Quake3World

Answer the question and ask one.

I start: what's the angle of the slope of a pile made with round marbles.

Are the bottom ones glued to the ground?

i dunno, going to take a quick guess of 45 degrees.

but that is geometry, not physics.

I am thinking of a pyramid of marbles, btw. But I haven't sketched it out, so i could be wrong.

Answer: You can't make a pile with round marbles.

I'm assuming we are ignoring that fact, stacking them in a pyramid.

Yeah, you're right, its geometry. Btw, they dont have to be marbles, just anything that has a spheric shape. I'm just wondering how many people here can answer this simple question. Oh, and its not 45 degrees.

ToxicBug wrote:Yeah, you're right, its geometry. Btw, they dont have to be marbles, just anything that has a spheric shape. I'm just wondering how many people here can answer this simple question. Oh, and its not 45 degrees.

Then I'll think about it a bit. But are we talking about a pyramidal shape here?

Sure, it has to be a pyramid. If you dump all the marbles/spheres/whatever in the same place from a truck, eventually it will look like a pyramid without having to actually stack it as a pyramid.

ToxicBug wrote:Sure, it has to be a pyramid. If you dump all the marbles/spheres/whatever in the same place from a truck, eventually it will look like a pyramid without having to actually stack it as a pyramid.

No it won't. It'll only do that if they'res some walls or something to obstruct a rolling marble to stop it from rolling otherwise it'll just keep spreading out. So, I'll ask again, are the marbles glued to the ground?

Just imagine that the spheres have enough friction to not roll away. Then do the problem.
Easy way to figure this out would be to take a bunch of quarters, lie them down in a pyramid on a table, and then figure the angle out.

And they dont' have to be a pyramid. You could feasibly stack the spheres (if you ignore the possibility of rolling away) into shapes other than a pyramid.

EDIT: DIdn't see your 'stack' comment earlier.

Well I would think the angle would depend on the "friction" as you say or whatever object is obstructing the marbles movments if friction isn't enough. The higher the friction the narrower the angle I would think. So if the bottom marbles were glued and aligned in a perfect square to make a pyramid it would be 90 degrees whereas if they aren't glued it would vary I'd think.

Kracus wrote:Well I would think the angle would depend on the "friction" as you say or whatever object is obstructing the marbles movments if friction isn't enough. The higher the friction the narrower the angle I would think. So if the bottom marbles were glued and aligned in a perfect square to make a pyramid it would be 90 degrees whereas if they aren't glued it would vary I'd think.

Ignore any sliding. Just imagine that you are stacking them with no slipping. And if they were glued it woudl not be 90 degrees.

Imagine building a pyramid with them. Again, take some coins, lie them on a table in a pyramid. Now project that idea into 3 dimensions.

if you were to dump them then it wouldn't be a constant slope but instead one that curves.

if you neatly stacked them then it would be a constant slope.

It wont curve because the indentation the marbles fall into with each progressive level is equal, so the height of every level after the first is constant.

Grandpa Stu wrote:if you were to dump them then it wouldn't be a constant slope but instead one that curves.

if you neatly stacked them then it would be a constant slope.

I think he is picturing nothing more than a pyramid of spheres.

Someone just do my suggestion with the coins and figure the angle out. I am grading research papers on cosmology right now (or at least I should be).

Well... I dunno Toxic, A pile of marbles has a very small critical angle (almost 0º) So I can't see how you could actualy "pile" any marbles although technicaly it might be considered a pile. As for friction and whatnot I won't exclude any known physics in the universe to get the desired awnser. The marbles are either glued to the ground (bottom ones) or they simply spread out too much.

30° / 60° - assuming hexagonal close packing
http://mathworld.wolfram.com/HexagonalClosePacking.html

it's the angle of repose.

Grandpa Stu wrote:it's the angle of repose.

Well a dumptruck dumping marbles all over the place is definitely going to throw it over.

Well, anyway, its 60°. This can be easily verified by a simple example. Take 3 circles, like tnf mentionned. Don't even need to draw them. Trace an imaginary line between the centres of the circles. You've got an equilateral triangle, which has 3 equal 60° angles. Easy as pi.

No, you weren't clear enough on the question.

I was assuming that the marbles would be staggered, with each marble sitting in the center of the three below it. That's the way they would be if they were in a pile with the bottom layer stuck to the ground.

In that case, the angle would be closer to 45 degrees.

Nevermind, I see what you're talking about.

Assuming that this isn't a trick question (ie you can't stack marbles) then it's 60 degrees because they'd make an equilateral triangle.




edit: Oh, i see it's already been posted. There was me feeling all clever too