What is the Weight Reduction with Each Added Pulley in a Pulley System?

AI Thread Summary
The discussion focuses on understanding the weight reduction achieved with each added pulley in a pulley system. The user is designing a complex pulley setup to lift approximately 200 lbs and seeks information on the equations related to mechanical advantage. Participants suggest consulting resources like Wikipedia for foundational knowledge on mechanical advantage. The conversation emphasizes the importance of understanding how pulleys can reduce the effort needed to lift heavy weights. Overall, the thread aims to clarify the mechanics behind pulley systems for effective weight lifting.
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I am working on making a system of pulleys and a lever. I am planning on using a complex pulley with a few blocks. I wanted to know what how much weight is taken off with the addition of each pulley. If anyone knows some of the equations involved it would be much appreciated. I was planning on lifting about 200 lbs.
 
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Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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