Question Re: Giant Hole Through the Earth

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Kartoffelkopf
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Question Re: Giant Hole Through the Earth

Postby Kartoffelkopf » Fri Mar 28, 2008 9:49 am UTC

This was the 'challenge question' for today's Physics class, quoted verbatim from the teacher. I decided to bring it here, because, well...

CHALLENGE QUESTION
Chris gets bored in Physics class and starts digging. Being a very good digger, he digs through the centre of the earth and out the other side. Terps (his girlfriend) soon starts to miss Chris and jumps through the hole after him. Describe her movement. Will she come out? (assuming she won't burn up in the core)

Written answers only.

Best/most creative answer at the end of term one (~2 weeks) will win A CAN OF COKE (and eternal glory).


Randomness is encouraged, but it must have scientific reasoning.

EDIT: Here was /b/'s answer, which was suitably epic.
No.

The core of the earth's gravitational pull will keep her stuck in the middle. She'll also weigh a fuckton, suspended in air. (Assuming the hole goes straight through the core and is wide enough to move around in.)

>> 03/28/08(Fri)05:54:45 No.60193870

Randomness is encouraged. Don't care if it's true or not. this is /b/ dammit

>> 03/28/08(Fri)05:56:28 No.60193983

EPIC FAIL THREAD IS FAIL.

>> 03/28/08(Fri)05:57:09 No.60194015

>>60193666
This, and that she will hit terminal velocity and die. So floating corpse in the middle of the Earth is my answer.

>> 03/28/08(Fri)05:57:17 No.60194029

>>60193870

Why the fuck would you want a random answer if a can of coke is at stake, retard?

What do you expect /b/ to say? No u? Would that be an acceptable answer? Or how about Needs more battletoads? Push button, recieve bacon? Is what you wanted from /b/ and answer or a pointless meme that will do nothing towards your goal of aquiring delicious coke?

tl;dr, you're a dumbass, answer is here. >>60193870


Thread closed due to fail and aids.

>> 03/28/08(Fri)05:57:23 No.60194038

>>60193666
You sir, are correct.

>> 03/28/08(Fri)05:59:13 No.60194169

>>60193511
OP are you stupid, he wouldnt even reach the core, the pressure would kill him.


if the hole previously existed, you would have to calculate if the woman has enough acceleration to escape the gravitational field of the core.

>> 03/28/08(Fri)06:00:42 No.60194275
File :1206698442.png-(127 KB, 320x240, 1206350092332.png)
127 KB

I think a more pressing issue is that if there was a giant hole puncturing the earth, all the gravity would escape.

>> 03/28/08(Fri)06:04:34 No.60194494
File :1206698674.gif-(653 KB, 400x225, aminos finger.gif)
653 KB

when you throw a ball in the air, it peaks and then returns back down, and, minus air resistance, ends up going down at the same speed that you threw it up

this would be the same if she jumped in the hole, she would slowly build up speed and then slowly lose it, but with air resistance she wouldnt return to the same height, but if she held onto like a ton going down and let going at the center, she would have enough speed to make it out
Last edited by Kartoffelkopf on Fri Mar 28, 2008 10:19 am UTC, edited 2 times in total.

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Re: Physics 'challenge question' ceptnotrly

Postby ian » Fri Mar 28, 2008 10:11 am UTC

She'll enter the world of hollow-earth and live happily ever after with the people of this place.

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Re: Physics 'challenge question' ceptnotrly

Postby evilbeanfiend » Fri Mar 28, 2008 10:55 am UTC

clearly she will travel with damped harmonic motion back and forth through the core until the drag from air resistance slows her enough to stop in the centre, she will be weightless here.

if you want non-physical answers this might not be the right forum
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Re: Physics 'challenge question' ceptnotrly

Postby ian » Fri Mar 28, 2008 11:00 am UTC

evilbeanfiend wrote:clearly she will travel with damped harmonic motion back and forth through the core until the drag from air resistance slows her enough to stop in the centre, she will be weightless here.

if you want non-physical answers this might not be the right forum


Well actually the question just says she won't be burned, not that that molten rock won't fill up the hole (and perhaps erupt)

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Re: Physics 'challenge question' ceptnotrly

Postby Kartoffelkopf » Fri Mar 28, 2008 1:38 pm UTC

evilbeanfiend wrote:if you want non-physical answers this might not be the right forum

I already tried /b/. :(

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Re: Physics 'challenge question' ceptnotrly

Postby taby » Fri Mar 28, 2008 2:54 pm UTC

evilbeanfiend wrote:clearly she will travel with damped harmonic motion back and forth through the core until the drag from air resistance slows her enough to stop in the centre, she will be weightless here.

if you want non-physical answers this might not be the right forum


Stole the words right out of my mouth.

