The Naked Scientists

The Naked Scientists Forum

Author Topic: Falling Again  (Read 5303 times)

Offline A Big Mug

  • Jr. Member
  • **
  • Posts: 21
    • View Profile
Falling Again
« on: 19/11/2005 01:37:05 »
A person in free fall from 100,000 feet in a short time reaches a velocity of 700 miles per hour.  By the time that person reaches 20,000 feet the increased air density slows them down to 120 miles per hour.  If that same person continued the free fall into the tunnel that runs right through the earth it would seem like:

1.  The air density would continue to increase causing drag to increase with a corresponding reduction in velocity.  If the sky divers speed slows from 700 mph to just 120 mph in only a 20 mile or so fall, how much slower would he be falling after continuing on another 3,980 miles to center of the earth?  I think the air density would be almost like a liquid near the center of the earth.  The sky divers velocity through the air near the center of the earth would be about nil.

2.  Once the sky diver passed into the tunnel more and more of the earth would be behind him.  This would decrease the gravitational pull on him.  In the center of the earth there would be no gravitational pull.

So, just when the diver gets to the greatest possible air density, with the greatest amount of drag, gravity will no longer be pulling him.

I think the sky diver could take a very very long time to ever get near the center of the earth.  Perhaps hundreds or thousands of years.  There is no way in the world the sky diver could ever come popping out the other side.

So what do you think?  I wish I knew how to calculate how great the air density would be when the column of air was 4000 miles high.  Granted, the air at the center of the air is not being pulled by gravity as much as the air higher up but there sure is a lot of air above the center.

Thanks for reading this.

Dave


 

Offline daveshorts

  • Moderator
  • Neilep Level Member
  • *****
  • Posts: 2583
  • Physics, Experiments
    • View Profile
    • http://www.chaosscience.org.uk
Re: Falling Again
« Reply #1 on: 19/11/2005 10:29:48 »
You are right he wouldn't come popping out the other side because if there is any air resistance then some of his original potential energy would be turned into heat by friction so there wouldn't be enough energy to get him out of the other side.

With the amount of gravity, it so happens that if you are inside the earth the gravity you feel is the same as standing on a planet with the radius you are standing at, all the stuff outside you cancells out, so the gravity does get smaller as you go in.

You  would probably go a few km out past the centre but not that far as you say,
 

Offline DoctorBeaver

  • Naked Science Forum GOD!
  • *******
  • Posts: 12656
  • Thanked: 3 times
  • A stitch in time would have confused Einstein.
    • View Profile
Re: Falling Again
« Reply #2 on: 19/11/2005 12:27:34 »
I thought gravity always acted as if it was coming from the centre of an object
 

Offline neilep

  • Withdrawnmist
  • Naked Science Forum GOD!
  • *******
  • Posts: 20602
  • Thanked: 8 times
    • View Profile
Re: Falling Again
« Reply #3 on: 19/11/2005 14:48:08 »
As a  firm believer in empirical study I took an apple and used a corer to put a hole in it...I found a spidey and dropped it through the apple...result ?...spidey was well and after consultation and a reward of a fly spidey went on his merry way. QED !...you're welcome !

Men are the same as women.... just inside out !!
 

Offline daveshorts

  • Moderator
  • Neilep Level Member
  • *****
  • Posts: 2583
  • Physics, Experiments
    • View Profile
    • http://www.chaosscience.org.uk
Re: Falling Again
« Reply #4 on: 19/11/2005 15:12:58 »
quote:
Originally posted by DoctorBeaver

I thought gravity always acted as if it was coming from the centre of an object


If the object is spherical then it does. If you are inside a spherical object the force is as if you were standing on a smaller sphere with the radius you are standing at - if you stand at the centre of the earth then there will be no net gravity as everything cancells.
 

Offline A Big Mug

  • Jr. Member
  • **
  • Posts: 21
    • View Profile
Re: Falling Again
« Reply #5 on: 19/11/2005 17:16:31 »
quote:
Originally posted by DoctorBeaver

I thought gravity always acted as if it was coming from the centre of an object

I think the attraction would be to the center of the objects mass as measured from where you are in the tunnel to the other end of the tunnel.  In this special case of the sky diver in the tunnel, the center of the objects mass would initially be the center of the earth.  As the sky diver fell down the tunnel the center of mass pulling him would slowly move to the far side of the tunnel.  At the same time the "felt" center of mass was moving away, a new gravitational attraction from the earth behind him in the tunnel would start to grow.  If the sky diver (tunnel diver?) ever arrived at the center of the earth the mass of the earth from all around him would be pulling on him equally.  

I picture the sky diver about 1/3 down the tunnel.  That would mean, I think, that the center of mass pulling on him would be located somewhere in the middle of the 2/3 portion of the earth ahead of him.  This would be on the far side past the actual center of the earth.  The radius of the center of mass would not be consistant of course because the shape of the earth is based on a sphere around the actual core.  So I think it would be more like a mushroom shape.  Please no jokes about mushrooms.

