Re: [math-fun] High school physics problem
[Eavesdroppers: Other respondents offered https://en.wikipedia.org/wiki/Granular_convection and "the Brazil nut effect".] On 2018-12-10 09:16, Henry Baker wrote:
Suppose we have a large container not 100% filled with ball bearings (all of exactly the same material & hence density) but with a wide & random variety of radii. The largest ball bearings are << the smallest dimension of the container, and the smallest ball bearings can get into every corner of the container.
Initially, the bearings of all sizes are equally distributed w.r.t. location within the filled portion of the container.
We're on Earth with its standard gravity g and standard atmospheric pressure & temperature (if that matters).
Now shake the container vigorously for quite a while (but not so vigorously enough that the balls become dented or heated!).
What is the resulting distribution of sizes after this shaking?
A. The same as before.
B. The larger balls become more likely in the upper layers.
C. The larger balls become more likely in the lower layers.
I don't have a proof, but I have an intuition about which answer is correct.
Has this problem been studied before?
In the New Jersey gravel pits. Shore dwellers' lots are plain white sand. Your cheapest driveway is a truckload of low grade gravel, with granularity ranging from pebbles all the way down to clay. You sink in if you try to drive (or even walk) on it. But after a few weeks of weather, and then initially light usage, all the big pebbles are on top. —rwg
So the interior of the earth is the finest powder, and we have to live on the top with all the big rocks? All those beautiful white sand beaches are just vying to sink beneath it all? Arise ye rocks of earth and sea, Climb to heights of majesty! And all ye mites of sand and dust, Descend to depths beneath the crust. Hilarie
From: Bill Gosper <billgosper@gmail.com>
[Eavesdroppers: Other respondents offered https://en.wikipedia.org/wiki/Granular_convection and "the Brazil nut effect".] On 2018-12-10 09:16, Henry Baker wrote:
Suppose we have a large container not 100% filled with ball bearings (all of exactly the same material & hence density) but with a wide & random variety of radii. The largest ball bearings are << the smallest dimension of the container, and the smallest ball bearings can get into every corner of the container.
Initially, the bearings of all sizes are equally distributed w.r.t. location within the filled portion of the container.
We're on Earth with its standard gravity g and standard atmospheric pressure & temperature (if that matters).
Now shake the container vigorously for quite a while (but not so vigorously enough that the balls become dented or heated!).
What is the resulting distribution of sizes after this shaking?
A. The same as before.
B. The larger balls become more likely in the upper layers.
C. The larger balls become more likely in the lower layers.
I don't have a proof, but I have an intuition about which answer is correct.
Has this problem been studied before?
In the New Jersey gravel pits. Shore dwellers' lots are plain white sand. Your cheapest driveway is a truckload of low grade gravel, with granularity ranging from pebbles all the way down to clay. You sink in if you try to drive (or even walk) on it. But after a few weeks of weather, and then initially light usage, all the big pebbles are on top. —rwg
um… from this? Arise, ye subterranean Winds, More to distract their guilty minds; And all ye filthy damps and vapours rise, Which use t'infect the earth, and trouble the skies.
On Dec 14, 2018, at 11:46 AM, Hilarie Orman <ho@alum.mit.edu> wrote:
So the interior of the earth is the finest powder, and we have to live on the top with all the big rocks? All those beautiful white sand beaches are just vying to sink beneath it all?
Arise ye rocks of earth and sea, Climb to heights of majesty! And all ye mites of sand and dust, Descend to depths beneath the crust.
Hilarie
From: Bill Gosper <billgosper@gmail.com>
[Eavesdroppers: Other respondents offered https://en.wikipedia.org/wiki/Granular_convection and "the Brazil nut effect".] On 2018-12-10 09:16, Henry Baker wrote:
Suppose we have a large container not 100% filled with ball bearings (all of exactly the same material & hence density) but with a wide & random variety of radii. The largest ball bearings are << the smallest dimension of the container, and the smallest ball bearings can get into every corner of the container.
Initially, the bearings of all sizes are equally distributed w.r.t. location within the filled portion of the container.
We're on Earth with its standard gravity g and standard atmospheric pressure & temperature (if that matters).
Now shake the container vigorously for quite a while (but not so vigorously enough that the balls become dented or heated!).
What is the resulting distribution of sizes after this shaking?
A. The same as before.
B. The larger balls become more likely in the upper layers.
C. The larger balls become more likely in the lower layers.
I don't have a proof, but I have an intuition about which answer is correct.
Has this problem been studied before?