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Re: Physics 'challenge question' ceptnotrly

Postby EricH » Fri Mar 28, 2008 8:08 pm UTC

evilbeanfiend wrote:clearly she will travel with damped harmonic motion back and forth through the core until the drag from air resistance slows her enough to stop in the centre, she will be weightless there.


Assuming the physics class is held at one pole or the other. Otherwise, Coriolis force...the drag is not just from air resistance, but from scraping down the east side of the hole. Same result, but damped a lot quicker. Also, remember that air pressure increases with depth. Interesting calculus problem--what would the air pressure be at the center of the earth? Gravitational force decreases with depth, but that means pressure just increases more slowly.

ian wrote:Well actually the question just says she won't be burned, not that that molten rock won't fill up the hole (and perhaps erupt)


Right, the question seems to presuppose that the hole could be held open. Digging though the Earth's core is rather like trying to dig a hole in the ocean--you'd better dig awfully fast. Realistically, she'd better be just a few microseconds behind the digger, or she's not going to make it.

So many errors from the /b/ thread, but I'll confine myself to this--it's not called terminal velocity because you die at that speed. I'd buy death by heat, or pressure (depending on the answer to the calculus problem I just mentioned), or even the bends, for Pete's sake, but not 'suffocation at terminal velocity.'
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Re: Physics 'challenge question' ceptnotrly

Postby SWGlassPit » Fri Mar 28, 2008 9:45 pm UTC

I recall reading something about this one time...don't remember the source.

Basically, neglecting air resistance and contact friction with the walls (in other words, anything that would slow you down in any way), a trip from one end to the other purely under the force of gravity would take about 45 minutes.

The interesting thing is that if you dig a hole that forms a straight line between any two points on the earth, e.g., New York to London, and travel this hole purely under the force of gravity, the time it would take to traverse the distance would be the same, regardless of the relative location of the two points.
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Re: Physics 'challenge question' ceptnotrly

Postby Mathmagic » Fri Mar 28, 2008 10:14 pm UTC

SWGlassPit wrote:The interesting thing is that if you dig a hole that forms a straight line between any two points on the earth, e.g., New York to London, and travel this hole purely under the force of gravity, the time it would take to traverse the distance would be the same, regardless of the relative location of the two points.

Except for the small fact that the two locations won't necessarily be directly opposite eachother, so you wouldn't be falling straight down the hole.
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Re: Physics 'challenge question' ceptnotrly

Postby uTP » Fri Mar 28, 2008 11:44 pm UTC

More or less meant as a joke:
I'd say she doesn't survives such a journey, due to the extremely high air pressure and gravitational force pulling her limbs apart at the centre of earth. So for a known period of time she or parts of her not disintegrated will be rushing from one side to the other, slowly ending their journey in the middle of the earth, because of air drag.

---

However, seeing as her boyfriend made it I assume the gravitational pull is neglectable in favor of her surviving and as she propably couldn't wait to see him again she fall with terminal velocity to the core, shoot straight up the other side and crawl the rest of the way up to the side he is resting. What then follows is free to imagination ;)...


[Edit] Added the first sentence, due to possible misunderstanding
Last edited by uTP on Sat Mar 29, 2008 9:03 pm UTC, edited 1 time in total.

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Re: Physics 'challenge question' ceptnotrly

Postby mrbaggins » Sat Mar 29, 2008 10:26 am UTC

Except for the small fact that the two locations won't necessarily be directly opposite eachother, so you wouldn't be falling straight down the hole.


