question on paper stacking

gkaby · 2017-04-09 18:55:53

ignoring all known laws of physics, how many pieces of paper can you stack without it melting?

skullz17

Gosha · 2017-04-09 18:58:32

42

EDIT:
also, if you ignore all physics laws - you lose the defenition of "paper"

gkaby

Sensei1 · 2017-04-09 19:12:37

When does it melt? When it gets too close to sun?

gkaby, skullz17

gkaby · 2017-04-09 19:18:46

you are forgetting that the sun is only on one side of earth! what if you stack the paper while its night time?!?!!??

hummerz5 · 2017-04-09 19:22:40

if you have large amounts of mass, deep internal pressure causes heat, so I suppose lots of paper makes gravity makes pressure makes heat makes melting?

gkaby

gkaby · 2017-04-09 19:25:56

humus you are forgetting that we are ignoring all known laws of physics..................................................
the paper might weigh 0 so there wont be pressure also if they are stacked to space eventually there wont be pressure because they wont be weighing down the initial pieces of paper that were stacked!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Sensei1 · 2017-04-09 19:27:39

If we make tall enough paper tower is it possible that it spins with the earth so fast that it gets hot and melts?
I don't really know physics all that well but since we're ignoring all the laws of physics... xD

EDIT: So we HAVE TO ignore all the laws of physics!?

gkaby

gkaby · 2017-04-09 19:31:36

what makes you think the earth is spinning?

hummerz5 · 2017-04-09 19:32:56

given that all materials have a melting point as defined by the laws of physics, if we remove those, there is no melting point.

so I guess your answer to how many is "no"

gkaby, Tomahawk, TaskManager

gkaby · 2017-04-09 19:34:58

well according to gosha, paper is not a material so therefore we dont know whether it doesnt have a melting point or not

Evilbunny · 2017-04-09 19:48:53

I give up, just tell me the answer.

Sensei1, Xfrogman43, gkaby

Koya · 2017-04-09 20:01:51

gkaby wrote:

you are forgetting that the sun is only on one side of earth! what if you stack the paper while its night time?!?!!??

Well the moon would knock it over, amateur.

gkaby

gkaby · 2017-04-09 20:06:20

Evilbunny wrote:

I give up, just tell me the answer.

I do not know the answer, that is why I asked the question

Koya wrote:

gkaby wrote:
you are forgetting that the sun is only on one side of earth! what if you stack the paper while its night time?!?!!??
Well the moon would knock it over, amateur.

you can stack it in a place outside of the moon's orbit

Sensei1 · 2017-04-09 20:19:11

I got an idea considering the laws of physics. Laws of physics aren't really laws right? They're just something we've made up, so could we agree that gravity and pressure and stuff like that still exist?

gkaby

Pingohits · 2017-04-09 20:21:21

well if you're ignoring all laws of physics then the paper wouldn't stack in the first place ya dingus

Xfrogman43, gkaby, Badoosh, Slabdrill

gkaby · 2017-04-09 20:27:07

sensei1 i mean as if their ostensible effects we see are being ignored

pingohit i said all known laws of physics

Master1 · 2017-04-09 21:08:59

what about the unknown law of physics where paper has a mass of 1,000,000 pieces of paper squared and if you place one on top of the other the pressure is equivalent to the gravity of a black hole and stacking just 2 pieces will cause the paper to instantly burst into flame and melt??

the answer is 2!

gkaby

gkaby · 2017-04-09 21:23:38

but if you are correct, the answer would be less than 2 because 2 will cause it to melt and i said without it melting

Sensei1

Evilbunny · 2017-04-09 21:45:50

gkaby wrote:

the answer would be less than 2

oh man I think we're getting close!

gkaby

Tomahawk · 2017-04-09 21:53:18

Ignoring all laws of physics, there are no forces holding atoms together. Gravity, paper and the universe wouldn't exist, soooo....

gkaby

HeyNK · 2017-04-09 22:17:05

^ Actually those are laws of chemistry, not physics. Two unrelated but often confused fields.

gkaby

LukeM · 2017-04-09 22:42:55

So... Im going to get a bit physicsy for something thats supposed to be ignoring physics, but this is the only way I can think of to do it...

Assumptions:
You are stacking towards the sun
The paper wont burn (only melt)
You are using .1mm thick paper (found here from a quick google)
The bottom of the stack is 20 degrees
All energy from the suns light is converted to heat (no other sources)
Ignoring the atmosphere or whatever

So...
Conduction formula: Q = kA(Thot - Tcold)t/d
Q = (thermal conductivity of paper)*(area of sheet)*(temperature difference)*(time)/(stack height)

Thermal conductivity of paper = 0.05 [1]
Paper is made from cellulose, which has a melting point of 265 degrees [2]
This means there is a difference of 245 degrees from top to bottom when it melts
Calculating for one second, to make it easier (and I couldnt find the right formula)

Q = 0.05 * A * 245 / h
Q = 12.25 * A / 0.001S
Q = 12250A / S

light energy = (fraction of total sun energy) * (total sun energy)
total sun energy = 3.86 × 10^26 watts [3]
fraction of total sun energy = (area of sheet) / (total surface area of sphere centered on the sun)
total surface area = 4 * pi * r^2
r = distance from earth to the sun - height
distance from earth to the sun = 149600000000 meters
fraction of total sun energy = A / (4 * pi * (149600000000 - 0.001S)^2)
light energy = (A / (4 * pi * (149600000000 - 0.001S)^2)) * (3.86*10^26)

