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Apples: CR4 Challenge (10/14/08)

Posted October 14, 2008 2:09 PM

This week's CR4 Challenge Question

You partially fill (up to ½ of its height) a bucket with apples of various sizes. Shake the bucket for several minutes. You notice that the biggest apples are on top. Why?

And the Answer is....

The larger apples cannot slip downward if the available space between the lower apples is not big enough. However apples smaller than the available space can slip down and larger apples will remain on top. By shaking the bucket several times, this process is repeated (smaller apples slip down, bigger apples remain on top), and eventually the system will settle such that the larger apples remain on top.

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#1

Re: Apples: CR4 Challenge (10/14/08)

10/14/2008 3:40 PM

The smaller apples fall to fill in the voids left inbetween the large apples. Much like shaking a bucket of sand and gravel mixed. the sand works its way to the bottom filling in the voids left behind in the rocks.

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#2

Re: Apples: CR4 Challenge (10/14/08)

10/14/2008 3:47 PM

This is similar to the question of why the large nuts move to the top of the can or why the larger grains of coffee also move to the top of the can. I've really never seen an explanation that I really liked.

The explanation that I have the most liking for is that it is related to the drag on the side of the container as the container is moved up and down. The container and its contents move up together but as the container is accelerated downward faster than the acceleration of gravity, the contents tend to lag behind. However, the friction with the side walls causes the contents there to move more with the container. This creates a downward "convection" along the wall. The contents along the wall tend to move downward which caused the contents on average to move upward in the rest of the container. The convective current downward tends to be as narrow as it can be which causes a net downward motion of smaller particles near the wall which results in a general trend of the larger particles moving upward.

I think it might also have to do with the size of the holes between particles. As the contents is shaken, holes between particles get larger. The smaller particles can most easily move into these holes, if only partially. After many cycles of vibration, the holes toward the bottom are smaller and filled with the smaller particles. This causes the larger particles in general to end up higher.

For more widely distributed particle sizes than a bucket of apples, the small particles would simply fill in the spaces between the larger ones. This would leave the spaces at the bottom more filled and the once at the top less filled. This would be a lower energy situation and would be the most stable situation.

None of these explanations seems to really explain the phenomena well though.

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#4
In reply to #2

Re: Apples: CR4 Challenge (10/14/08)

10/14/2008 11:06 PM

Ya,

it is fact in plitics too. Large nuts go up and up to top and rule the countries.

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#11
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Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 6:25 AM

Jim's right about the convection created at the sides of the walls. It is indeed easier, and takes less energy for the smaller apples to move down. I remember seeing a study done by someone, maybe at MIT or somewhere and it being telecasted on Discover years and years ago, when i was kiddier than i am now :P.

One would also think it has a bit to do with momentum, as the bucket is moving up and down with the same velocity and all the apples having the same acceleration, the smaller apples have lower momentum while the bigger apples have higher momentum thereby creating a relative motion between the two and resulting in the smaller apples filling the void.

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#13
In reply to #2

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 6:41 AM

First, I'm not clear that this is valid for a bucket full of apples, the question in my mind is whether the size range is sufficient for this to take place. Unfortunately, I don't have sufficient apples spare to perform an experiment to verify the effect - contributions from someone with a decent supply would be much appreciated (any ambiguity here is deliberate)

As regards the general effect, I too have never seen a simple explanation that I like - indeed, most of those I have seen are demonstrably incorrect.

The one that raises most hackles for me is the one that involves minimisation of potential energy in the final state, because in so many cases it is demonstrably untrue.
. Consider pebbles on the beach (or in your garden soil) - these do indeed tend to rise to the top. But the state of minimum potential energy is with the pebbles at the bottom with the interstices surrounded by sand (or soil).

Number two in the "suspect" list of is the effect of the sides of the container, because such effects must be trivial on the beach or in the garden.

To my mind the least bad I have seen is as follows:
. When one of the items rotates (or rocks), other items can move to occupy the space underneath. Larger objects will tend to retain any rotational motion for longer than smaller ones - you can model this in terms of the ratio of surface area to volume, meaning that equivalent external effects have a smaller relative impact on the movement of the large object than they do on smaller ones; alternatively, you can consider the effect of increased radius of inertia. The first mechanism means that both upwards motion (relative to other objects) and rocking will be more persistent; the second only affects rocking.
. Either way the upwards tendency of the larger objects will persist beyond that of smaller ones.
. . So far, however, this is no explanation at all, because downwards relative motions should be equally persistent. We need to add that a significant proportion of upwards motions are initiated from a locally compacted state, in which the proportionate effects on large and small objects are very similar.

Gyroscopes at dawn, anyone?

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#14
In reply to #13

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 6:49 AM

I refuse to believe that you do not posses sugar lumps/tongs/granulated sugar/ for experimenting with. Nobody in their right mind would request you place said lumps in the Earl Grey, but this one is ripe for experimentation. Oddly, it coincides with a question elsewhere titled 'Probablity' - I forget who's interesting question, but it relates to half pills put back in a bottle. My endeavours at present are concentrated on the Pils, it seems to be of more practical use .

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#16
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Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 7:34 AM

Kris

I know this works when there is a wide range of sizes and in a relatively large vessel. It is the specific case of items covering a relatively small range and being a substantial proportion of the size of the vessel that arouses suspicion. (There are also some claims in the responses in this thread that I doubt, but you can't cover everything).

The experiment needs rounded objects with diameters between (say) 0.2 and 0.25 the diameter of the vessel.

BTW1 . As we don't encourage our visitors to bring their horses into the house, the only lump sugar is kept in the stables.
BTW2 . I hope this is Pilsner Urquell or similar, as the vessels will not be the correct sizes or shapes for the experiment - so the proper purpose will be for drinking

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#18
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Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 7:52 AM

Hi Fyz,

The experiment needs rounded objects with diameters between (say) 0.2 and 0.25 the diameter of the vessel.

