Ron Paul Posted October 31, 2012 Share Posted October 31, 2012 (edited) The picture is Earth, and what you see is a hole that goes through it in a straight direction. You throw a ball down this hole, and you wonder what will happen. * The earth will not collapse under it's weight * There is no burning center of the Earth. There is no magma, or water. It is a hole, with nothing blocking it. * You're dropping the ball from a location that has ground, to another location with ground I.E Chicago - Beijing * Gravity is normal * No physical force will interfere with this ball (Rocks, mounds of dirt, etc) * The ball will not be destroyed by pressure or any sort. * The Earths rotation will not effect the ball in any shape or form. Will it go to the other side? Will it stay stuck in the middle? Will it come back to you? Picture: If you need any clarification, ask I'll try to explain everything. Edited November 4, 2012 by Ron Paul Link to comment Share on other sites More sharing options...
LazaHorse Posted October 31, 2012 Share Posted October 31, 2012 (edited) It will oscillate indefinitely between your position and the same position on the other side of the center of the Earth. Long story short, the conservation of energy requires that the ball remain at a constant energy. It's potential energy reaches a maximum at either end of the Earth, but the equilibrium there is not stable. It's kinetic energy becomes a maximum at the center, but because it is moving, it has no equilibrium. You learn this in a high school physics class? It's a very intricate problem that can be simplified (maybe over-simplified) into three separate force diagrams. Real. Edited November 1, 2012 by LazaHorse Link to comment Share on other sites More sharing options...
BranHorse Posted October 31, 2012 Share Posted October 31, 2012 So its a straight hole correct? It would get stuck on the side due to the earths rotation. So it would get stuck about a third of the way down not in the middle. Think of a ride at the fair that spins and forces you into your seat unable to move....something like that. Also, the ball would have to be made of PURE UNOBTANIUM in order to withstand the pressures. Link to comment Share on other sites More sharing options...
BranHorse Posted October 31, 2012 Share Posted October 31, 2012 It will oscillate indefinitely between your position and the same position on the other side of the center of the Earth. Long story short, the conservation of energy requires that the ball remain at a constant energy. It's potential energy reaches a maximum at either end of the Earth, but the equilibrium there is not stable. It's kinetic energy becomes a maximum at the center, but because it is moving, it has no equilibrium. You learn this in a high school physics class? It's a very intricate problem that can be simplified (maybe over-simplified) into three separate force diagrams. Also that ^^^^ BUT MORE UNOBTAINIUM!!!!!!! Link to comment Share on other sites More sharing options...
jajolt Posted October 31, 2012 Share Posted October 31, 2012 It would Bounce back and forth and finally float in the center because of gravity Link to comment Share on other sites More sharing options...
PerryThePlatypus Posted October 31, 2012 Share Posted October 31, 2012 What have BP been doing again. On a serious note it depends since your hole runs from Chicago to Beijing it would loose momentum and stop depending on how hard you can roll it because your hole is horizontal , it depends on the hole. Also it is vertical the ball will make it to the other side of the earth because it's moving fast enough that the g force of the ball is so heavy that gravity won't stop it as it is moving too fast and it is too light Link to comment Share on other sites More sharing options...
LazaHorse Posted October 31, 2012 Share Posted October 31, 2012 (edited) My answer was wrong. I didn't read and figured you were asking from North to South Pole. As Branflake said, when you go from one side to the other you are going against the centripetal "imaginary" force caused by a difference of reference frames between the ball and the earth. As such there is a distance r from the center of the Earth at which the gravitational force equals the centripetal force. The ball will oscillate around that point until it eventually comes to rest there. Unless of course I forgot something else, in which case yolo I regret nothing. *EDIT* What have BP been doing again. On a serious note it depends since your hole runs from Chicago to Beijing it would loose momentum and stop depending on how hard you can roll it because your hole is horizontal , it depends on the hole. Also it is vertical the ball will make it to the other side of the earth because it's moving fast enough that the g force of the ball is so heavy that gravity won't stop it as it is moving too fast and it is too light Stop watching Star Trek, you're not watching it correctly. Do you even... know what g force is? The only g-force you would ever consider with this is air resistance which would work against the fall of the ball, not with it. Likewise, gravitational pull wouldn't work against the ball's fall, but is the initiator for it. Please stop. Real. Edited November 1, 2012 by LazaHorse Link to comment Share on other sites More sharing options...
BranHorse Posted October 31, 2012 Share Posted October 31, 2012 My answer was wrong. I didn't read and figured you were asking from North to South Pole. As Branflake said, when you go from one side to the other you are going against the centripetal "imaginary" force caused by a difference of reference frames between the ball and the earth. As such there is a distance r from the center of the Earth at which the gravitational force equals the centripetal force. The ball will oscillate around that point until it eventually comes to rest there. Unless of course I forgot something else, in which case yolo I regret nothing. http://www.youtube.com/watch?v=I-5UFp2dsqk Link to comment Share on other sites More sharing options...
