Imagine the Empire State building with a big harness around it. An extremely large and strong tower arches over it with a cable hanging down an attached to the harness.
Would it be possible to build a series of gears and pulleys attached to a hand crank that would very slowly lift the whole building over time? If so, how long would it take to lift it?
Could I? No, I’m not sufficiently adept at such things. But yes, given enough gears to reduce distance in order to increase torque, I would think that you could. The only limiting factor I can see is the loss to friction, which might increase with the more gears you have interfacing with each other. Or pulleys. Pulleys might work better.
Are we assuming that the ESB is already snapped off at ground level, or does this contraption have to break it loose from its foundation?
It needs to be broken loose from its foundation. Once we get this far, I figure we might as well use the pulleys and gears to do all of the work.
That’s gotta be one heck of a cable - 19-stranded unobtanium, at a guess.
The empire state building weights 365,000 tons. cite
A pulley system works as a force multiplier. We’ll say that a person can safely exert a force of 200.lbs (1/10 of a ton) on the crank by himself, for easy calculations.
We’ll also pretend that the building has been removed from its foundation. I don’t know its tensile strength, and the amount of force necessary to break it from its foundation would likely cause it to break somewhere in the middle and render everything else invalid.
Such a system would seem to require 3,650,000 pulleys. However, the pulleys and cable themselves have weight. Since you didn’t say this part, I’m going to say that our goal is to lift the building one foot (12.0in) from the spot its foundation used to rest on. This would mean that we would need a minimum of 3,650,000 feet, or 691 miles, of cable. We really need more to go around the top of each pulley, though, and we haven’t gotten into the weight of the rope or the pulleys, but I’m keeping this a strict algebra problem, so we’ll ignore these in favor of an inelegant estimation.
We’re about ready for the calculation. We’ll say that the crankshaft is the same length as the radius of one of the pulleys inside. (A longer crankshaft would serve the same purpose as a few of the pulleys inside, trading length for force). We’ll say that our man can wind up 3" of cable every second. That may seem slow, but with 200lbs holding it in place, anyone’d be hard pressed to turn it that fast for long, and our poor man or woman is going to have to turn it for some time. 14,600,000 seconds, or, in more easily readable terms, just under one hundred and sixty-nine days for the feat of lifting the building 12 inches above the ground. Sounds like a new fitness program to me! The actual time is more than this because we have assumed weightless pulleys, a weightless rope, and a frictionless system.
Of course, the reality of the building is such that it’s designed to support it’s weight from the bottom, and that wherever you’re lifting it from is now having to support forces that it was never designed to going in directions the designers of the building never anticipated. I suspect heavily that it’d break in two before you got even an inch off the ground. But, well, it’s fun to dream, yes?
Friction loss sets a practical limit to how much mechanical advantage you can get from any sort of gearing or pulleys (any engineers out there who know what the limit is?)
If you want to get extreme, you could have the following: Having cut the Empire State Building loose from it’s fundation, a cofferdam is built around the tower, 2000 feet high and massive enough to withstand tremendous pressure. You then get to carry twenty pounds of mercury at a time up a set of stairs to the top of the cofferdam and pour it in. After several millenia, you fill the cofferdam with enough mercury to float the building.
Practically speaking, the physical size of the gears or pulleys that are large enough to handle the load would create frictional losses greater than the output of one person. So, no, it can’t be done.
However, if we assume zero mass, unlimited strength, and zero friction in our machinery then it could be done. And since we’re dreaming, I’d like a trillion dollars. And a pony.
How about that “long enough lever” thing?
Basically the same deal as the pulleys. You have to have an infinitly stiff level or it will just bend when you put a force on it.
“Give me a fulcrum on which to rest, and I will move the earth.”
Anyone who has snapped off a half inch drive socket when using a cheater pipe knows this is wishful thinking. You can certainly design the lever for mechanical advantage but no substance will be hard enough to serve as a fulcrum or have the tensile strength to serve as a lever.
I like the mercury filled cofferdam idea.
Eureka!
It could be done with cables and pulleys. 365,000 tons. You can easily lift a ton with a hand cranked ratchet comealong. Just place 365,000 of these around the periphery. Walk to each one and crank it to one ton of tension, lather, rinse, repeat. 30 seconds for each comealong, 12 hours a day. You would have lifted the building in less than nine months.
It’s much easier to work with energy rather than force. A 365,000 ton weight at 12-inch height has a potential energy of 10[sup]9[/sup] joule. Divide that by the typical sustained power output of a human being (about 50W) and you get 228 days. If you work at it 12 hours a day, you’ll need twice as many days. This of course ignores friction of the pulleys, so in reality it would take a bit longer.