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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
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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%.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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United States24782 Posts
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.
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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.
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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
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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?
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United States24782 Posts
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.
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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 @___@).
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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
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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.
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EPT
