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The hole through the center of earth?





D'Artagnan
I've seen this question in another forum and in a magazine, i think the questiong is just amazing, but reading peoples theories is more amazing Smile


What if someone could make a hole in the earth: from one side to another, let's say from north pole to south pole, passing right throught the center of earth. Then this same person (who have much spare time Razz) place ping-pong ball right in the middle of this hole, and let it fall down. What would happen to the ping-pong ball?
Bikerman
D'Artagnan wrote:
I've seen this question in another forum and in a magazine, i think the questiong is just amazing, but reading peoples theories is more amazing Smile


What if someone could make a hole in the earth: from one side to another, let's say from north pole to south pole, passing right throught the center of earth. Then this same person (who have much spare time Razz) place ping-pong ball right in the middle of this hole, and let it fall down. What would happen to the ping-pong ball?

Well, the scientific answer is that it would melt Smile
However, assuming we take heat and other considerations out of the question then it would pass slightly beyond the centre before gravity took effect and it would then 'bounce' back and forward until it came to rest in the centre. Because of wind resistance and low mass then the ball would not go too far beyond the centre - perhaps a better case would be a lead ball.
Cmink32
I am actually really surprise that I found this topic because I actually had this conversation with my CISCO teacher today. Agreeing with Bikerman we would have to first take heat and any obstacles out of consideration. But if you could someone make a tube like structure through the earth, allowing for a clear passage to the other side a very remarkable thing would happen. I will try not to put to much physics into this explanation but I can't promise anything.

When an object, any object, be it lead, plastic, rubber, or a person, falls due to gravity alone they accelerate at 32ft per second squared. This means that for every second you fall you are falling 32 feet per second faster up to a maximum speed of 17,700 mpd. As the object falls towards the center of the earth it would accelerate until it reaches the exact center of the given path. At this point it would begin to slow down at a rate of 32ft per second every second it continues going. This means that it would not see a huge decease in speed after passing the center of the path but rather it would see a decrease in speed directly opposite the increase that it saw falling, causing it to come to a complete stop right as it reached the surface on the other side of the planet in about 42 minutes. The truly remarkable aspect of this is that the hole would not have to be straight through the planet for this to work.

For example, it you made a hole from New York to Paris, once again taking heat out of the equation, the trip would still take about 42 minutes because gravity would only be able to propel you to a lower speed before you passed the half way point and gravity began to slow you down again.

Hopefully I didn't confuse anyone to bad. If you have any questions about any of this please ask.
Bikerman
No, fraid not.
The thing that this leaves out is air resistance. Any body falling in air has a 'terminal velocity' which is much less that the velocity it could attain in vacuum. Drop a ping pong ball off a tall building, for example, and it will never get above (at a guess) about 30mph. Drop a man out of a plane and the terminal velocity is around 120mph.
This means, of course, that no object would ever get close to the maximum speed you quote.

Your CISCO teacher has also made another basic mistake when doing the sums. The 'force' of gravity actually depends on the mass and square of distance. As you move through the earth g actually increases slightly until you get to the outer core (this is because the core is much denser than the mantle and crust - the calculation is complex but trust me on this - we went through it in some detail at the science forums). At the boundary of the outer core g has a value of around 10.8 m/sē (as compared to about 9.8 at the surface). Gravity then drops in a straight line until it reaches a value of 0 at the exact centre of the earth...

The final problem with this scheme is that if the path were not straight (ie straight through the earth) then the falling object would be in more or less constant contact with the surface through which it was moving (be it a tube or whatever). This would, of course, generate friction which would further limit the terminal velocity. This means, of course, that the object - whatever it was, would never arrive at the destination. It would have slowed to zero well before and began to fall back towards the centre. It would repeat this over and over until, finally, it settled at the centre.
Cmink32
Guess I am going to have to bust out some physics equations. Hold on tight, here we go.


Starting out your acceleration would be initially effected by the amount of gravity on earth surface. This would be


g=GM/R(squared)=9.8m/s (squared)


and you are correct that acceleration would become progressively less as you got closer and closer to the center. But your weight would also become less and less as you got closer. But seeing as this trip though the center would never be possible anyways you must take air resistance and temperature out of it. This, in turn, would cause us to take out density of the planet, because the only way for a spinning body of the earth's size to be the same density would be if it was the same temperature uniformly and if there was no air in the hole. So as for the gravity as you wall through here it is.

g=GM(r)/r (squared)

M(r)=p(4/3) pi r (cubed)

p=M/(4/3) pi R(cubed)

g=GMr (cubed)/r(squared)R(cubed)= g(r/R)

This also bring up the point that in a sphere the power of gravity would be proportional to the distance you are from the center in our given situation. So if positive r is, from the center of the earth, outward,

F=-mg(r/R)=-kr


This would cause the object to travel back and forth through the center of the earth.

