PDA

View Full Version : What will Gravity do in this case?



Physics95
2014-Jan-13, 07:09 PM
Lets say we somehow dig a well/bore all the way from N-pole to S-pole creating a tunnel along the earths axis open at both ends. What will gravity do to a ball dropped from N-pole into this tunnel? Where will it end resting?

NEOWatcher
2014-Jan-13, 08:26 PM
This sounds like a homework question.

With that in mind (we don't like to answer homework questions), I would like to say that there are plenty of answers out there. Each one of them takes into account various factors, most importantly, atmosphere. Then there is the premise of a hole anyway, is it even possible. We tend to get very detailed here, so it might not be what you're looking for.

If it's not a homework question, then I apologize. But; some additional discussion (and what kind of factors you are interested in) will help us get a feel for why you are interested and expand your thoughts other than just answering a question.

Physics95
2014-Jan-14, 05:53 AM
The origin of this question was out of curiosity.

Its an eyebrow raising thing for me to see you have questioned the possibility of such a thing. I guess most breakthroughs in science have emerged from the figment of imagining the impossible.

I registered in this site with an excitement that my questions will find some answers, but it seems I am at the wrong place. Thank you.



This sounds like a homework question.

With that in mind (we don't like to answer homework questions), I would like to say that there are plenty of answers out there. Each one of them takes into account various factors, most importantly, atmosphere. Then there is the premise of a hole anyway, is it even possible. We tend to get very detailed here, so it might not be what you're looking for.

If it's not a homework question, then I apologize. But; some additional discussion (and what kind of factors you are interested in) will help us get a feel for why you are interested and expand your thoughts other than just answering a question.

Noclevername
2014-Jan-14, 02:15 PM
I guess most breakthroughs in science have emerged from the figment of imagining the impossible.

Most breakthroughs in science have come from careful observations and experiments, being open minded about possibilities, and not jumping to conclusions when something happens differently or one gets an answer different than one expects.

Strange
2014-Jan-14, 02:39 PM
Lets say we somehow dig a well/bore all the way from N-pole to S-pole creating a tunnel along the earths axis open at both ends. What will gravity do to a ball dropped from N-pole into this tunnel? Where will it end resting?

The ball will accelerate (at a decreasing rate) until it reaches a maximum velocity at the center of the Earth. It will start slowing and then come to s stop at the same height you dropped it from (assuming for simplicity you have also sucked he air out of the hole - quite an engineering challenge you have taken on here...)

One of the interesting things about this is that the time taken for the ball to make that journey, about 42 minutes, is exactly the same as a satellite orbiting at the Earth's surface. In fact, that is true for any tunnel through the earth (assuming we can ignore friction).

Back to your ball. As you didn't raise enough money from Kickstarter to create a vacuum in the tunnel, your ball will be slowed by air resistance and so it will not quite get all the way to the surfcae before falling back. It will then oscillate with damped harmonic motion until it comes to rest at the center of the Earth.

This ignores minor practical problems like precession, Coriolis forces, heat, etc.

Some more analysis here: http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/earthole.html
And a model to play with: http://www.geogebra.org/en/upload/files/nikenuke/tunnel07.html

NEOWatcher
2014-Jan-14, 05:49 PM
I registered in this site with an excitement that my questions will find some answers, but it seems I am at the wrong place. Thank you.
No; you are in the right place.

Part of the reason I responded in the way that I did was because simple (well, simple to us) questions like that from the first post of someone is usually someone looking for homework help.

The other reason I responded the way I did was to get a feel for your knowledge of it to begin with. We can answer from the simple to the very detailed. I hope that your "eyebrows' being raised is because you just didn't understand that there are a lot of things that can be consered as levels of answers.

But; thanks to your response, we can continue to move forward and I extend a welcome. I hope that Strange's response helps. It's about the level I would have started with.

Physics95
2014-Jan-15, 07:03 PM
Thank You!


No; you are in the right place.

Part of the reason I responded in the way that I did was because simple (well, simple to us) questions like that from the first post of someone is usually someone looking for homework help.

The other reason I responded the way I did was to get a feel for your knowledge of it to begin with. We can answer from the simple to the very detailed. I hope that your "eyebrows' being raised is because you just didn't understand that there are a lot of things that can be consered as levels of answers.

But; thanks to your response, we can continue to move forward and I extend a welcome. I hope that Strange's response helps. It's about the level I would have started with.

corner
2014-Jan-15, 07:20 PM
As you're drilling through the poles, there will be no lateral force pressing the ball into the sides of the shaft. That would not be the case if you drilled from somewhere else.

Physics95
2014-Jan-15, 07:21 PM
Thank you for your reply. So I guess gravity in this case can give us a reciprocating motion for free at least for some time.

I would also imagine that the ball when at rest will be floating in air (assuming that its place of rest is the center of earth's gravity).


The ball will accelerate (at a decreasing rate) until it reaches a maximum velocity at the center of the Earth. It will start slowing and then come to s stop at the same height you dropped it from (assuming for simplicity you have also sucked he air out of the hole - quite an engineering challenge you have taken on here...)

One of the interesting things about this is that the time taken for the ball to make that journey, about 42 minutes, is exactly the same as a satellite orbiting at the Earth's surface. In fact, that is true for any tunnel through the earth (assuming we can ignore friction).

Back to your ball. As you didn't raise enough money from Kickstarter to create a vacuum in the tunnel, your ball will be slowed by air resistance and so it will not quite get all the way to the surfcae before falling back. It will then oscillate with damped harmonic motion until it comes to rest at the center of the Earth.

This ignores minor practical problems like precession, Coriolis forces, heat, etc.

Some more analysis here: http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/earthole.html
And a model to play with: http://www.geogebra.org/en/upload/files/nikenuke/tunnel07.html

Trebuchet
2014-Jan-15, 09:24 PM
Just thinking about this again, I suspect Coriolis forces and such, if not ignored, will cause the ball to be bouncing off the walls of the tube even if it is evacuated, slowing it down even more.

Noclevername
2014-Jan-15, 09:26 PM
Just thinking about this again, I suspect Coriolis forces and such, if not ignored, will cause the ball to be bouncing off the walls of the tube even if it is evacuated, slowing it down even more.

If the ball falls down the exact center of the rotational axis, it should avoid that.

NEOWatcher
2014-Jan-16, 07:21 PM
If the ball falls down the exact center of the rotational axis, it should avoid that.
Yes. There is also the issue of variations in gravitational pull. The path wouldn't be exactly straight. The hole would need to be wide enought to accomodate this.

Trebuchet
2014-Jan-17, 01:43 AM
If the ball falls down the exact center of the rotational axis, it should avoid that.

What if you drop a pumpkin instead? (Sigh. Nine months to go. Whoa, only nine months to go! I'd better get building!)

Noclevername
2014-Jan-17, 01:57 AM
What if you drop a pumpkin instead?

It would get vacuum-desiccated, and the outgassing might skew the path of its fall. Besides, pumpkins are for flinging, not dropping!