Physics In the Playground

[noparlpf]

The whole question is based on the Dragons Hoard problem: You have a practically infinite amount of gold and can take with you as much as you can carry. Based on the gear soldiers tend to carry, let's say you would take 40 kilos of gold to take home with you. You end up pretty exhausted, but damn, it's gold!

But what if you had a cart? How much more could you take if you are willing to do the same amount of work to get it home?
Obviously that depends on both the cart and the terrain you are moving on. If the cart collapses under the weight of the gold or the wheels sink into the ground, you are obviously not going anywhere. And if you have to cross very uneven ground, you probably could end up with even less gold than you could carry on your back, since you would have to basically carry the cart over the obstacles as well. And then there's the friction of the axle. If you have roughly cut wood on wood, it would obviously be a lot more than if you had steel ball bearings.

But any educated guess?

A wood-on-wood axle shouldn't be all that bad. Heating and compression tend to smooth out hard woods. Worse than ball bearings, but not awful. Depends on whether we're talking rough-cut like Stone Age or rough-cut like handmade with good-quality metal manual tools.

[Jimorian]

As a rough guess, I'd say a rickshaw scaled cart and load would work. So let's call it somewhere between 1x and 2x body weight, might be able to push that to 3x. That's enough to make a difference, but small enough to be able to unpack and haul it manually in chunks, plus manhandle the cart over/around obstacles.

[Drolyt]

How does fire work? I get (at least at a Chem 101 level) how the reaction between the fuel and the oxidizer creates heat, but where does the light come from? I ask for perhaps a silly reason: I was trying to figure out a pseudo-scientific explanation for psychokinesis or magical fire, and this got me thinking when I realized I didn't really understand where the light part of fire was coming from. I realize this this is more chemistry than physics, but I figured it fit here and I'm curious.

[noparlpf]

How does fire work? I get (at least at a Chem 101 level) how the reaction between the fuel and the oxidizer creates heat, but where does the light come from? I ask for perhaps a silly reason: I was trying to figure out a pseudo-scientific explanation for psychokinesis or magical fire, and this got me thinking when I realized I didn't really understand where the light part of fire was coming from. I realize this this is more chemistry than physics, but I figured it fit here and I'm curious.

I'm not totally sure, but here's a guess. Light in chemical reactions is usually produced by the excitation of electrons. You get some energy, electrons move to higher-energy positions, then lose some energy and drop back to their base state, and that excess energy is released as a photon of some wavelength/color.

[Drolyt]

I'm not totally sure, but here's a guess. Light in chemical reactions is usually produced by the excitation of electrons. You get some energy, electrons move to higher-energy positions, then lose some energy and drop back to their base state, and that excess energy is released as a photon of some wavelength/color.

That makes sense I think. Hmm, coming up with a sciency explanation for magical fire is harder than I thought. I think it would have to be that there was some sort of magical fuel involved. Like using magical energy to create psuedo methane or something.

[factotum]

As far as I know, the flame is caused by light being emitted by the hot combustion gases. Note that you would get light by sufficiently heating anything, so if your pyromancer basically just superheats air to produce his flame, you'd also get some sort of light from that--I've no idea what colour that light would be, mind you, because different elements produce different colours. The normal "yellow" flame that you regularly see is that colour due to hot carbon atoms coming off the thing that's burning, for instance. My guess would be that the hot air would give off light mainly from the emission spectrum of nitrogen, since that's its largest component, but I don't know what colour what would be!

[Drolyt]

As far as I know, the flame is caused by light being emitted by the hot combustion gases. Note that you would get light by sufficiently heating anything, so if your pyromancer basically just superheats air to produce his flame, you'd also get some sort of light from that--I've no idea what colour that light would be, mind you, because different elements produce different colours. The normal "yellow" flame that you regularly see is that colour due to hot carbon atoms coming off the thing that's burning, for instance. My guess would be that the hot air would give off light mainly from the emission spectrum of nitrogen, since that's its largest component, but I don't know what colour what would be!

What you said got me thinking so I looked up why hot things glow and I think I understand it pretty well now (the heat energy causes electrons to move into higher energy states, then the electrons move back into lower energy states releasing photons) but I haven't the foggiest idea what that would look like if you just superheated air without a fuel, I'm thinking not much like a wood fire, but maybe I'm wrong?

[noparlpf]

As far as I know, the flame is caused by light being emitted by the hot combustion gases. Note that you would get light by sufficiently heating anything, so if your pyromancer basically just superheats air to produce his flame, you'd also get some sort of light from that--I've no idea what colour that light would be, mind you, because different elements produce different colours. The normal "yellow" flame that you regularly see is that colour due to hot carbon atoms coming off the thing that's burning, for instance. My guess would be that the hot air would give off light mainly from the emission spectrum of nitrogen, since that's its largest component, but I don't know what colour what would be!

The internet suggests purplish. I'll take its word for it as it's been a few years since I did a lab with the different sorts of gases in tubes.

