F***ing Pulleys, How Do They Work?

Everyone acts like it’s obvious that pulleys do a physically possible thing, but personally, I’ve never understood why you can lift a 100kg object straight up by pulling it with less force than what it weighs.

“Pulleys let you move the rope twice as far as the load moves, so you’re spreading your pull force over a 2x longer distance, so you can use half the force, it’s just conservation of energy!”

No, f*** you, that doesn’t explain why a wheel on the rope means I’m allowed to pull the rope half as hard to lift the same weight.

If you want to know the secret explanation I learned while procrastinating today, read on...

Ok imagine there’s a 100kg man lying in a hammock that has 2 supporting ropes. You’re on the left holding one rope, and there’s a tree on the right holding the other rope.

In this setup, you only lift 50kg of vertical weight, because you’re in a symmetrical configuration with the tree. Tada!

(That’s actually the trick to all “simple machines” — you take advantage of the fact that the ground/trees/etc are always game to lift or push against the full weight of objects, if the configuration provokes an equal & opposite reaction force.)

So yeah, you can lift the hammock a foot or two by lifting the rope over your head, and you’ll still only need ~half the lifting force you’d normally need for 100kg. Though note you have to raise your arms by 2ft to get the guy to lift 1ft, because the midpoint of the rope is the average height of your hands and the tree’s connection point, and the tree’s connection point hasn’t moved. I guess the “conservation of energy” guy was onto something there.

This simple hammock setup is a legit proof of concept of the core magic of the pulley. You’re just getting a tree or other fixed object to partner with you on bearing the weight of the lift. That’s it. It’s really quite simple, until the f***ing wheels get involved…

At this point, since our hammock proof of concept isn’t a genuine Pulley™, we have to deal with various little problems:

1. Puller’s configuration: Your arms aren’t long enough to pull much, or you have to keep walking toward higher ground as you pull

2. Rope needing to slide around the load: If the person in the hammock is attached to a fixed point on the rope (not spanning a bunch of width across it) and you try to pull up, you only have two options: (a) Pull straight up, but the tree’s half of the rope goes slack and now you’re pulling all 100kg, or (b) Treat the whole system as a pendulum/swing, giving it a very leftward-angled tug, which is a workable setup, but you lose the tree’s assistance as the hammock swings higher toward the horizontal configuration at the top of its arc. Realistically, you don’t want to attach the load to a fixed point on the rope. The rope needs to slide around the load as it lifts. Your friend is just going to have to accept getting rope burned.

3. Wasteful horizontal force component: The rope makes a V shape (as long as you’re not letting it go slack, which you can’t if you want to activate the tree’s component of lift), which means you have to add an additional wasted component of force pulling at the hammock (and the tree) horizontally. You can mitigate this issue if you stand right next to the tree and pull straight up, as long as the rope can slide relative to your load, but then problem 1 above becomes extra annoying — e.g. if you were hoping to walk your end of the rope up a ramp, it’s not going to be maximally efficient.

Alright, let’s add a wheel.

Now we’ve solved problems 2 and 3. The rope can easily slide around the load, keeping your friend’s upward journey smooth and balanced. And there’s no more wasteful horizontal force component — that’s not because of the wheel per se, it’s because you connected the rope to the ceiling.

And there’s no extra lift-force-easing magic here that the hammock setup didn’t already have. The load in this setup feels to you like 50kg because the ceiling plays the role of the tree from before, splitting the weight with you equally in a symmetrical configuration.

Finally, we’ll solve problem #1 by adding a second wheel, so now you can stand in the same place while you pull. The second wheel doesn’t do anything to the force, it just redirects the direction.

IMO the wheels are a shiny distraction. The hammock proof of concept is what it’s all about. Pulleys are just a way to use wheels to share the load with fixed objects like trees and ceilings.

In conclusion, f*** pulleys. But next time you see a hammock, consider impressing your friends with your efficient lifting abilities.

P.S. For fancier pulleys whose mechanical advantage is 3:1 or higher, the proof of concept is a hammock with 3 or more ropes that are all connected to the ceiling, except for one at a time that you hold. You can walk around the rafters pulling on one of the ropes at a time, with 1/3 or 1/n of your load's full weight, by a small enough bit at a time that the other ropes still maintain their tension.

Then the upgrade you get by licensing the Pulley™ intellectual property is that a single long rope's tension-spreading property makes the "pull on 3 sub-ropes in turn" process maximally efficient.