Angular Frequency is:

w= square root of k over m

period of time is:

T=2 pi multiplied by the square root of m over K

So for our given situation the length of the trip to one side and back is:

T=2pi multiplied by the square root of mR/mg = 2pi multiplied by the square root of R/g

Where R=63.78x10(to the sixth power)m

and T=5068sec or 84.5 minutes

You would accelerate towards the center till you hit a speed of 7900 m/s ~17,700 Mph. This would cause you to reach the other side at ~42 minutes and a subsequent return to the other side in about ~42 minutes. But of course this hypothetical journey would never be possible. But this equation can also be put to any hole that is not through the direct center an as I stated before you would get an amazing result as your answer. The time it would take to fall through any whole that connects two point on earth surface in a linear fashion would take ~42 minutes one way.



p.s. I major in physics Smile
newolder
D'Artagnan wrote:
I've seen this question in another forum and in a magazine, i think the questiong is just amazing, but reading peoples theories is more amazing Smile


What if someone could make a hole in the earth: from one side to another, let's say from north pole to south pole, passing right throught the center of earth. Then this same person (who have much spare time Razz) place ping-pong ball right in the middle of this hole, and let it fall down. What would happen to the ping-pong ball?

This concise explanation should help: http://www.yale.edu/phys180/lecture_notes/180_Lect_31/sld007.htm

The ping-pong ball (in the absence of friction) reaches the opposite pole in 42 minutes.

http://hyperphysics.phy-astr.gsu.edu/Hbase/mechanics/earthole.html
and
http://digg.com/general_sciences/42_Minutes_to_Anywhere_Express_Elevator_Through_the_Earth
Bikerman
Ed, come on mate - it's a load of baloney. It is such an idealised version of events that all the interesting physics goes out of the water. Assuming uniform density for the earth makes this, at best, an A level question. It would be a much more challenging problem to deal with the real variation in g as you go 'down'. Fancy a go? Smile

Cmink32 - physics major you may well be, but speaking as a lecturer (not in physics), had you handed me this as an assignment I would strongly suspect that you had copied it from the hyperphysics site* and given you an F. There's nothing wrong with using other sources in assignments but the golden rule applies - cite your sources.

* (
The give-away is twofold:
a) The sequencing of your working matches exactly with the hyperphysics site.
b) You use p for rho - ρ - (density) without explanation.
)
The_Longshot
Could this "hole" be applied to the moon? And/or be made to act like a Faraday Flashlight? The body need to have a rational spin, I think.
metalfreek
If you were able to drill a hole through the earth than drop a ball in it than it will move simple harmonically (SHM). The ball will fall from north pole to the south pole and than return to north pole again and this process continues hence creating a simple harmonic motion.
killianvillian
I vote for Cmink32's as the most convincing answer to invest my twinkie into.

I only say that because it seems to hint the most clearly at the fact that so many realities have to be removed to even consider it possible. Which means to me, that every answer is equally wrong for even trying.

But also, this one gets more positive points by acknowledging this the most clearly.

So if i havent won on this account yet, my ridiculous conlusion is that if we made a hole in the middle of the earth, so many problems would occur with the climate, gravity (from density loss of course), religious war, zombie war, war on war action, that there wouldn't really be a condition to stand next to the hole and drop the ping pong ball in.

Lets be thankful if we have the last ping pong around and play together in flatland.

To be sure, the equation that solves for this problem is:

g+h*l/e = 34.443

confirm or deny.
TrueFact
Why don't you look to the bigger picture (excluding heat and melting the ball)?

I'm not a physics expert, but simply what causes the gravity? it is the mass of earth spinning around itself, right?

When you dig that hole, there's no more mass spinning in the center to drag the ball towards it! In other words, the ball will roll over on the hole wall. So you can add air resistance and friction against the walls.

Anyways, From my point of view, assume the that the exact center of earth is vacuum and the ball will be, practically, affected by the mass around the hole walls.