In the New Jersey gravel pits. Shore dwellers' lots are plain white sand. Your cheapest driveway is a truckload of low grade gravel, with granularity ranging from pebbles all the way down to clay. You sink in if you try to drive (or even walk) on it. But after a few weeks of weather, and then initially light usage, all the big pebbles are on top. —rwg
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Or maybe "Arise, ye sons of MIT", but it doesn't have the same scansion. OK, Hilarie, I give up. On Fri, Dec 14, 2018 at 4:06 PM Cris Moore <moore@santafe.edu> wrote:
um… from this?
Arise, ye subterranean Winds, More to distract their guilty minds; And all ye filthy damps and vapours rise, Which use t'infect the earth, and trouble the skies.
On Dec 14, 2018, at 11:46 AM, Hilarie Orman <ho@alum.mit.edu> wrote:
So the interior of the earth is the finest powder, and we have to live on the top with all the big rocks? All those beautiful white sand beaches are just vying to sink beneath it all?
Arise ye rocks of earth and sea, Climb to heights of majesty! And all ye mites of sand and dust, Descend to depths beneath the crust.
Hilarie
From: Bill Gosper <billgosper@gmail.com>
[Eavesdroppers: Other respondents offered https://en.wikipedia.org/wiki/Granular_convection and "the Brazil nut effect".] On 2018-12-10 09:16, Henry Baker wrote:
Suppose we have a large container not 100% filled with ball bearings (all of exactly the same material & hence density) but with a wide & random variety of radii. The largest ball bearings are << the smallest dimension of the container, and the smallest ball bearings can get into every corner of the container.
Initially, the bearings of all sizes are equally distributed w.r.t. location within the filled portion of the container.
We're on Earth with its standard gravity g and standard atmospheric pressure & temperature (if that matters).
Now shake the container vigorously for quite a while (but not so vigorously enough that the balls become dented or heated!).
What is the resulting distribution of sizes after this shaking?
A. The same as before.
B. The larger balls become more likely in the upper layers.
C. The larger balls become more likely in the lower layers.
I don't have a proof, but I have an intuition about which answer is correct.
Has this problem been studied before?
In the New Jersey gravel pits. Shore dwellers' lots are plain white sand. Your cheapest driveway is a truckload of low grade gravel, with granularity ranging from pebbles all the way down to clay. You sink in if you try to drive (or even walk) on it. But after a few weeks of weather, and then initially light usage, all the big pebbles are on top. —rwg
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Purcell and Shakespeare are grand, I'd not reduce them to doggerel. My inspriation was "arise ye sons of MIT". Always hated that phrase. Hilarie
um... from this?
Arise, ye subterranean Winds, More to distract their guilty minds; And all ye filthy damps and vapours rise, Which use t'infect the earth, and trouble the skies.
On Dec 14, 2018, at 11:46 AM, Hilarie Orman <ho@alum.mit.edu> wrote:
So the interior of the earth is the finest powder, and we have to live on the top with all the big rocks? All those beautiful white sand beaches are just vying to sink beneath it all?
Arise ye rocks of earth and sea, Climb to heights of majesty! And all ye mites of sand and dust, Descend to depths beneath the crust.
Hilarie
From: Bill Gosper <billgosper@gmail.com>
[Eavesdroppers: Other respondents offered https://en.wikipedia.org/wiki/Granular_convection and "the Brazil nut effect".] On 2018-12-10 09:16, Henry Baker wrote:
Suppose we have a large container not 100% filled with ball bearings (all of exactly the same material & hence density) but with a wide & random variety of radii. The largest ball bearings are << the smallest dimension of the container, and the smallest ball bearings can get into every corner of the container.
Initially, the bearings of all sizes are equally distributed w.r.t. location within the filled portion of the container.
We're on Earth with its standard gravity g and standard atmospheric pressure & temperature (if that matters).
Now shake the container vigorously for quite a while (but not so vigorously enough that the balls become dented or heated!).
What is the resulting distribution of sizes after this shaking?
A. The same as before.
B. The larger balls become more likely in the upper layers.
C. The larger balls become more likely in the lower layers.
I don't have a proof, but I have an intuition about which answer is correct.
Has this problem been studied before?
In the New Jersey gravel pits. Shore dwellers' lots are plain white sand. Your cheapest driveway is > a truckload of low grade gravel, with granularity ranging from pebbles all the way > down to clay. You sink in if you try to drive (or even walk) on it. But after a few > weeks of weather, and then initially light usage, all the big pebbles are on top. âr> wg
_______________________________________________
Well, yours is better than the original. I want to put another "and" in front of the second line to make it iambic tetrameter throughout. On Fri, Dec 14, 2018 at 5:29 PM Hilarie Orman <ho@alum.mit.edu> wrote:
Purcell and Shakespeare are grand, I'd not reduce them to doggerel. My inspriation was "arise ye sons of MIT". Always hated that phrase.
