no. the size of a pully makes little difference to its action on a rope as the only thing changing is how much of the rope is in contact with the pully and since the pully rotates it makes it no easier or harder to pull the rope.
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A lever is an adaptation of a stick or tree branch. A pulley is an adaptation of a wheel.
A pulley system is made up of a pulley and a rope. A pulley is, in essence, a wheel with a groove going all the way around it so that a rope or a cable can fit in it securely. One could also run an indented track around a wheel.
Very simple the answers in your own question.Stationary pulleys works on its own axle of rotation while the Movable pulleys move with Load like the one in cranes.
a coumpound pulley is when there is a fixe pulley and movable pulley working together
Archimedes invent the compound pulley around 250 BC. The invention was to utilize leverage to make moving a heavy object easier.