That would seem to be sensible, but this is CR4 question-land. Is there a basis for suggesting the 0.2/0.5 ? My inclination was to think about relative size of apples to each other. I don't have that other thread's link to hand,but it's worth looking up for the sensible bits (title is "Probablity" or similar, I'll check when I'm back next).

The question is (perhaps wrongly) leading me to think about packing density in a finite space. If all apples are the same shape, packing density is the same in an infinite volume, but with a limited ratio of object to container size maybe there is an argument that works to explain this phenomena. Whatever the case ( bad choice of word) there are some subtle aspects to the question and finding a clear answer.

Until later, I shall return to my Pils in a cow horn...............

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#19
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Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 7:54 AM
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#25
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Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 10:22 AM

think about packing density in a finite space

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#26
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Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 10:46 AM

Round bucket, larger apple = better packing density at edge. Taking that for final PE considerations, the large apple should fall to the bottom. So I can't see where this leads

I believe this is why the solutions that have so far been favoured depend on the difference between the initial upwards acceleration and the subsequent settling effects. The initial upward acceleration each time is driven from the base of the bucket, and is pretty-much independent of apple size. The interactions during settling depend more on the surface area of the apple, so they should have proportionately (~R-1/3) less effect on larger items of similar density.

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#28
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Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 11:36 AM

Extreme case perhaps, and, only considering one cylindrical "slice" the thickness of the apples diameter (also not considering vertical shuffling):-

Packing density ratio of 28 to 25.

Can you come up with any counter examples?

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#33
In reply to #28

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 4:04 PM

I think that 9:8 might be a closer approximation?

Here are some relatively simple regular tightly-packed examples:
1 -> 100%
3 -> 64.6% [= 3/(1+1/cos(30))2]
4 -> 68.6% [= 4/(1+sqrt(2))2]
7 -> 77.8% [= 7/9]
19 -> 76% [= 19/25]
Infinity -> 90.7% [= ∏/2/sqrt(3)]

So I agree that the local irregularity sits over a general increase in packing density - but I doubt this applies in the region of interest (bucket diameter about 5-times the diameter of the apple).
In addition, there is no question that where the density is changing on a continuous basis it is falling monotonically as you reduce apple size. Then there are sudden jumps to a closely-packed peak, which may (or not) be higher than the previous one.

But this is not really the basis of my objection to the explanation - which is that the idea that externally derived shaking will tend to reduce the potential energy of the final (stationary) system to its lowest level. This is demonstrably untrue for sands and for soils that are disturbed by rain or by tides. For the case of a shaken bucket of apples, I rather expect the position of the C of G to fall initially and then to rise - but I'm perfectly prepared to be found wrong on this.

BTW, I once worked for a company whose Chief Industrial Engineer had used energy arguments to show that "vibratory bowl feeders could not possibly work" - and his staff were so scared of him that attempts to authorise purchase of such feeders always failed. (My division, one of only three that is still trading, persuaded our supplier to accept a different description - but even there we made certain that the units were switched off whenever he visited, and a spurious explanation of their purpose was ready to trip off the tongue.)

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#40
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Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 4:36 AM

SHAPE OF THE BUCKET OF NO IMPORTANCE. Size more of a factor - small ones go down.

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#65
In reply to #26

Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 1:32 AM

still do not agree - shape of the bucket is not relevant - the effect is not influenced by the shape of the container - Unless it is small relative to the size of individual particles. Specific gravity and size differences for the particles are the controlling factors. Don't bring red herrings in.

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#67
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Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 2:01 AM

Not unless you're dealing with something like a baking pan... Oooo! Baked apples! Screw the challange!!!

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#72
In reply to #67

Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 6:12 AM

Are you suggesting that the effect is driven by cosmological corkscrews?

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#23
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Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 8:39 AM

I think thats what I said I just simplified it.

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#79
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Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 6:55 AM

This is misleading - the size of the container would have a minimum but there is no maximum and shape of the container has nothing to do with it! It is an interaction between the shape of the particles, their relative size as well as the specific gravities in the case of mixtures. Look at the scree on a mountain side no container still the same effect!

I seem to remember an angle of 30 degrees being quoted but not sure. This is also a problem when dealing with bulk solids when they reach an angle of repose. It can also be a problem when emptying hoppers as bridging takes place - I believe a similar angle of repose is found. We had to use vibrators to stop this.

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#81
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Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 7:19 AM

Angle of repose of scree is not some fixed number. Amongst other factors, it depends upon the 'angle of friction' of the material. 'Choking' in hoppers is not uncommon and relates to differences in static/dynamic effect. In underground mining it's not uncommon to resort to dynamite to resolve such problems. Come back to an ore-chute after a days stoppage and it may well be blocked - Mr big-bad may be your best option. Vibration is, however, a less dramatic solution for flour or whatever.

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#3

Re: Apples: CR4 Challenge (10/14/08)

10/14/2008 10:54 PM

Actually, if you think about it, the bucket will have to be friggen BIG

you wouldn't be picking small apples, you'd be picking the larger ones, and maybe the minimum you'd be picking are 1/2 the size of the larger ones, any smaller, and they'd get ejected in the sorting machine.

Now, to shake the apples so the smaller ones fall between the cracks/spaces of the larger ones, the larger ones will have to move apart and seperate considerably, and the bucket would have to still retain the apples as they come back down, so you'd have to lift and allow the apples to exit the top of the bucket, space out then try and juggle back into the small opening.

The smallest of apples I eat are about 2-3" diameter, so to shake the smaller ones to the bottom would be 1 hell of a mean feat.

Could you please provide a video of yourself or someone successively doing this?

I don't mean using something to simulate apples, but using real apples, and prove that this "Challenge" is actually able to be done?

Please don't try this during picking time on a orchard, you'd possibly get sacked for damaging the produce

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#5

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 12:00 AM

They have a larger mass and the movement allows them to squeeze upwards while gravity pulls the smaller one downward. is my guess.

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#6

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 12:34 AM

Oh, man!!! Don't be so flippant, man!!! It's the work of Lothar, dude! King of the apples!!! Ya see, this is why the apple was the forbidden fruit! They can think, dude! They can really think; and the big ones climb to the top - and are probably plotting their revenge right now!!!

