Static Equilibrium: Why Does Changing Pulley Position Affect Relative Angles?

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Discussion Overview

The discussion revolves around the behavior of pulley systems in static equilibrium, specifically examining how changing the position of pulleys affects the relative angles between them. The focus is on comparing systems with different numbers of pulleys (2, 3, and 4) and the implications of these configurations on the angles maintained under static conditions, while considering factors such as friction.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that in a 3-pulley system, changing the position of one pulley does not affect the relative angles, while in a 4-pulley system, it does.
  • Another participant requests a specific example to clarify the initial claim regarding the effect of pulley position on angles.
  • A correction is made regarding the number of pulleys, indicating that the original claim should refer to 2 and 3 pulleys instead of 3 and 4.
  • One participant emphasizes the importance of the magnitude and direction of forces acting on the central ring, suggesting that in a static scenario, the forces must sum to zero, leading to a unique solution for angles in certain configurations.
  • It is proposed that in a two-pulley case, moving one pulley allows the ring to adjust freely, maintaining the required angles, whereas in a three-pulley case, this may not be possible.
  • A participant suggests that mathematical proof may be sought to support the claims made about the angles changing with pulley movement.
  • Another participant expresses confusion about the request for proof, questioning the premise of the angles changing if the angles are altered.

Areas of Agreement / Disagreement

Participants express differing views on the behavior of angles in pulley systems, with some agreeing on the mechanics of force balance while others seek clarification and proof. The discussion remains unresolved regarding the specific conditions under which angles change or remain constant.

Contextual Notes

There are limitations in the discussion, including potential misunderstandings about the number of pulleys involved and the assumptions regarding force application and movement of the pulleys. The mathematical relationships and conditions necessary for static equilibrium are not fully explored.

Kevin de Oliveira
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I have a 3 pulley system statically balanced hanging weights at a determined relative angle (we are taking into account friction). If I change the position of one pulley, angles will remain the same. However, if I have a 4 pulley system, at the same conditions, changing one's position will affect the relatives angles between them all.

I would like to know why that happen. Why, with 3 pulleys, changing one's position will not affect their relatives angles and not with 4 pulleys?
 
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Kevin de Oliveira said:
I have a 3 pulley system statically balanced hanging weights at a determined relative angle (we are taking into account friction). If I change the position of one pulley, angles will remain the same. However, if I have a 4 pulley system, at the same conditions, changing one's position will affect the relatives angles between them all.

I would like to know why that happen. Why, with 3 pulleys, changing one's position will not affect their relatives angles and not with 4 pulleys?
Can you please present a specific example?
 
Here an example attached.
Just a correction, instead of 3 it's 2 and 4 it's 3.
In that example, there are only 2 pulleys. If I apply the same conditions in 3 pulleys, angles will change.

Thank you for you reply
 

Attachments

Sorry. I still don't get what you are asking.
 
I think I understand what he's asking...

Forget about the position of the pulleys for the moment. What matters is the magnitude and direction/angles of the forces acting on the central ring (see solution 1). Since it's a statics problem the vertical and horizontal components must sum to zero. The forces are fixed so in general (but not always) there will only be one solution for the angles.

In the two pulley case: If one pulley is moved the ring is also free to move horizontally and vertically so the forces acting on it stay at the angles required for the static solution.

In the three (or more) pulley case it's not always possible for the ring to move to maintain the required angles. However it _is_ possible to move a pulley in such a way that it preserves the angles.
 
Last edited:
For example in this set up the top pulley can be moved from position A to position B without changing any of the angles. If it's moved in any other direction the angles change and a new static solution will have to be found..

FBD.jpg
 
Thank you dor your reply. But can we mathematically prove it?

And just to add, I suppose that it's because there is one force applied on each side. In another word, if I apply an odd quantity of forces on the horizontal axis, the angles will no longer be the same. not sure if this physically makes sense
 
As I see it.. In the three pulley case you are asking us to prove that the angles change if you change the angles.
 
Yes
 

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