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Author Topic:   Throwing Stuff Down A Mineshaft
elianna 
Suspended Member (Idle past 4063 days)
Posts: 4
Joined: 01-06-2009


Message 1 of 69 (493296)
01-08-2009 6:20 AM


Throwing Stuff Down A Mineshaft
Two guys were hiking in the mountains when they came across an old mine shaft going straight down into the ground.

"Wow," said the first guy. "I wonder how deep it is?"

"I dunno," said the second.

"Let's find out." With that, he dropped a rock down the hole. They waited and waited, but didn't hear it hit bottom.

"Hmm. Let's try a bigger rock," said the first guy, and tossed a watermelon-sized stone down the hole. They waited a couple of minutes, but didn't hear it hit either. So, they looked around for something bigger to throw down and came across an old railroad tie, which they lifted together and dumped down the hole. Then suddenly, as they waited to hear it hit, a goat streaked between the two of them and jumped straight down the mineshaft.

While they stood there scratching their heads in amazement, a third guy came up the path and asked them if they'd seen a goat.

"Yeah, just now," said one of the first two guys. "It just ran up and jumped down this hole."

"Oh, well then it couldn't have been my goat," said the third guy. "My goat was tied to an old railroad tie."

Edited by Adminnemooseus, : No reason given.


http://reseller.name

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Parasomnium
Member (Idle past 1202 days)
Posts: 2191
Joined: 07-15-2003


Message 2 of 69 (493299)
01-08-2009 6:38 AM
Reply to: Message 1 by elianna
01-08-2009 6:20 AM


Thought experiment
Nice one!

Now a theoretical question: what would you expect to happen with something they throw in the hole if it was a hole that went all the way to other side of the earth? (Let's just ignore the hot core of the earth and assume it's cold and solid, with the hole going right through it.)


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iano
Member (Idle past 447 days)
Posts: 6165
From: Co. Wicklow, Ireland.
Joined: 07-27-2005


Message 3 of 69 (493308)
01-08-2009 7:52 AM
Reply to: Message 2 by Parasomnium
01-08-2009 6:38 AM


Re: Thought experiment
Off the top of my head.

It would fall towards the centre with it's rate of acceleration decaying all the way. It would come to a halt(after an infinite amount of time) right in the centre of the earth.

?

Edited by iano, : No reason given.


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Parasomnium
Member (Idle past 1202 days)
Posts: 2191
Joined: 07-15-2003


Message 4 of 69 (493311)
01-08-2009 8:00 AM
Reply to: Message 3 by iano
01-08-2009 7:52 AM


Re: Thought experiment
You're on the right track, but you must ask yourself when exactly its acceleration starts to decay...

(Added by edit: it has something to do with WHY the acceleration starts to decay at a certain moment.)

Edited by Parasomnium, : No reason given.


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iano
Member (Idle past 447 days)
Posts: 6165
From: Co. Wicklow, Ireland.
Joined: 07-27-2005


Message 5 of 69 (493320)
01-08-2009 8:47 AM
Reply to: Message 4 by Parasomnium
01-08-2009 8:00 AM


Re: Thought experiment
Flailing wildly around again.

Lets see. Rockets can escape gravitational pull by getting further away from earth. So I suppose acceleration due to gravity increases as you head nearer the centre of the earth.

You drop something from the surface and its acceleration increases all the way to the centre. It overshoots due to momentum but (decaying acceleration due to gravity) pulls it back towards the centre where it overshoots again - but to lesser degree.

In theory this would go on forever - with ever diminishing overshoot

??


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cavediver
Member (Idle past 2149 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 6 of 69 (493323)
01-08-2009 8:54 AM
Reply to: Message 5 by iano
01-08-2009 8:47 AM


Re: Thought experiment
So I suppose acceleration due to gravity increases as you head nearer the centre of the earth.

That's the magic gravity gnome that lives at the centre of the Earth. ;)

What is it that causes the gravity? And if you are halfway to the centre of the Earth, where is that thing that causes the gravity?


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Larni
Member
Posts: 3992
From: Liverpool
Joined: 09-16-2005


Message 7 of 69 (493325)
01-08-2009 9:02 AM
Reply to: Message 6 by cavediver
01-08-2009 8:54 AM


Re: Thought experiment
If you get half way to the center would the mass behind you begin to exert gravitational influence on you?