Hilarie
um... from this?
Arise, ye subterranean Winds, More to distract their guilty minds; And all ye filthy damps and vapours rise, Which use t'infect the earth, and trouble the skies.
On Dec 14, 2018, at 11:46 AM, Hilarie Orman <ho@alum.mit.edu> wrote:
So the interior of the earth is the finest powder, and we have to live on the top with all the big rocks? All those beautiful white sand beaches are just vying to sink beneath it all?
Arise ye rocks of earth and sea, Climb to heights of majesty! And all ye mites of sand and dust, Descend to depths beneath the crust.
Hilarie
From: Bill Gosper <billgosper@gmail.com>
[Eavesdroppers: Other respondents offered https://en.wikipedia.org/wiki/Granular_convection and "the Brazil nut effect".] On 2018-12-10 09:16, Henry Baker wrote:
Suppose we have a large container not 100% filled with ball bearings (all of exactly the same material & hence density) but with a wide & random variety of radii. The largest ball bearings are << the smallest dimension of the container, and the smallest ball bearings can get into every corner of the container.
Initially, the bearings of all sizes are equally distributed w.r.t. location within the filled portion of the container.
We're on Earth with its standard gravity g and standard atmospheric pressure & temperature (if that matters).
Now shake the container vigorously for quite a while (but not so vigorously enough that the balls become dented or heated!).
What is the resulting distribution of sizes after this shaking?
A. The same as before.
B. The larger balls become more likely in the upper layers.
C. The larger balls become more likely in the lower layers.
I don't have a proof, but I have an intuition about which answer is correct.
Has this problem been studied before?
In the New Jersey gravel pits. Shore dwellers' lots are plain white sand. Your cheapest driveway is > a truckload of low grade gravel, with granularity ranging from pebbles all the way down to clay. You sink in if you try to drive (or even walk) on it. But after a few weeks of weather, and then initially light usage, all the big pebbles are on top. —r> wg
_______________________________________________
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
It's been revised to "arise all ye of MIT". On the beaches, it's the wind, waves, and sun that grinds and bleaches the rocks into sand. On 14-Dec-18 17:28, Hilarie Orman wrote:
Purcell and Shakespeare are grand, I'd not reduce them to doggerel. My inspriation was "arise ye sons of MIT". Always hated that phrase.
Hilarie
um... from this? Arise, ye subterranean Winds, More to distract their guilty minds; And all ye filthy damps and vapours rise, Which use t'infect the earth, and trouble the skies.
On Dec 14, 2018, at 11:46 AM, Hilarie Orman <ho@alum.mit.edu> wrote:
So the interior of the earth is the finest powder, and we have to live on the top with all the big rocks? All those beautiful white sand beaches are just vying to sink beneath it all?
Arise ye rocks of earth and sea, Climb to heights of majesty! And all ye mites of sand and dust, Descend to depths beneath the crust.
Hilarie
From: Bill Gosper <billgosper@gmail.com>
[Eavesdroppers: Other respondents offered https://en.wikipedia.org/wiki/Granular_convection and "the Brazil nut effect".] On 2018-12-10 09:16, Henry Baker wrote:
Suppose we have a large container not 100% filled with ball bearings (all of exactly the same material & hence density) but with a wide & random variety of radii. The largest ball bearings are << the smallest dimension of the container, and the smallest ball bearings can get into every corner of the container.
Initially, the bearings of all sizes are equally distributed w.r.t. location within the filled portion of the container.
We're on Earth with its standard gravity g and standard atmospheric pressure & temperature (if that matters).
Now shake the container vigorously for quite a while (but not so vigorously enough that the balls become dented or heated!).
What is the resulting distribution of sizes after this shaking?
A. The same as before.
B. The larger balls become more likely in the upper layers.
C. The larger balls become more likely in the lower layers.
I don't have a proof, but I have an intuition about which answer is correct.
Has this problem been studied before?
In the New Jersey gravel pits. Shore dwellers' lots are plain white sand. Your cheapest driveway is > a truckload of low grade gravel, with granularity ranging from pebbles all the way > down to clay. You sink in if you try to drive (or even walk) on it. But after a few > weeks of weather, and then initially light usage, all the big pebbles are on top. —r> wg
_______________________________________________
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (5)
-
Allan Wechsler -
Bill Gosper -
Cris Moore -
Hilarie Orman -
Mike Speciner