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airtown
Profile Blog Joined May 2009
United States410 Posts
Last Edited: 2010-11-27 23:47:44
November 27 2010 23:35 GMT
#1
1. If a reinforced hole was drilled straight through the moon and a ladder was added, would the pull of gravity increase or decrease as you climbed down towards the center?

2. What happens if you heat up wood to very high temperatures inside a chamber without oxygen (edit: not necessarily a vacuum, perhaps a chamber with helium or something)?

***
http://www.gwu.edu/~nsarchiv/news/20010430/northwoods.pdf
Adeny
Profile Blog Joined January 2009
Norway1233 Posts
November 27 2010 23:41 GMT
#2
Homework? Pretty interesting questions regardless.

1 - I'd think the pull would stay the same but distributed in other directions as you're leaving some of the mass behind you.
2 - IDK.
ZeaL.
Profile Blog Joined April 2009
United States5955 Posts
November 27 2010 23:42 GMT
#3
1) Gravity should increase proportional to r^2
2) ??
Archas
Profile Blog Joined July 2010
United States6531 Posts
November 27 2010 23:42 GMT
#4
If this is a homework thread, it's pretty subtly prompted. O_o

Question 1 intrigues me greatly; I never thought about it before.

As for question 2, heating wood in a vacuum is very difficult in the first place, since wood is not a good conductor of heat, and the only way to heat wood in a vacuum is through conducting heat radiation through the wood. Assuming you could get it done, there'd be no fire, since fire requires oxygen. The wood would just degrade steadily and release gases; once the process completes, you'd have a very high-grade chunk of charcoal remaining.
The room is ripe with the stench of bitches!
quirinus
Profile Blog Joined May 2007
Croatia2489 Posts
Last Edited: 2010-11-27 23:59:02
November 27 2010 23:42 GMT
#5
1. Decrease I think?

2. It carbonizes? Pyrolyses




Edit:

1. There's a theorem (forgot the name, but some famous physicist showed it) that shows that only the mass under the height you're standing should be used to calculate the pull, so you'd have less mass that pulls you, but you'd be closer to the center. (I think the same theorem says that the mass under your height can be assumed to be located at the center - if it's uniformly spherically distributed) The net result would be that it pulls you less, as obviously, if you were at the center, you'd have to feel no force, as the same force "pulls" you from all directiones.
It's not that hard to show/prove it too.

2. http://en.wikipedia.org/wiki/Charcoal, happened naturally a long time ago...
All candles lit within him, and there was purity. | First auto-promoted BW LP editor.
airtown
Profile Blog Joined May 2009
United States410 Posts
November 27 2010 23:43 GMT
#6
On November 28 2010 08:41 Adeny wrote:
Homework?

Nope.
http://www.gwu.edu/~nsarchiv/news/20010430/northwoods.pdf
hacklebeast
Profile Blog Joined April 2010
United States5090 Posts
Last Edited: 2010-11-27 23:49:48
November 27 2010 23:43 GMT
#7
1, net pull would decreace untill you are weightless in the center
2. it melts, assuming that "very high" means something hotter than humans can make.

the pull decreaces because as you move into the center because all of the matter that you pass starts pulling you backwards. At the center the pull of any matter is perfectly countered by matter on the opposite side, so there is no prevailing foce (ignoring the fact that the moon is not a perfect sphere.)
Protoss: Best, Paralyze, Jangbi, Nal_Ra || Terran: Oov, Boxer, Fantasy, Hiya|| Zerg: Yellow, Zero
MetalFace
Profile Joined September 2010
United States75 Posts
November 27 2010 23:45 GMT
#8
I haven't taken a physics class in years, but from what I remember:

1) I think as you get closer to something, the gravitation attraction you'll feel is stronger, so as you get closer to more of the moon, the pull of gravity would increase.

2) This one I'm not so sure of, but I think it might be called gasification. Pretty much the natural gas in wood can be extracted from it through a process involving heating up wood in a sealed container.

I'm not sure on either of those though. Good luck with whatever project you're doing where you heat up wood in the middle of the moon.
Archas
Profile Blog Joined July 2010
United States6531 Posts
Last Edited: 2010-11-27 23:47:03
November 27 2010 23:46 GMT
#9
On November 28 2010 08:45 MetalFace wrote:
I'm not sure on either of those though. Good luck with whatever project you're doing where you heat up wood in the middle of the moon.

It's clearly a terrorist plot to turn the Moon into a flaming meteor and crash it into Washington D.C.
The room is ripe with the stench of bitches!
bbq ftw
Profile Joined September 2010
United States139 Posts
November 27 2010 23:50 GMT
#10
1. If a reinforced hole was drilled straight through the moon and a ladder was added, would the pull of gravity increase or decrease as you climbed down to the center?

