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On June 05 2015 16:23 helpman176 wrote:
Is it flawed because of wrong usage of statistics or because we have reason to believe that we are living in the first 5%?
If I get this right, the assumptions are:
1) There is a finite number of humans that will ever live. (Fair enough)
2) Me right now is a randomly selected human of all humans that ever lived. (Highly dodgy)
3) Earth population and life-span will stay roughly the same in the future. (Potentially inaccurate, but not out of the question I guess)
Then they say that if we rank the humans chronologically: there is a 5% likelyhood that I am one of the first 5% of all humans to ever live. (which is true ofc, if you take the above assumption) Then you formulated it as a probability, not a likelihood, which is highly dodgy in this case.
Well, that is what I got in a quick summary. Can others expand and elaborate what I missed? ty.
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You missed upon the fact that a lot of people are really bad at maths and not really capable of judging statistics, as long as there are numbers that look like they make sense, they are so bedazzled that they do not find the stealthy problems in the arguments, that are not in the numbers, but hidden in the words. There is simply no connection in their head between those words and the numbers, if something is maths, it must only be about the numbers and the words are merely flavour text around it (text problems in school tend to work this way, too). Thus if the numbers fit, the statement must be true.
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Ok, silly physics question I was wondering about and it has been to many years since I had physic classes so I need some help ;D
I have a guy who is 2m tall and weights 100kg. I shrink him to 1.5cm height. Could he jump from unlimited heights without hurting himself?
First we need to find out his terminal velocity.
Assuming his original projected area is 0.33m^2 his drag coefficient is 0.5 and his body volume is 99 Liters
http://www.wolframalpha.com/input/?i=v=sqrt((2*(100*(1/8)^(log(200/1.5)/log(2))-1.225*0.099*(1.5/200)^3)*9.81)/(1.225*0.33*(1.5/200)^2*0.5)
We get a terminal velocity of 8.5272 m/s.
Wondering from what height the 2m person must fall to achieve that speed:
using v=a*t and s=0.5*m*t^2 -> 3.70m
Next calculating the kinetic Energy: 0.5*m*v^2 at 8.5272 m/s.
Original person: 3635 Joule
Shrinked: 0.001549 Joule
Now I am not sure how to proceed. Do you need to calculate the surface area of his feet that he is landing on to see how destructive the impact is? I assume you need to because it hurts a lot more to punch the wall with the tip of your little finger then it does to punch it with the palm of your hand at the same speed.
So let's assume the 2m guy's feet are 7cm*30cm
Original guy: (0.5*100*8.5272^2)/(0.07*0.3*2) = 86563 Joule/m^2
Shrinked: 0.001549/(0.07*0.3*2*((1.5/200)^2)) = 655 Joule/m^2
Any mistakes, wrong assumptions?
I am especially wondering about the last step, if it makes sense to look at the surface area of the feet as a 2 dimensional area that absorbs the energy even though in reality it's an elastic system with joints and muscles and stuff.
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The terminal velocity of a regular sized human is about 70 to 80 m/s, so something is wrong from the beginning here. I'm guessing you're missing a 0 somewhere
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On June 05 2015 21:40 oGoZenob wrote:
The terminal velocity of a regular sized human is about 70 to 80 m/s, so something is wrong from the beginning here. I'm guessing you're missing a 0 somewhere
The first equation is already for the shrinked guy. Terminal velocity for the original guy with the assumed values for drag and projected area is 98m/s or 352km/h, which is a realistic value for head first fall. I couldn't find the drag coefficient for feet first fall so I used 0.5 which I found as an estimation for head first fall.
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You are doing it way too hard. You don't need any of the logs in the speed calculation, as long as you assume that he is falling long enough to achieve terminal velocity, you just need to equal the drag force with the gravtiational force. I also don't know why you would need his body volume, that is irrelevant to both of the forces involved.
We will calculate stuff very roughly, ignoring changes in density of the atmosphere and changes in gravitational pull due to being closer to earth, because those don't really matter if we talk about landing at terminal velocity.
Gravitational Force = m*g
Drag Force = 0.5 C*A*rho* v²
==> v= Sqrt((2*m*g)/(C*A*rho))
(Is there no better way to input formulas into this forum? I assume it can't process LaTeX?)