Well, I guess you guys are better than me to do the mat Smile

But, is it practically right?
Bikerman
No...the 'spinning' part is wrong. Gravity is caused by mass - spinning or not. The spinning motion produces another force which subtracts from gravity - we call it centrifugal force but that is a bit of a misnomer since what is really happening is that a body at the equator tries to carry on moving in a straight line, whilst gravity pulls it down to earth..
At the centre of the earth (presuming the earth was a perfect sphere of uniform density) then there would be an equal 'pull' of gravity from every direction. This would cancel to leave no net gravitational attraction.
killianvillian
Any ideas what effects the loss of the magnetic field would have on this situation.

Without a rotating liquid center, we would have a hard time dropping ping pong ball with all the cancer in us and whatnot.
Bikerman
killianvillian wrote:
Any ideas what effects the loss of the magnetic field would have on this situation.

Without a rotating liquid center, we would have a hard time dropping ping pong ball with all the cancer in us and whatnot.

The loss of the Earth's magnetic field would have little, if any, effect on this scenario. Despite the lunatic theories of some internet trolls, we are actually held down by gravity, not magnetism. I have seen websites which seriously propose that there is no such thing as gravity and that what we perceive as gravity is actually some form of electromagnetism. Laugh? I nearly bought a round.

Not sure what the reference to cancer means...
leontius
This concept has been proposed before actually... http://en.wikipedia.org/wiki/Gravity_train

Quote:
A gravity train is a theoretical means of transportation intended to go between two points on the surface of a sphere, following a straight tunnel that goes directly from one point to the other through the interior of the sphere.

In a large body such as a planet, this train could be left to accelerate using just the force of gravity, since, during the first half of the trip (from the point of departure until the middle), the downwards pull towards the center of gravity would pull it towards the destination. During the second half of the trip, the acceleration would be in the opposite direction relative to the trajectory, but (ignoring the effects of friction) the speed acquired before would be enough to cancel this deceleration exactly (so that the train would reach its destination with speed equal to zero).


Also we don't have to pierce right through the center of the earth; a hypocycloid is fine and the tunnel can be made from anywhere to anywhere.
ocalhoun
leontius wrote:

Also we don't have to pierce right through the center of the earth; a hypocycloid is fine and the tunnel can be made from anywhere to anywhere.

Hm, that could be used to make a very energy-efficient train... You have to ignore extreme difficulties in building it though.
killianvillian
Quote:
Not sure what the reference to cancer means...


I was just trying to be brief. But i was referring to the fact that extra solar radiation that is normally deflected by the magnetosphere, would now enter, and we would die before being able to test this theory.

*cough*

Ill be quiet now...
manlear
Cmink32 wrote:
I am actually really surprise that I found this topic because I actually had this conversation with my CISCO teacher today. Agreeing with Bikerman we would have to first take heat and any obstacles out of consideration. But if you could someone make a tube like structure through the earth, allowing for a clear passage to the other side a very remarkable thing would happen. I will try not to put to much physics into this explanation but I can't promise anything.

When an object, any object, be it lead, plastic, rubber, or a person, falls due to gravity alone they accelerate at 32ft per second squared. This means that for every second you fall you are falling 32 feet per second faster up to a maximum speed of 17,700 mpd. As the object falls towards the center of the earth it would accelerate until it reaches the exact center of the given path. At this point it would begin to slow down at a rate of 32ft per second every second it continues going. This means that it would not see a huge decease in speed after passing the center of the path but rather it would see a decrease in speed directly opposite the increase that it saw falling, causing it to come to a complete stop right as it reached the surface on the other side of the planet in about 42 minutes. The truly remarkable aspect of this is that the hole would not have to be straight through the planet for this to work.

For example, it you made a hole from New York to Paris, once again taking heat out of the equation, the trip would still take about 42 minutes because gravity would only be able to propel you to a lower speed before you passed the half way point and gravity began to slow you down again.

Hopefully I didn't confuse anyone to bad. If you have any questions about any of this please ask.


Basically what he is trying to say is, you will never get through the middle of the earth. You will get stuck in the middle by the enormous gravitational pull.
japfart
cmink32 looks like you got bikerman jelous bikerman jelousieeeeeeeeeeeeeeeeee hahaha i like it cmink
chatrack
Due to gravity the ball slide closer to side walls and finally rolls over it in a spiral path
pscompanies
Wow. The Hollow Earth Theory.
BigGeek
I just got done reading this whole post and I have to say I didn't think Bikerman came across a jealous............he was just pointing out that cmink got his info from somewhere else, and didn't site his sources. I actually think he demonstrated that he is quite a bit more knowledgeable about this as he knew where cmink got the info in his post from.