 

Offline DoctorBeaver

  • Naked Science Forum GOD!
  • *******
  • Posts: 12656
  • Thanked: 3 times
  • A stitch in time would have confused Einstein.
    • View Profile
Re: Falling Again
« Reply #6 on: 19/11/2005 19:23:51 »
Sorry but I can't resist it... if the tunnel was narrow there wouldn't be MUSHROOM for him to move about

*hangs head in shame* [V]

Veni, Vidi, Velcro. I came, I saw, I got stuck.
 

Offline A Big Mug

  • Jr. Member
  • **
  • Posts: 21
    • View Profile
Re: Falling Again
« Reply #7 on: 19/11/2005 20:41:40 »
quote:
Originally posted by DoctorBeaver

Sorry but I can't resist it... if the tunnel was narrow there wouldn't be MUSHROOM for him to move about

*hangs head in shame* [V]

Veni, Vidi, Velcro. I came, I saw, I got stuck.

That's OK.  I could tell from reading your other posts that you are a real fungi.
 

another_someone

  • Guest
Re: Falling Again
« Reply #8 on: 20/11/2005 11:50:32 »
I assume that all of you are discussing what happens if he drops through from the north or south pole, otherwise the rotation of the Earth would have him bouncing off the side of the tunnel.
 

Offline A Big Mug

  • Jr. Member
  • **
  • Posts: 21
    • View Profile
Re: Falling Again
« Reply #9 on: 21/11/2005 17:39:59 »
quote:
Originally posted by another_someone

I assume that all of you are discussing what happens if he drops through from the north or south pole, otherwise the rotation of the Earth would have him bouncing off the side of the tunnel.

Good point.  I thought I had a bead on how to calculate the increase in air pressure with depth but alas it was to no avail.  I was hoping a mining site would have some type of calculation available.  The other item I was hoping to find is the the number of atmospheres of pressure that air would turn to liquid.  It seems like the pressure toward the middle of the tunnel might be sufficient.  I wish now I had paid more attention in every single class I ever took in school.  Ever wish you could go back and do it again?  I do.
 

Offline hderycke

  • First timers
  • *
  • Posts: 2
    • View Profile
Re: Falling Again
« Reply #10 on: 29/11/2005 20:27:49 »
quote:
Originally posted by A Big Mug
Good point.  I thought I had a bead on how to calculate the increase in air pressure with depth but alas it was to no avail.  I was hoping a mining site would have some type of calculation available.  The other item I was hoping to find is the the number of atmospheres of pressure that air would turn to liquid.  It seems like the pressure toward the middle of the tunnel might be sufficient.  I wish now I had paid more attention in every single class I ever took in school.  Ever wish you could go back and do it again?  I do.


Isn't air pressure related to gravity? As you enter the atmosphere and go down, pressure increases because you have more and more air on top of you, which is being pulled towards the planet. But once you breach the surface, the gravitational pull on the air decreases, all the way to zero once you're at the center (or at least, the gravitational pull of the surrounding planet cancels out).
 

another_someone

  • Guest
Re: Falling Again
« Reply #11 on: 30/11/2005 07:35:59 »
quote:
Originally posted by hderycke
Isn't air pressure related to gravity? As you enter the atmosphere and go down, pressure increases because you have more and more air on top of you, which is being pulled towards the planet. But once you breach the surface, the gravitational pull on the air decreases, all the way to zero once you're at the center (or at least, the gravitational pull of the surrounding planet cancels out).



And how do you propose that the air pressure beneath the surface layer that has already accumulated above your head is dissipated?

Air pressure is created by the accumulated downward force of the air above you.  That gravity beneath the surface of the Earth is less than that above the surface of the Earth would mean that there is less additional pressure to accumulate than might otherwise be, but in the absence of an upward force, you would still be subject to the full downward force that has already been accumulated by the weight of air above you.

You could not explain the pressure of water at the depths of the oceans if you only took account of the immediate gravitational pull acting solely upon the local water at that depth.  The pressure deep under water is caused by the cumulative weight of water above, and even if the bottom depths of water were at zero gravity, it would still have the weight of the water above that was not at zero gravity.
 

Offline hderycke

  • First timers
  • *
  • Posts: 2
    • View Profile
Re: Falling Again
« Reply #12 on: 30/11/2005 18:54:14 »
quote:
Originally posted by another_someone

And how do you propose that the air pressure beneath the surface layer that has already accumulated above your head is dissipated?

Magical fairy dust?
quote:
Air pressure is created by the accumulated downward force of the air above you.  That gravity beneath the surface of the Earth is less than that above the surface of the Earth would mean that there is less additional pressure to accumulate than might otherwise be, but in the absence of an upward force, you would still be subject to the full downward force that has already been accumulated by the weight of air above you.

Thanks.
 

The Naked Scientists Forum

Re: Falling Again
« Reply #12 on: 30/11/2005 18:54:14 »

 

SMF 2.0.10 | SMF © 2015, Simple Machines
SMFAds for Free Forums