Equal tension on rope in a pulley system?

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Discussion Overview

The discussion centers around the behavior of tension in a massless, frictionless rope within a pulley system. Participants explore the implications of Newton's second law in this context and consider variations when friction is introduced.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that if the rope is massless and frictionless, the tension must be equal on both sides of the pulley due to the application of Newton's second law.
  • Others elaborate that since each tiny section of the massless rope has zero mass, the net force must also be zero, leading to identical tensions throughout the rope.
  • A participant introduces the idea that if friction is present, the tension may differ between the two sides of the pulley, especially when the pulley is accelerating.
  • Some participants emphasize that the assumptions of masslessness and frictionlessness are critical to the conclusions drawn about tension equality.

Areas of Agreement / Disagreement

Participants generally agree on the implications of a massless and frictionless rope leading to equal tension. However, there is disagreement regarding the effects of friction and acceleration on tension differences in practical scenarios.

Contextual Notes

The discussion relies on the assumptions of masslessness and frictionlessness, which may not hold in real-world applications. The implications of introducing friction and acceleration are not fully resolved.

negation
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Suppose the rope involved in the pulley is massless and experience no friction.

Why is the force on the right hand side equal to the tension experienced by the rope on the left hand side?
 
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Apply Newton's second law, F=ma, with m=0.
 
negation said:
Suppose the rope involved in the pulley is massless and experience no friction.

Why is the force on the right hand side equal to the tension experienced by the rope on the left hand side?

Newton's second law.

If the rope is massless then each tiny section of the rope must be massless. The net force on that tiny incremental section [in the tangential direction] is equal to the difference in tension, if any, between the two ends of the section.

But, by Newton's second law: f=ma. We know that the mass of the section is zero. So the net force must be zero. So the tensions at each end must be identical.

Apply this logic incrementally from one end of the rope to the other. The tension must be the same throughout the length of the rope.

[Edit: I see that Meir Achuz beat me to it]
 
Last edited:
That explanation is for a massless rope. You also can consider the same section of massless rope described above but with friction from contact with the pulley acting on it. In this case there would be a difference of tension in the rope when the pulley is accelerating.

Since the rope is frictionless as well as massless then this is also the reason that forces are the same on both sides of the pulley.
 

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