Springs and Hooke's Law -- Unequal forces applied to the two ends....

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Discussion Overview

The discussion revolves around the application of Hooke's Law to a spring or rigid rod subjected to unequal forces at both ends. Participants explore the implications of the forces on the tension within the spring or rod, considering scenarios where the object is not stretching but is accelerating. The conversation includes technical reasoning and conceptual clarifications regarding the behavior of tension along the length of the object.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how Hooke's Law can be applied when a spring is pulled with different forces from each end, suggesting that the net force on a segment may be zero.
  • Another participant seeks clarification on whether the spring is stretching or not, leading to a discussion about the distinction between stretching and movement.
  • There is a proposal that the scenario may be analogous to a rigid rod with forces applied at both ends, prompting questions about how tension varies along the rod.
  • Participants discuss the implications of acceleration on the rod and whether all parts experience the same acceleration despite varying tension.
  • One participant suggests that the difference in tension must be consistent for all parts to maintain the same acceleration, leading to further inquiry about how tension varies along the rod.
  • The concept of tension being distributed over the local cross-section of the rod is introduced, with participants reflecting on their understanding of tension at specific points.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the application of Hooke's Law and the behavior of tension in the context of unequal forces. Multiple viewpoints are presented, and the discussion remains unresolved regarding the precise nature of tension and its implications for the system described.

Contextual Notes

There are limitations in the assumptions made about the spring or rod's behavior, particularly regarding the conditions under which Hooke's Law is applicable and the effects of acceleration on tension. The discussion does not resolve these complexities.

Utilite
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Okay here is my question.
Assume that you are pulling a spring with 3N from one end and 5N from the other one. How can we apply Hooke's Law in this case? And let's assume that the spring isn't stretching anymore just to simplify things, but it is accelerating.
If we divide the spring into eight segments. I feel like the net force on the end of third segment is zero (3N is applied to first segment). If that idea is true then we can apply Hooke's Law to each side.
But I couldn't prove that idea and the springs got me really confused.
 
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Utilite said:
And let's assume that the spring isn't stretching anymore just to simplify things, but it is accelerating.
What do you mean by that? Is the spring stretching or not?
 
nasu said:
What do you mean by that? Is the spring stretching or not?
It isn't stretching but it is moving. Like when you stretch a spring hold it and move it around.
 
But what keeps the spring stretched?
 
So, you are talking about a rigid rod with a force of 5 N applied at one end and a force of 3 N applied in the opposite direction at the other end, and you are asking how the tension in the rod varies with position along the rod from one end to the other. Is that correct?
 
Chestermiller said:
So, you are talking about a rigid rod with a force of 5 N applied at one end and a force of 3 N applied in the opposite direction at the other end, and you are asking how the tension in the rod varies with position along the rod from one end to the other. Is that correct?
Yes that is kind of what i am asking. And also we know that the rigid rod stretched a bit as some force is applied. Can we calculate the stretching using Hooke's Law?
 
nasu said:
But what keeps the spring stretched?
I don't know doesn't the spring stretch when you pull it with some force on different ends. (We first stretched it by pulling it then it stabilized then it started moving around) Perhaps it doesn't it just accelerates(?). I got really confused with springs.
 
Utilite said:
Yes that is kind of what i am asking. And also we know that the rigid rod stretched a bit as some force is applied. Can we calculate the stretching using Hooke's Law?
Yes. But first, let's look at the rod. Let M be the mass of the rod. In terms of M, what is the acceleration of the rod? Are all parts of the rigid rod experiencing the same acceleration?
 
Chestermiller said:
Yes. But first, let's look at the rod. Let M be the mass of the rod. In terms of M, what is the acceleration of the rod? Are all parts of the rigid rod experiencing the same acceleration?
yes definitely. the rod is accelerating with 2N/M. since it is rigid every part is accelerating with same acceleration but how is that possible if tension changes from one point to another
 
  • #10
Utilite said:
yes definitely. the rod is accelerating with 2N/M. since it is rigid every part is accelerating with same acceleration but how is that possible if tension changes from one point to another
Well, let's just see. Suppose we divide the rod into 8 parts like you did in your first post. What is the mass of each part? Now, suppose we do a free body diagram on the part immediately adjacent to the 5 N end. The tension of the right end of this segment is 5 N, and call the tension on the left end of this segment T. What is the 2nd law force balance on this segment?
 
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  • #11
A small slice of the rod accelerates due to difference in the tension on the two sides.
So if all the parts are to have same acceleration, the difference need to be the same, and not the tension itself.
What does this tell you about the way the tension varies along the rod?

Edit
Sorry, Chet posted a second before. :)
 
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  • #12
Chestermiller said:
Well, let's just see. Suppose we divide the rod into 8 parts like you did in your first post. What is the mass of each part? Now, suppose we do a free body diagram on the part immediately adjacent to the 5 N end. The tension of the right end of this segment is 5 N, and call the tension on the left end of this segment T. What is the 2nd law force balance on this segment?
Yes now I get it it is just like two masses connected with a string. I was thinking about the tension on a very little dL as just from one side. But now it is actually from two sides. Then what do we mean as tension on some point?
 
  • #13
Utilite said:
Yes now I get it it is just like two masses connected with a string. I was thinking about the tension on a very little dL as just from one side. But now it is actually from two sides. Then what do we mean as tension on some point?
I don't follow your question. The tension is distributed over the local cross section of the rod, at each location.
 
  • #14
Chestermiller said:
I don't follow your question. The tension is distributed over the local cross section of the rod, at each location.
I am sorry I couldn't state my question properly but it doesn't matter now. I got what I was looking for you have been very helpful thank you.
 

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