That's why we ignore friction for these problems :P
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Re: Physics 'challenge question' ceptnotrly

Postby dardy_7 » Sat Mar 29, 2008 11:26 am UTC

Yr. 12 Physics answer: she would float in equalibrium because all the gravitational forces around her would be in balance
More importantly what type of shovel is this guy using and where can i buy one?
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Re: Physics 'challenge question' ceptnotrly

Postby evilbeanfiend » Sat Mar 29, 2008 1:21 pm UTC

uTP wrote:I'd say she doesn't survives such a journey, due to the extremely high air pressure and gravitational force pulling her limbs apart at the centre of earth.


there are no significant gravitational forces at the centre of the earth
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Re: Physics 'challenge question' ceptnotrly

Postby Xanthir » Sat Mar 29, 2008 3:14 pm UTC

evilbeanfiend wrote:
uTP wrote:I'd say she doesn't survives such a journey, due to the extremely high air pressure and gravitational force pulling her limbs apart at the centre of earth.


there are no significant gravitational forces at the centre of the earth

Geez, even if there was, I can hardly see why it would pull her limbs apart. Certainly it would just crush her. Unless her limbs are being pulled off by the gravity that is escaping thanks to *someone* puncturing the core...
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Re: Physics 'challenge question' ceptnotrly

Postby mavman2k8 » Sat Mar 29, 2008 5:21 pm UTC

ok I'm not a physicist, so please correct my mistakes on this ...

first of all: why does everyone say, that all of the earths gravitational pull pulls towards the center of the earth ? Most of the time for modeling purposes it makes no difference, but isn't actually every point of the "earth" that is occupied by mass pulling with the same strength ?
Ok so now with this assumption, forgetting for a moment that the earth doesn't stand still, and that the hole likely filled up with something resisty like air, lava or stuff, when the girl jumps into the hole that goes directly through the middle of the "earth", and is not in any way hindered in her movement by any form of mass that jumps in her way to toast her or give her the whole "you just ran headfront into a wall"-feeling, the gravitational force of the earth that acts on her in directions orthogonal to her movement, always amounts to zero, because we can safely assume, that the mass is spread out evenly across the ball that is earth and so there is always the same amount of mass in all orthogonal directions.
So this only leaves to check how the gravitational pull is along a straight line of lenght 2*(insert earth radius here). Since at both ends she is accelerated by 9.81 meters per second per second (inwards, i.e. we go from 9.81 to -9.81), and the whole thing seems so symmetrical I would guess this is just linear interpolation, isn't it ?
So now the next guess, because i'm to lazy to do integrating and stuff, although it's just one-dimensional i.e. school stuff, is that she'll make it barely out of the whole on the other side, grab on to some grass or whatever they have on the ground in kangaroo country and be happy with her boyfriend... except that this probably took so long that she, having forgotten her diving equipment, ran out of gas while flying through the vacuous hole ... O2 to be precise.

ok now lets slowly improve the modeling, the earth moves again, and the hole was digged orthogonal to the rotation axis of said movement. now girlfriend jumps in and starts her journey down the hole with the same acceleration downwards as before, but with an addes speed component in the direction of the movement of the earths surfaces where the hole is ... i.e. she'll quickly begin grinding against the eastern wall of the hole (because the earth rotates to the east [?] and the earth rotates slower towards the center, i.e. she'll be to fast in eastern direction) which slows her quite a bit and forces her to walk/climb back up from some point that i do not want to compute.

am i correct up to this point ? please help me physicists :)

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Re: Physics 'challenge question' ceptnotrly

Postby uTP » Sat Mar 29, 2008 5:26 pm UTC

Xanthir wrote:
evilbeanfiend wrote:
uTP wrote:I'd say she doesn't survives such a journey, due to the extremely high air pressure and gravitational force pulling her limbs apart at the centre of earth.


there are no significant gravitational forces at the centre of the earth

Geez, even if there was, I can hardly see why it would pull her limbs apart. Certainly it would just crush her. Unless her limbs are being pulled off by the gravity that is escaping thanks to *someone* puncturing the core...


was a bit of guessing at that part ..., sry if it's utterly idiotic.

I guess I thought you could treat the core as a kind of blackhole in the sence of gravitation. However, was i wrong at thinking her limbs would be pulled apart, due to the difference in gravitation, if she was falling into a blackhole? (sry for offtopic, just bugs me a bit)

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Re: Physics 'challenge question' ceptnotrly

Postby evilbeanfiend » Sat Mar 29, 2008 5:52 pm UTC

mavman2k8 wrote:ok I'm not a physicist, so please correct my mistakes on this ...

first of all: why does everyone say, that all of the earths gravitational pull pulls towards the center of the earth ? Most of the time for modeling purposes it makes no difference, but isn't actually every point of the "earth" that is occupied by mass pulling with the same strength ?


