in the same direction constantly.
  • #1
Feynmanfan
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I don't know how to solve this rigid solid problem

Let there be a rod hanging of a string fixed to a certain point. Why is not possible for both the string and the rod to be in the same direction all the time. (it is common sense that it's impossible but how can I prove it?)

Thanks a lot!
 
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  • #2
"Be in the same direction" is a little unclear to be honest. Think about separate x,y and z components of the rod and the string. Assuming the setup is perfect (i.e the string is attached to the rod at the center of one of its ends, no exturnal forces are acting on it other then gravity, uniform density of both parts etc) there is no reason why it wouldn't hang straight down their y axis. If there was to be any exturnal force... i.e wind, then the rod (being of bigger size) would exprience a larger force and hence you would get turning forces which would change the rods direction. Maybe I'm missing something here
 
  • #3
also... you said "to be in the same direction all the time"... what is changing over time to make any difference?
 
  • #4
I think that the others said it you cannot get a clear answer to an unclear question --- plus your name sake would NEVER do that. !
 
  • #5
Feynmanfan said:
I don't know how to solve this rigid solid problem

Let there be a rod hanging of a string fixed to a certain point. Why is not possible for both the string and the rod to be in the same direction all the time. (it is common sense that it's impossible but how can I prove it?)

Thanks a lot!
Basically, in this case, you can regard the string as a MULTIPLE pendulum (more correctly a chain), each component pendulum having one degree of freedom. Adding to that the degree of freedom the stiff rod has, what you're basically asking is why a system with multiple (practically, infinite) degrees of freedom won't behave as a system with only one degree of freedom...
 
  • #6
I believe by "Be in the same direction" he means the string and pendulum stay lined up, acting as a single longer pendulum. Prove why they won't.
 

FAQ: Unsolvable: The Physics of a Hanging Rod and String Dilemma Explained

What is the "hanging rod and string dilemma"?

The hanging rod and string dilemma is a classic physics problem in which a rod is suspended by two strings attached to its ends. The question is, what is the tension in the strings and how does it vary along the length of the rod?

Is the hanging rod problem actually unsolvable?

Yes and no. The problem can be solved using basic principles of physics, but the solution involves a complex mathematical formula that cannot be easily solved or expressed in simple terms. Therefore, it is often referred to as "unsolvable" for practical purposes.

What are the key factors that affect the tension in the strings?

The tension in the strings is affected by the weight of the rod, the distance between the strings, and the angle at which the strings are attached to the rod. These factors determine the distribution of weight and force along the rod, which in turn affects the tension in the strings.

Can the hanging rod and string dilemma be applied to real-life situations?

Yes, this type of problem can be seen in real-life situations such as suspension bridges or flagpoles. However, in these cases, the problem is solved using more advanced techniques and engineering principles.

Why is the hanging rod and string dilemma important for scientists to study?

The hanging rod and string dilemma is a good example of how seemingly simple physical problems can have complex and counterintuitive solutions. It also highlights the importance of understanding and applying mathematical principles in physics. By studying this problem, scientists can gain a deeper understanding of tension, weight distribution, and other fundamental concepts in physics.

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