How a movable pulley increases mechanical advantage?

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Discussion Overview

The discussion revolves around understanding how a movable pulley increases mechanical advantage, particularly in the context of physics and engineering principles. Participants explore the mechanics behind the pulley system, including the relationship between input force and the movement of the load.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about why a movable pulley provides a mechanical advantage of roughly 2, seeking clarification on the mechanics involved.
  • Another participant explains that a mechanical advantage of 2 implies that pulling 2 feet of rope raises the object by 1 foot, suggesting that the force required is half the weight of the object.
  • A different participant compares the operation of a movable pulley to that of a lever, indicating that pulling the rope twice as far results in the same height increase for the load.
  • One participant suggests using a free body diagram to illustrate the forces at play, noting that the tension in the rope is equal on both sides of the pulley, leading to a requirement of half the weight in force to lift the object.

Areas of Agreement / Disagreement

Participants present various explanations and interpretations of how a movable pulley works, but there is no consensus on a single explanation or model. The discussion remains exploratory with multiple viewpoints expressed.

Contextual Notes

Some assumptions about the ideal conditions of the pulley system are not explicitly stated, and the discussion does not resolve the mathematical details or the implications of the free body diagram mentioned.

eagermind
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Firstly, I'm sorry for posting this here it seems like the best place possible, but I'm not quite so sure I didn't see a section for civil engineering. So I don't understand why a movable pulley increases the mechanical advantage. This occurs in a situation when one end of the string is fixed and the input force is on the other end of the string, through the pulley. From the pulley hangs the mass. I just simply don't understand why there is a mechanical advantage of roughly 2. Please help me wrap my mind around why this occurs?
 
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a mechanical advantage of 2 means that you pull 2 ft of rope and the object raises 1 ft so that then implies you used a force equivalent to half the weight of the object to raise the object.
 
It works the same way as a lever ... but you'll have to draw a series of diagrams to see this. If the mechanical advantage is 2x then you also have to pull the rope twice as far to raise the block the same height.

Without the pulley - if you pull the rope 1m, the rope holding the weight gets shorter by 1m, and the weight goes up 1m, and you do mg in work. If you loop the rope around a pulley on the weight, then if you pull the rope 1m, the rope gets shorter by 0.5 m on each side of the pulley, and so the weight goes up 0.5m and you have done mg/2 in work, moving the same distance ... so the force must be half.
 
You could also draw a free body diagram about the floating pulley...

It should have two force vectors upwards for the rope and 1 down for the weight of the object. The tension on one end of the rope is equal to the other. So an object of weight P, requires you to tug perfectly parallel with force P/2.
 

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