Pretty sure it decreases.

Logic is a bit iffy but:

Gravity at surface of moon is some finite value.
Gravity at the middle of the moon is zero (there's no mass within the sphere defined by r=0)

Assuming that the gravity vs radius is continuous (no abrupt breaks) one can surmise gravity is decreasing.

In addition, bad over simplified math says:

the sphere defined by r=x where x is your current position has volume proportional to x^3. Sphere volume assuming constant density, therefore volume proportional to mass, mass proportional to x^3

the denominator of gravity term is x^2 -- x is also the distance from moon's center of mass (center) from current position

gravity proportional to x^3/x^2 = x

lower x, lower gravity = decreases


2. interesting question, i have no idea.
Slayer91
Profile Joined February 2006
Ireland23335 Posts
Last Edited: 2010-11-27 23:58:56
November 27 2010 23:57 GMT
#11
On November 28 2010 08:45 MetalFace wrote:
I haven't taken a physics class in years, but from what I remember:

1) I think as you get closer to something, the gravitation attraction you'll feel is stronger, so as you get closer to more of the moon, the pull of gravity would increase.


As you reach the dead centre, the gravitational affects of each part of mass will all cancel out, and you'd feel no force.
It is stronger with respect to r^2 only if the mass pulling you is all in one direction.

I assume the wood would vapourise eventually, even without combustion.
AcrossFiveJulys
Profile Blog Joined September 2005
United States3612 Posts
November 27 2010 23:59 GMT
#12
1) gravitational pull will linearly decrease as you approach the center until the pull is zero. Intuitively, this is because the volume "under" you decreases cubically as you move towards the center while the gravitational pull (of the decreasing mass under you) increases quadratically as you move towards the center.
Blisse
Profile Blog Joined July 2010
Canada3710 Posts
Last Edited: 2010-11-28 00:04:24
November 28 2010 00:01 GMT
#13
1. Would need to ask which pull of gravity, Earth's, or the Moon's. Questioning why the same question could not have been Earth instead of the Moon.


FG = (G x m1 x m2) / r^2 have anything to do with this? Cause I don't know if UND means infinite or zero...

2. Do you mean if say you placed it on an electric heater or something similar?
There is no one like you in the universe.
sheaRZerg
Profile Blog Joined June 2009
United States613 Posts
Last Edited: 2010-11-28 00:05:15
November 28 2010 00:03 GMT
#14
On November 28 2010 08:42 quirinus wrote:
There's a theorem (forgot the name, but some famous physicist showed it) that shows that only the mass under the height you're standing should be used to calculate the pull, so you'd have less mass that pulls you, but you'd be closer to the center.


You can use Gauss' law for gravity, much like you would for the electric charge. That is what you are describing for part 1. So the gravitational acceleration would be less on the interior of the sphere than at the surface.

Edit: http://en.wikipedia.org/wiki/Gauss'_law_for_gravity
"Dude, just don't listen to what I say; listen to what I mean." -Sean Plott
airtown
Profile Blog Joined May 2009
United States410 Posts
November 28 2010 00:05 GMT
#15
On November 28 2010 09:01 vica wrote:
1. Would need to ask which pull of gravity, Earth's, or the Moon's. Questioning why the same question could not have been Earth instead of the Moon.

2. Do you mean if say you placed it on an electric heater or something similar?

1. Ignore any outside pulls of gravity

2. Um, idk. Does it matter?
http://www.gwu.edu/~nsarchiv/news/20010430/northwoods.pdf
airtown
Profile Blog Joined May 2009
United States410 Posts
November 28 2010 00:10 GMT
#16
Found this, which seems to be relevant: http://en.wikipedia.org/wiki/Shell_theorem#Inside_a_shell

Can someone put it into laymans terms? I'm only in algebra 2.
http://www.gwu.edu/~nsarchiv/news/20010430/northwoods.pdf
MoltkeWarding
Profile Joined November 2003
5195 Posts
November 28 2010 00:16 GMT
#17
The pull of gravity would increase, but be more evenly distributed in different directions, so there would be a net decrease, assuming that the mass of the moon were equally distributed throughout its body. If we can imagine a moon with its mass heavily concentrated at the core, it's possible that the net pull would increase.
MetalFace
Profile Joined September 2010
United States75 Posts
November 28 2010 00:16 GMT
#18
"net gravitational forces acting on the point mass from the mass elements of the shell cancel out"
-from the wiki page you linked.

