MA of pulley - movable vs. immovable

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azor ahai

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I am not really satisfied with the short-cut to find the mechanical advantage of a pulley that sets it equal to the number of vertical strings attached to that object. Is this true only for movable pulleys and untrue for fixed pulleys?

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In general, for every V-shaped pulley there is a mechanical advantage of 2, and for every A-shaped pulley there is no mechanical advantage
I believe the V-shaped ones are movable but the A shaped ones are not
 
Four_pulleys.svg


It is more about how much you pull versus how much the mass moves.
Just think about how far the mass would move if you pull 1 meter of rope. (1/2meter=2MA, 1/3meter=3MA)

#3 is a combination "V shape and A shape" and gives a mechanical advantage of 3.
 
Four_pulleys.svg


It is more about how much you pull versus how much the mass moves.
Just think about how far the mass would move if you pull 1 meter of rope. (1/2meter=2MA, 1/3meter=3MA)

#3 is a combination "V shape and A shape" and gives a mechanical advantage of 3.

I understand that the input distance is inversely proportional to the output distance, but usually I wouldn't be given the s-value like the diagrams you provided.

However, I think I understand that it is only movable pulleys that we're concerned with. That first example has an immovable pulley, so it doesn't contribute. The second has one movable pulley with two vertical ropes, so it has twice the MA. Third example has three vertical ropes attached to the movable pulleys, so it has 3x the MA. etc.
 
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