there are 3 reasons. 1st of all the planet is more or less spherical, 2nd the distribution of mass within the earth is more or less rotationally symmetric. 3rd it doesn't matter how many different things gravitaional fields you are in, what matters is what the force sums to.
if you do the maths for a sphere with uniform mass then you find the centre of gravity is at the centre of the sphere, the mass to the left or right of you all cancels out.

however it is also true that the planet isn't perfectly spherical and isn't of uniform density so there is slight variation in both the magnitude and direction of the gravitational force.
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Re: Physics 'challenge question' ceptnotrly

Postby Charlie! » Sat Mar 29, 2008 5:55 pm UTC

Trying to explain the "no gravitation force in the core" thing, Newton proved this really cool thing, that if you're inside a solid sphere (of any thickness) of matter, all the gravitational forces balance out and there's no attraction. So if the core were hollow, the secret alien society down there would have to live in a weightless environment.

A similar thing would happen to Terps if she were in this hole through the earth. The mass all around her, assuming it didn't cave in and squish her like an ant, would balance out so that she would feel essentially no gravitational force.



Also, why would you post /b/ 3@%(* in here? You're in Physics (3rd or 4th year high school?), which I assume means the average age of 4chan is younger than you.

Lastly, I say she burns up because of air resistance on the first pass, which you can pretty easily look at by assuming she's made of water, calculating the work done by simple F = v2*coefficient air resistance on her, and looking at how much energy it would take to raise a body mass of water from room temp to boiling (hint: do that last bit in calories and convert to joules at the end).
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Re: Physics 'challenge question' ceptnotrly

Postby evilbeanfiend » Sat Mar 29, 2008 6:00 pm UTC

i've never heard of people spontaneously combusting while skydiving, terminal velocity really ain't that fast (wikipedia reckons about 120 mph)
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Re: Physics 'challenge question' ceptnotrly

Postby EricH » Sat Mar 29, 2008 6:05 pm UTC

mavman2k8 wrote:Ok so now with this assumption, forgetting for a moment that the earth doesn't stand still, and that the hole likely filled up with something resisty like air, lava or stuff, when the girl jumps into the hole that goes directly through the middle of the "earth", and is not in any way hindered in her movement by any form of mass that jumps in her way to toast her or give her the whole "you just ran headfront into a wall"-feeling, the gravitational force of the earth that acts on her in directions orthogonal to her movement, always amounts to zero, because we can safely assume, that the mass is spread out evenly across the ball that is earth and so there is always the same amount of mass in all orthogonal directions.
So this only leaves to check how the gravitational pull is along a straight line of lenght 2*(insert earth radius here). Since at both ends she is accelerated by 9.81 meters per second per second (inwards, i.e. we go from 9.81 to -9.81), and the whole thing seems so symmetrical I would guess this is just linear interpolation, isn't it ?


Assuming the Earth is a constant density (which isn't true), then the acceleration anywhere in the tube is proportional to the distance from there to the center. In other words, when she has fallen 1/4 of the way down, (1000 miles) she is only accelerating at 3/4 g.

mavman2k8 wrote:So now the next guess, because i'm to lazy to do integrating and stuff, although it's just one-dimensional i.e. school stuff, is that she'll make it barely out of the whole on the other side, grab on to some grass or whatever they have on the ground in kangaroo country and be happy with her boyfriend... except that this probably took so long that she, having forgotten her diving equipment, ran out of gas while flying through the vacuous hole ... O2 to be precise.

ok now lets slowly improve the modeling, the earth moves again, and the hole was digged orthogonal to the rotation axis of said movement. now girlfriend jumps in and starts her journey down the hole with the same acceleration downwards as before, but with an addes speed component in the direction of the movement of the earths surfaces where the hole is ... i.e. she'll quickly begin grinding against the eastern wall of the hole (because the earth rotates to the east [?] and the earth rotates slower towards the center, i.e. she'll be to fast in eastern direction) which slows her quite a bit and forces her to walk/climb back up from some point that i do not want to compute.

am i correct up to this point ? please help me physicists :)


Yes--the force pushing her to one side of the hole is Coriolis force. Like centrifugal force, it appears when we translate Newton's laws into a rotating reference frame. (See this cartoon.)
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Re: Physics 'challenge question' ceptnotrly

Postby mavman2k8 » Sat Mar 29, 2008 6:29 pm UTC

physics is fun :P

now give me some funnier problems to think about ... where it's actually surprising what will happen ... not the laser through grid stuff they show you in high school ... something weirder :P

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Re: Physics 'challenge question' ceptnotrly

Postby niko7865 » Sat Mar 29, 2008 9:52 pm UTC

Something weird? Fusion of atomic nuclei.