That aside, I thought that this was gonna be one of those hollow earth conspiracy theory posts, and I was gonna jump in and blow it out bey pointing out all the seismic work done to map out the continent and sea floor thicknesses, the depth of the plates as they subduct all the way through the mantle, the islands on the core mantle boundry mirroring the continents on the surface and so on, and so forth and point out that the hollow earth theory is BS, and only an uneducated person might think that.....but it was about a theorietical problem in none reality. Oh well!

But I also found out that there are those that think that gravity doesn't exist.....that's a new one. Wonder how that works......ummm on second thought I really don't want to know Laughing Shocked
soljarag
interesting topic... I would love to see a computer simulation of this test!
tony
Great discussion topic! Wouldn't it be fantastic if we could travel through the earth to the other side of the world and back? It would be quite a bit faster than today's air travel but making the hole would be an incredibly difficult task. Has anyone here hard of the Kola SuperDeep Borehole? It's the deepest hole ever drilled and even so it was only about 12 km deep. When you drill that deep, temperature becomes a huge problem. Here's the wikipedia page on the Kola Superdeep Borehole: http://en.wikipedia.org/wiki/Kola_Superdeep_Borehole
Chinmoy
that would rewrite many maths and physics books..lol
Bikerman
Chinmoy wrote:
that would rewrite many maths and physics books..lol
Err...why?
Quote:
I just got done reading this whole post and I have to say I didn't think Bikerman came across a jealous
Nope, Bikerman isn't jealous at all. I frequently partake in discussion with people who know FAR more than I do, and I have no problem with that. Ed (newolder), for example, has probably forgotten more maths than I know.
The point I was trying to make is that this, as a theoretical exercise, is not really difficult, or particularly interesting - in fact it is a sub-A level question. All the things that make it an interesting 'real world' proposition have been 'idealised out'.
a) We know that gravity is much more complex for the earth than for an ideal sphere of uniform density. In fact I went to a fair bit of effort to calculate how g varies with depth. That would make it a far more interesting physics problem and a more accurate model.
b) Air resistance is not a trivial factor. You can propose evacuating a tunnel 2000 miles long (or whatever), but the difficulties of getting any sort of reasonable vacuum would be immense.
c) Friction is also not a trivial factor. How are you going to avoid thermal problems from friction when the train is moving at many times the speed of sound over the 'track'. Maglev would be one possible option.
skippythegoat
i guess technically, an axis would be a big hole going through the center of the earth, but if there literally was a whole, it would just be a core, or emptyness, because there isnt really a way to do that in a sphere. to everyone else, it would be flipped or lopsided...
lucian0127
I think guatemala city has answer the questions, this city has a deep and biggest hole in earth... look at the image below.

ocalhoun
lucian0127 wrote:
this city has a deep and biggest hole in earth... look at the image below.

Biggest, hm?
Afraid I must disagree;
The biggest hole* is an impact crater in Australia:

It has a 15 mile (24km) diameter and goes down to 16,400 ft (5,000m).

*Not counting holes filled with water
menino
Interesting that if you fall through the hole at 32ft per second you would reach the other side in 42 minutes.

Question is that when you fall, you have gravity taking you to the center, but when coming out the other side, shouldnt you have gravity going against you?
Bikerman
menino wrote:
Interesting that if you fall through the hole at 32ft per second you would reach the other side in 42 minutes.

Question is that when you fall, you have gravity taking you to the center, but when coming out the other side, shouldnt you have gravity going against you?

*sigh* Have you read the thread or did you just not understand it? It is all explained.
lucian0127
ocalhoun wrote:

Biggest, hm?
Afraid I must disagree;
The biggest hole* is an impact crater in Australia:

It has a 15 mile (24km) diameter and goes down to 16,400 ft (5,000m).

*Not counting holes filled with water


Wow! Thanks for that information mate, i'd never heard that one before Shocked
HalfBloodPrince
menino wrote:
Interesting that if you fall through the hole at 32ft per second you would reach the other side in 42 minutes.

How would it reach the other side? Gravity pulls from the center inwards. Once the ball passes the center it would require an even larger body than the Earth on the other side to pull it. Since that isn't there, it would eventually stabilize right in the middle. Or am I missing something?
Bikerman
HalfBloodPrince wrote:
menino wrote:
Interesting that if you fall through the hole at 32ft per second you would reach the other side in 42 minutes.

