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Author Topic:   Throwing Stuff Down A Mineshaft
Parasomnium
Member
Posts: 2224
Joined: 07-15-2003


Message 16 of 69 (493335)
01-08-2009 9:34 AM
Reply to: Message 13 by Coragyps
01-08-2009 9:31 AM


O yeah, the goat...
Don't worry, you'll bump into it, no doubt.

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iano
Member (Idle past 1940 days)
Posts: 6165
From: Co. Wicklow, Ireland.
Joined: 07-27-2005


Message 17 of 69 (493338)
01-08-2009 9:49 AM
Reply to: Message 8 by Parasomnium
01-08-2009 9:03 AM


Re: Thought experiment
No air?? I had been neglecting air.
Overshoot(#1) has momentum(#1) due to being dropped from the surface of the earth. This momentum carries the object past the centre despite the pull of gravity towards centre (now acting on the overshooter) - but not back to the surface. Thus overshoot(#2) has less momentum 'powering' it so it doesn't overshoot as far past centre as overshoot(#1)
??

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Larni
Member (Idle past 164 days)
Posts: 4000
From: Liverpool
Joined: 09-16-2005


Message 18 of 69 (493339)
01-08-2009 9:57 AM
Reply to: Message 12 by cavediver
01-08-2009 9:28 AM


Re: Thought experiment
Just a thought, but what happens to the gravitational energy inside the sphere?
If every point is the equivalent of being in free fall does all of that energy increase the mass of the sphere or is the gravity actually cancelled out (having no ability to do work)?
I appreciate this probably sounds like nonsense

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Parasomnium
Member
Posts: 2224
Joined: 07-15-2003


Message 19 of 69 (493340)
01-08-2009 10:00 AM
Reply to: Message 17 by iano
01-08-2009 9:49 AM


Re: Thought experiment
If there's no air resistance, there's no reason why it wouldn't fall all the way to the opposite side, to the same height it was released from, and then fall back, again to the same height, etc. In other words, without air resistance, it would endlessly oscillate between both extremes without diminishing amplitude.
You could rescue the goat by just grabbing it the moment it pops back up. You could also wait a few hours to see it pop up repeatedly, and then grab it, because it would pop up just as high each time. Of course, without air, you wouldn't really be rescuing it, because it would've suffocated *, but you get the idea...
* and so would you, by the way
Edited by Parasomnium, : No reason given.
Edited by Parasomnium, : No reason given.

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Huntard
Member (Idle past 2295 days)
Posts: 2870
From: Limburg, The Netherlands
Joined: 09-02-2008


Message 20 of 69 (493347)
01-08-2009 10:37 AM
Reply to: Message 17 by iano
01-08-2009 9:49 AM


Re: Thought experiment
Hello Iano,
As Parsamonium has explained, the only way this could happen is if there was air. It would be due to the friction and resistance of the air that you'd slow down.
This is also the reason that a feather drops slower then a ball of lead. If dropped in a vacuum, they will both drop at the same speed and hit the ground simultaneously.

I hunt for the truth

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 21 of 69 (493348)
01-08-2009 10:40 AM
Reply to: Message 14 by Parasomnium
01-08-2009 9:32 AM


Re: Thought experiment
Are you sure about this?
Oh, very sure I can take you through the integration if you like...

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Larni
Member (Idle past 164 days)
Posts: 4000
From: Liverpool
Joined: 09-16-2005


Message 22 of 69 (493349)
01-08-2009 10:46 AM
Reply to: Message 19 by Parasomnium
01-08-2009 10:00 AM


Re: Thought experiment
If there's no air resistance, there's no reason why it wouldn't fall all the way to the opposite side, to the same height it was released from, and then fall back, again to the same height, etc. In other words, without air resistance, it would endlessly oscillate between both extremes without diminishing amplitude.
Would'nt there be some loss of energy in heat that would slow it down eventually?

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Stile
Member
Posts: 4295
From: Ontario, Canada
Joined: 12-02-2004


Message 23 of 69 (493350)
01-08-2009 10:50 AM
Reply to: Message 18 by Larni
01-08-2009 9:57 AM