(Specifically the quantum tunneling part)
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Re: Physics 'challenge question' ceptnotrly

Postby SWGlassPit » Sat Mar 29, 2008 10:13 pm UTC

mathmagic wrote:
SWGlassPit wrote:The interesting thing is that if you dig a hole that forms a straight line between any two points on the earth, e.g., New York to London, and travel this hole purely under the force of gravity, the time it would take to traverse the distance would be the same, regardless of the relative location of the two points.

Except for the small fact that the two locations won't necessarily be directly opposite eachother, so you wouldn't be falling straight down the hole.



Imagine, if you will, a frictionless train with massless wheels riding perfectly smooth rails along that path. The travel time will be the same regardless of the locations of the points.
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Re: Physics 'challenge question' ceptnotrly

Postby Mathmagic » Sat Mar 29, 2008 10:24 pm UTC

SWGlassPit wrote:
mathmagic wrote:
SWGlassPit wrote:The interesting thing is that if you dig a hole that forms a straight line between any two points on the earth, e.g., New York to London, and travel this hole purely under the force of gravity, the time it would take to traverse the distance would be the same, regardless of the relative location of the two points.

Except for the small fact that the two locations won't necessarily be directly opposite eachother, so you wouldn't be falling straight down the hole.



Imagine, if you will, a frictionless train with massless wheels riding perfectly smooth rails along that path. The travel time will be the same regardless of the locations of the points.

Sorry, somehow I skimmed over the disclaimer at the beginning about ignoring friction and air resistance. :)
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Re: Physics 'challenge question' ceptnotrly

Postby Oort » Sun Mar 30, 2008 2:07 am UTC

The centripedal/coriolis/centrifugal/whatever force will keep her on the east side of the hole all the way. Therefore (assuming she is a very good climber and runner) she can use this for traction, allowing her to scale the hole. Unless she's frictionless.

Or, alternatively, she can take an extremely massive object with her, than drop it after she reaches the halfway point. When I say extremely, I mean so large that it will iincrease her acceleration speed. The moon (compressed to fit into her handbag) perhaps.

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Re: Physics 'challenge question' ceptnotrly

Postby roundedge » Sun Mar 30, 2008 12:36 pm UTC

I know your teacher wants written answers only, but this is not really for you to turn in, this is more to ground the conversation.

I know most of the physicists here have seen this stuff, but I felt like doing it anyways, just to demonstrate that, damn it, science works.
WARNING: Calculus ahead
Spoiler:
at any point inside a solid massive uniform sphere, the gravitational acceleration at that point is a=-GM/r2 where r is the distance of the point from the center, and M is the mass contained in the sphere of radius r. Note that the gravitational pull from the mass outside of this sphere of radius r cancels itself out.

The mass contained within the sphere of radius r is M=µ(4/3)πr3 where µ is the density of the sphere.

so a=-Gµ(4/3)πr, Fgrav=-Gmµ(4/3)πr
but we have to include air friction!
so let's just say that the force due to air friction is just proportional to velocity
Ffric=-yv
now F=-Gmµ(4/3)πr-yv, a=-Gµ(4/3)πr-Yv (let Y=y/m)
dr2/d2t=-Gµ(4/3)πr-Y(dr/dt)
r''+Yr'+Gµ(4/3)πr=0
assume r has the form ezt
you get z2+Yz+Gµ(4/3)π=0
use the quadratic equation z=(-Y±sqrt(Y2-(42/3)Gµπ))/2
there's your solution for the motion of this girl
et*(-Y±sqrt(Y2-(42/3)Gµπ))/2
now, analysis is important:
unless the air friction coefficient is huge, z will be a complex number, and the girl will undergo harmonic motion, because eit=cos(t)+isin(t)
it's also interesting to note that her motion has nothing to do with her weight, only her shape.