Pretty much, the forces of gravity inside a sphere will cancel each other out, like everyone's pretty much been saying. So as you go inside the moon, the forces will be stronger, but the directions will start to cancel each other out, until you get to the middle where all of the forces will be cancelled.
SpiritoftheTunA
Profile Blog Joined August 2006
United States20903 Posts
November 28 2010 00:16 GMT
#19
you don't need the shell theorem, but the general idea of the answer to problem 1 is that any mass distributed outside of the radius you're currently at (say the moon's radius is 10 and you're at 8), you'll feel the pull of only the stuff below you (the radius 8 sphere, not the full moon). this is a linear relationship, so basically

if 'a' is the radius of the moon, and the gravitational pull at the surface is F = G*m1*m2/a^2, you just have to multiply the whole thing by a factor of your radius from the center in order to get the gravitational force for anything under the surface.

so ends up working out as F = r*G*m1*m2*/a^2 (where r is the only variable in this case, your radial distance from the center of the moon)
posting on liquid sites in current year
SpiritoftheTunA
Profile Blog Joined August 2006
United States20903 Posts
Last Edited: 2010-11-28 00:48:24
November 28 2010 00:21 GMT
#20
On November 28 2010 09:16 MoltkeWarding wrote:
The pull of gravity would increase, but be more evenly distributed in different directions, so there would be a net decrease, assuming that the mass of the moon were equally distributed throughout its body. If we can imagine a moon with its mass heavily concentrated at the core, it's possible that the net pull would increase.

This actually isn't the case, even if 90% of the moons' mass were within its innermost 10% sphere, the gravitational pull would decrease as you go towards the center because you still will no longer feel the downward pull of all of the ground you're digging under. as long as the mass is distributed radially symmetrically, your gravitational attraction towards the very center should never increase as you dig into the mass. (actually it might not increase towards the center no matter what)


EDIT: actually that was severely wrong see post below me for details
posting on liquid sites in current year
susySquark
Profile Blog Joined May 2010
United States1692 Posts
Last Edited: 2010-11-28 00:41:28
November 28 2010 00:40 GMT
#21
To question 1, it of course depends on how the mass of the moon is distributed. If you assume that the moon's mass is evenly distributed across its volume then the answer is simple:

Since volume, and therefore mass (because volume * density = mass), is proportional to r^3, and gravitational effects is proportional to 1/r^2, decreasing r reduces the gravitational force because of the amount of mass you lose more than it increases because of the closer distance.

You ignore the "shells" of mass that are above you because of Gauss's law. Enclosed mass is all that matters.

Voila!

Question 2, since the process of burning requires oxygen, and the chamber is filled with an inert gas, you would eventually just get liquid wood when it got hot enough. Before that though, http://en.wikipedia.org/wiki/Charcoal
hypercube
Profile Joined April 2010
Hungary2735 Posts
November 28 2010 00:47 GMT
#22
On November 28 2010 09:21 SpiritoftheTunA wrote:
This actually isn't the case, even if 90% of the moons' mass were within its innermost 10% sphere, the gravitational pull would decrease as you go towards the center because you still will no longer feel the downward pull of all of the ground you're digging under. as long as the mass is distributed radially symmetrically, your gravitational attraction towards the very center should never increase as you dig into the mass. (actually it might not increase towards the center no matter what)


This is incorrect, check out the exact math in the previous posts. The effect of getting closer to 90% of the mass would outweigh losing the attraction of the other 10%.
"Sending people in rockets to other planets is a waste of money better spent on sending rockets into people on this planet."
SpiritoftheTunA
Profile Blog Joined August 2006
United States20903 Posts
November 28 2010 00:48 GMT
#23
On November 28 2010 09:47 hypercube wrote:
Show nested quote +
On November 28 2010 09:21 SpiritoftheTunA wrote:
This actually isn't the case, even if 90% of the moons' mass were within its innermost 10% sphere, the gravitational pull would decrease as you go towards the center because you still will no longer feel the downward pull of all of the ground you're digging under. as long as the mass is distributed radially symmetrically, your gravitational attraction towards the very center should never increase as you dig into the mass. (actually it might not increase towards the center no matter what)


This is incorrect, check out the exact math in the previous posts. The effect of getting closer to 90% of the mass would outweigh losing the attraction of the other 10%.

Yeah, my bad, I wasn't thinking properly. Thanks for the heads-up.
posting on liquid sites in current year
quirinus
Profile Blog Joined May 2007
Croatia2489 Posts
Last Edited: 2010-11-28 01:03:59
November 28 2010 01:02 GMT
#24
On November 28 2010 09:10 4iner wrote:
Found this, which seems to be relevant: http://en.wikipedia.org/wiki/Shell_theorem#Inside_a_shell

Can someone put it into laymans terms? I'm only in algebra 2.


