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I've read a little bit on the science of a space elevator and it's a surprisingly difficult problem. To have a working space elevator, it would need to be at least to the Geosynchronous orbit, 22,000 miles up, probobly a bit beyond that for buoyancy. The highest balloon is some 25 miles - so that's less than 1/10th of 1% of the distance. The strongest ...


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If the cable of the "elevator" is not connected to a point on earth, then the satellite must be in a geostationary orbit (or it will float away); this implies that if you now attach something to the platform (increasing the pull on the cable) you will pull the satellite down to earth. And as @lionelbrits pointed out, the pulling part of a space elevator ...


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About 50 years ago in Reader's Digest there was an article about a Soviet airplane pilot who bailed out at high altitude. He fell into a snow-filled ravine and survived. If the angle of the snow is high enough it is no big deal. At Squaw Valley I have seen skiers do drops that might have been 100 feet. If the landing is steep enough it is OK. It is ...


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There's no uniform density of heated air. It depends on the temperature (higher T -> lower density) but also on the ambient air pressure. In Denver, cold air is less dense, because the ambient pressure is lower. But this same effect also increases the density of hot air, by the same percentage. So, the result is that the lift of a balloon decreases with ...


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So I found the answer....I was not taking the final step of multiplying The difference in density between the surrounding air and the heated air and then multiplying by the envelope volume. I was just focusing on the difference and getting stuck there. I chose Denver because it's a mile above sea level with a known air density. I could have chosen Mt Everest ...


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Given the imprecision in these numbers, that means that you can lift anywhere between 0 and 0.1 kg per m^3 of air. Per Wikipedia, a typical hot air balloon holds 2,800 m^3 of air in the envelope, so it can suspend something between 0 and 280 kg in the basket. A typical human weighs under 100kg, so you could probably lift between one and three people with a ...


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Nice theoretical answers (I can certainly appreciate them, I'm a mathematician). But why delve into theory when experiment is available? In this video you can see a skier jump from more than 200 feet and get head first into the snow, without a helmet. The video starts with the aftermath, if you want to see the jump right away fast forward to about 1 ...


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This is another chance to use one of my favorite approximations ever! I first offered it as an answer to a question about how deep a platform diver will go into the water. Now is the chance to use it again! Issac Newton developed an expression for the ballistic impact depth of a body into a material. The original idea was expressed for materials of ...


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@SeƱor O gives a very good answer, but he assumes an ideal deceleration. Based on a viewing of the scene, Anna sinks a little under a meter, while Kristoff doesn't sink more than half a meter. Since they fell about 200 feet (about 60 m), my initial estimate for their impact velocity is (assuming no air resistance): $v = \sqrt{2gh} = \sqrt{2*60*9.8} ...


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As a very rude guess, fresh snow (see page vi) can have a density of $0.3 g/cm^3$ and be compressed all the way to about the density of ice, $0.9 g/cm^3$. Under perfect conditions you could see a 13 feet uniform deceleration when landing in 20 feet of snow, or about 4 meters. Going from $30 m/s$ to $0m/s$ (as @Sean suggested in comments), you'd have ...


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Ballpark (based on the iron starting out at 0 degrees Kelvin and melting at 1538 and the earth's radius of about 6000000 meters and the mass of a fly about 12 milligrams and velocity of a fly about 2 meters per second) (EDIT: Also based on the assumption of no radiative cooling of the sphere, i.e., perfect transfer of fly-bumping into heating the sphere and ...


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The fog you are seeing is condensation of atmospheric water, not sublimed $CO_2$. The water fog is made very near the boiling surface, and then sinks slowly, exactly as it does in rainclouds. Therefore, just because you can see fog gathering on the floor does not mean that the $CO_2$ is confined there. The $CO_2$ molecules have a speed, in random ...


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So I think there's a couple things going on here, all related to fluid dynamics. I'm not entirely sure, but I'll start with the fluttering. There are two types of fluttering you could be seeing. The first is if it could flutter like a flag in the wind as the paper drops sideways or moves diagonally through the air. This is a result you can derive in fluid ...


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If you want to do it in 1 million years then your basic problem is kinetic energy. The gravitational potential energy of the Earth around the Sun is $-GM_{\odot}M_{E}/(1au) = -5.3\times 10^{33}$ J. To get to Proxima Centauri within 1 million years requires a relative velocity of at least 1.27 km/s. So I'm not sure how exact an answer you need. The main ...


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Some rough estimates (you can dig up more accurate numbers): The oceans contain about 321 million cubic miles of water (source: http://oceanservice.noaa.gov/facts/oceanwater.html), or 3.5e20 U.S. gal. 1 gal seawater contains roughly enough deuterium to provide the same energy as 300 gal of gasoline (maybe slightly less - that's the part for your homework!), ...


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Lets start with some assumptions. You probably have the beam from a laser pointer in mind so the hole size you want to burn is about $4\,\text{mm}$ in diameter. Lets assume that it's roughly $-5^\circ\text{C}$ ($23^\circ\text{F}$) outside. One final assumption, and this one is just a guesstimate, lets assume that due to thermal conductivity you need to ...



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