How would it reach the other side? Gravity pulls from the center inwards. Once the ball passes the center it would require an even larger body than the Earth on the other side to pull it. Since that isn't there, it would eventually stabilize right in the middle. Or am I missing something?
Yes, you are missing inertia. The astronaut has been accelerating for some time. He stops accelerating when he reaches the middle. He then has a lot of slowing down to do, which will take him most of the way up to the surface. In the end, of course, the energy lost to friction (heat) would make the distance smaller and smaller...but it would take considerable time. Then there are assumptions such as the magnetic field is even (it isn't), and that it's actually feasible to travel at space-shuttle speeds (it isn't, yet anyway), and that we could build it (not even close - our deep mines go down a very few miles...)...
eday2010
menino wrote:
Interesting that if you fall through the hole at 32ft per second you would reach the other side in 42 minutes.

Question is that when you fall, you have gravity taking you to the center, but when coming out the other side, shouldnt you have gravity going against you?


You wouldn't come out the other side. Gravity would pull you back to the middle. I also assume that since gravity is strong enough to pull everything towards the Earth and to keep the moon in orbit, that at the center, the gravity is strong enough to crush you.
ocalhoun
eday2010 wrote:

You wouldn't come out the other side. Gravity would pull you back to the middle.

You would come close though, before gravity began to pull you back to the center. A (relatively) small boost at the exit of the hole could get you to the other side. How close you get to the other side depends on your ratio of weight to friction (air resistance).

Bikerman makes a good point in that you would reach some very high speeds, and it would be very difficult to prevent burning up due to heat from air friction. (Especially since the air at the center of the hole would presumably be much denser.)

The hole would work so much better if you pumped all the air out of it!
Bikerman
eday2010 wrote:
You wouldn't come out the other side. Gravity would pull you back to the middle. I also assume that since gravity is strong enough to pull everything towards the Earth and to keep the moon in orbit, that at the center, the gravity is strong enough to crush you.
No, you have a basic misconception. Gravity at the centre is effectively zero because equal mass is acting on you in all directions which 'cancels out'.
Starrfoxx
The pictures of that crater are humungous!
LittleBlackKitten
My take on this theory;

Burning to a crisp from heat aside, I believe the force at which gravity would pull you down at a constant lessening rate would in fact slow you down, then after you pass the core, those slowing effects double as you progress on, as you're fighting gravity. I elieve you (or the poor ping pong ball) would eventually settle in on the core, where you would promptly die (either from oxygen in the blood or heat as well) from the sheer stress on your body from the gravitational forces shoving you from all sides into the center.
ocalhoun
LittleBlackKitten wrote:

Burning to a crisp from heat aside, I believe the force at which gravity would pull you down at a constant lessening rate would in fact slow you down,

No, gravity would still be accelerating you until you reached the center of the Earth. The rate of that acceleration would slow down, yes, but you're still being accelerated until you reach the center.
Bikerman
LittleBlackKitten wrote:
My take on this theory;

Burning to a crisp from heat aside, I believe the force at which gravity would pull you down at a constant lessening rate would in fact slow you down, then after you pass the core, those slowing effects double as you progress on, as you're fighting gravity. I elieve you (or the poor ping pong ball) would eventually settle in on the core, where you would promptly die (either from oxygen in the blood or heat as well) from the sheer stress on your body from the gravitational forces shoving you from all sides into the center.
You have some serious misconceptions regarding the basics.
a) How can a force acting positively along the axis of movement slow the body down? (Answer - it can't). The body accelerates (theoretically) until it reaches the centre, after which gravity then acts negatively along the same axis decelerating the body.
b) In reality the heat would have killed any living organism well before it reached the centre. There is an increase in temperature of 25-30(C) for each km you go 'down', so within a very small distance you would be cooked, and in not much further distance you would be liquified/sublimated.
c) There is no 'stress' produced at the centre of the earth from gravity. You can imagine all the different forces cancelling out to leave no overall force acting at all.
eday2010
ocalhoun wrote:

No, gravity would still be accelerating you until you reached the center of the Earth. The rate of that acceleration would slow down, yes, but you're still being accelerated until you reach the center.


Gravity would accelerate you until you hit terminal velocity, which is 122 mph if you are falling free-fall style. If you pull your arms in, you'll go faster, and if you dive head first, you'll go even faster, but neither will cause you to burn up, and the max speed reached by a person was 624 mph.
Bikerman
I presume you mean Kittinger's freefall. The actual speed was probably 614mph, according to Kittinger himself, though various claims exist, up to 724 mph. I'm not sure where the 624mph comes from - never seen that before..
ocalhoun
eday2010 wrote:
ocalhoun wrote:

No, gravity would still be accelerating you until you reached the center of the Earth. The rate of that acceleration would slow down, yes, but you're still being accelerated until you reach the center.