As you can see, this scales linearly with Sqrt (m/A), which are the only numbers that change when you shrink a person. Let's go with a shrinkage factor of 100 for easy maths. m scales with length³, A scales with length². Thus, your terminal velocity scales with Sqrt (l³/l²)), or Sqrt (l). With a shrinkage factor of 1/100, your terminal velocity would be Sqrt (1/100)= 10% of that of a normal sized man.
I'd say drop the whole energy/area calculations, they don't make a lot of sense. The main problem the way your legs are able to absorb a shock working like a spring, and i have no idea how shrinking would influence that. I'd just guess that you can safely absorb roughly the same speed, possibly more. The question now is what happens to a person that hits the ground at ~8m/s.
Possibly you could calculate the force that your legs need to bring up to reduce that speed to 0 over the length of half a leg? That seems reasonable, i'll go take a look at that in ~ 1 hour when i have time again.
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It's actually impressively accurate.
Air resistance force scales with area of the thing (so the length squared), and with the square the speed:
F_res ~ A*v^2 = L^2*v^2
Gravitational pull obviously scales with the mass which is proprtional to the volume, or the length cube. (I guess you dont want to shrink him maintain mass...)
F_grav ~ m = L^3
Equating the two (terminal velocity has drag = gravitational pull), we get
L^2*v^2 ~ L^3 --> v ~ sqrt(L)
That is, the terminal velocity scales as the square root of the length. Here, he wishes to scale down the size a factor 0.01 roughly, which translates into a factor 10 smaller terminal velocity, which fits with both of your numbers. Great!
To continue with the question whether he dies. To land and stay on your feet, you need to apply a force sufficient to de-accelerate your speed to 0 within a distance roughly that of your length L. Knowing that breaking distance goes as square of the velocity, and inversely with acceleration we get the required de-acceleration from the persons legs to be
L ~ v^2/a_needed
ie
a_needed ~ v^2/L
inserting the formula for v above, we get
a_needed ~ sqrt(L)^2/L ~ 1
That is, the leg acceleration needed to catch the fall is constant, it does not depend on how you scale the guy. 1km, 1m or 1mm. Same acceleration needed, cool!
The acceleration the persons legs can apply is proportional to his cross section area of his muscles (scales as L^2), and inversely proportional to his mass (scales as L^3), thus
a_legs = F_legs/m ~ L^2/L^3 = 1/L
Ie, the smaller the guy, the quicker he can accelerate. This is "why can a cricket jump 10x his height" calculation.
It now shows that smaller things can catch their fall much better (which we already knew from reality). Let's say that your small guy has L=1. Set all the proportionality constants to 1 and we get
a_needed = v^2/L = 1
a_legs = 1/0.01 = 1
ie a ratio of 1. Now for a big guy, L=100, you get
a_needed = v^2/L = 1
a_legs = 1/100 = 0.01
ie, leg acceleration is 1% of needed. Splat. The corresponding speed v_corr at which the big guy get same ratio as the small guy is
a_needed = 0.01
needs
v_corr^2 = 0.01*L
which mean
v_corr = sqrt(0.1)
which mean that
v_corr = sqrt(0.01/100) = 1/100.
Keeping in mind that the terminal velocity of the big guy was sqrt(L) = 10, ten times as large as v_corr.
So in conclusion, if a 2m person falls at terminal velocity of 55m/s (source), the fall for someone that is 2cm long, but otherwise identically built, corresponds to a fall at 5.5m/s for the big guy. After having fallen for time t (in vacuum) on the earth surface, you have traveled t^2*g/2, and have a speed of g*t. You will have 5.5m/s after 0.55 seconds falling, which will have taken you
d_corr = (0.55m/s)^2*(10m/s^2)/2 = 1.5m.
So the terminal velocity fall for the guy downscaled a factor 100 (around 55m/s*sqrt(0.01) = 5.5m/s in agreement with your calculation) is like a fall of 1.5 meters for the full size guy.
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Mwahaha, Cascade already did what i intended to do later, so i can lazy off now.
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Sorry, I did what Simberto said he would do in an hour. 
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On June 05 2015 23:05 Simberto wrote:
Mwahaha, Cascade already did what i intended to do later, so i can lazy off now.
Haha, seems like we have the physics section of this thread well covered. :D
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On June 05 2015 08:30 TMagpie wrote:Show nested quote +On June 05 2015 08:23 Sent. wrote:On June 04 2015 23:35 oGoZenob wrote:
if a stateless person murders another stateless person someone while swimming in international waters, who has the authority to juge him ? Depends on local law (check general provisions of your national penal code) but I guess any state has the autorithy as long as the murderer is within it's territory. International waters has no local law since its shared by all. Stateless would mean no one has to take responsibility for them. This leaves it to large international organizations to take action using abstract terms like "Human Rights" or other such relative intangibles.
