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Math Help - A Question About Atoms

  1. #1
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    A Question About Atoms

    I'm having a hard time conceptualizing something. Here is the situation: say there is a soft rubber ball that has a hollow center, not solid. A normal hand-sized bouncy ball that works fine as long as it maintains its integrity. Say that it is lying on the floor. Now say a kid comes into the room, bends down and picks the ball up between his index finger and thumb, and in the process squeezes the ball, deforming it at the point of contact.

    I want to relate what is going on here in terms of atoms. As best I can conceptualize this, we have, at first, a collection of atoms lying on the floor. This collection of atoms is what we call the ball, and the collection is taking up coordinates in space. Okay. Now another collection of atoms comes into the room (the room is also a collection of atoms, but ignore that, to keep this "simple"). This newly arrived collection of atoms is the kid. The atoms comprising the kid's index finger and thumb undergo an interaction with the collection of atoms comprising the ball, such that the entire collection of atoms of the ball feels an attraction to the finger atoms and in the process moves to a different coordinate space.

    What is the explanation for what is going on here?

    Conceptually (and generally), I see an attraction between the two collections (the ball atoms moving with the finger atoms), and I also see a repulsion (some of the ball atoms moving away from the finger atoms even as the overall collection of ball atoms is moving with the fingers, which causes the appearance of deformation).

    How can this concept be expressed in terms of electrons? For the attraction, I think that the electrons in the fingers are repulsing electrons in the ball, which sets up an attractive force between the ball and fingers. But what is driving the atoms of the ball away at the point of interaction, to produce the deformation? The best I can figure out is that first there is the initial attraction caused by the electrons in the ball leaving the area in great quantities, creating positive ions, and then a follow up interaction caused by these positive ions leaving the area (causing the deformation). I'm not sure what is causing the positive ions to leave the area. And I'm not sure if this is even what's happening. Nothing like this is addressed in any of the books that I have. (Actually, I'm still studying classical physics, and began wondering about how to at least conceptualize what is happening at the atomic scale)
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    Quote Originally Posted by spiritualfields View Post
    I'm having a hard time conceptualizing something. Here is the situation: say there is a soft rubber ball that has a hollow center, not solid. A normal hand-sized bouncy ball that works fine as long as it maintains its integrity. Say that it is lying on the floor. Now say a kid comes into the room, bends down and picks the ball up between his index finger and thumb, and in the process squeezes the ball, deforming it at the point of contact.

    I want to relate what is going on here in terms of atoms. As best I can conceptualize this, we have, at first, a collection of atoms lying on the floor. This collection of atoms is what we call the ball, and the collection is taking up coordinates in space. Okay. Now another collection of atoms comes into the room (the room is also a collection of atoms, but ignore that, to keep this "simple"). This newly arrived collection of atoms is the kid. The atoms comprising the kid's index finger and thumb undergo an interaction with the collection of atoms comprising the ball, such that the entire collection of atoms of the ball feels an attraction to the finger atoms and in the process moves to a different coordinate space.

    What is the explanation for what is going on here?

    Conceptually (and generally), I see an attraction between the two collections (the ball atoms moving with the finger atoms), and I also see a repulsion (some of the ball atoms moving away from the finger atoms even as the overall collection of ball atoms is moving with the fingers, which causes the appearance of deformation).

    How can this concept be expressed in terms of electrons? For the attraction, I think that the electrons in the fingers are repulsing electrons in the ball, which sets up an attractive force between the ball and fingers. But what is driving the atoms of the ball away at the point of interaction, to produce the deformation? The best I can figure out is that first there is the initial attraction caused by the electrons in the ball leaving the area in great quantities, creating positive ions, and then a follow up interaction caused by these positive ions leaving the area (causing the deformation). I'm not sure what is causing the positive ions to leave the area. And I'm not sure if this is even what's happening. Nothing like this is addressed in any of the books that I have. (Actually, I'm still studying classical physics, and began wondering about how to at least conceptualize what is happening at the atomic scale)
    Everything here depends on the electromagnetic force.

    Atoms can be (more or less) conceptualized as tiny little spheres with positive charge at the center and a spherical cloud (shell) of negative charges around it. So when two atoms come into contact the electron shells repel each other. (I'll ignore the effects of the redistribution of the electron clouds due to the electromagnetic interaction. If you are interested, search under the term "Van der Waals interaction.") This repulsion is why the ball deforms in the first place.