Yeah, I was talking about this theorem. Haha, thought Newton proved it.

Also, What Moltke says is more realistic, since the density does increase towards the center. Depends how much it increases though.

also, what I love about science and people in it is this:

On November 28 2010 09:48 SpiritoftheTunA wrote:
Show nested quote +
On November 28 2010 09:47 hypercube wrote:
On November 28 2010 09:21 SpiritoftheTunA wrote:
This actually isn't the case, even if 90% of the moons' mass were within its innermost 10% sphere, the gravitational pull would decrease as you go towards the center because you still will no longer feel the downward pull of all of the ground you're digging under. as long as the mass is distributed radially symmetrically, your gravitational attraction towards the very center should never increase as you dig into the mass. (actually it might not increase towards the center no matter what)


This is incorrect, check out the exact math in the previous posts. The effect of getting closer to 90% of the mass would outweigh losing the attraction of the other 10%.

Yeah, my bad, I wasn't thinking properly. Thanks for the heads-up.


When someone is wrong, they just admit it and usually thank people for correcting them - and are genuinely thankful.
All candles lit within him, and there was purity. | First auto-promoted BW LP editor.
Blisse
Profile Blog Joined July 2010
Canada3710 Posts
Last Edited: 2010-11-28 01:12:49
November 28 2010 01:05 GMT
#25
On November 28 2010 09:05 4iner wrote:
Show nested quote +
On November 28 2010 09:01 vica wrote:
1. Would need to ask which pull of gravity, Earth's, or the Moon's. Questioning why the same question could not have been Earth instead of the Moon.

2. Do you mean if say you placed it on an electric heater or something similar?


1. Ignore any outside pulls of gravity

2. Um, idk. Does it matter?


1. I'm asking which gravity, the gravity of the Earth on the person, or the gravity of the Moon on the person... I'm assuming it's the gravity of the Moon, since the discussion wouldn't exist if it was the Earth. Why didn't you use the Earth as the object instead though?

2. It's so I can understand the question better... anyways, it should just vaporize.ophy.
There is no one like you in the universe.
airtown
Profile Blog Joined May 2009
United States410 Posts
November 28 2010 01:20 GMT
#26
On November 28 2010 10:05 vica wrote:
1. I'm asking which gravity, the gravity of the Earth on the person, or the gravity of the Moon on the person... I'm assuming it's the gravity of the Moon, since the discussion wouldn't exist if it was the Earth. Why didn't you use the Earth as the object instead though?

2. It's so I can understand the question better... anyways, it should just vaporize.ophy.

1. The Moon, but Earth would work as well.

Btw, thanks for the answers everyone.
http://www.gwu.edu/~nsarchiv/news/20010430/northwoods.pdf
Archaic
Profile Blog Joined March 2008
United States4024 Posts
Last Edited: 2010-11-28 01:23:21
November 28 2010 01:21 GMT
#27
On November 28 2010 09:10 4iner wrote:
Found this, which seems to be relevant: http://en.wikipedia.org/wiki/Shell_theorem#Inside_a_shell

Can someone put it into laymans terms? I'm only in algebra 2.

To put it simply, you would be essentially weightless if you on the inside of a hollow planet. At the center this is obvious. However, when you are shifted towards a side (assuming it is a perfect circle), the pull is *still* equal on all sides because though you are getting further from the other side, the amount of mass on that side increases, essentially balancing out the pull, still rendering you weightless.
Sorry if that is confusing...

Oh, this might be incorrect... It's based on memory from a year ago.
Ecrilon
Profile Blog Joined October 2009
501 Posts
November 28 2010 01:21 GMT
#28
The moon is presumably used for this question to avoid the very good point that Moltke brings up. The moon is actually quite uniform in density and lacks the iron core that earth does. Getting closer to the moon's center clearly decreases the amount of gravity you feel whereas if the question were posed for earth, it would be sightly more ambiguous.

Wood is largely carbon/water. As everyone has said, water will vaporize, carbon will turn into charcoal.
There is but one truth.
Almeisan
Profile Joined November 2010
50 Posts
Last Edited: 2010-11-28 01:52:20
November 28 2010 01:51 GMT
#29
No.1 is Newton's shell theorem. The part of the sphere outside of the radius you are from the center neutralizes itself. In the middle all gravity neutralizes each other. Only the mass of the inner sphere counts.
I think I remember that Newton's proof wasn't valid or just flawed. But the theorem is true.


