Friction in Pulley System: Calculations?

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Discussion Overview

The discussion revolves around the role of friction in a pulley system, particularly when a string is pulled without slipping. Participants explore whether frictional forces act on the string by the pulley and how this affects calculations involving torque and tension, considering different assumptions about the mass of the string and pulley.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that static friction is necessary for the string to turn the pulley, while others argue that it does not typically appear in calculations since it does no work.
  • There is a discussion about whether static friction contributes to torque calculations, with some asserting that it does provide torque if the pulley has mass.
  • Concerns are raised about the implications of assuming a massless string, suggesting that this could imply no friction and thus prevent the pulley from turning.
  • Some participants clarify that static friction transmits tension from the string to the pulley without restricting the string's motion.
  • It is noted that typical assumptions in introductory courses include massless strings and frictionless pulleys, but the presence of friction can lead to different tension values on either side of the string.
  • Participants discuss the conditions under which friction is considered, particularly in relation to the mass of the pulley and the normal force acting on it.

Areas of Agreement / Disagreement

Participants express differing views on the role of static friction in calculations and the implications of massless assumptions. There is no consensus on whether static friction should be explicitly considered in torque calculations, indicating ongoing debate.

Contextual Notes

Limitations include assumptions about the mass of the string and pulley, the nature of friction, and the conditions under which torque is calculated. These factors remain unresolved and are subject to interpretation based on different scenarios.

boredaxel
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If a string around a pulley is pulled without slipping, I am wondering if there is any frictional force acting on the string by the pulley. If there is, will it appear in calculations? Thanks in advance
 
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boredaxel said:
If a string around a pulley is pulled without slipping, I am wondering if there is any frictional force acting on the string by the pulley.
Sure, otherwise the string couldn't turn the pulley.
If there is, will it appear in calculations?
Not usually. (It's static friction and does no work.)
 
but wouldn't the static friction appear in torque calculation? Also what if the string is assumed to be massless, doesn't that implies no friction and so the pulley shouldn't be able to turn?
 
boredaxel said:
but wouldn't the static friction appear in torque calculation?
No, it just transmits the string tension to the pulley.
Also what if the string is assumed to be massless, doesn't that implies no friction and so the pulley shouldn't be able to turn?
No.

Typical assumptions (in intro courses) are that strings are massless (and thus have the same tension throughout) and that pulleys are frictionless (not between string and pulley, but about the axle of the pulley).
 
Doc Al said:
No, it just transmits the string tension to the pulley.

Care to explain this? I can't really visualize it. Thanks
 
The pulley moves with the string because the pulley is on bearings and free to rotate. Thus it doesn't restrict the motion of the string except by its own inertia when accelerating. It is the static friction between the string and the pulley that makes the pulley rotate.
 
boredaxel said:
but wouldn't the static friction appear in torque calculation?

Hi boredaxel! :smile:

If the pulley has mass, and if you need to calculate the energy or angular momentum of the pulley, then yes, the friction is an external force on the pulley, and will provide a torque to the pulley.

But exam questions usually (though not always :wink:) say that pulleys are massless.
Also what if the string is assumed to be massless, doesn't that implies no friction and so the pulley shouldn't be able to turn?

Friction depends on the normal force on the pulley, and (if the string is bent round the pulley) there will always be a normal force, even if the string is massless.
Doc Al said:
Typical assumptions (in intro courses) are that strings are massless (and thus have the same tension throughout) …

Hi Doc Al! :smile: May I qualify that?

A massles string with no obstructions will have the same tension throughout (while a massive string hanging vertically will of course have more tension at the top) …

but a string touching anything (like a pulley) with friction will have different tension on either side, even if the string is massless. :wink:
 
tiny-tim said:
If the pulley has mass, and if you need to calculate the energy or angular momentum of the pulley, then yes, the friction is an external force on the pulley, and will provide a torque to the pulley.
Absolutely, but you generally don't need to explicitly consider static friction. The forces exerted on the pulley are represented by the tensions in the string.

but a string touching anything (like a pulley) with friction will have different tension on either side, even if the string is massless. :wink:
But not if the pulley is massless, a common assumption as you point out. I was waiting for the OP to bring up the issue of a massive pulley so I could qualify my statement. :wink: (One step at a time.)
 
Doc Al said:
I was waiting for the OP to bring up the issue of a massive pulley so I could qualify my statement. :wink: (One step at a time.)

ah … I guessed that's what you were thinking … but I noticed the OP had mentioned torque, so I assumed his pulley already had mass. :wink:
 

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