Unraveling the Mystery of Pulleys: Understanding Force and Distance Ratios

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The discussion focuses on understanding the mechanics of pulleys, specifically the relationship between force and distance ratios. A participant expresses confusion about a type of pulley that allows for a doubling of force when pulling on the rope, while the distance moved is halved. They struggle to grasp why this occurs and mistakenly conclude that the rope must have increased in size. The conversation encourages participants to tackle specific problems to clarify their understanding of these principles. Overall, the thread aims to demystify the physics behind pulley systems and their operational mechanics.
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So, there are is a type which I couldn't understand.
1: (I don't know this type name is, so tell me please)
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So, the books says if you push the rope, you will double your force, but instead, for every x distance you push, it will go x/2 distance(their work is the same), which I couldn't fiqure(How to spell the word?) out why. And when I think about it, I get to the weird conclusion that the rope must have increased its' size.
And it got much worse when I tried to solve this:
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(it is 1600N)
 

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