When you get to the middle (say hi to Doug Maclough) would you be in free fall?

Edited by Larni, : Spacing


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Parasomnium
Member (Idle past 1202 days)
Posts: 2191
Joined: 07-15-2003


Message 8 of 69 (493326)
01-08-2009 9:03 AM
Reply to: Message 5 by iano
01-08-2009 8:47 AM


Re: Thought experiment
Nearly spot on! You only need to explain why it overshoots less far each time. (Hint: what happens if there's no air?)

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cavediver
Member (Idle past 2149 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 9 of 69 (493328)
01-08-2009 9:16 AM
Reply to: Message 7 by Larni
01-08-2009 9:02 AM


Re: Thought experiment
If you get half way to the center would the mass behind you begin to exert gravitational influence on you?

Absolutely. And it all works out beautifully - everything in the shell from the surface down to your radius exactly cancels out. So the stuff that's behind you exactly balance the equivalent stuff on the other side of the planet, leaving just the mass that is below you that is relevant. So if you are 2000km from the centre, your gravitational acceleartion is the same as standing on a planet with radius 2000km (assuming same density). Cool :cool:

Even better, just think what happens if you are inside a hollow shell of matter. By the above, there is no gravity at all! You are weightless anywhere inside the shell, yet anything outside the shell feels the inward gravitational pull as normal! This is the gravitational analogue of the Faraday Cage effect.


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cavediver
Member (Idle past 2149 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 10 of 69 (493329)
01-08-2009 9:21 AM
Reply to: Message 5 by iano
01-08-2009 8:47 AM


Re: Thought experiment
So I suppose acceleration due to gravity increases as you head nearer the centre of the earth.

Just to be clear, if I wasn't before - this is wrong. As is

You drop something from the surface and its acceleration increases all the way to the centre.

You are describing the velocity, not the acceleration.

The acceleration decreases all the way to the centre, where it is zero. As you overshoot, the acceleration grows again (linearly with depth) but in the opposite direction.

But as Parasomnium explains, your picture of what happens is correct.


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Larni
Member
Posts: 3992
From: Liverpool
Joined: 09-16-2005


Message 11 of 69 (493330)
01-08-2009 9:25 AM
Reply to: Message 9 by cavediver
01-08-2009 9:16 AM


Re: Thought experiment
You are weightless anywhere inside the shell, yet anything outside the shell feels the inward gravitational pull as normal!

That's one hell of a good trick!

Is it something like being a massive lagrange point covering the volume of the inside of the sphere?

Sometimes I really do wish I had the brains to have study physics rather than psychology :(


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cavediver
Member (Idle past 2149 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 12 of 69 (493331)
01-08-2009 9:28 AM
Reply to: Message 11 by Larni
01-08-2009 9:25 AM


Re: Thought experiment
Is it something like being a massive lagrange point covering the volume of the inside of the sphere?

Yes, it is - though I hadn't thought of it that way - and it's a state of neutral equilibrium.


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Coragyps
Member
Posts: 5493
From: Snyder, Texas, USA
Joined: 11-12-2002
Member Rating: 3.5


Message 13 of 69 (493332)
01-08-2009 9:31 AM


Won't somebody think about the poor litte goat??!!

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Parasomnium
Member (Idle past 1202 days)
Posts: 2191
Joined: 07-15-2003


Message 14 of 69 (493333)
01-08-2009 9:32 AM
Reply to: Message 9 by cavediver
01-08-2009 9:16 AM


Re: Thought experiment
Even better, just think what happens if you are inside a hollow shell of matter. By the above, there is no gravity at all! You are weightless anywhere inside the shell, yet anything outside the shell feels the inward gravitational pull as normal! This is the gravitational analogue of the Faraday Cage effect.

Are you sure about this? I would have thought that as long as you are not in the exact centre of gravity, you would fall toward it, overshoot, fall back, overshoot again, etc.


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Larni
Member
Posts: 3992
From: Liverpool
Joined: 09-16-2005


Message 15 of 69 (493334)
01-08-2009 9:33 AM
Reply to: Message 13 by Coragyps
01-08-2009 9:31 AM


Being pulled down a well is the penalty for being a goat.

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