If you want to do these unholy experiments, man, you'd be a lot safer using tangerines!!!

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#7
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Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 2:11 AM

I mustent be hanging around in the right forums, you been missing from "General population" for a while.

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#8
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Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 3:30 AM

vermin has been jumping up and down on the opposition ;

It seems intuitively right that the little ones would fall lower, but that's not exactly an explanation. When vermin jumps about, there's always space for smaller thing to fall in the void beneath him. If you go digging on a pebble beach you'll likely find sand beneath the pebbles. Even if vermin was slightly denser he would probably rise, but their must be a cut-off limit in vermins density versus ability to jiggle upwards. I suspect such a limit is related to how vigorously he's shaken and how deeply he's buried.

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#92
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Re: Apples: CR4 Challenge (10/14/08)

10/21/2008 1:10 PM

Unfortunately the General was caught with another' wife. He was demoted to Kernel.

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#93
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Re: Apples: CR4 Challenge (10/14/08)

10/21/2008 2:13 PM

Are you sure he wasn't subjected to Corporal punishment?

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#94
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Re: Apples: CR4 Challenge (10/14/08)

10/21/2008 3:39 PM

Unless you are a human rights lawyer, in which case it is of Major interest, that should remain a Private matter.

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Re: Apples: CR4 Challenge (10/14/08)

10/21/2008 11:27 PM

You obviously have a good Command of your vocabulary! Soldier on! I Recon I shall have to Salute you for your Intelligence.

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#96
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Re: Apples: CR4 Challenge (10/14/08)

10/22/2008 7:30 AM

If we are to cope with the Field in/of the next challenge, we need to work hard to Marshall our resources.

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#97
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Re: Apples: CR4 Challenge (10/14/08)

10/22/2008 8:45 AM

Someone should summon the Sargeant-at-Arms...

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#98
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Re: Apples: CR4 Challenge (10/14/08)

10/22/2008 2:43 PM

Yes, if this line of punnery continues, it shall resemble my last National Guard summer camp. We didn't stay in barracks that year, and it was an in-tents experience.

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#99
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Re: Apples: CR4 Challenge (10/14/08)

10/22/2008 3:44 PM

Enough, I too can't take any more of this Barracksing.

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#100
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Re: Apples: CR4 Challenge (10/14/08)

10/22/2008 3:52 PM

Well, as they used to say in the Cavalry, if you're not a-horse, you're a-foot.

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#9

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 5:56 AM

If you look at the bucket as a system and determine its center of gravity, an "unordered" bucket will have a higher center of gravity than an "ordered" bucket. As the smaller objects in any collection of equal density objects move toward the bottom, the center of gravity moves down. The entropy of the latter system is less.

An interesting experiment is to perform the same shake with a can of marbles including large steelies and small plastic balls. If the plastic balls have a density small enough such that the average density of a given volume of plastic balls is less than the average density of the steelies in the same volume, the plastic balls will move toward the top.

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#10

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 6:11 AM

Yes pebbles on the beach was my first thought, so how does that relate to apples? Well as they are tossed into the air, just like the incoming tide, or wave, an even force (acceleration) is being applied, resulting in all the apple reaching the same height? When they start to fall gravity takes over, each falling at the same rate, but when they hit the bottom, it's mass plus acceleration then we have an equal and opposite force, so the larger mass rebounds further, till they eventually rise to the top. Wow, I think that's what happens? Yes vermins been missing for a while good to see him back.

Regards JD.

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#12

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 6:37 AM

the larger apples meet in such a way as to form a large gap between any three adjacent, which probably has to do with some trigonometric feature i can't right now specify. at any rate, this creates a series of sieves amongst any three adjacent apples and this serves to sort the apples by size, with the smaller ones being able to pass through the sieves. most likely a parallel explanation is that the larger apples have more buoyancy because the microscopic area of contact with adjacent apples is greater compared to their mass (even though their mass per surface area is greater) again related to what is probably the differential of their curvature at the contact point. with more contact area there is more force to act against gravity. ordinarily, the force of friction relative to weight is irrelevant since the increased weight serves both to increase the normal force and inertia - they cancel out - but here the force is normal to gravity instead of aligned with it so the increased surface area does create more friction.

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#15

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 7:17 AM

Being a confessed apple addict I believe that a couple of things might be overlooked. First shaking the bucket for several minutes will bruise all the apples. Second smaller apples usually are much denser which can actually create a smaller heaver apple, larger apples tend to be aire with larger cavities around the core & seeds. Remember its not always the size that matters but weight. This brings me to another interesting observation along these line. I have noticed that old buried tires through the years seem to migrate up and out of the ground on there own, in non seismic areas?

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#17

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 7:50 AM

Apparent Density. This is why rocks come to the surface in the spring thaw and stream flow grades particles by size. http://en.wikipedia.org/wiki/Sedimentation

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#20

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 7:57 AM

A fundamental concept in the paint industry. Gets more complex if the spheres are different materials with different densities Try the following

SPECIFIC GRAVITY or DENSITY

This is a primary area for confusion We can have "Relative Density' or "Specific GravIty" the preferred term. Density tends to be a rather loose term - it may refer to the density of a fog, a crowd or a forest So let us see what the dictionary says

SPECIFIC GRAVITY

The ratio of the density of a substance to the density of a reference substance it is an abstract number that is unrelated to any units. For solids and liquids specific gravity is numerically equal to density but for gases it is not, because of the difference between the densities of the reference substances, which are usually water (mg/cc) for solids and liquids and air (0.00129 g/cc or 1.29 g/L at 0°C and 760 mm) for gases.

The specific gravity of a gas is the ratio of its density to that of air. Since the specific gravity of air = 1.0 (1.29/1.29) this is usually stated to indicate the comparison but with the gas under consideration For example the density of hydrogen is 0.O89 g/l its specific gravity is 0.069, (i.e. 0.089/l.29). The specific gravity of solids and liquids is the ratio of their density to that of water at 4C, taken as 1 0, as 1 cc of water weighs 1 gram. Thus a solid or liquid with a density of 1 5 g/cc has a specific gravity of 1.5/1 or 1.5.

