Why Is the Tension in a Rope Not Zero When Pulled Equally from Both Ends?

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Homework Help Overview

The discussion revolves around understanding the concept of tension in a rope when it is pulled from both ends with equal forces. Participants are exploring why the tension is not zero despite the forces being equal and opposite, and what this implies about the nature of tension itself.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the definition of tension and how it relates to the forces applied at each end of the rope. There are attempts to clarify whether the sum of forces or the nature of the forces acting on the rope defines tension.

Discussion Status

The discussion is active, with participants providing insights into the nature of tension and the forces involved. Some have offered clarifications about the relationship between the forces applied and the resulting tension, while others are still grappling with the concepts being discussed.

Contextual Notes

There appears to be some confusion regarding the definitions and calculations related to tension, particularly in the context of a massless rope and the implications of Newton's third law. Participants are working through these assumptions without reaching a definitive conclusion.

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Homework Statement


If the two ends of a rope in equilibrium are pulled with forces of equal magnitude and opposite direction, why is the total tension in the *not* zero?



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The Attempt at a Solution


If there are two vectors with same magnitude and opposite direction their sum is zero. So, at the middle point that has to be in equilibrium. Are they asking what the sum is at the end of one side of the rope? Should I be taking the absolute value of each vector and adding them to equal a non zero number?
 
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DrummingAtom said:
If there are two vectors with same magnitude and opposite direction their sum is zero. So, at the middle point that has to be in equilibrium. Are they asking what the sum is at the end of one side of the rope?
No, they are checking that you understand what 'tension in a rope' means. That the net force on the rope is zero happens to be true, but that's not what defines tension.
Should I be taking the absolute value of each vector and adding them to equal a non zero number?
Nothing like that. You just have to know that tension is the force that the rope exerts. If each end is pulled with a force F, what's the tension in the rope?
 
doc al said:
nothing like that. You just have to know that tension is the force that the rope exerts. If each end is pulled with a force f, what's the tension in the rope?

T = F1+F2 Right?
 
DrummingAtom said:
T = F1+F2 Right?
Nope!

What force does the rope exert? You and I are playing tug of war. We both pull our ends with a force F. What force does the rope exert on each of us? (Recall Newton's 3rd law.)
 
Doc Al said:
Nope!

What force does the rope exert? You and I are playing tug of war. We both pull our ends with a force F. What force does the rope exert on each of us? (Recall Newton's 3rd law.)

The rope would be an equal opposite force on us, a force toward the center.
 
DrummingAtom said:
The rope would be an equal opposite force on us, a force toward the center.
Right. So what will be the tension in the rope in terms of F?
 
Doc Al said:
Right. So what will be the tension in the rope in terms of F?

Hmm, well:

If T2= -F2 and T1 = -F1.

And Ttotal = T2 + T1 then

Ttotal = -F2 + -F1

How's that?
 
DrummingAtom said:
Hmm, well:

If T2= -F2 and T1 = -F1.

And Ttotal = T2 + T1 then

Ttotal = -F2 + -F1

How's that?
Not quite it yet. For one, there's no T1 and T2 (at least for the usual 'massless' rope) or Ttotal, there's just a single tension. And there's nothing to calculate. If I pull on the rope with a force F, then the rope pulls back on me with a force F. And thus the tension in the rope is simply F.

What's confusing to most--and is the point of this question--is that in order for a tension to be created in the rope both ends must be pulled with the same force. And the tension created is just F, not 2F.
 
Doc Al said:
Not quite it yet. For one, there's no T1 and T2 (at least for the usual 'massless' rope) or Ttotal, there's just a single tension. And there's nothing to calculate. If I pull on the rope with a force F, then the rope pulls back on me with a force F. And thus the tension in the rope is simply F.

What's confusing to most--and is the point of this question--is that in order for a tension to be created in the rope both ends must be pulled with the same force. And the tension created is just F, not 2F.

Ahh, it's making more sense now. That explanation helps a lot. Thank you.
 

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