Gravity would accelerate you until you hit terminal velocity, which is 122 mph if you are falling free-fall style. If you pull your arms in, you'll go faster, and if you dive head first, you'll go even faster, but neither will cause you to burn up, and the max speed reached by a person was 624 mph.

Assuming we don't pump the air out of it, yes.
Hm, supposing we prevented the Earth's core from entering it, we would still have a bigger problem than air... It would tend to fill up with water.
JOHNNYTREMPs
Ive just got one question for bikerman, can you tell me if the rotation of the earth would have any effect on the travel of the ball?
kelseymh
JOHNNYTREMPs wrote:
Ive just got one question for bikerman, can you tell me if the rotation of the earth would have any effect on the travel of the ball?


Now that's a good question, and one which is almost always neglected in these discussions! To make the calculation simple, we'll work the problem in the frame of a distant observer, watching the Earth rotate (we could do it in a frame attached to the rotating Earth, but it's more complex), and let's put everything right at the equator, so that the rotational axis, tunnel, and ground are mutually perpendicular.

The angular velocity is 360 degrees per day; the circumference is about 25,000 miles, so at the equator the linear velocity due to rotation is just over 1,000 miles per hour. Since the Earth rotates as a rigid body, the angular velocity (degrees per second) is constant. That means as you go deeper, the linear velocity drops, and is exactly zero at the center of the Earth. For example, 3,200 miles down (halfway), the linear velocity will be just ~500 miles per hour.

At the top of the tube, the ball will share the Earth's rotation at the local surface (since you or a machine is holding the ball in place over the hole, and you or that machine are standing still on the ground, etc.).

But the ball is falling freely. The only force is gravity, and it is acting perpendicular to the direction of rotation (that's why I wanted to do this problem at the equator!), which means it cannot change the ball's original tangential velocity. So as the ball falls, it will be moving sideways faster than the walls of the tube around it, and will crash into the side wall.

Suppose that you make the ball just fit in the tube, so that it's sliding through rather than freely falling. Then the tube walls will be pushing on the ball with a sideways force. That force can (and will!) change the ball's tangential velocity as it falls.
JOHNNYTREMPs
thanks. it was a little hard to understand, but i think i got it.
Bikerman
I can't improve on Mike's description so I won't try. Smile
kelseymh
JOHNNYTREMPs wrote:
thanks. it was a little hard to understand, but i think i got it.


It's a hard problem (one that I would assign to a freshman physics course, probably late first quarter or second quarter).

If you want to think about it qualitatively, picture holding a tube in your hand and drop a ping-pong ball through it. If you move the tube to one side while the ball is falling, the ball will hit the side of the tube, right? From the ball's perspective, that's just what is happening -- it's "just falling," but the tube is moving to the side as it falls.
Bikerman
It is also suprisingly deep because it begs the question - does gravity act instantly? (ie does the 'attractor' for the falling ball exert its influence immediately, or does the change in the direction of 'pull' take some time to 'get there').
(Granted that in this particular scenario the difference is probably immesurably small).
ocalhoun
kelseymh wrote:


But the ball is falling freely. The only force is gravity, and it is acting perpendicular to the direction of rotation (that's why I wanted to do this problem at the equator!), which means it cannot change the ball's original tangential velocity. So as the ball falls, it will be moving sideways faster than the walls of the tube around it, and will crash into the side wall.


So, does that mean that all vertically traveling bodies on Earth are subject to this effect?
(ie, if you shot a ball up into the sky, would it therefore move slower than the Earth's rotation and tend to move a little sideways? Hm... perhaps it would be simpler to think about that as being on a rotating planet that doesn't have an atmosphere.)
Maybe it's just too small to notice on the usual scales...
Bikerman
The effect is certainly real and is illustrated nicely by Focault's Pendulum

The problem with real world examples is that, of course, the atmosphere is dynamic. It is. itself, 'moving', so any calculation would have to factor the relative movement of the atmosphere to make any sense.
kelseymh
ocalhoun wrote:
kelseymh wrote:

But the ball is falling freely. The only force is gravity, and it is acting perpendicular to the direction of rotation (that's why I wanted to do this problem at the equator!), which means it cannot change the ball's original tangential velocity. So as the ball falls, it will be moving sideways faster than the walls of the tube around it, and will crash into the side wall.