Since weights of liquids and gases vary with temperature it is necessary to specify both temperatures involved except for rough or approximate values. Thus the specific gravity` of alcohol should be given as 0.7893 at 20/4C, the first temperature referring to the alcohol and the latter to the water. At 15.56C the specific q gravity of alcohol is 0 816.

In the case of gases the pressure would also be a consideration hence the temperature and pressure at which the reading was taken must be quoted.

A density will always show a mass/volume relation ship. `

Specific Gravity is the relationship to a set reference substance.

Densities of some common substances follow

grams/cm3 grams/liter SG

Sulphur 2.06 2.06

Aluminium 3.7 3.7

Sodium 0.967 0.967

Glycerol 1.27 1.27

Water 1.0 1.0

chlorine 3.214 2.486

Carbon dioxide 1.977 1.529

Air 1.293 1.0

Oxygen 1.429 1.105

Hydrogen 0.089 0.069

"APPARENT DENSITY", "BULK DENSITY" OR "PACKING DENSITY"

Relative density applies to the solid mass of the substance but when substances are divided into smaller particles then the apparent volume changes because of the voids between the particles. The mass of a given volume of a substance in this condition is referred to by various terms such as "Apparent Density", "Bulk Density" or "Packing Density". The term:"bulking value" is sometimes used. These refer to the weight of a given volume of powder/granules as such. In other words, it is the weigh of a given volume as presented. Think of corn it can be In the form of a grain, flour, a cornflake or a piece of popcorn. Consider Iron, it can come in various forms such as bars, wire, filings or wire wool. These groupings can all be the same substance they just have different forms The volume of a given weight of these will differ considerably.

This concept is mostly of use to shippers and packers. When loading a vehicle or a ship- to the weight In other, words it can there is a limit to the volume - it will take as well as get too full of too heavy. By careful composition of a mixed load, the maximum advantage can be achieved Sometimes the term 'tamped' is quoted this means that It the substance has been vibrated or compacted to make It pack as closely as possible. In order to save space substances are compressed.

It is important for the paint maker to remember that paint is sold and applied on a volume basis but It is manufactured on a weight basis. It would be very difficult to measure the pigments extenders by volume. Using weight allows a measurement that is more accurate and repeatable. Using volume, without precautions, can lead to inaccuracies. Apart from the complication of the voids in solids, in the case of liquids, their susceptibility to volume change with temperature can lead to errors

At all times the paintmaker must be aware of volume/weight considerations as surface coatings are applied at specific thickness and so the volume not the weight is of concern.

Of prime consideration is the specific gravity - in other words how much do you get for your money In the case of titanium dioxide, 1 litre weighs 4.1 kgs, in the case of talc or clay 1 litre weighs 2.8 kgs , for chalk 2 5 kgs. and for barytes 4 34 kgs. When considering cost efficiency of pigments, it is actually the cost per litre which is of concern not the cost per kilo. The weight for any given volume of each type of pigment is different! Appended is a list of some of the more common ones

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#21

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 8:07 AM

Along with the laws of gravity and friction, I think we should also take into account the laws of inertia and kinetic energy. once all the apples have started to move upward they want to remain moving upward. the apples with the larger mass are harder to get moving, but are also harder to stop moving by both gravity and friction of the bucket. As all the apples move upward the smaller apples on the bottom will strike the larger ones (and smaller ones as well. which is why we need to shake for several minuets.) on top of the thus transferring some of their energy to move up to the ones on top of them causing them to move downward sooner than the ones on top of them filling in the voids sooner than the larger ones. After multiple repetitions of this, soon all of the smaller apples have fallen to the bottom first having lost most of their upward kinetic energy to the larger ones on top. In order for this phenomenon to occur we must have a few things, 1) larger and smaller particles of a shape so as to create voids 2) enough force to allow all the particles to move and create holes in the structure enough so that smaller particles can slip down and fill those voids 3) enough room for the particles to move enough to allow smaller particles to slip in to voids. Hence if we had all the same size apples in a bucket and we shook without enough force to move the apples or had a stuffed completly full with a lid allowing no room for movement, no apples would move to the top or bottom.

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#22

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 8:37 AM

Don't rightly know but, you are going to bruise your apples. You should consider using them for something usefull like making nice hard apple cider instead of wasting them on such nonsense...

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#24
In reply to #22

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 9:54 AM

We'll just use them right after for just sort of a thing and consider it to be part of the mashing process prior to fermenting.

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#27

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 11:07 AM

The apples are a slurry mixed with air. The apples are more dense. The mixture with smaller apples has a greater proportion of the more dense material and falls to the bottom when shaken, not stirred...

Mr. Gee

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#29

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 12:07 PM

Here the boyancy and gravitation works to separate the bigger one than smaller one.As we go on skaking the bucket the bigger aple staret flooting on upper level than the smaller apple.At the same time the smaller aple starts comming down and the larger apple remain on upper level.

B.K.P

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#30

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 12:21 PM

Why? Because the smaller apples are already mashed into applesauce is why. Shake a bit longer, most of the larger ones will be gone too. The packing density of applesauce is much higher than that of apples, so the larger apples will stay afloat on this sea of applesauce longer. Eventually you'll have to grate some cinnamon sticks on top of it and serve, preferably chilled. Like a decent martini: shaken, not stirred, and chilled.

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#31

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 2:35 PM

I use this process in my work every day. I run heavy equipment in a quarry. This process works on boulders of any size. Many are over 40 tons. I need to separate oversize boulders before loading trucks for the crusher. No shaking involved just dropping, either on the ground or against a sloped bank. The larger rocks most often end up on top making them easier to separate. When doing dirt road repair I spread buckets of material along a stretch. Then come along with the bucket slightly raised and leave the smaller stuff for the road surface.

