Monkey on a rope, I'm the monkey. Real world.

[california_jobcase]

From Learjeff:

If you have to pull 1 foot to raise 1 foot, there’s no mechanical advantage.
…
The rope you’re pulling came down 6 inches; you went up 6 inches. Ergo, mechanical advantage of 2.

I’m trying to believe the mechanical advantage of two , but this contradicts itself- 6 inches input and six output is the same as one foot and one foot.

[Hampshire]

@ZenBeam

If you start with 100 feet of rope, you’re hanging 50 feet below it. If you pull it all the way through so that you reach the pulley, you’ve pulled 100 feet of rope, and only risen 50 feet.

This is it in a nutshell. W=Fd (Work = force * distance) You’ve pulled 2x the amount of rope and only moved x and essentially were only pulling 1/2 your weight in doing so.
A similar setup is a see-saw with a central pivot point. To raise a 50# kid 3 feet up you have to push your end down 3 feet with 50# of force. Make your end of the see-saw twice as long and you can lift him using 25# of force but have to push down 6 feet.

[Arthur_See_Clarity]

@california_jobcase

From Learjeff:

I’m trying to believe the mechanical advantage of two , but this contradicts itself- 6 inches input and six output is the same as one foot and one foot.

You excised the important part, that I’ve pulled one foot of rope past me. That one foot had to come from both sides of the rope, ergo six inches on either side, thus I only rose up six inches despite pulling a foot.

[Martin_Hogbin]

So, Arthur See Clarity, are you now convinced that with a single pulley you have to pull yourself up twice as far but the pulling force required is half as much?

[Xema]

@Martin_Hogbin

… you have to pull yourself up twice as far but the pulling force required is half as much?

It would be more accurate to say “you have to pull twice as much rope …”.