This is how it looks like in German Criminal Code:
(1) German criminal law shall apply to offences committed abroad against a German, if the act is a criminal offence at the locality of its commission or if that locality is not subject to any criminal jurisdiction.
(2) German criminal law shall apply to other offences committed abroad if the act is a criminal offence at the locality of its commission or if that locality is not subject to any criminal law jurisdiction, and if the offender:
(...)
2. was a foreigner at the time of the offence, is discovered in Germany and, although the Extradition Act would permit extradition for such an offence, is not extradited because a request for extradition within a reasonable period of time is not made, is rejected, or the extradition is not feasible.
It's regulated in a similar way in Polish law so I'm willing to take a bet that it's like this at least in any country from continental Europe. Note that a stateless person is also a foreigner. Obviously an extradition is not an option in this case so the local criminal law should apply.
I think it's understandable why the law allows to punish such people. They're criminals and shouldn't go unpunished just because they killed someone abroad.
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On June 05 2015 23:08 Cascade wrote:Show nested quote +On June 05 2015 23:05 Simberto wrote:
Mwahaha, Cascade already did what i intended to do later, so i can lazy off now. Haha, seems like we have the physics section of this thread well covered. :D
That's still a 8m/s to 0 deceleration in roughly 1cm, which means about 320G.
The leg strength is enough to absorb the impact, but a second check would be needed to verify the brains are not leaking through the ears.
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On June 05 2015 23:19 Oshuy wrote:Show nested quote +On June 05 2015 23:08 Cascade wrote:On June 05 2015 23:05 Simberto wrote:
Mwahaha, Cascade already did what i intended to do later, so i can lazy off now. Haha, seems like we have the physics section of this thread well covered. :D That's still a 8m/s to 0 deceleration in roughly 1cm, which means about 320G. The leg strength is enough to absorb the impact, but a second check would be needed to verify the brains are not leaking through the ears.
The same proportionality analysis generalises for all those. Any inertial force (such as the brain pushing at the skull) will scale as the mass, while the "holding together" force (such as the ears) will scale as the cross section of something. You can see this in practice from small animals having roughly proportional skin thickness to larger animals. They tend to switch to exoskeleton, but that is a different reason.
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Hm, that is really interesting, but does sound a bit weird too. That would mean that on average, smaller things can take a proportional amount of lot higher accelerations. If a human can survive 10g, can a mouse take a 100?
This sounds weird, i am going to take a look at all of this.
Edit: Why can't i find out how much g-force a mouse can take? I can't believe that noone ever did experiments on that.
This sounds like what i am looking for, but i don't know how to access it 
http://www.ncbi.nlm.nih.gov/pubmed/1131134
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TL doesn't support experiments that you don't have ethics approval for.
In general, forces that holds things together are electromagnetic forces, and cancel out over large distance due to cancelling charges. They only act over a small surface, an area. While inertia and gravity act through mass, that doesn't cancel out, so the full volume gets to count.
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Oh, wow that paper! :o don't think you'd get ethics for that today. But cold war and space race and things change that I guess. Paper from 75, so may not have been scanned. Maybe they just transcribed the abstract. Anyway, they say that the limit was inversely positional to body weight, and had similar Gs to the 1cm guy, but larger animals, so I'd say it looks largely consistent with the calculations.
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Yes, but it still sounds really weird to have such a linear relationship between size and ability to survive g-forces. Thus i am looking for actual data that would support that.
Hm, true, i kind of overlooked that last sentence in my flurry to try to find the whole text. They didn't say inversely proportional, they said "inversely related", which if i interpret it correctly would just mean "The heavier the less it can take", but there are a lot of different curves with such a behaviour.
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Yeah, large animals are more heavily affected by gravity than smaller animals.
That is because on the cellular level, gravity has almost no effect.
You need to centrifuge at >1000g to separate organelles within a cell and more than 100000g are needed to separate proteins.
Mice can withstand 100g, fish can withstand ~1000g, insects can withstand >200000g.
The smaller the organism, the more important are things like surface tension, Brownian motion, viscosity, etc.
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What do you think of all the editing?
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This is getting chaotic with all of the editing.
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EPT