I think the smaller stuff can tumble into voids and the larger stuff tends to remain near the surface.

As you can see I'm no engineer but I thought everyone may enjoy a "real life" example of this process at work.

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#74
In reply to #31

Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 6:27 AM

That is a practical view - it is also of interest that the slope of heap is fairly constant (irrespective of size of particles or mix)

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#32

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 3:50 PM

The apples on the bottom are suffocating. Since the big ones are stronger than the small ones, they bully their way to the top for the fresh air.

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#34

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 4:06 PM

You guys make it to difficult,

During the shaking /vibration more spaces are created that a small apple/object can fall into vs the larger object.

By the time the space is large enough for the larger apple/object a smaller apple/object has already had room and gravity took its course.

As more and more small voids are filled with small apples/objects moving down the larger apples/objects are moved up by the same energy that makes the voids.

In unequal density the heaver massed object imparts more velocity to the lighter object while slowing its own. (it pushes them out of the way) until the ratio of masses finds equilibrium. (sinks or floats to some degree)

This should work up to where the pressures make non elastic deformation (apple sauce) or quantum effects kick in or just turn off the gravity.

Clear as mud?

Brad

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#35

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 4:43 PM

It worries me when I read about friction on the side of a container alternately preventing motion by friction (drag is experienced by an object moving through a fluid - friction is experienced by an object moving against a surface) and then at the same time promoting a non-thermally induced convection current. Same thing with sorting by momentum objects going the same speed - objects in freefall fall with the same acceleration regardless of mass. The density of the apples is also approximately the same large to small. Any differences are insignificant as long as we ignore age. Toss a bunch of apples of the same kind, large and small into a tub of water. You will observe that they have the same percentage of volume above the water.

OK, that stuff aside, let's evaluate a couple other ideas not yet discussed and one that has been. First, keep in mind that as we shake a container of apples we begin the apples moving relatively with respect to eachother. Depending upon the shape of the container, how you hold the container, how you support the weight, how you produce the shaking motion, some apples from one area will be accelerated more than from another. We start a flow of apples. We induce, by the shaking, relative motion between apples. Now keep in mind the excellent comment someone made about the smaller apples able to fit into the open spaces more easily and drop into now open holes more easily than the larger apples that are too big for many of those voids. Since we now have a flow and some apples are moving more and faster than others, these holes become more available. Also consider the big apples. To visualize the effect more starkly, imagine a container of sand. Take a 10cm diameter right cylinder and try to push it end first into the sand. Not easy to do because of all those little bits of sand in the way. Now take a right cyclinder with a diameter of 0.1 cm and push it into the sand. It is very easy to do. Now look at the big apple. Remember that we have things moving in a sort of a flow. Once on top, it is difficult for the big apple to re-enter the flow because it is big and has more smaller and equally dense objects below it and not enough big holes. It would have to push the smaller apples out of the way and up the sides of the container to get back in. Having the same density, it cannot do this and remains on the top. Over time, more and more of the big apples get stuck on the top and are unable to force their way back into the flow. When the skaking, and thus the flow of apples, stops, the apples have been sorted by size - largest on top, at least to some degree.

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#36
In reply to #35

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 5:29 PM

i am one of those who pointed out what you are saying, namely, the smaller apples able to fit into the open spaces. i am curious as to whether, as well, the comment i made about friction between the apples and between the apples and the sides of the bucket due to an increased area of contact at the microscopic level - being greater with the larger apples due to their having less curvature (which would only matter if the surface is not perfectly sheer and non-elastic but being subject to some deformation) - would also contribute to the larger apples not being able to fall as freely. As i mentioned, the friction in question is produced by a force normal to that of gravity so the usual considerations of mass canceling out the effects of larger surface area do not apply. Obviously, the "moving sieve" effect is the major one, and i do think that one can derive the "packing density" principle from that (and do you agree that the two are equivalent?), but, would not the larger contact area of a large apple contribute to at least a minute, perhaps practically insignificant, degree?

James H Waters, PhD

Clinical Psychology and Neuropsychology

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#76
In reply to #36

Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 6:40 AM

Interesting point and probably pertinant.

There is an old party trick where you take a glass of rice full to the brim. If you now force a chopstick into this quickly there is a wedge effect and you can pick the whole glassfull up on the end of the stick. If you push the stick in slowly you can also remove it easily - obviously there is no wedging.

This must be similar to tampimg which should be used to ensure a proper bulk density is measured.

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#78
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Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 6:49 AM

That hints toward several other interesting phenomena - stabbing a potato with a straw (staw doesn't buckle), and the question of why will a piece of spaghetti break into three bits when stressed. Dang....they google too easy.

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#48
In reply to #35

Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 7:20 AM

As succinctly pointed out by Randall in #38, the mechanism in question is the difference between upwards and downwards movement and/or filling. To my mind, your explanation does not clarify this.

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#56
In reply to #35

Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 4:38 PM

Your explanation does not agree with a demonstration I recall, where there was a vibrating sand bath. A metal key and a cork were placed on the sand surface and the key sank, whereas the cork floated. In fact the sand simulated a liquid. If a large solid sand sphere (big apple) were to be placed in this fluidic sand (small apples), it would sink because the density of the solid is greater than the average density it would displace. I see no reason for the large apple to rise as a result of agitation alone.

But stationary particles do not behave like a liquid. A silo filled with particles, does not exhibit a increasing pressure on the base as the height of its contents is increased. In fact the base pressure becomes independent of the fill depth as the fill depth increases. Support for the particles comes from the silo walls which carry a significant vertical load. If the contents are let out from the centre of the base, a self supporting dome can develop into which no particles will fall. The friction of the walls and between the particles is enough to support the contents. It is friction that makes it difficult to push a large cylinder into sand.

It is easy to conceive a container which prevents the sorting from happening. A cylinder just big enough to contain the largest apple will never allow anything to pass it, so it cannot rise.

