What is the formula for calculating mechanical advantage in a pulley system?

AI Thread Summary
To calculate the mechanical advantage in a pulley system, the Ideal Mechanical Advantage (IMA) can be determined using the formula IMA = output force / input force. The tension in each rope supporting the load is equal, and the mechanical advantage can be found by dividing the weight of the load by the number of ropes supporting it. Some participants express confusion over this method, suggesting that it may not be accurate. Clarifying the relationship between the load weight and the number of supporting ropes is essential for understanding mechanical advantage. Accurate calculations are crucial for effective pulley system design.
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The tension of each rope supporting the weight of the load is the same. Divide the weight of the load by the number of ropes supporting it.
 
Divide the weight of the load by the number of ropes supporting it? That doesn't seem right to me. I'm looking for a quick way to identify the Ideal Mechanical Advantage (IMA) = output force / input force.
 

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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