How a movable pulley increases mechanical advantage?

[eagermind]

Firstly, I'm sorry for posting this here it seems like the best place possible, but I'm not quite so sure I didn't see a section for civil engineering. So I don't understand why a movable pulley increases the mechanical advantage. This occurs in a situation when one end of the string is fixed and the input force is on the other end of the string, through the pulley. From the pulley hangs the mass. I just simply don't understand why there is a mechanical advantage of roughly 2. Please help me wrap my mind around why this occurs?

 

[jedishrfu]

a mechanical advantage of 2 means that you pull 2 ft of rope and the object raises 1 ft so that then implies you used a force equivalent to half the weight of the object to raise the object.

 

[Simon Bridge]

It works the same way as a lever ... but you'll have to draw a series of diagrams to see this. If the mechanical advantage is 2x then you also have to pull the rope twice as far to raise the block the same height.

Without the pulley - if you pull the rope 1m, the rope holding the weight gets shorter by 1m, and the weight goes up 1m, and you do mg in work. If you loop the rope around a pulley on the weight, then if you pull the rope 1m, the rope gets shorter by 0.5 m on each side of the pulley, and so the weight goes up 0.5m and you have done mg/2 in work, moving the same distance ... so the force must be half.

 

[jehake12]

You could also draw a free body diagram about the floating pulley...

It should have two force vectors upwards for the rope and 1 down for the weight of the object. The tension on one end of the rope is equal to the other. So an object of weight P, requires you to tug perfectly parallel with force P/2.