(12250A / S) = (A / (4 * pi * (149600000000 - 0.001S)^2)) * (3.86*10^26)
(12250 / S) = (3.86 × 10^26) / (4 * pi * (149600000000 - 0.001S)^2)
(12250 / S) * (4 * pi * (149600000000 - 0.001S)^2) = (3.86*10^26)
12250 * 4 * pi * (149600000000 - 0.001S)^2 = 3.86S*10^26
49000 pi * ((1.496*10^11)^2 - (0.002S*1.496*10^11) + (0.001S)^2) = 3.86S*10^26
154 * (2.24*10^22 - 3S*10^8 + (S^2)*10^-6) = 386S*10^21
(345*10^22) - ((effectively 0) + (386*10^21))S + (10^-6)S^2 = 0

Quadratic equation solver (because I CBA to do it myself): S = 3.86*10^29 or 8.94

That ^ seems wrong... I probably made a mistake somewhere but I cant be bothered to find it atm, maybe ill check later
If its not, then your answer is 3.86*10^29 sheets

Citations:
1: http://www.engineeringtoolbox.com/therm … d_429.html
2: https://en.wikipedia.org/wiki/Cellulose
3: https://en.wikipedia.org/wiki/Solar_con … _radiation

gkaby

Abelysk · 2017-04-09 22:51:35

How many papers does it take to get to the center of a paper

gkaby

hummerz5 · 2017-04-09 23:09:12

^ the fraction of total sun energy is also dependent on how far away the stack is. We would take up much more of the sun's expounding energy if we were on its surface as opposed to where we are now. you took that into account in your numbers. nice.

also, if we were on the surface of the sun, wouldn't there just be heat in general as opposed to light energy probably handled this as well with the whole r = distance - height thing

btw what happened to your A in that above equation?

I mean, i still think the internal combustion would be an issue well before your stack was heated up by the sun's light. edit: perhaps my knowledge of physics is wrong. I mean Earth has its thing because of how it was formed, right? Then I read this xkcd that says the mole of moles has its thing because meat naturally has lots of energy. What does paper have? Enough? idk
well I just... uh...
how would the weight of the stack affect where it was positioned? if we were out in a cornfield, would the papers (assuming they wouldn't fall over) settle a hole in the ground? Also, since we're assuming these papers won't fall over, let's just pretend they're one continuous block. Given that an object's center of gravity follows a smooth curve and that earth rotates, would the giant block be somehow spun off of Earth? "A satellite in such an orbit is at an altitude of approximately 35,786 km (22,236 mi) above mean sea level" [0]. Meanwhile, your stack of 10^29 sheets at .1mm thickness would be 2.3984928 × 10^22 miles tall [1]. I bring this orbit up because they're essentially the height where they aren't being pulled up or down... well, they are, but they're falling around. Here, you're so far away that you'd be falling away from the Earth... your stack would fly away.

Does your conductance formula mean that the entire stack is engulfed? Would that mean that Earth itself would be engulfed? I mean, if the conductance had to get all the way down to Earth to vaporize the whole stack, that'd be a lot of melting mass.

now for some reason I'm assuming that we have paper that is falling to earth. I guess that's if the whole stack reached melting point? Or perhaps if we assume regular paper again?
1 sheet of printer paper: 4.5 grams ([2])
number of pages below geosynchronous orbit: 35785400000
( I still don't know what the area of a sheet is, so we're just assuming a page of printer paper now?)

161,034,300 kg of paper below the fall-to-earth height (if my physics is solid) -- but, earth is 5.972 × 10^24 kg [1] so it's really not as damaging as I thought.

earth's surface area: 196.9 million mi² [1]. Surface area of all those pages: 833.464583 square miles -- so we could do some damage, but not a whole lot. We could cover New York (304.6 mi²) twice [1] but I mean that's just new york right
0: https://en.wikipedia.org/wiki/Geosynchronous_orbit
1: google search (built-in conversion tool!)
2: http://ansuz.sooke.bc.ca/entry/12

gkaby

Tomahawk · 2017-04-09 23:10:39

HeyNK wrote:

^ Actually those are laws of chemistry, not physics. Two unrelated but often confused fields.

While I meant the forces that hold individual atoms together, the study of all fundamental forces is taught in physics and not chemistry.

"Unrelated" my ****.

hummerz5, gkaby

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#1 2017-04-09 18:55:53

question on paper stacking

#2 2017-04-09 18:58:32, last edited by Gosha (2017-04-09 18:59:24)

Re: question on paper stacking

#3 2017-04-09 19:12:37

Re: question on paper stacking

#4 2017-04-09 19:18:46

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#5 2017-04-09 19:22:40

Re: question on paper stacking

#6 2017-04-09 19:25:56, last edited by gkaby (2017-04-09 19:26:12)

Re: question on paper stacking

#7 2017-04-09 19:27:39, last edited by Sensei1 (2017-04-09 19:28:36)

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#8 2017-04-09 19:31:36

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#9 2017-04-09 19:32:56

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#10 2017-04-09 19:34:58

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#11 2017-04-09 19:48:53

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#12 2017-04-09 20:01:51

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#13 2017-04-09 20:06:20

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#14 2017-04-09 20:19:11

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#15 2017-04-09 20:21:21

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#16 2017-04-09 20:27:07, last edited by gkaby (2017-04-09 20:28:36)

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#17 2017-04-09 21:08:59

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#18 2017-04-09 21:23:38

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#19 2017-04-09 21:45:50

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#20 2017-04-09 21:53:18

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#21 2017-04-09 22:17:05

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#22 2017-04-09 22:42:55

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#23 2017-04-09 22:51:35

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#24 2017-04-09 23:09:12, last edited by hummerz5 (2017-04-09 23:12:32)

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