So where does this leave me? I believe that the sorting phenomenon may occur in a certain region of apple/bucket diameter ratio - not too large or big apples will sink, not too small or passing of apples would be restrictive. What drives the bigger apples upward? The only thing I can think of is that apple/apple friction and apple/bucket friction play a role in some sort of ratcheting effect which favours smaller apples

I hope the answer, when it comes, is more convincing than the postings to date!

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#37

Re: Apples: CR4 Challenge (10/14/08)

10/15/2008 6:00 PM

I could be mistaken but the effect happens without the container so most likely the container cancels itself out or has no effect.

Brad

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#38

Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 2:52 AM

Don't all the arguments about smaller apples slipping into voids more easily than bigger apples apply to apples moving up just as well as down?

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#47
In reply to #38

Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 7:11 AM

Nicely put.

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#51
In reply to #38

Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 11:32 AM

Yes but the difference you forgot is gravity, more go down than up. While the larger apples go more up because the smaller apples going more down displace them.

The larger apples have the same mass density per the same internal volume but total mass/weight/volume is more per unit for the eg. stated above they have a harder time going down but in going up their greater mass takes more energy to change direction/velocity. The smaller masses change direction/ velocity with less energy.

So thus the larger apple when going up changes direction slower due to its mass, gravity effects both size masses the same but the interaction with other apples is different and the smaller apples flow underneath the larger when it rises.

An object with a high enough mass density will push the moving objects below it out of the way for the same reason, it changes direction even slower needing more energy to do so as gravity pulls it down the energy of the moving masses is not enough to change its direction but they move out of the way.

This is just based on observation and basic physics

work calls

Brad

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#52
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Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 11:50 AM

"the larger apple when going up changes direction slower due to its mass" Galileo (and subsequently Newton) would have something to say about this hypothesis.

"based on observation and basic physics" or perhaps not...

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#53
In reply to #52

Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 12:56 PM

An object in motion stays in motion unless acted upon by an outside force. You read but you do not comprehend and that is my fault.

Object A with mass 100 and velocity 10 strikes object B of mass 50 and stationary to the frame of reference. Both A and B are spherical and of uniform density. The vector of A does not change when it strikes B so what is the new velocity of A and B?

A has a velocity in it's original vector has a velocity of 5 and B has a velocity of 10 on the same vector. thus energy is conserved. Newton.

In the real world it is not so simple because you have factors that can mitigate, dissipate and focus forces. By dissipate I mean converting motion into heat or entropy.

The model can be so complex that short of a super computer only statistics are available. The problem with statistics is like any tool it does what the user tells it to.

And yes vertical motion will cause the larger|denser object to ascend through the loose matrix. But random motion does not. Gold nuggets would be much easier to find if they did. I enjoy panning for gold.

Brad

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#54
In reply to #53

Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 3:40 PM

Ad hominem comments do not increase your credibility.

In addition, this is not what you actually wrote previously (which appeared to relate to the movement of the objects independently of each other) although it is possible that it is what you meant.

Be that as it may, what you are now saying does not assist understanding of the situation under discussion. Indeed, according to my reading, the system as you describe it would perfecly fit the Earth's atmosphere, with the shaking bucket replacing the thermally-heating ground and different size apples the gas molecules of which the atmosphere is composed. Now, the linear kinetic energy of a molecule is independent of its mass. Hence, the velocity of the lighter molecules at a given height is greater than that of heavier ones - as indeed you have supposed. But gravity applies equal downward acceleration to all molecules, so we would expect the lighter gases to have higher relative concentrations as we ascend. And that is exactly what is observed - exactly the opposite of what you are supposedly trying to explain.

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#55
In reply to #54

Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 4:22 PM

Gravity effects mass the same, the environment does not.

No I'm not explaining Brownian motion. And your perception obviously doesn't match mine. As stated this fails at the quantum level. Even some large molecules can't seem to decide if they are a particle a wave or both.

So what have you separated with this effect? In panning for gold there are many techniques that add to or minimize the effect. In compacting ground that is to dry it is also observable except in powder acts more like a liquid, and of course working the fields the rocks always rise. Had the chance this summer to observe some quick sand up close (put my arm down in it) and it does not work there much like powder.

Ad hominem comments do not increase your credibility.

Nor yours. I didn't realize I attack anyones beliefs or credibility. Only that I understood this effect different and it works for me in a repeatable simple way.

So we agree to disagree then? I'll waste no more of your time Sir guest.

Brad

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#57
In reply to #55

Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 4:41 PM

Now darn et you made me realize I for got to explain something I took for granted.

The Voids size is related to the pressure gradient, Less material on top less weight|mass and larger voids for the same energy. So as you go down the voids get smaller from the random motion. In a gas or soluble fluids the gradient is not localised enough to cause this effect normally.

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#69
In reply to #57

Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 5:37 AM

Just got to this - that is truly an additional perception. => GA.
I don't know whether it is sufficient to explain the effect, but it is certainly plausible - the basis for doubt is whether the additional mass of the larger particles (and therefore penetration) would allow them to open up their own holes and thereby negate the effect.

Perhaps someone with access to a dynamic simulator could clarify this for us (starting from ideally elastic spheres of equal density and zero friction)?

Regarding your comment about the lack of significance in a gas, I think the reason that we would not expect this to be significant in the Earth's atmosphere would be the extremely small particle size, which even at ground level would only account for about 0.1% of volume. So, if it does work out, this effect would only become significant in very deep (and dense) atmospheres.
Were its atmosphere stationary, Jupiter might have been a candidate, but I imagine any modelling work will have taken the mixing effects of storms into account - which (given Jupiter's size) would almost certainly outweigh the effect of diffusion. (We would need a large planet at a much greater distance from its star.)

You also mention liquids; as you imply, they are rather incompressible, so I would agree that other (chemical-interaction related?) solubility effects will almost certainly dominate.

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#75
In reply to #69

Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 6:31 AM

Perhaps someone with access to a dynamic simulator....

The KrisDelTM Bucket-U-Like* is currently available for hire...........

*Please note that no liability is accepted for the consequence of projectile vomiting after excessive peanut consumption.

