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Maximum power available from an infinite source with specified dimensions.?

A) Given present-day materials engineering, how much power could be drawn from a pair of six-inch cubes rotating against each other with a period of 6.9 seconds and infinite torque Assume that failure of the cubes is not an issue. Since in principle power could be drawn in balance from both sides of the Device, it would be legitimate to assume that anchoring one end to the earth is also not a requirement. However if you do choose to anchor one end (preferred), assume granite.

B) Same question, but using say late eighteenth/early nineteenth-century British metallurgy.

C/D) Is this enough information to determine a rough minimum size for the first stage of such a coupling device? If so what would it be? Is anchorage to the earth a first-order problem or does the strength of the six-inch square holes swamp other considerations?

Notes:

a) I'm hoping for answers within a factor of two or so, preferably in horsepower or watts..

b) I don't know the answer myself.

c) The power source in question resides in Terry Pratchett's book _Thud_

Update:

@Domenic - Please, the infinite source is clearly fantastic. The question hinges on how much torque could be transmitted by a six-inch square shaft with a coupling depth of six inches, given the known properties of realistic materials and stipulating that the shaft itself is not the limiting factor. It's an engineering question, not a scientific one.

Update 2:

@oillfieldtrash - Obviously such a source doesn't exist, except in a book of fantastic satire (or satirical fantasy) written by Terry Pratchett. It's an artifact of untold age and its existence is simply a given. But to get any use out of it the present inhabitants would have to couple to it using available technology, which is pre-steam. They have iron and steel. The thing is that since the device consists of a pair of six-inch cubes, the available surface to couple to is quite small and therefor the amount of torque that can be exerted is severely limited by the strength of available materials. So how strong can you make a six-inch square hole six inches deep? My hunch is that the maximum power you could get back then might be a few hundred horsepower, and even that might be way high because of how slowly the thing is turning. The fact that it *is* turning and cannot be stopped is another complication of course, but that way lies madness. Does that help?

3 Answers

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  • 10 years ago
    Favorite Answer

    Let's see, you have an infinite amount of torque applied to an indestructible square shaft. That would appear to make it possible to produce an infinite amount of power.

    What am I missing?

  • 10 years ago

    Meaningless. A rotating 6" cube has energy only in it's rotational KE, and that is only a few Joules.

    The term "torque" applies only to the rotational KE, and is also quite small.

    Assuming granite, the mass of the cube is about 10 kg.

    period of 7s, ω = 2π/7

    simplifying to a sphere

    KE = ½Iω² = ½cMR²ω² = ½(10)(2/5)(.08)²(2π/7)² = 0.01 Joule

    edit, looking at your added details, why didn't you state the actual problem initially instead of all that nonsense. What does coupling depth mean? what is the diameter of this coupling and how are they connected? what is the material.

  • Anonymous
    10 years ago

    This another of the psuedo-scientific propositions that pop up to confound

    others. Basically there is no viable energy input, no conversion of energy,

    no transformational energy. So there is no energy input = no energy output

    question is kaput.

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