Re: Thought experiment
I'm not really sure what you're asking, but I'll have a go at it.
Larni writes:
Just a thought, but what happens to the gravitational energy inside the sphere?
By "gravitational energy", I'm guessing you mean Potential Energy. That is, the kind of energy an object has because of some other object's gravitational force. Like a book on a shelf has more Potential Energy then a book on the floor.
But the "mass of the sphere" is unaffected. The Potential Energy comes from the mass of the sphere. It's not the energy that makes the mass, it's the mass that makes the energy. The book on the shelf has more Potential Energy than the book on the floor, but neither book gains or loses mass, and neither does the Earth (not even a teeny-tiny bit).
You are essentially correct that the Potential Energy at the centre of a hollow sphere cancels out*. Think of it as every tiny point in the mass of the sphere is pulling you a tiny bit towards it. (In fact, every tiny point of everything that has mass is actually pulling you a tiny bit towards it, but that's just a side point).
On the surface, you have all the tiny points in the mass "below" you, that's why you're pulled "down".
Inside the hollow part, you have all the tiny points actually pulling you away towards the surface. Given a perfect sphere, each point on one side has an equal point on the exact opposite side that cancels out. Add in a bit of air resistance and no matter where you are in the centre area, you'll eventually "float" to the centre of the sphere.
Now think of a non-perfect hollow sphere (or obloid-type thing I think the word is). With a bit of air resistance, you'll still float to one spot... the centre of mass. You can get the same effect using a perfect hollow sphere with you in the middle and, say, 5-million people all in one country on the outside (and no one else anywhere else). The mass of those 5-million people would actually pull you a bit towards them... right to the centre of mass of the sphere-plus-the-people.
Now for an interesting addition... if you're on the surface of an earth that was massive enough, you'ed actually be pulled towards the centre with enough force to crush your bones against the ground.
And taking this massive-concept to a hollow sphere... if it were massive enough, it would pull your body apart and splatter you all over the inside walls
Also... even though the earth is pulling us to it's centre, we're actually also pulling the earth towards our centres. It's just that the size of the earth is so much that it's extremely negligible.
But, if you want to use exact-precision, you can say that you pull the earth out of orbit everytime you jump up. (Of course, as you push off with your jump you push the earth away, and then pull it back towards you with the force of gravity).
The amount the earth moves is ridiculously small... like milli-milli-micron-milli-half-an-electron type small... but it's calculable.
*Note: By "cancels out" we don't mean that the forces go away. It's that the forces are equal-but-opposite. The forces are all still there, and all as strong as they were before, it's just that there's no movement as a result of those forces.
Edited by Stile, : Added clarity on what "cancels out" means

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Stile
Member
Posts: 4295
From: Ontario, Canada
Joined: 12-02-2004


Message 24 of 69 (493353)
01-08-2009 10:53 AM
Reply to: Message 22 by Larni
01-08-2009 10:46 AM


Re: Thought experiment
(Heat is caused by friction... and you only have friction if you're hitting something... which is what the air resistance is)
So, if you remove air resistance, you remove friction and also remove heat-loss.
You do still have ambient heat-loss from your body-temperature into the air, but this has no affect on the energy of the motion. It only has an affect on the energy of your body. You'd just die from starvation eventually... then that heat loss stops

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Stile
Member
Posts: 4295
From: Ontario, Canada
Joined: 12-02-2004


Message 25 of 69 (493355)
01-08-2009 10:58 AM
Reply to: Message 21 by cavediver
01-08-2009 10:40 AM


Re: Thought experiment
I, um.. would like to see the integration on this
If you're in a hollow shell (perfect sphere).. and the hollow part has a radius of 100 meters.
If you're out by the edge (say, 90m from the centre of mass), you'll be pulled towards the centre of mass until you reach equilibrium (at the centre of mass).
Or, perhaps I'm defining "weight" incorrectly?
I'm assuming that you're not "weightless" if you're being pulled towards the centre of mass... you just feel like you have very little weight. But the only place you actually feel truly "weightless" would be at the centre of mass, no?
Edited by Stile, : Fixed a confusing typo where I put "fell" instead of "feel"

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iano
Member (Idle past 1940 days)
Posts: 6165
From: Co. Wicklow, Ireland.
Joined: 07-27-2005


Message 26 of 69 (493357)
01-08-2009 11:02 AM
Reply to: Message 19 by Parasomnium
01-08-2009 10:00 AM


Re: Thought experiment
Aah yes! Very good
Deep breath..

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iano
Member (Idle past 1940 days)
Posts: 6165
From: Co. Wicklow, Ireland.
Joined: 07-27-2005


Message 27 of 69 (493358)
01-08-2009 11:06 AM
Reply to: Message 10 by cavediver
01-08-2009 9:21 AM


Re: Thought experiment
Gotcha.
What a funny picture that - oscillating between the opposite sides of the globe - forever. Question for you then: approximately what frequency would this occur at?

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 28 of 69 (493359)
01-08-2009 11:15 AM
Reply to: Message 27 by iano
01-08-2009 11:06 AM


Re: Thought experiment
what frequency would this occur at?
0.0002 Hz

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iano
Member (Idle past 1940 days)
Posts: 6165
From: Co. Wicklow, Ireland.
Joined: 07-27-2005


Message 29 of 69 (493363)
01-08-2009 11:35 AM
Reply to: Message 28 by cavediver
01-08-2009 11:15 AM


Re: Thought experiment
The ultimate cavediving...
Thanks. I must have been bunking off the day they thought calculus
Edited by iano, : No reason given.
Edited by iano, : ...and spelling

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Parasomnium
Member
Posts: 2224
Joined: 07-15-2003


Message 30 of 69 (493365)
01-08-2009 11:42 AM
Reply to: Message 21 by cavediver
01-08-2009 10:40 AM


Re: Thought experiment
I can take you through the integration if you like...
My mathematical skills are rather rickety, so I probably couldn't follow your explanation.
But I was under the impression that you can do the maths for the gravitational effects of any massive object by treating it as a point mass. The point mass of a hollow sphere would be located in its exact centre (its centre of gravity), in which case we would be talking about a similar situation as that of our hypothetical hole in the earth. As long long as the path through the centre of gravity is free, you would just oscillate along this path between extremes, inside the sphere, as you would through the hole.
But I'm open for suggestions that would convince me otherwise.

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