Author
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Topic: Throwing Stuff Down A Mineshaft
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Parasomnium
Member Posts: 2224 Joined: 07-15-2003
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Message 2 of 69 (493299)
01-08-2009 6:38 AM
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Reply to: Message 1 by elianna 01-08-2009 6:20 AM
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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.)
This message is a reply to: | | Message 1 by elianna, posted 01-08-2009 6:20 AM | | elianna has not replied |
Replies to this message: | | Message 3 by iano, posted 01-08-2009 7:52 AM | | Parasomnium has replied |
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Parasomnium
Member Posts: 2224 Joined: 07-15-2003
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Message 4 of 69 (493311)
01-08-2009 8:00 AM
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Reply to: Message 3 by iano 01-08-2009 7:52 AM
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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.
This message is a reply to: | | Message 3 by iano, posted 01-08-2009 7:52 AM | | iano has replied |
Replies to this message: | | Message 5 by iano, posted 01-08-2009 8:47 AM | | Parasomnium has replied |
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Parasomnium
Member Posts: 2224 Joined: 07-15-2003
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Message 8 of 69 (493326)
01-08-2009 9:03 AM
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Reply to: Message 5 by iano 01-08-2009 8:47 AM
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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?)
This message is a reply to: | | Message 5 by iano, posted 01-08-2009 8:47 AM | | iano has replied |
Replies to this message: | | Message 17 by iano, posted 01-08-2009 9:49 AM | | Parasomnium has replied |
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Parasomnium
Member Posts: 2224 Joined: 07-15-2003
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Message 14 of 69 (493333)
01-08-2009 9:32 AM
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Reply to: Message 9 by cavediver 01-08-2009 9:16 AM
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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.
This message is a reply to: | | Message 9 by cavediver, posted 01-08-2009 9:16 AM | | cavediver has replied |
Replies to this message: | | Message 21 by cavediver, posted 01-08-2009 10:40 AM | | Parasomnium has replied |
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Parasomnium
Member Posts: 2224 Joined: 07-15-2003
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Message 16 of 69 (493335)
01-08-2009 9:34 AM
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Reply to: Message 13 by Coragyps 01-08-2009 9:31 AM
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O yeah, the goat...
Don't worry, you'll bump into it, no doubt.
This message is a reply to: | | Message 13 by Coragyps, posted 01-08-2009 9:31 AM | | Coragyps has not replied |
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Parasomnium
Member Posts: 2224 Joined: 07-15-2003
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Message 19 of 69 (493340)
01-08-2009 10:00 AM
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Reply to: Message 17 by iano 01-08-2009 9:49 AM
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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.
This message is a reply to: | | Message 17 by iano, posted 01-08-2009 9:49 AM | | iano has replied |
Replies to this message: | | Message 22 by Larni, posted 01-08-2009 10:46 AM | | Parasomnium has not replied | | Message 26 by iano, posted 01-08-2009 11:02 AM | | Parasomnium has not replied |
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Parasomnium
Member Posts: 2224 Joined: 07-15-2003
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Message 30 of 69 (493365)
01-08-2009 11:42 AM
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Reply to: Message 21 by cavediver 01-08-2009 10:40 AM
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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.
This message is a reply to: | | Message 21 by cavediver, posted 01-08-2009 10:40 AM | | cavediver has replied |
Replies to this message: | | Message 32 by cavediver, posted 01-08-2009 12:46 PM | | Parasomnium has replied |
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Parasomnium
Member Posts: 2224 Joined: 07-15-2003
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Message 31 of 69 (493375)
01-08-2009 12:35 PM
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Reply to: Message 23 by Stile 01-08-2009 10:50 AM
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Re: Thought experiment
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 I'm not convinced that this would be what happened. If the forces from all sides cancel out, as you explain, then the net force on you would be zero. The rest of what you say makes excellent sense. "Ignorance more frequently begets confidence than does knowledge: it is those who know little, not those who know much, who so positively assert that this or that problem will never be solved by science." - Charles Darwin.
This message is a reply to: | | Message 23 by Stile, posted 01-08-2009 10:50 AM | | Stile has seen this message but not replied |
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Parasomnium
Member Posts: 2224 Joined: 07-15-2003
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Message 43 of 69 (493392)
01-08-2009 1:52 PM
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Reply to: Message 32 by cavediver 01-08-2009 12:46 PM
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Re: Thought experiment
cavediver writes: Parasomnium writes: 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. Only if you are located outside the shell. Once inside the shell, you experience no force whatsoever at any point. There is no "floating" towards the centre. It's straightforward calculus, just integrating hoops from pole to pole. Thanks for enlightening me, Cavediver, I didn't know that. If I'm correct you're a physicist of some kind (I'm too lazy to look it up in old messages), so I'll take your word for it. "Ignorance more frequently begets confidence than does knowledge: it is those who know little, not those who know much, who so positively assert that this or that problem will never be solved by science." - Charles Darwin.
This message is a reply to: | | Message 32 by cavediver, posted 01-08-2009 12:46 PM | | cavediver has not replied |
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