Mechanical Advantage: Pulley Systems & Archimedes' Ship

[BogMonkey]

I'm fairly fascinated by the idea of mechanical advantage using pulley systems. Using this pulley system
http://www.swe.org/iac/images/plly_071.jpg
as an example I read that this provides a mechanical advantage of 4. If I'm only putting say 20N force in and the block weights 80N where is the other 60N coming from?

I read that Archimedes claimed he could move a ship with enough pulleys and the king challenged Archimedes to put his claim to the test and Archimedes actually managed to move a ship with pulleys. What kinda pulley system would he have used in that scenario?

 

[russ_watters]

I'm fairly fascinated by the idea of mechanical advantage using pulley systems. Using this pulley system
http://www.swe.org/iac/images/plly_071.jpg
as an example I read that this provides a mechanical advantage of 4. If I'm only putting say 20N force in and the block weights 80N where is the other 60N coming from?

You're applying a force of 20N to 4 strands at the same time.

 

[DannoXYZ]

It's leverage, similar to gearing or levers. You condense a lot of motion into a smaller movement. If you have a lever, like a crowbar, you can move your hand 4x as much as the object the other end of the bar is moving. With gearing, you can have 4:1 gearing where the motor spins 4x for every rotation of the output shaft.

With the block & tackle, you pull on the rope with 4x the movement of the lower-pulley. So 4ft of cable-pull gets condensed into 1ft of lift for 4:1 leverage.