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#84
In reply to #69

Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 12:04 PM

Perhaps someone with access to a dynamic simulator

Phun seems to be doing a half reasonable job for the 2D disc experiment. All parameters are left at default except the two cams which joggle the apples around are speeded up from default 15 rpm a bit (200ish and slightly different). Also there strength has been increased to infinity.

Start position:-

After 15 minutes:-

I don't think that the bottom row of "apples" is ever going to shift without joggling a bit harder, but, for the moment I'm just going to leave it over the weekend and see what happens.

I believe that playing around with this could give some useful insights, because you can mess around with friction, mass, size etc.

For those that don't know phun is a free 2D physics simulator. Just google for "phun". I see that it's now at a much later version than the one I'm using.

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#85
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Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 12:35 PM

Thanks for the Modeler info

Brad

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#86
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Re: Apples: CR4 Challenge (10/14/08)

10/18/2008 7:01 AM

Thanks Randall.

If the discs are of applish size, maybe 50-rpm would have been more appropriate (I wouldn't imagine shaking a full bucket at more than a full cycle in a second (and presumably simulation time will be related to number of events rather than to elapsed time?). Plus, I don't understand what "strength" means here - is that the dimension of the cams, or can you control that separately? Are the discs rough or smooth (I think the smooth condition would best support U_V's theory)?

Either way, assuming that the simulation proceeds beyond preliminary mixing, there could be interesting results. (Is it possible to stop periodically and measure the position of the CofG? I'd be especially interested to see whether it first goes down and then up - if only because I would love to demonstrate the "reduction of static PE" camp as being overly simplistic (dynamic PE would also be interesting - for equal density discs this would likely be better behaved, although I wouldn't count on it; however, I'm still dubious that it is a reasonable predictor, as practical demonstrations give the same outcome even when the larger discs had very high density).

Fyz

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#87
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Re: Apples: CR4 Challenge (10/14/08)

10/18/2008 8:25 AM

Did you read Kris' link to the article about the Brazil nut effect. I think that completely blew the "reduction of static PE" theory (which I originally subscribed to) out of the water.

Strength here is just that: the strength of the motor if I didn't make them strong they would not lift all those discs.

I'm on a different computer here and unless I can get my son interested I don't think I'll be able to try anything else until I get some free time on Monday.

Phun is essentially a game, so it runs real time (unless the computer can't process all the calculations in time).

Another thing about the simulation I have left running is that the sides of the "bucket" are fixed (I'm only jiggling the bottom).

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#88
In reply to #87

Re: Apples: CR4 Challenge (10/14/08)

10/18/2008 9:02 AM

Yes, I read Kris's link, which demonstrates that the practical case is not fully driven by potential energy.
What I am looking to do is discriminate whether U_V's sparse and elegant mechanism (that relies on hole-size gradient alone) is adequate foe all cases, or whether the general case requires the more complex ones that involve rocking and friction.

The way that U_V's proposed mechanism (in the absence of friction) treats PE would be a reasonable predictor that would give some confidence. On the other hand, a direct run with 10x density for the large spheres would be would be more conclusive.

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#89
In reply to #84

Re: Apples: CR4 Challenge (10/14/08)

10/20/2008 1:43 AM

This is unfortunate: nothing is really moving. There was no indication that anything like this might happen late Friday night: I'm going to download the latest version and start again.

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#58
In reply to #55

Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 5:22 PM

I owe you an apology - I was guilty of misreading your statement "You read but you do not comprehend and that is my fault" to include a negation that was not there. You were not guilty of ad hominem, and I apologise for saying you were. Neither was I - at least not intentionally.

Now, returning to the apples and air; in the size ranges of interest (either for apples or kinetic theory of gases) we can take the mechanical (non-wave) approximation for the behaviour without loss of accuracy, so I shall treat this as an amusing aside - but capable of being red (pun intended) as a herring nonetheless.

What I was trying to point out was that there was nothing whatever in your statements that didn't apply identically to atmospheric gases (including Brownian motion). That seems to remain the case, so it constitutes a proof of the argument that what you have written does not provide an explanation of the rising of large apples (or for that matter the separation of gold in panning, both of which I know to occur in practice).

So, given that I believe we have proof that the previous generalities can't hack it, we need to search for an explanation that exploits the particular characteristics of the various situations. A final note - I would not bother to argue this with you if I did not believe that you are as well equipped to handle it as any - once you decide more depth to be necessary.

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#62
In reply to #58

Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 12:20 AM

Thank you for the clarification, accepted, and now that I understand what you where referring to please allow me to retract my "back at you".

I think I've figured a way to 2 dimensionality model this effect. The wave machines in physics class made me think of it.

Lets see If my visual thought process can communicate it correctly.

say a smooth surface 2X2 foot, two parrellel sides have solid rails say 1/2 inch tall. Mount on frame with one non rail side low and the other non rail side high making a 45o from level surface. On the lower side mount a moveable rail that can vibrate paralel to the 45o surface. Use a variable speed (a Pot will do) controler.

Now cover the 45o surface with Checkers sized plasitc pieces and afew of larger diamiter same thinkness etc. plastic.

Now verious sized pucks can be made to observe the effect. By placing large pucks beside and away from the wall|rail the bucket input could be considered. Also one could mark each puck for tracking and visualy record the entire process.

This should be a 2D model, the 45os is a variable paramiter and just a place to start. By changing the vibration, size, and the slope a clearer understanding my be found.

Only one possible faital assumption- that it will reproduce the desired effect.

(the spell checker errored out so please excuse any of my poor spelling I missed)

Off to Heliarc|TIG|GTAW class.

Brad

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#63
In reply to #62

Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 12:34 AM

What a bunch of Apple-pan-dowdies!!! If you would just look at Kris' three pictures on #44, it would all be answered!

When a larger object is moved up and down (while surrounded by smaller objects), it creates space within which the smaller objects fall. The process of falling into the smaller spaces displaces the larger object in the only direction it can be displaced, up.

DUUUUUUUUUUUUHHHHHHHH!!!!

