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>>Would I figure this by calculating the volume of two cylinders, one 20 inches smaller
>>diamter-wise than the other? (Pi*d)*h, twice?
Yes, you'd want to subtract one cylinder from the other. But it'd be (Pi*d^2)*h/4, twice. Pi*d gives you the circumference, not the area.
You'd be laying about 40 (Pi*d/[bagwidth]) bags per course, I think, if that helps compute the effort involved.
>>How big a hole in the yard does this make? Big enough for a pool?
This may be a stupid answer, but...it would make a circular hole 16 feet across, right? Which would be, oh, 200 square feet or so.
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Interesting fact about a relativistic rocket: Its total mass will *not* increase as the rocket accelerates. It can't increase; conservation of energy = conservation of mass. So in fact the rocket's mass must decrease as it vents exhaust (which must carry *some* amount of mass/energy away).
How do you square this with the fact that fast-moving objects have higher masses? Well, there must be a lot of potential energy in the rocket fuel, which will be released when the fuel "burns" (or decays if it's nuclear, or whatever). That means the fuel has more rest mass than the exhaust it's turned into.
(A bucket of gasoline and a tank of oxygen, for instance, have slightly more total rest mass than the waste products you get by burning the gasoline with the oxygen. The hydrogen in an H-bomb weighs about a hundredth more than the helium it becomes after fusion. That extra hundredth-weight of a tiny bit of hydrogen, expressed as radiant energy, will vaporize a city.)
So to an outside observer, the slow-moving rocket has a lot of really heavy fuel. As the rocket accelerates, the fuel burns into lighter exhaust--while the rocket *minus* the fuel gets heavier and heavier. But the total system always has the same mass if you add fuel, exhaust and rocket together--and the mass of the rocket plus remaining fuel gradually decreases. Once the fuel's all gone, you have a trail of light exhaust, and an empty rocket that's much heavier than an empty rocket at rest, but lighter than a rocket at rest with a full tank.
*I* think that's interesting, anyway. Took me a while to figure out what was really going on in that picture when I took special relativity. Usually they just tell you that objects get heavier as they accelerate, but that only works if something else is doing the accelerating...a particle in a cyclotron for instance. You're pouring mass/energy into it as you accelerate it, so it can get heavier without violating conservation laws. |
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