    How then can the ball be picked up? It isn't attraction, it's repulsion again. But taking a step outward to see the surfaces involved gives you the idea a bit better: if you are pressing inward on a sphere your fingers sink into it somewhat. Your fingers will not slide over the surface anymore since they are stuck inside the indentation. It has nothing to do with any sort of an attraction.

    Even if you aren't deforming the ball we can still make a similar argument: the surfaces of the ball and your fingers aren't perfectly smooth, so there will always be some places where your fingers are "sunk" into the surface of the ball.

    -Dan
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    Thanks for that information topsquark. About this:
    How then can the ball be picked up? It isn't attraction, it's repulsion again. But taking a step outward to see the surfaces involved gives you the idea a bit better: if you are pressing inward on a sphere your fingers sink into it somewhat. Your fingers will not slide over the surface anymore since they are stuck inside the indentation. It has nothing to do with any sort of an attraction.
    With big world physics (keeping atoms out of it), the way I was looking at it was this: two systems on opposite sides of the ball, with a finger exerting a force on the ball on each side, and the ball exerting a reactive force on the fingers. Because the mass of the finger is greater, the ball is accelerated (deformed), and this happens on each side of the ball. Is this correct? [edit...in thinking more about this, both the finger and ball are accelerated, only the ball more so because of its smaller mass, right?...too bad they don't make talking books that can say yey or nay ]

    But in terms of atoms what is the explanation?

    I have heard of van de Waals interactions. I came across the description, of all places, in my biology book. It came up in the discussion of molecules, and specifically using gecko lizards as an example, stating that it is van de waals interactions that enable a gecko to "stick" to a vertical wall. Supposedly, (anything in a biology book I take with a grain of salt), the atoms in the molecules of the surface of the wall and the gecko's feet undergo these interactions. That even when molecules and atoms are electrically neutral, the electrons are in constant motion and so regions build up where the distribution within the atoms and molecules are not symmetrical, causing "hot spots" of positive and negative charges to build up that allow atoms and molecules to stick to each other. This is how the gecko can remain stable on a vertical wall. But this sounds like an attractive kind of charge. [edit: I hadn't even thought about this when I originally posted my question. But I can visualize it in my head now...though it still seems like it's an attraction]
    Last edited by spiritualfields; July 15th 2007 at 08:46 PM.
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    Quote Originally Posted by spiritualfields View Post
    With big world physics (keeping atoms out of it), the way I was looking at it was this: two systems on opposite sides of the ball, with a finger exerting a force on the ball on each side, and the ball exerting a reactive force on the fingers. Because the mass of the finger is greater, the ball is accelerated (deformed), and this happens on each side of the ball. Is this correct? [edit...in thinking more about this, both the finger and ball are accelerated, only the ball more so because of its smaller mass, right?...too bad they don't make talking books that can say yey or nay ]
    Don't think in terms of mass and acceleration, think about force. The finger is exerting more force than the surface of the ball can. Thus there is deformation.

    Quote Originally Posted by spiritualfields View Post
    But in terms of atoms what is the explanation?
    Think of the surface of the ball as two parallel vertical lines. When the fingers press inward, the surfaces deform, making the vertical lines look more like an hourglass shape. The fingers are in the indented portion of the hourglass. Now to pick this thing up what do we do? We simply raise the hand. This exerts more force on the upper surfaces (the points of contact above the fingers) than it does on the lower. But the atoms in the finger are repelling the atoms in the ball. So the ball's reaction to the upward force from the fingers is to accelerate the ball upward.

    Quote Originally Posted by spiritualfields View Post
    I have heard of van de Waals interactions. I came across the description, of all places, in my biology book. It came up in the discussion of molecules, and specifically using gecko lizards as an example, stating that it is van de waals interactions that enable a gecko to "stick" to a vertical wall. Supposedly, (anything in a biology book I take with a grain of salt), the atoms in the molecules of the surface of the wall and the gecko's feet undergo these interactions. That even when molecules and atoms are electrically neutral, the electrons are in constant motion and so regions build up where the distribution within the atoms and molecules are not symmetrical, causing "hot spots" of positive and negative charges to build up that allow atoms and molecules to stick to each other. This is how the gecko can remain stable on a vertical wall. But this sounds like an attractive kind of charge. [edit: I hadn't even thought about this when I originally posted my question. But I can visualize it in my head now...though it still seems like it's an attraction]
    Van der Waals forces are attractive, you've got that right. I don't know if geckos do or do not use them.