So, does that mean that all vertically traveling bodies on Earth are subject to this effect?


Yes, indeed. As Bikerman noted, the Foucault pendulum is the classic demonstration of this. However, for most applications the effect is just too small to notice (the ratio of distances from the center of the earth). The long-range guns on battleships, for example, have to take Coriolis effects into account.
yagnyavalkya
By digging deep holes one can harness geothermal energy
ocalhoun
yagnyavalkya wrote:
By digging deep holes one can harness geothermal energy

Only in places where said geothermal energy is close to the surface. In most places, digging a hole that deep would not be cost effective, and might not be possible at all with current technology.


Digging a hole to pump a coolant/heating fluid through in order to take advantage of the thermal mass though... now that's a more practical idea. You don't have to dig very far to find levels that will stay at constant temperature no matter what the outside weather -- or even outside season -- is.
By using that constant-temperature mass, you can cool things off during the summer, and/or heat things up in the winter.
ie, you get some of the temperature-regulation benefit of underground construction without the problems involved in building underground.

In this example, you can see that the temperatures are much more stable as depth below ground increases:

(X = depth)
(The exact numbers will vary by climate and by soil type.)
therimalaya
We can use the hole for different purpose like transportation, transmission on energy... and more...
cresvale
That's just impossible
chatrack
Hi,
Yes It is theoretically possible. Or it remain as a thought problem. I think we can computer stimulate
and find what actually happen. Do you know any stimulation programs that can help us ?

I think the pressure at the lower regions of earth will raise to so high that , density of air become
too much. The falling object soon attain a Terminal Velocity.

So it eventually land at the center of the earth, slowly. Finlay rest some were near center of earth.

I think so Rolling Eyes
EEThomas
Cmink32 wrote:
Guess I am going to have to bust out some physics equations. Hold on tight, here we go.


Starting out your acceleration would be initially effected by the amount of gravity on earth surface. This would be


g=GM/R(squared)=9.8m/s (squared)


and you are correct that acceleration would become progressively less as you got closer and closer to the center. But your weight would also become less and less as you got closer. But seeing as this trip though the center would never be possible anyways you must take air resistance and temperature out of it. This, in turn, would cause us to take out density of the planet, because the only way for a spinning body of the earth's size to be the same density would be if it was the same temperature uniformly and if there was no air in the hole. So as for the gravity as you wall through here it is.

g=GM(r)/r (squared)

M(r)=p(4/3) pi r (cubed)

p=M/(4/3) pi R(cubed)

g=GMr (cubed)/r(squared)R(cubed)= g(r/R)

This also bring up the point that in a sphere the power of gravity would be proportional to the distance you are from the center in our given situation. So if positive r is, from the center of the earth, outward,

F=-mg(r/R)=-kr


This would cause the object to travel back and forth through the center of the earth.

Angular Frequency is:

w= square root of k over m

period of time is:

T=2 pi multiplied by the square root of m over K

So for our given situation the length of the trip to one side and back is:

T=2pi multiplied by the square root of mR/mg = 2pi multiplied by the square root of R/g

Where R=63.78x10(to the sixth power)m

and T=5068sec or 84.5 minutes

You would accelerate towards the center till you hit a speed of 7900 m/s ~17,700 Mph. This would cause you to reach the other side at ~42 minutes and a subsequent return to the other side in about ~42 minutes. But of course this hypothetical journey would never be possible. But this equation can also be put to any hole that is not through the direct center an as I stated before you would get an amazing result as your answer. The time it would take to fall through any whole that connects two point on earth surface in a linear fashion would take ~42 minutes one way.



p.s. I major in physics Smile


Good post. Only next time use 63.78 x 10^5 m or 6.378 x 10^6 m. This mistake actually confirms that you used a website to get this info because you and that website { http://hyperphysics.phy-astr.gsu.edu/Hbase/mechanics/earthole.html } make the same mistake. You should never trust another persons calculations unless you have done them yourself. A good physics major would know this.
cr8agame
It would be almost impossible to have a hole through the centre of the earth as the core will pull the object in and you couldn't get out the other side. Also, depending on the drill you use the heat will be so intense the drill would just melt.

