Does Pulley Mass Affect Rope Tension Symmetry?

Click For Summary

Discussion Overview

The discussion revolves around the effects of pulley mass on rope tension in a pulley system, specifically examining whether tension is symmetric on either side of the pulley. The conversation includes theoretical considerations, mathematical reasoning, and conceptual clarifications regarding friction, torque, and acceleration in both massless and massive pulley scenarios.

Discussion Character

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

Main Points Raised

  • Some participants propose that if a pulley is massless and frictionless, the tension will be the same throughout the string.
  • Others argue that if the pulley has mass, a net torque is required to accelerate it, leading to different tensions on either side of the pulley.
  • A participant questions whether torque needs to be considered if there is no friction on the rope going over the pulley, suggesting that the pulley could still roll easily.
  • Another participant clarifies that if there is no slipping of the rope on the pulley, the linear acceleration is related to angular acceleration, which might imply equal acceleration on both sides.
  • Some participants express confusion about the relationship between tension, pulley mass, and block masses, questioning how to derive the tensions in relation to the masses and acceleration.
  • A later reply emphasizes that the net torque on the pulley is determined by the difference in tensions, indicating that the tensions cannot be the same if the pulley has mass.

Areas of Agreement / Disagreement

Participants generally disagree on whether the mass of the pulley affects the symmetry of tension in the rope. While some assert that tension is the same in massless scenarios, others maintain that a massive pulley leads to differing tensions due to the need for torque. The discussion remains unresolved regarding the implications of pulley mass on tension symmetry.

Contextual Notes

Limitations include assumptions about friction and slipping, as well as the dependence on definitions of a "frictionless" pulley. The discussion does not resolve the mathematical relationships or the conditions under which tensions may be equal or different.

Who May Find This Useful

This discussion may be useful for students and enthusiasts of physics, particularly those interested in mechanics, pulley systems, and the dynamics of forces and torques.

iva
Messages
21
Reaction score
1
Hi there,

If a pulley system made of 2 same mass blocks (on a a table, one hanging), a disk pulley with mass but no friction on the string nor pulley axis, does it mean that the Tension on the rope is the same on either side of the rope? Everywhere I've read implies this, and it makes sense to me because the rope is 1 continuous object and if the pulley is frictionless then surely there is nothing that should make the tension be different on either side of it? But I'm not sure if the mass of the pulley should affect this.

And then what if the pulley was massless, surely in that situation the tension should be the same throughout?

Thank you
 
Physics news on Phys.org
If the pulley is massless and frictionless, then the tension will be the same throughout the string (treating the string as massless). But if the pulley has mass, then a net torque is required to accelerate it--so the tension will be different on each side of it.

(When we speak of a frictionless pulley we mean no friction on its axis. There must still be static friction of string on pulley, otherwise the pulley will not turn.)
 
Thanks, but do you still need to consider Torque even if there is no friction on the rope going over the pulley? I'm just thinking that if you have this pulley that just rolls easily (I'm thinknig of some sports equipment where often the rope doesn't go over the pulley because there is dirt on it, but when i rub sillicone over the pulley and clean it it rolls perfectly)

Also if the string doesn't slip on the pulley, doesn't this mean that Linear accel = radius * angular accel, meaning that the acceleration on both sides would have to be the same?
 
Last edited:
iva said:
Thanks, but do you still need to consider Torque even if there is no friction on the rope going over the pulley?
If you really mean 'no friction on the rope', then the tension will be same on both sides of the pulley. But the pulley will not turn! It's as if it wasn't there. Its mass is irrelevant. This is generally not what is meant by a 'frictionless pulley'.
I'm just thinking that if you have this pulley that just rolls easily (I'm thinknig of some sports equipment where often the rope doesn't go over the pulley because there is dirt on it, but when i rub sillicone over the pulley and clean it it rolls perfectly)
What makes a pulley roll easily is no friction on its axis, not no friction between the rope and the pulley.
 
Thanks, OK i realize I'm mixing up and confusing friction with slipping ( as I've just learned about the slipping factor that if there is no slipping then linear acceleration is related to angular acceleration by radius * angular acceleration)
So if there is no slipping of the rope on the pulley doesn't the formula

linear acceleration = radius * angular acceleration

then suggest that the acceleration on either side of the pulley will be the same? and if the mass of the 2 blocks are the same then that should give the same tension?

Thanks again :)
 
iva said:
Thanks, OK i realize I'm mixing up and confusing friction with slipping ( as I've just learned about the slipping factor that if there is no slipping then linear acceleration is related to angular acceleration by radius * angular acceleration)
So if there is no slipping of the rope on the pulley doesn't the formula

linear acceleration = radius * angular acceleration

then suggest that the acceleration on either side of the pulley will be the same?
Even with slipping the acceleration of the rope (and attached masses) would be the same (in magnitude).
and if the mass of the 2 blocks are the same then that should give the same tension?
No. Assuming the pulley has mass, then the tension on each side of the pulley cannot be the same.
 
So if the acceleration is the same either side, then what this means is that the Tension is a result of the pulley mass PLUS each of the block masses separately?? Sort of like

T1 = (Mass block1 + mass pulley) * linear acceleration and

T2 = (Mass block2 + mass pulley) * linear acceleration ?

This result doesn't make sense though, because if the masses are the same I'm going to end up with the 2 tensions being the same and with the one block hanging from the pulley it can't be

thanks for your patience
 
Last edited:
iva said:
So if the acceleration is the same either side, then what this means is that the Tension is a result of the pulley mass PLUS each of the block masses separately?? Sort of like

T1 = (Mass block1 + mass pulley) * linear acceleration and

T2 = (Mass block2 + mass pulley) * linear acceleration ?

This result doesn't make sense though, because if the masses are the same I'm going to end up with the 2 tensions being the same and with the one block hanging from the pulley it can't be
Not sure where you got those equations. The angular acceleration of the pulley is governed by:
Net Torque = I*alpha

The net torque will be: (T1 - T2)r

Only the two masses are linearly accelerated. You need three equations--one for each object--to describe things. Then you can solve for the acceleration and the tensions.
 
Thanks yes i got the rotational equation when i started working this out
but then got confused with the tensions , wanting to make the tension for both sides the same as well as the accelerations, but now it makes sense. The pulley system is not as intuitive or straight forward as I thought it would be

Thanks for helping me with this
 

Similar threads

Undergrad What is the free-body diagram for a massless pulley in free fall?
  • · Replies 31 ·
2
Replies
31
Views
5K
Graduate Does the Relation ##T_2 = T_1 e^{\mu \theta}## Hold for an Accelerating Capstan?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Moment of Inertia of Massless Pulley w/String & Mass m Attached
  • · Replies 14 ·
Replies
14
Views
4K
Graduate 1 pulley with mass, 1 mass on the cord, 1 external force, no gravity
  • · Replies 16 ·
Replies
16
Views
3K
Undergrad How Does Mass Affect the Direction of Rotational Motion in a Pulley System?
  • · Replies 2 ·
Replies
2
Views
1K
High School Limiting case for an Atwood's machine
  • · Replies 9 ·
Replies
9
Views
898
Undergrad Understanding the physics of a bosun's chair and mechanical advantage
  • · Replies 6 ·
Replies
6
Views
4K
Undergrad Distance Traveled by an object on a pulley
  • · Replies 17 ·
Replies
17
Views
5K
Undergrad Equal tension on rope in a pulley system?
  • · Replies 3 ·
Replies
3
Views
7K
Undergrad Wall strength and tension on rope-pulley system
  • · Replies 6 ·
Replies
6
Views
4K