    The concept is this: when the electron clouds of two atoms are close to each other, the electrons from one atom repel the electrons from the other. This leaves the positive nuclei of the atoms slightly unsheilded on the side where the electrons aren't, creating a slight positive charge on one side of the atom and a slight negative side on the other. This is called a "dipole" and dipoles attract each other by lining up charges + - + - + ...

    Van der Waals forces operate similarly, but don't need the atoms to be all that close to each other. In this case the dipole is formed by random fluctuations in the electron cloud, rather than repulsion. Two atoms (at a distance) are briefly attracted to each other when one forms a dipole. As you can imagine this is much weaker than the dipole situation I mentioned above. But it is sufficient to solidify even the noble gases if you cool them enough. (Except for Helium: Helium has no solid state except under tremendous pressures.)

    -Dan
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    Don't think in terms of mass and acceleration, think about force. The finger is exerting more force than the surface of the ball can. Thus there is deformation.
    If I leave the acceleration out, and think only of forces, I see this scenario: with respect to the ball, there are two forces (looking at only one side of the ball), one exerted by the finger on the ball, and a force that counters this (acting like a friction force), that is opposite in direction but less in magnitude than the finger force. Since the force exerted by the finger is greater than the force exerted by this "friction force", the ball at the point of contact moves in the direction of the finger force, and so the ball is deformed, until the "friction force" is great enough to negate the force exerted by the finger. "Friction force" doesn't seem like the right terminology, but I t don't know what else to call this force.

    With respect to the finger, the reactive force of the ball on the finger tries to move the finger backward but finger's friction force (or whatever it's called) cancels out of the force exerted by the ball, with enough left over to keep moving toward the ball.

    In my book there is an example of a horse pulling a sled, with "friction forces" being the force that counters the action/reaction forces that the horse and sled are exerting on each other. That's why I'm using the term "friction force" to represent the resistance of the ball and fingers. Maybe inertia would be a better term.
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    Quote Originally Posted by spiritualfields View Post
    If I leave the acceleration out, and think only of forces, I see this scenario: with respect to the ball, there are two forces (looking at only one side of the ball), one exerted by the finger on the ball, and a force that counters this (acting like a friction force), that is opposite in direction but less in magnitude than the finger force. Since the force exerted by the finger is greater than the force exerted by this "friction force", the ball at the point of contact moves in the direction of the finger force, and so the ball is deformed, until the "friction force" is great enough to negate the force exerted by the finger. "Friction force" doesn't seem like the right terminology, but I t don't know what else to call this force.

    With respect to the finger, the reactive force of the ball on the finger tries to move the finger backward but finger's friction force (or whatever it's called) cancels out of the force exerted by the ball, with enough left over to keep moving toward the ball.

    In my book there is an example of a horse pulling a sled, with "friction forces" being the force that counters the action/reaction forces that the horse and sled are exerting on each other. That's why I'm using the term "friction force" to represent the resistance of the ball and fingers. Maybe inertia would be a better term.
    "Reactive" force is a decent term. It's actually closer in spirit to a "normal" force, since the force at any point on the ball from the hand is perpendicular to the surface of the ball at that point.

    -Dan
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    It's actually closer in spirit to a "normal" force, since the force at any point on the ball from the hand is perpendicular to the surface of the ball at that point.
    Thanks for all the information, topsquark. I'll think of it as having the same effect as a normal force, with the main difference being that the source of the force is the ball itself, and with itself as the object of the force.

    I'm not completely pleased with my physics book. It's a college physics text for non-physicists. There are many examples and exercises, so there is a lot of practice available with plugging numbers into the equations, but explanations seem a little skimpy. And there is an insidious deception (by way of ommision) at work. I self-teaching myself about physics because I want to understand (or at least know a little better) the nature of reality. There are alot of things I don't know, but one thing that I do know is that there are no balls, no fingers, in reality. An honest physics book, in my opinion, would at least mention, as it takes the reader into the section on motion and forces, that it's all an illusion, based on convention and familiarity, and not fundamentally real. Just temporal arrangements, forming patterns.