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Re: Physics 'challenge question' ceptnotrly

Postby Charlie! » Sun Mar 30, 2008 6:49 pm UTC

evilbeanfiend wrote:i've never heard of people spontaneously combusting while skydiving, terminal velocity really ain't that fast (wikipedia reckons about 120 mph)


Oh, right, because of conduction, heat will get pulled out of her faster than she accumulates it. nvm then.
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Re: Physics 'challenge question' ceptnotrly

Postby ian » Sun Mar 30, 2008 7:26 pm UTC

roundedge wrote:it's also interesting to note that her motion has nothing to do with her weight, only her shape.


change her mass to that of the earth and wanna see if that holds true?

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Re: Physics 'challenge question' ceptnotrly

Postby Mathmagic » Sun Mar 30, 2008 8:20 pm UTC

ian wrote:
roundedge wrote:it's also interesting to note that her motion has nothing to do with her weight, only her shape.


change her mass to that of the earth and wanna see if that holds true?

Sure. The mass of the object is canceled by the m*a term in the equation of motion. The mass of the person is still inconsequential to the motion.
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Re: Physics 'challenge question' ceptnotrly

Postby roundedge » Sun Mar 30, 2008 10:38 pm UTC

actually, I was wrong, the Y term is equal to y/m, so there is a mass dependency, but I'm not sure how do conceptualize what exactly is going on with that.

In addition, if her mass were comparable to that of the earth, her acceleration wrt the center of the earth would change, because you'd have to include the acceleration of the earth towards her, which I had assumed was negligible in this scenario.

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Re: Physics 'challenge question' ceptnotrly

Postby Thunderbird4! » Mon Mar 31, 2008 2:29 am UTC

It is quite clear that she will survive since it is well known that the Earth is, in fact, flat. Once reaching the other side she will live out the rest of her life with the mermaids, unicorns and Olympian Gods that inhabit the other side of our flat Earth.

(Before I get ravaged by someone who can't tell, this is completely not serious and appealing to the most creative/funniest aspect of the question.)
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Re: Physics 'challenge question' ceptnotrly

Postby Korandder » Mon Mar 31, 2008 6:51 am UTC

Perhaps she help answer the question: What sex is Great A'Tuin, the turtle which supports the four elephants which support the world on their backs?

Sorry but I would much rather prefer to be reading Discworld than trying to finish an essay on the Jovian moon Europa.
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Re: Physics 'challenge question' ceptnotrly

Postby Celeritas » Mon Mar 31, 2008 2:21 pm UTC

Assuming we are talking about an average physics college class, she should stop missing Chris, climb back out and take advantage of the ratio of male to female physics students. Her movement would then be the shortest route to the pub.

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Re: Physics 'challenge question' ceptnotrly

Postby EricH » Mon Mar 31, 2008 8:34 pm UTC

Oort wrote:The centripedal/coriolis/centrifugal/whatever force will keep her on the east side of the hole all the way. Therefore (assuming she is a very good climber and runner) she can use this for traction, allowing her to scale the hole. Unless she's frictionless.


Correct--although, on the way up, it's the west side of the hole. (She doesn't switch sides in the middle, it's just a feature of the coordinate system.)

Oort wrote:Or, alternatively, she can take an extremely massive object with her, than drop it after she reaches the halfway point. When I say extremely, I mean so large that it will increase her acceleration speed. The moon (compressed to fit into her handbag) perhaps.


Incorrect. This is another error that was in the /b/ quote--I guess I should have addressed it, too....
There are two ways I can interpret your statement: 1) a massive object will increase her terminal velocity, so she falls faster through the air in the hole, or 2) since we're neglecting air resistance, a massive object will make her fall faster, because of gravity, so dropping it in the middle means less mass is coming up, and thus she can go fast enough to go all the way through.
Version 2 is false (see also Galileo); she is in free fall throughout the trip, so letting go of the extra mass at the midpoint will have exactly zero effect. It will continue traveling with her, all the way back up.
Version 1 is true, but the massive object continues to help on the way back up, so there's no good reason to drop it. In this case, in fact, letting go of the neutronium-filled handbag at the halfway point means that she slows down, and it keeps going without her.

Edit: She slows down a lot. See my next post.
Last edited by EricH on Tue Apr 01, 2008 2:57 am UTC, edited 1 time in total.
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Re: Physics 'challenge question' ceptnotrly

Postby tower668 » Tue Apr 01, 2008 1:24 am UTC

Has anyone considered how Chris actually dug the hole? Once he hit the center he would no longer have anything to stand on... so then how exactly does he dig upwards?