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#68
In reply to #63

Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 2:09 AM

I thought I over stated that? Oh well here I go again. .................. Not!

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#73
In reply to #63

Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 6:21 AM

Kris's pictures show that the upwards effect can be sufficient to overcome large differences in density - but there is no indication as to the cause of the effect. Interesting, and relevant enough not to require marking off-topic - but not I think an answer to the challenge (and not claimed as such by Kris)

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#77
In reply to #73

Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 6:43 AM

....It simply shows the phenomena, so didn't really answer anything. It saved me from fooling around with sugar cubes and posting pictures. 'Off-topic' is such a malleable phrase....I notice that Cadbury has re-introduced the Whispa Bar - as with Aero, it's fascinating how the bubbles get distributed. My concentration has been directed elsewhere, especially to the fact that they only do this with milk chocolate. It wouldn't really seem 'right' with dark chocolate, but it would be interesting to taste. I suspect the melt-ability has them foxed. Until this subject degenerates to apple-bobbing and toffee-apples, I shall spectate.........hang on......what if I did apple bobbing with various sizes in a small barrel ? Would the apples somehow stratify themselves regardless of individual, and presumably similar density ? So many questions, so little time.................

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#80
In reply to #77

Re: Aero Bar

10/17/2008 7:09 AM

Hi Kris

I doubt there would be any problem producing aerated plain chocolate bars with a bubble density similar to that of the aero bar*. So I imagine its absence is more likely related to the sizes (and profitability) of the respective markets for plain and for milk chocolates. That still means you are unlikely to get to taste it unless you can commission someone with appropriate equipment to do it for you (it comes somewhere below koala meat on my list of priorities, and that thought is enough to make me contemplate turning vegetarian)

* This is based on how similar the distribution of bubbles is in the aero-bar to what is found in in all sorts of foamed plastics mouldings (expanded polystyrene being an exception because its production process is more akin to making rice-cake biscuits)

cheers

Fyz

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#82
In reply to #80

Re: Aero Bar

10/17/2008 7:22 AM

.........somewhere below koala meat........

If I can stop laughing, I may reply !

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#83
In reply to #82

Re: Aero Bar

10/17/2008 7:48 AM

That'll be pretty far down, I reckon - koalas, given their diet, must taste something akin to a mentholyptus cough drop. Gimme a Violet Crunch any day!

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#70
In reply to #62

Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 5:50 AM

The model should produce the desired effect - but the organisation of the movement of the base means that the observed effect might be due to other causes. However, if you could apply the pseudo-thermal energy by vibrating a vertical side...

that class is a bit specialised. Take care during the practicals...

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#71
In reply to #70

Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 6:10 AM

P.S. I was that pesky guest - for some reason I was having trouble logging in.

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#59
In reply to #53

Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 5:23 PM

An object in motion stays in motion unless acted upon... Which play is required?

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#64
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Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 12:48 AM

Fast play, just watch the slow motion replay.

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#66
In reply to #38

Re: Apples: CR4 Challenge (10/14/08)

10/17/2008 1:40 AM

???????????????

How are we going to decide whether the big one are going up against the small ones going down

We move into the realm of the ridiculous

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#39

Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 3:55 AM

Reading the replies, the one I find most interesting is the one by FYZ. When the apples drop, and strike the bucket bottom, due to the apples irregular shape they will strike or bounce at a point away from their centre of gravity, this will cause them to rotate, the apple of the large mass will then force the smaller apples to the bottom?

Regards JD.

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#41

Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 5:38 AM

Looks like object density may not be critical. (Tks to http://users.monash.edu.au/~rhodes/education.htm#top)

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#42
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Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 6:03 AM

Apparently you liked the red X pic so much you had to post 3 more...awww, nuts! Brazil or otherwise.

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#44
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Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 6:17 AM

LOL ! Lucky I can find the page again.......

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#45
In reply to #42

Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 6:17 AM

I had the three red Xs too until after I'd visited the site they were on: then they mysteriously appeared. Maybe they're such big pics. that they only rise to the top when they're shaken up a bit.

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#60
In reply to #42

Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 5:48 PM

Well, if Kris likes red X pics so much...

If he wants more, I can make some.

He could also take photos of divorced communists...

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#43
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Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 6:09 AM

From the Brazil nuts article:-

Much to their surprise, the researchers found that at normal pressure both the heaviest and the lightest of the big balls moved to the top ahead of balls of intermediate weight, Mobius says.

I wonder how that intermediate weight (density of the slowest rising balls) related to the density of the surrounding particles.

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#46
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Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 6:20 AM

Yes, it suggests a failry complex interplay of all the factors.

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#49
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Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 7:26 AM

That is getting horribly like the particles going to the centre when swirling a bucket of water.

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#50
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Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 7:54 AM

And to quote the site:

"The mechanism responsible for this effect is not entirely understood."

So it is, then, with the apples...

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#61

Re: Apples: CR4 Challenge (10/14/08)

10/16/2008 10:56 PM

Even though this analogy may be flawed, I believe we can compare this with the viscosity of fluids. The apples with the larger diameters are like a fluid with high viscosity, or resistance to flow. The smaller apples are like a fluid with lower viscosity. As the bucket is shaken, in the up phase, motion is transferred from the bucket to all the apples, and it lifts them all equally. In the down phase, the bucket is lowered by your hands, but gravity is what moves the apples. Because the smaller apples encounter less resistance, they "flow" towards the bottom quicker.

As I said the analogy is probably flawed, most analogies are. I'll have to ruminate on this some more...

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#90

Re: Apples: CR4 Challenge (10/14/08)

10/20/2008 5:05 AM

Hi,

It's about gravity and probability effects space for smallest apple dropped when bucket shaking for couples second. Therefore the big apple is always on top.

Enjoy your hot coffee...

Cheers ,

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#91
In reply to #90

Re: Apples: CR4 Challenge (10/14/08)

10/20/2008 11:25 PM

No, no, no! I think if we're really going to get to the bottom of this, we need to resort to apple sauce.

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