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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.

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    $\begingroup$ Yes the baby could drop 20 inches to raise the man 1 inch. $\endgroup$ Dec 31, 2020 at 4:47
  • $\begingroup$ 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. $\endgroup$
    – DKNguyen
    Dec 31, 2020 at 4:58
  • $\begingroup$ 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. $\endgroup$
    – Luaan
    Dec 31, 2020 at 17:13

2 Answers 2

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I think there's two key pieces needed to intuitively understand pulleys. The first is that, if you focus on the tension on the rope, you see that there are many ropes going between the pulleys, and just one going to the person doing the lifting. So, since the force of tension is the same all along the rope, the N ropes going back and forth between the pulleys generate N times the force.

The second intuition is that the puller and the heavy object are not the only actors in this game. The top pulley is attached to something. It's attached to some strong rig. You'll find that its the rig that provides the "missing" force that causes intuitive problems. While there may be only one rope being pulled on, all of the other tension forces holding up the heavy object pull down on the strong rig it is attached too. If that breaks, no number of pulleys will help you lift. Its that support that helps you sum all of the forces to equal 0.

The one thing you can't cheat is energy. Energy is conserved in a pulley system. So if you're pulling with 1/10th the force, you better be doing it over 10x the distance. And, indeed, if you work the math, that's what happens.

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    $\begingroup$ Also, while not actually a pulley system, its worth looking at chain hoists. They actually use gearing, rather than pulleys, but they are very easy to see in operation, and can help with the feeling as-if there's no way you could be lifting a heavy object. $\endgroup$
    – Cort Ammon
    Dec 31, 2020 at 5:03
  • $\begingroup$ Yes, it was that "get something for nothing" (seemingly) that was hard to understand. If the mechanical advantage is offset by requiring one to pull for a longer distance (kind of a "mechanical disadvantage", if you will), then that does make sense, thanks. $\endgroup$
    – Hank Igoe
    Dec 31, 2020 at 5:08
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The total energy that you will end up spending is the same. The difference is that with a pulley you can use less force but more extended in time, so you can have a low power motor to raise a heavy weight. But it will take much longer with a smaller force, so the total energy spent will be the same.

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