A simple movable pulley not at equilibrium

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    Equilibrium Pulley
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Discussion Overview

The discussion revolves around the behavior of a movable pulley system when it is not in equilibrium. Participants explore the effects of applying a pulling force greater than what is required for equilibrium, specifically focusing on the resulting acceleration of the weight and the tension in the rope.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant describes a scenario involving a movable pulley and questions the effects of pulling harder than the equilibrium force.
  • Another participant states that the tension in the rope is uniform and explains that the upward force on the pulley/mass equals twice the tension.
  • A third participant proposes that increasing the pulling force to the weight of the object results in a uniform tension of mg, leading to an upward acceleration of the weight at g.
  • A later reply confirms the correctness of the previous participant's understanding.

Areas of Agreement / Disagreement

Participants generally agree on the mechanics of the system, particularly regarding the uniform tension and the resulting acceleration when the pulling force exceeds the equilibrium condition.

Contextual Notes

The discussion does not address potential limitations or assumptions regarding the system, such as the effects of friction or the mass of the pulley.

Who May Find This Useful

Individuals interested in mechanics, particularly those studying pulley systems and forces in non-equilibrium conditions.

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Note: This is not a homework question. I have constructed this question to help me understand a concept.

If I have an object hanging off a single (frictionless, negligible mass) movable pulley, the equilibrium system entails me pulling on the free end of the (frictionless, negligible mass) rope with half as much force as the object weighs.

What happens if I pull harder than that?

See the attached GIF. What would be the behavior of the weight? Would it accelerate up? If so, at what acceleration? What would be the tension in the left side of the rope?

Every resource I have access to that mentions pulleys keeps talking about pulleys in this type of setup in equilibrium. I am interested in furthering my understanding in regards to pulleys not in equilibrium.

Thank you for any help.
 

Attachments

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The tension is uniform throughout the rope. The upward force on the pulley/mass will equal twice the tension. To find the acceleration, just add the vertical forces and apply Newton's 2nd law.
 
So me increasing my pulling force from an equilibrium inducing (1/2)mg to mg will cause the rope to have a uniform tension of mg, thus making the total upward force 2mg (the tension of the rope being a uniform "mg"). This accelerate the weight, which weighs mg, upwards at acceleration = g.

Is that correct?
 
Yes, that's correct.
 

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