    I'm going to continue to use the physics book that I have (it does have a preponderance of examples and exercises, with answers for the odd-numbered exercises). But I also want to know what is really happening, not some song and dance pony show, so I ordered Richard Feynman's Lectures on Physics, and should be receiving it today. I had wanted to hold off a little while longer on that collection, because I've read that calculus is a must to completely understand the lectures. I'm in the process of going through my third pass of my precalculus book, and was only dipping my fingers in, so to speak, the physics book that I have, just to give myself some preliminary physics background. I had intended to get about halfway through my calculus book before starting the Feynman lectures. However, I don't want to wait any longer, as I can see that reading this physics book (that I have) is going to leave me with countless gaps and glossed over explanations.

    I'll start getting into my calculus book now, while continuing to sweep one last time through my precalculus book, and use the Feynman lectures and the college physics book concurrently.

    BTW, congratulations on getting engaged!
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    Quote Originally Posted by spiritualfields View Post
    Thanks for all the information, topsquark. I'll think of it as having the same effect as a normal force, with the main difference being that the source of the force is the ball itself, and with itself as the object of the force.

    I'm not completely pleased with my physics book. It's a college physics text for non-physicists. There are many examples and exercises, so there is a lot of practice available with plugging numbers into the equations, but explanations seem a little skimpy. And there is an insidious deception (by way of ommision) at work. I self-teaching myself about physics because I want to understand (or at least know a little better) the nature of reality. There are alot of things I don't know, but one thing that I do know is that there are no balls, no fingers, in reality. An honest physics book, in my opinion, would at least mention, as it takes the reader into the section on motion and forces, that it's all an illusion, based on convention and familiarity, and not fundamentally real. Just temporal arrangements, forming patterns.

    I'm going to continue to use the physics book that I have (it does have a preponderance of examples and exercises, with answers for the odd-numbered exercises). But I also want to know what is really happening, not some song and dance pony show, so I ordered Richard Feynman's Lectures on Physics, and should be receiving it today. I had wanted to hold off a little while longer on that collection, because I've read that calculus is a must to completely understand the lectures. I'm in the process of going through my third pass of my precalculus book, and was only dipping my fingers in, so to speak, the physics book that I have, just to give myself some preliminary physics background. I had intended to get about halfway through my calculus book before starting the Feynman lectures. However, I don't want to wait any longer, as I can see that reading this physics book (that I have) is going to leave me with countless gaps and glossed over explanations.

    I'll start getting into my calculus book now, while continuing to sweep one last time through my precalculus book, and use the Feynman lectures and the college physics book concurrently.

    BTW, congratulations on getting engaged!
    First of all, thanks!

    Second, you will likely enjoy the Feynman Lectures. (I did, and still do.) But you will have a problem with your intentions almost immediately.

    The problem is that if I designed a course that explained Physics using the most accurate models of reality that we've been able to construct you wouldn't even make it past the first day of the course. It's too much to handle all at once: quantum field theory mystifies even the experts and it's impossible with our present level of understanding to even work out the solution to the simplest realistic problem with it.

    The standard programme of Physics education is to start with the simple stuff. First a description of what happens to "point" particles, which introduces Newton's laws, the conservations laws, etc. Then as the basic fields of study are introduced the "blinders" are slowly taken away and the Physics becomes more and more realistic until at the graduate level of study you are basically working with the cutting edge of our understanding of how the Universe works.

    Feynman disagreed with this concept. He felt it should be possible to educate a student in such a way that the cutting edge would be possible to be taught from the start. As he was one of the best, if not the best, Physics instructor of all time I pay attention to this principle. One of his mottos was "If it can't be be explained simply then we don't really understand it." To my mind the issue is that we really don't understand the more advanced fields of Physics. And even Feynman's Lectures are somewhat of a failure: I find that they are good, but they are difficult to learn from. (But provide and excellent review and a very interesting point of view from which to learn Physics.)

    If you are looking for a good text to learn from I would recommend either Tipler or Serway. (Many people find Serway to be difficult but I've always thought it to be an excellent text provided you are taking the course from a good professor. It's not a good one for learning Physics on your own.)

    -Dan
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    If you are looking for a good text to learn from I would recommend either Tipler or Serway. (Many people find Serway to be difficult but I've always thought it to be an excellent text provided you are taking the course from a good professor. It's not a good one for learning Physics on your own.)
    Thanks for the information on the Tipler and Serway books. I do have the Serway book, and am self-teaching myself, so I just ordered a used copy of the Tipler book, extended version. In reading some of the reviews for the Tipler book, there were some positive reviews for people who are teaching themselves.
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