But assuming he is a really good digger, I would say that his girlfriend would have a very fun ride, assuming the hole stays open, yo-yo-ing back and forth until she becomes weightless and crawls out (on the east side?) ... hopefully remembering which way she is suppose to go.

The real question that should be answered is how long would she be yo-yo-ing for ...

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Re: Physics 'challenge question' ceptnotrly

Postby EricH » Tue Apr 01, 2008 2:55 am UTC

tower668 wrote:Has anyone considered how Chris actually dug the hole? Once he hit the center he would no longer have anything to stand on... so then how exactly does he dig upwards?


And, indeed, where does he put the material he's removing? Perhaps he compresses it into a strong wall around the sides of the hole, to protect himself from the heat and pressure?

tower668 wrote:But assuming he is a really good digger, I would say that his girlfriend would have a very fun ride, assuming the hole stays open, yo-yo-ing back and forth until she becomes weightless and crawls out (on the east side?) ... hopefully remembering which way she is suppose to go.

The real question that should be answered is how long would she be yo-yo-ing for ...


Without air resistance, the question has already been answered--by roundedge and calculus.

Change the problem to include calculating the air resistance.... And the ride isn't very fun. Because the pressure goes up as she falls, and the acceleration of gravity goes down, her terminal velocity rapidly decreases. Ballpark estimate, after 10 hours or so, she's fallen about 270 miles, she's down to 94% gravity, she's under 8 3/4 atmospheres of pressure (equivalent to a dive of ~230 feet) and her terminal velocity is around 13 miles an hour. Without breathing gear, this is where she dies, because oxygen is toxic at that pressure.
Something over a year later, her corpse drifts gently into the vicinity of the Earth's center. That is, within 50 miles or so. She's down to 1% of surface gravity, under around 67 atmospheres of air pressure, equivalent to a dive of maybe 2000 feet. She's still 'falling', if you want to call it that, at about one foot per minute (terminal velocity for a human, with that much pressure and that little gravity). She will never be 'yo-yo-ing', because her motion will be completely damped out by air resistance.

So, really, the neutronium handbag is her only solution for keeping up speed; if she lets go of it at the midpoint, she won't get anywhere near the surface again. (She'd need a heat shield anyway--by the midpoint, holding on to it, she'll be moving at the same speed as a space shuttle beginning re-entry, through that 60-odd atmospheres of air pressure... The numbers get ridiculously high. You know how they say falling a hundred feet onto water is almost the same as falling on concrete? At these speeds and pressures, air is like that.) Assuming she holds together, she'll stop rising in a matter of seconds, and again, drift verrry slowly toward the center of the Earth.
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Re: Physics 'challenge question' ceptnotrly

Postby idobox » Wed Apr 02, 2008 9:06 pm UTC

Assuming there is no air in the hole, and that it is curved so that Coriolis force won't push her against the wall, there is still a huge hazard:
We get an ohmic conductor traveling pretty fast in a variable magnetic field. I don't know the strength of the earth's magnetic field, and I am not sure anyone knows it, and neither do I know the resistivity of an average teenager, so I cannot give numerical values, but I guess she will experience strong induction that will cook her while falling.
She will also experience Foucault's force that will slow her down. But as the different parts of her body have different conductivity, this force won't be equal everywhere. And because her cooked body should end up as charcoal with low cohesion, her corpse will probably disperse in chunks.
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Re: Physics 'challenge question' ceptnotrly

Postby BlackSails » Wed Apr 02, 2008 9:56 pm UTC

Yes, she will come out the other side, as long as she jumps in, rather than stepping in.

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Re: Physics 'challenge question' ceptnotrly

Postby Mathmagic » Wed Apr 02, 2008 10:04 pm UTC

BlackSails wrote:Yes, she will come out the other side, as long as she jumps in, rather than stepping in.

How do you figure?
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Re: Physics 'challenge question' ceptnotrly

Postby BlackSails » Wed Apr 02, 2008 10:31 pm UTC

mathmagic wrote:
BlackSails wrote:Yes, she will come out the other side, as long as she jumps in, rather than stepping in.

How do you figure?


Assuming no air resistance, you will oscillate between the two ends. If you jump in, you will oscillate between just above the earth, to just above the earth on the other side. This way he can easily kick off the side of the tunnel at the end, and make it onto land.


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