Understanding Pulleys, Strings, and Tensions: Common Doubts and Clarifications

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    Pulley Tension
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Discussion Overview

The discussion revolves around the concepts of pulleys, strings, and tensions, focusing on the behavior of massless and massive pulleys and strings, the effects of friction, and the implications for tension in various scenarios. Participants explore theoretical aspects, practical implications, and clarify common doubts related to these mechanics concepts.

Discussion Character

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

Main Points Raised

  • Some participants propose that a massless pulley can rotate with zero net torque, similar to a massless string accelerating with zero net force.
  • There is a discussion about whether tension in a massless string remains the same when moving over a pulley, with some noting that friction can lead to unequal tensions if the pulley has friction.
  • Some participants argue that if a pulley is massless and the string has mass, the tensions at the endpoints of the string over the pulley should be the same, while others suggest that the tensions must be unequal due to the mass of the string.
  • The role of friction between the string and the pulley is debated, with some asserting that friction affects tension, while others claim it is irrelevant for massless systems.
  • Participants discuss how the length of the string over the pulley may influence tension, with differing views on whether equal lengths result in equal tensions.
  • There is an exploration of how the presence of mass in the pulley or string affects the net forces and tensions, with some participants questioning how a net force of zero can coexist with unequal tensions.
  • One participant notes that tension varies along the arc of a string wrapped around a pulley, while remaining constant outside of that arc.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the effects of mass, friction, and the conditions under which tensions are equal or unequal. The discussion remains unresolved, with no consensus reached on several key points.

Contextual Notes

There are limitations in the discussion regarding assumptions about the nature of friction, the definition of massless versus massive systems, and the specific conditions under which tensions are analyzed. Some participants also express uncertainty about the implications of these concepts in practical scenarios.

Who May Find This Useful

This discussion may be of interest to students and educators in physics, particularly those exploring mechanics, as well as individuals seeking clarification on the behavior of pulleys and strings in various contexts.

  • #31
jbriggs444 said:
The frictional force at the axle would be multiplied by the radius of the axle to get the resulting frictional torque.

So you would have:

Iα = (T2-T1)R - fr​

Where T1 is the one tension, T2 is the other tension, R is the pulley radius, r is the axle radius and f is the frictional force at the axle.

Thanks...Things are getting clearer...Now please consider a frictionless pulley with sufficient friction between string and pulley.

Why do we write net torque on the pulley as (T2-T1)R ?

The tangential force acting on the pulley is friction F and not the tension in the string.Tension doesn't act on the pulley.

So,the torque on the pulley is FR.

But,since the friction F is equal to the difference in the tensions at the two ends of the arc we write the torque as (T2-T1)R .

Is my understanding correct ?
 
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  • #32
Tanya Sharma said:
But,since the friction F is equal to the difference in the tensions at the two ends of the arc we write the torque as (T2-T1)R .

Is my understanding correct ?

Yes.

Note that there is some lack of rigor talking about "friction F" as if it had a well-defined value. Force is a vector. The friction between the string and the pulley is not a single well defined vector whose magnitude is "F". Instead, it is spread out (and may not be spread out evenly) over the surface of the pulley. Fortunately for our purposes, every incremental bit of string that is stretched out over the surface of a circular pulley contributes its frictional force with a moment arm of length R at right angles to the incremental force. So we can safely shrug, treat the net tangential F as if it were a simple number and correctly conclude that its value is T2-T1.
 
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  • #33
Thanks jbriggss...The explanation is simply wonderful.

Loosely speaking,this is how I thought that the net friction would be equal to the difference in tensions.

The forces acting on a tiny bit of a string are the net tension difference,say dT and friction f .Now,since the string is massless,the net force on every bit of the string should be zero.So we have dT=f .Summing them along the arc,we get ΔT=F or T2-T1 =F.

Is it correct to think in this manner ?
 
  • #34
Tanya Sharma said:
Loosely speaking,this is how I thought that the net friction would be equal to the difference in tensions.

The forces acting on a tiny bit of a string are the net tension difference,say dT and friction f .Now,since the string is massless,the net force on every bit of the string should be zero.So we have dT=f .Summing them along the arc,we get ΔT=F or T2-T1 =F.

Is it correct to think in this manner ?

Yes. This is a good way to come up with a number "F" that is, in some perfectly reasonable sense, the total friction.

The lack of rigor that I had in mind comes up when multiplying this "F" by R to try to compute torque. The result has units of torque and actually gives the right torque in the case at hand, but it would not be a justifiable computation in the case of arbitrary (non-circular) pulleys. There are also complications if the string is wrapped in a slanted or crooked path around the pulley.
 
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  • #35
Tanya Sharma said:
Loosely speaking,this is how I thought that the net friction would be equal to the difference in tensions.

The forces acting on a tiny bit of a string are the net tension difference,say dT and friction f .Now,since the string is massless,the net force on every bit of the string should be zero.So we have dT=f .Summing them along the arc,we get ΔT=F or T2-T1 =F.

Is it correct to think in this manner ?

Yes. This is a good way to come up with a number "F" that is, in some perfectly reasonable sense, the total friction.

The lack of rigor that I had in mind comes up when multiplying this "F" by R to try to compute torque. The result has units of torque and actually gives the right torque in the case at hand, but it would not be a justifiable computation in the case of arbitrary (non-circular) pulleys. There are also complications if the string is wrapped in a slanted or crooked path around the pulley.
 
  • #36
Thank you jbriggs
 

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