No.2 is complex as we are talking about biochemistry. At certain temperature, which isn't very high, protein will unfold. I don't know what cellulose will do at high temperatures. But as a polymer it may very well fall apart. But as it gets warm enough the solids will melt and even vaporize. Then they will form plasma.
jamesr12
Profile Blog Joined April 2010
United States1549 Posts
November 28 2010 01:57 GMT
#30
1) decrease

2) no clue
http://www.teamliquid.net/forum/viewmessage.php?topic_id=306479
micronesia
Profile Blog Joined July 2006
United States24701 Posts
November 28 2010 03:13 GMT
#31
On November 28 2010 10:20 4iner wrote:
Show nested quote +
On November 28 2010 10:05 vica wrote:
1. I'm asking which gravity, the gravity of the Earth on the person, or the gravity of the Moon on the person... I'm assuming it's the gravity of the Moon, since the discussion wouldn't exist if it was the Earth. Why didn't you use the Earth as the object instead though?

2. It's so I can understand the question better... anyways, it should just vaporize.ophy.

1. The Moon, but Earth would work as well.

Btw, thanks for the answers everyone.

What is this for? Generally blogs where you just ask random questions without giving any background (as well as pure hw blogs) are not allowed.
ModeratorThere are animal crackers for people and there are people crackers for animals.
Empyrean
Profile Blog Joined September 2004
16998 Posts
November 28 2010 03:27 GMT
#32
He posted that it wasn't for homework, but to be honest, I don't believe him.

It's started some interesting discussion regardless, so meh.
Moderator
SubtleArt
Profile Blog Joined January 2010
2710 Posts
November 28 2010 03:36 GMT
#33
2. This ones pretty easy. The wood would heat to a point where it vaporizes because the intermolecular bonds break. It wouldn't combust because theres no oxygen to react with.

1. I have no idea
Morrow on ZvP: "I'm not very confident in general vs Protoss because of the imbalance (Yes its imbalanced, get over it)."
zobz
Profile Joined November 2005
Canada2175 Posts
Last Edited: 2010-11-28 04:23:27
November 28 2010 04:22 GMT
#34
Edit: reading problems
"That's not gonna be good for business." "That's not gonna be good for anybody."
bellweather
Profile Blog Joined April 2009
United States404 Posts
November 28 2010 04:45 GMT
#35
Really enjoyed thinking about #1. Assuming you were to "jump" into the hole you dug through the moon, I imagine you'd oscillate and at some point reach equilibrium at the center... or would your momentum carry you to the other side?
A mathematician is a blind man in a dark room looking for a black cat which isnt' there. -Charles Darwin
micronesia
Profile Blog Joined July 2006
United States24701 Posts
November 28 2010 05:06 GMT
#36
On November 28 2010 13:45 InsideTheBox wrote:
Really enjoyed thinking about #1. Assuming you were to "jump" into the hole you dug through the moon, I imagine you'd oscillate and at some point reach equilibrium at the center... or would your momentum carry you to the other side?

Without friction it would be a harmonic oscillator just like a spring, going back and forth from surface to surface. With friction it would be a damped oscillator, would bounce back and forth less and less, and would eventually come to rest at the center.
ModeratorThere are animal crackers for people and there are people crackers for animals.
Z3kk
Profile Blog Joined December 2009
4099 Posts
November 28 2010 05:11 GMT
#37
I'm proud to say that I actually understand what you guys are saying!

Very interesting and/or brain-stimulating questions indeed :> Getting me in the mood for homework (and dropping the distractions @___@).
Failure is not falling down over and over again. Failure is refusing to get back up.
LaSt)ChAnCe
Profile Blog Joined June 2005
United States2179 Posts
November 28 2010 05:32 GMT
#38
moltke and susy gave the correct explanation(s) for 1, 2 i didn't know but after some logical thought (thanks, physics class!) i remembered that as things get hot, they eventually melt, then vaporize
unbal3
Profile Joined September 2010
Korea (South)131 Posts
Last Edited: 2010-11-28 08:34:31
November 28 2010 08:13 GMT
#39
1. pull would increase, obviously

2. The chemicals that compose the wood will liquefy then evaporate (or just sublimate, depends), turn into plasma, and eventually undergo atomic fission or fusion. there will be a short period of time where the more reactive components of wood go through chemical reactions, but eventually all bonds will break well before they become plasma.


what are the point of these questions, btw? seems to me as though you could have just typed these in google and got the answers there.

edit: as to #1, never mind, idk what i was thinking. gravity would decrease, not increase as you approach the center.
hp.Shell
Profile Blog Joined April 2010
United States2527 Posts
November 28 2010 08:53 GMT
#40
Please PM me with any songs you like that you think I haven't heard before!
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