PerryThePlatypus Posted October 31, 2012 Share Posted October 31, 2012 My answer was wrong. I didn't read and figured you were asking from North to South Pole. As Branflake said, when you go from one side to the other you are going against the centripetal "imaginary" force caused by a difference of reference frames between the ball and the earth. As such there is a distance r from the center of the Earth at which the gravitational force equals the centripetal force. The ball will oscillate around that point until it eventually comes to rest there. Unless of course I forgot something else, in which case yolo I regret nothing. *EDIT* What have BP been doing again. On a serious note it depends since your hole runs from Chicago to Beijing it would loose momentum and stop depending on how hard you can roll it because your hole is horizontal , it depends on the hole. Also it is vertical the ball will make it to the other side of the earth because it's moving fast enough that the g force of the ball is so heavy that gravity won't stop it as it is moving too fast and it is too light Stop watching Star Trek, you're not watching it correctly. Do you even... know what g force is? The only g-force you would ever consider with this is air resistance which would work against the fall of the ball, not with it. Likewise, gravitational pull wouldn't work against the ball's fall, but is the initiator for it. Please stop. so your saying that the hole is a vacuum ? GeForce is put on someone/thing when they are travelling at speed and making sharp turns/manoeuvres , in this case because the ball is travelling so quick by the time it gets to the centre where the pull is strongest the ball is travelling too quick to be stopped by the pull, If the hole is a vacuum then the ball can travel at even faster speeds because of the lack of air resistance in the hole, of course it couldn't be a vacuum because the earth has an atmosphere Link to comment Share on other sites More sharing options...
LazaHorse Posted October 31, 2012 Share Posted October 31, 2012 (edited) so your saying that the hole is a vacuum ? GeForce is put on someone/thing when they are travelling at speed and making sharp turns/manoeuvres , in this case because the ball is travelling so quick by the time it gets to the centre where the pull is strongest the ball is travelling too quick to be stopped by the pull, If the hole is a vacuum then the ball can travel at even faster speeds because of the lack of air resistance in the hole, of course it couldn't be a vacuum because the earth has an atmosphere There is not g-force on the ball except for air resistance. Did you read the problem? He is DROPPING the ball INTO the hole. The initial DROP is caused by gravity which BY DEFINITION cannot be a g-force. The gravity pulls the ball toward the center during which the centripetal force caused by the change of reference frame and the air resistance of the hole push the ball back toward the surface. Once it passes the equilibrium point I spoke of earlier where centripetal force = gravitational force, the ball will decelerate back toward that equilibrium point. It will go back and forth around it until the air resistance eventually brings it to rest. Sharp turns or maneuvers? Wth kind of drunken NASCAR induced science are you learning? BY THE WAY. Fuck Branflake, I was right at first. Centripetal force changes direction at the origin, pushing the ball back the other way. The ball will go from one end to the other and back and forth until air resistance (if you honestly want to consider that, which you shouldn't btw) slowly takes away energy and it stops at the center. *EDIT* Here's a PROFESSIONAL write-up on relativity including the tunnel through the Earth thought-experiment. http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity/index.html Also, interesting note, the force of gravity on the ball is constant in magnitude but changes direction (at the center) as it goes through the Earth. This is due to the fact that an object's gravity is a "potential" and thus cannot differ when the mass is equally distributed throughout the object. That can be proved with Laplace's/Poisson's equation: http://en.wikipedia.org/wiki/Gravitational_potential Real. Edited November 1, 2012 by LazaHorse Link to comment Share on other sites More sharing options...
Jadis Posted October 31, 2012 Share Posted October 31, 2012 (edited) nerd herd up in hurr I pose a new question. Assuming the diameter of the Earth is still the same, the ball is dropped from the radius of the Earth at the hole, and that Earth's mass is, well... let's just say normal for simplicity's sake. What would be the maximum velocity reached by the ball? Also, assume that the Earth is spherical. *runs off to Google* edit:yeh dat iz fast alrite Edited October 31, 2012 by Jadis Link to comment Share on other sites More sharing options...
BranHorse Posted October 31, 2012 Share Posted October 31, 2012 Doesn't matter earth is spinning like my rims bitch. http://motores.com.py/foro/index.php?attachments/spinners-gif.161306/ Link to comment Share on other sites More sharing options...
PerryThePlatypus Posted October 31, 2012 Share Posted October 31, 2012 Atleast I'm not a quaar Link to comment Share on other sites More sharing options...
LazaHorse Posted October 31, 2012 Share Posted October 31, 2012 (edited) Atleast I'm not a quaar [video=youtube;pD_imYhNoQ4] Real. Edited November 1, 2012 by LazaHorse Link to comment Share on other sites More sharing options...