[Knaight]

As far as I know, the flame is caused by light being emitted by the hot combustion gases. Note that you would get light by sufficiently heating anything, so if your pyromancer basically just superheats air to produce his flame, you'd also get some sort of light from that--I've no idea what colour that light would be, mind you, because different elements produce different colours.

It's more complicated than that. In addition to the emission spectra of the elements involved are the emission spectra of molecules. Generally speaking, molecules have several tight bands of multiple spectra which will look like a fairly continuous color spectrum to the naked eye. Fortunately, at the heat usually involved in combustion reactions (though by no means always involved), you can generally approximate with black body radiation, though it won't be completely accurate.

[Yora]

Watching some videos of the meteor strike, I noticed the same green glow before it exploded, that I'd also seen when we had a meteor here in Germany in November (looked it up on a meteor-report database to confirm there actually was one at that time and direction I've seen it).

What exactly is it? I would assume some type of plasma formed from gases in the atmosphere that are super-compressed in front of the meteor and heat up to glow. What is it that causes the green color?

[noparlpf]

Watching some videos of the meteor strike, I noticed the same green glow before it exploded, that I'd also seen when we had a meteor here in Germany in November (looked it up on a meteor-report database to confirm there actually was one at that time and direction I've seen it).

What exactly is it? I would assume some type of plasma formed from gases in the atmosphere that are super-compressed in front of the meteor and heat up to glow. What is it that causes the green color?

What was the meteor made of? Or does it happen for any sort of meteor regardless of material, if it's big enough, or whatever?

[factotum]

You'd expect green flames if the meteor had any copper content, certainly.

[Yora]

What was the meteor made of? Or does it happen for any sort of meteor regardless of material, if it's big enough, or whatever?

After some serching, I found that the glow is not created only by air in front of the meteor being super-compressed, but also by tiny particles being torn of the surface and burning up. (Which is the reason the meteorite itself doesn't get hot, since hot particles are no longer in contact with it.
Blue-green color is caused by magnesium.

Apparently there are other colors as well, it apparently was pure coincidence that the one in the videos and the big one I saw myself both were magnesium-rich.

[noparlpf]

You'd expect green flames if the meteor had any copper content, certainly.

Yeah, that's what I was thinking. Copper can also produce greenish plasma under certain conditions, I think. Or maybe that was certain copper-containing compounds. I forgot.

After some searching, I found that the glow is not created only by air in front of the meteor being super-compressed, but also by tiny particles being torn off the surface and burning up. (Which is the reason the meteorite itself doesn't get hot, since hot particles are no longer in contact with it.)
Blue-green color is caused by magnesium.

Apparently there are other colors as well, it apparently was pure coincidence that the one in the videos and the big one I saw myself both were magnesium-rich.

Was that a general thing for meteorites, or do they have pieces of this one yet?

[Yora]

General. But the videos I've seen show a clear green color just before it starts exploding.

---

I just found this quote from a medieval book about geography/cosmology:

"The sky is so far away from us that a stone would fall for 100 years before reaching us."

How far away would that be?

Let's assume "a stone" is a 1 kg sphere of average granite (2.70 g/cm³).

1. What is the distance this stone would travel in 100 years at terminal velocity? (Assuming the entire distance is filled with air at sea level pressure.)

2. What is the distance this stone would travel in 100 years, assuming a constant acceleration of 9.78 m/s² (and ignoring air resistance)?

3. If the Earth and stone were static and unmoving, with no other bodies to have gravitational pull on them, what distance would the stone have to be released at to result in a drop of 100 years?

I also think I really should send this one to Randall Munroe. Especially for an estimate of what would happen if the stone from #2 hits the earth.

Edit: #2 doesn't seem to work. The number I got is a hundred times the speed of light and then relativity kicks in, messing everything up.

[Bryn]

Yeah, accelerating at 1g for that long requires the relativistic formulae for constant proper acceleration. I don't have time to do the LaTeX now but I'll write up a solution to that this evening.

[Yora]

Even then, I see the end of all life of Earth and possible melting of the crust if a 1kg object impacts at 99% speed of light.

The impact calculator websites I found peak at 72 km/s. What I need is 290.000 km/s.

[Jimorian]

Hmm, I wonder if the gravitational potential energy equation would work for any known distance (and again assuming gravity is constant throughout the fall). Potential energy is linear with distance, and when something falls, that energy gets converted to kinetic energy (1/2mv^2) which does need relativistic terms to work as you approach C. I'm wondering if the linear nature of potential as it converts simply gets subsumed into the relativistic version of kinetic, or whether it needs its own relativistic term past a certain point.

As far as impact, those extra decimal places really start to matter. We might survive a .99C impact, but a .9999C one could take us out completely. I'm sure some science fiction writers have worked out the math from time to time.

I do remember somebody somewhere worked out what it would take to truly "blow up" a planet so that the pieces scattered into space, and it was a really enormous number.

So yes, let's ask Randall and have him do all the math.

[IthilanorStPete]

He already did.


Stupid cat.

[Yora]

Yeah, too similar, might probably not be doing that one.

But the distance of the sky in that quote is a different matter alltogether and still interesting in itself. Maybe he'll still do that.