I don't think we will ever make a hole through the centre of the earth.
crystalkey
I agree with the first response. It would just melt, or be caught on a rough sided surface on the way down. I'm assuming that the sides of the hole are not perfectly smooth here ...
stagga
Quote:
A frequently asked question!
If it were possible to dig a hole through the earth; and then jump in (ignoring the effect of air friction), you would pass right through the earth, and emerge at the other side. At the center, there would be no gravitational attraction, because the gravity from all sides would cancel out. But you would have developed a very high velocity at that point. The velocity would be sufficient to carry you right through to the other side, at which point, the acceleration you made in falling through the hole would be matched by the earth's pull of gravity, and you would come to a halt; only to fall back through again. In effect, without air resistance; you would form a perfect oscillating pendulum, falling from side to side like a yo-yo. Of course, air friction would slow you down, until you came to rest at the earth's center: a rather hot and unpleasant place to be.

Hypothetically, if it were possible to bore a hole through the earth (entirely impractical) and build an evacuated tube; the whole journey from side to side would only take about 90 minutes - cheap and quick transport, eh?
In fact the tube would not have to go through the center; but a journey through a tangential tunnel from, say Los Angeles to London would also take only 90 minutes.


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Pande
No, as cmink mentioned it would only slow you as much as it sped you up to begin with.
abhinavm24
well any such weird ideas are never going to turn in to reality for first!
but out of curiosity if it ever happens to someone to get it done,
it possible to dig a hole in solid structures only.(You just can't drill a hole in fluids).
Sorry but the innner core of earth is purely made up of fluid material mix and is probably never going to solidify in near future in response to extreme heat and pressure it is under.
Smile
Radar
I understand the concept of a hole through the Earth as a thought experiment.

What I'm really surprised at is the suggestions that we can use it for practical purposes. Once you talk about drilling an impossible hole, practical uses just go out of my mind.
ocalhoun
Radar wrote:

What I'm really surprised at is the suggestions that we can use it for practical purposes. Once you talk about drilling an impossible hole, practical uses just go out of my mind.

Suppose humans colonized a planet or moon with a solid, not molten, core...
Then it might be practical. If you could minimize friction through the tube (say, by pumping the air (if any) out of it and suspending the vehicle via mag-lev), it could be an extremely efficient means of long-distance transport.
kelseymh
ocalhoun wrote:
Radar wrote:

What I'm really surprised at is the suggestions that we can use it for practical purposes. Once you talk about drilling an impossible hole, practical uses just go out of my mind.

Suppose humans colonized a planet or moon with a solid, not molten, core...
Then it might be practical. If you could minimize friction through the tube (say, by pumping the air (if any) out of it and suspending the vehicle via mag-lev), it could be an extremely efficient means of long-distance transport.


Only if the asteroid or moon in question is not spinning. Otherwise, you will collide with the wall rather quickly due to the azimuthal velocity difference as a function of depth.
ocalhoun
kelseymh wrote:
ocalhoun wrote:
Radar wrote:

What I'm really surprised at is the suggestions that we can use it for practical purposes. Once you talk about drilling an impossible hole, practical uses just go out of my mind.

Suppose humans colonized a planet or moon with a solid, not molten, core...
Then it might be practical. If you could minimize friction through the tube (say, by pumping the air (if any) out of it and suspending the vehicle via mag-lev), it could be an extremely efficient means of long-distance transport.


Only if the asteroid or moon in question is not spinning. Otherwise, you will collide with the wall rather quickly due to the azimuthal velocity difference as a function of depth.

What if the hole was curved to allow for this?
kelseymh
ocalhoun wrote:
kelseymh wrote:
[[...]Only if the asteroid or moon in question is not spinning. Otherwise, you will collide with the wall rather quickly due to the azimuthal velocity difference as a function of depth.

What if the hole was curved to allow for this?

Unless the tube is directly along the Earth's rotational axis, it has to curve outward (i.e., toward the surface), and thereby stops being a "hole through the center". In fact, the only way to compensate perfectly is to remain on the surface the whole time, and go around :-/
ocalhoun
kelseymh wrote:
ocalhoun wrote:
kelseymh wrote:
[[...]Only if the asteroid or moon in question is not spinning. Otherwise, you will collide with the wall rather quickly due to the azimuthal velocity difference as a function of depth.

What if the hole was curved to allow for this?

Unless the tube is directly along the Earth's rotational axis,

...well, still useful, if not quite as convenient. *shrug*
codegeek
It would go into a simple harmonic motion. First, it accelerates toward the centre due to gravity. Then, when it reaches the centre, it would continue moving due to its inertia of motion. However, since gravity is still pulling it toward the centre, it would decelerate, finally it would start accelerating towards the centre again, and the process would continue.

However, this is highly theoretical, because it ignores all the other forces that must be taken into consideration.
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