Jadis Posted October 31, 2012 Share Posted October 31, 2012 Spoilers for you nerdz [spoiler=bitch i aint no nerd]So maximum velocity should be at the center of the Earth. Mean estimates of Earth's radius yield 6371km D=0.5 * a * t^2 (Distance fallen over period of time. Solve for t.) V = a * t (Velocity equation. Solve for V.) I got about 11.2km/s dat shit craycray Link to comment Share on other sites More sharing options...
LazaHorse Posted October 31, 2012 Share Posted October 31, 2012 (edited) Spoilers for you nerdz [spoiler=bitch i aint no nerd]So maximum velocity should be at the center of the Earth. Mean estimates of Earth's radius yield 6371km D=0.5 * a * t^2 (Distance fallen over period of time. Solve for t.) V = a * t (Velocity equation. Solve for V.) I got about 11.2km/s dat shit craycray Close, but centripetal force is not constant with r (distance from the Earth) so the constant velocity equations of motion do not apply. The velocity would be slightly lower. Real. Edited November 1, 2012 by LazaHorse Link to comment Share on other sites More sharing options...
Jadis Posted October 31, 2012 Share Posted October 31, 2012 Close, but centripetal force is not constant with r (distance from the Earth) so the constant velocity equations of motion do not apply. The velocity would be slightly lower. Oooo... Didn't think about that. However, gravity increases as you become closer to the center of mass. So wouldn't the object's velocity be higher? edit: Ah I see what you're saying. The equation for distance would not apply? Link to comment Share on other sites More sharing options...
LazaHorse Posted October 31, 2012 Share Posted October 31, 2012 (edited) Oooo... Didn't think about that. However, gravity increases as you become closer to the center of mass. So wouldn't the object's velocity be higher? edit: Ah I see what you're saying. The equation for distance would not apply? Actually gravity doesn't increase. Gravitational potential is the same throughout the mass (check the above wiki I posted). However, centripetal force is not constant and decreases as you get closer. Acceleration thus is not constant but actually increases on the way to the center (a = g - c where c is decreasing) until it reaches g at the center. The acceleration isn't constant, but instead starts slightly lower than g and increases to g at the center of the Earth. Thus you cannot use the constant velocity equations. Real. Edited November 1, 2012 by LazaHorse Link to comment Share on other sites More sharing options...
Plastered Posted October 31, 2012 Share Posted October 31, 2012 Where's Cookie? Link to comment Share on other sites More sharing options...
mccaincracker Posted October 31, 2012 Share Posted October 31, 2012 Where's Cookie? in the dumpster at panera bread LOL !!! Link to comment Share on other sites More sharing options...
iDigitaL- Posted October 31, 2012 Share Posted October 31, 2012 My brain is about to explode >.> Link to comment Share on other sites More sharing options...
PerryThePlatypus Posted October 31, 2012 Share Posted October 31, 2012 Quaars ! A quaar came into a bar talking about a hard drive, well after I dragged him to Donegal on the back of my van he knew all about a hard drive then. Link to comment Share on other sites More sharing options...
Cookie Posted October 31, 2012 Share Posted October 31, 2012 Actually gravity doesn't increase. Gravitational potential is the same throughout the mass Actually you're wrong, the person who said it would increase is actually correct in some aspect. Since the density fluxuates through the cores, you'll get a different gravity reading almost every 5 minutes. If you would like a better example I can write one in a little bit as I am pressed for time at the moment. Also here's some pictures for your edification; Link to comment Share on other sites More sharing options...
WhyYouNoDie? Posted October 31, 2012 Share Posted October 31, 2012 (edited) This whole thread is fucking bullshit. It makes me notice that my school has a science program that talks about nothing but the melting of water for 3 weeks. We have learned nothing that is actually interesting or complicated. Edited October 31, 2012 by WhyYouNoDie? Link to comment Share on other sites More sharing options...
LazaHorse Posted October 31, 2012 Share Posted October 31, 2012 (edited) Actually gravity doesn't increase. Gravitational potential is the same throughout the mass Actually you're wrong, the person who said it would increase is actually correct in some aspect. Since the density fluxuates through the cores, you'll get a different gravity reading almost every 5 minutes. If you would like a better example I can write one in a little bit as I am pressed for time at the moment. Also here's some pictures for your edification; [ATTACH=CONFIG]7633[/ATTACH] [ATTACH=CONFIG]7634[/ATTACH] My mistake, I wasn't being specific. I was talking about the example I was giving for the idealized case where you treat the Earth as a ball of constant mass density and no geographic variation at the surface. That's not the case, but it does simplify the hypothetical. The result is similar for both. You are right though, thank you for correcting me. Correct me if I'm wrong, but in each layer you re-treat the gravitational pull from the inner layers as a point source right? Real. Edited November 1, 2012 by LazaHorse Link to comment Share on other sites More sharing options...
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