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 
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 
) place ping-pong ball right in the middle of this hole, and let it fall down. What would happen to the ping-pong ball? | 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
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 ) 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
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.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.
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.
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 | 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
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 ) 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_EarthEd, 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?
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.
) 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.
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.
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.
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
But, is it practically right? 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.
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.
| 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...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. | 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. | 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... | 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.cmink32 looks like you got bikerman jelous bikerman jelousieeeeeeeeeeeeeeeeee hahaha i like it cmink
Due to gravity the ball slide closer to side walls and finally rolls over it in a spiral path
Wow. The Hollow Earth Theory.
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 
interesting topic... I would love to see a computer simulation of this test!
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 that would rewrite many maths and physics books..lol
| 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.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...
