# Intuitive explanation of the MA (mechanical advantage) of pulleys?

https://en.wikipedia.org/wiki/Pulley

Is there an intuitive explanation for how pulleys create a mechanical advantage? It seems too good to be true, like there must be some catch.

And if it is true, then one could string a bunch of them in a row to create, say, a 20:1 mechanical advantage. Then that would mean a 10 pound baby using nothing but its own body weight to hang from the rope could easily lift a 190 pound man who is hanging from a rope attached to the hook below the pulley, but that seems impossible, at least intuitively.

Can someone please explain this? I have a math degree so feel free to use vector calculus, linear algebra, etc if that would help, though a completely intuitive explanation is fine also.

• Yes the baby could drop 20 inches to raise the man 1 inch. Dec 31, 2020 at 4:47
• The catch is that you sacrifice distance/speed for force or force for distance/speed, thereby conserving energy. That is the catch. Instead of pulleys, what if you imagine a lever instead? It does the same thing. The difference between a lever and a gear is that a gear is a round lever (think an infinite number of levers extending outward from the gear's center to make a round solid gear), and the difference between a gear and a pulley is that a gear uses its teeth to drag other gears, but a pulley uses rope to drag other pulleys. Dec 31, 2020 at 4:58
• Pulleys multiply the force; energy is still conserved. The same thing happens with all the other simple machines - the lever (like in a door) and the inclined plane (like in a wedge). You're trading distance for moment - you can transfer a long movement into a much stronger short movement and vice versa. Dec 31, 2020 at 17:13