Simplifying Mathematics: Introducing Vectors and Vector Addition

Mathematics, Physics
[caption id="attachment_23153" align="alignright" width="480"] Magnetic vector force field[/caption] We all know how to add, subtract, multiply and divide ordinary numbers, even if basic units are attached to them such as gallons, apples, feet, tons, and so forth. 4+3 = 7 5 lbs x 3.2 = 16 lbs These two examples illustrate pure numbers in the first instance, and simple quantities in the second instance. But What About Direction? What if we toss in direction? Imagine a huge square, 5 miles on a side. We have to travel along the perimeter to travel from Point A to Point B, and then on to our destination, Point C (see the image). We thus travel 10 miles to reach Point C. If we could travel "as the crow flies", we would only have…
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The Chemical Bond – What Model Can We Choose to Represent It?

The Chemical Bond – What Model Can We Choose to Represent It?

Chemistry, Physics
Atoms and molecules are small indeed. Until recently, catching even a glimpse an atom was impossible. It still is impossible to see a chemical bond. Despite that, we know quite a few chemical reactions and can predict how many more will turn out. But we could know ever so much more about the scientific world of the very small if we had a very close bond model. We will discuss three bond models that have been used in the past, and to some extent still are used. 1. The rigid model. 2. The spring model. 3. The force / charge model. See the images associated with article. Each depicts one of the models discussed below. The Rigid Model One can depict a diatomic molecule by joining two balls with a…
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Why is My Potato Salad Mushy? Heat Capacity

Food, Physics
If you have a curious mind, you look at everyday matters differently. You ask yourself questions others do not care about. What is spider silk made of? What happens when water boils? Why do canned whole tomatoes look so perfect? Why are buttercups so bright? Are there dust storms on Mars? But NOW we ask: Since others make delicious potato salad, why is my potato salad mushy? The Challenge Potato salad is one of the most satisfying foods out there. It is low-cost and complements even simple meals. But it can detract from a meal if the potatoes are too hard, or if the potato salad is better called mashed potato salad. Such results obviously involve potato variety, size, and uniformity of the cut pieces. But more is involved. Temperature…
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Initiating a Fission Chain Reaction: What is Critical Mass?

Physics, Technology
[caption id="attachment_19651" align="alignright" width="600"] One basic fission reaction[/caption] What is critical mass? Before we answer that question, we want to discuss the topic of fission, itself. When we speak of atomic bombs, we do not usually mean hydrogen bombs or fusion bombs in which the nuclei of hydrogen atoms fuse together.¹ Rather, we mean fission bombs, in which large atoms of radioactive (unstable) elements are torn apart to produce smaller atoms with the release tremendous energy. One simple atomic explosion reaction is written, 1 n + 235U → [236U] → 92Kr + 141Ba + 3 n The above equation informs us that one energetic neutron properly striking an atom of uranium, isotope 235, produces, first and temporarily, an ordinarily stable atom of uranium, isotope 236. [caption id="attachment_19652" align="alignleft" width="300"] Uraninite…
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Converting Gas Temperature to Particle Velocity

Chemistry, Physics
[caption id="attachment_18761" align="alignright" width="440"] Atoms or Molecules of Gas[/caption] Unlike liquids or solids, whose atoms or molecules have greater correlation with each other, gas atoms and molecules move somewhat independently of each other. This is to be expected. A gas occupies a much greater volume than a corresponding liquid. This independent behavior allows us to calculate the root-mean-square velocity of gas particles directly from temperature. Tweaking the Ideal Gas Law We derive this equation from another well-known equation, the Ideal Gas Law equation. Algebraically, that equation is written: PV = nRT where P is pressure, V is volume (not velocity), n is the number of moles of gas, R is the ideal gas constant and T is the temperature. By combining the above equation with derivatives of Boltzmann's equation, we…
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Deriving Basic (Circular) Trigonometric Functions

Mathematics, Physics
[caption id="attachment_18674" align="alignright" width="401"] Figure 1[/caption] Draw two intersecting lines in space, illustrated below. The mathematician will not want to leave this simple drawing without completely pointing out its features and labeling those features. We do so to begin our understanding of basic (circular) trigonometric functions. [caption id="attachment_18675" align="alignleft" width="387"] Figure 2[/caption] We label the point of intersection of course – P will do. But the intersection produces what looks like slices in a pie. The size of those slices of pie were determined by how the two lines intersected, how "wide apart" the lines are. We label these as angles α (alpha) and β (beta). Superimposing a Circle [caption id="attachment_18676" align="alignright" width="387"] Figure 3[/caption] The title of this paper is understanding basic circular trigonometric functions. So at this stage,…
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What IS the Kinetic Isotope Effect and How Is It Useful?

Chemistry, Physics
[caption id="attachment_18280" align="alignright" width="460"] The simplest atom.[/caption] Matter and the atoms that make it up consists of electrons, protons, and neutrons. The center or nucleus of each atom consists of at least one positively charged proton. Usually the nucleus includes neutrons, which are uncharged. Negative electrons are found in orbitals well outside the nucleus. Their number equals the number of protons in the nucleus. Such atoms have a net charge of zero. Elements The number of protons determines what element an atom is. One proton identifies hydrogen, two protons helium, three lithium, four beryllium, five boron, six carbon, and so on. Each of these elements possesses a unique chemistry. The quantity of protons equals the quantity of electrons, so everything's set, right? Well, no! The number of neutrons in all…
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Comparing ⁴He with ²H₂ – An Atom with a Molecule?

Astronomy, Physics
The title of this article may seem a bit strange. How do we begin comparing a helium-4 atom with a molecule of deuterium hydrogen? It may become more apparent if we examine illustrations of the two species. Note the similarities and the differences. If you do, comparing ⁴He with ²H₂ should not seem so strange. Helium-4 Helium is element number two in the periodic table. This means helium has an atomic number of two—it has two protons. Protons are positively charged. Now an atom is neutral, thus electrical neutrality dictates a helium atom also has two electrons. The only variable is the number of neutrons. Helium-4 (sometimes written ⁴He) is a very stable form of helium and has two neutrons. Deuterium or Heavy Hydrogen Atomic hydrogen (symbol H) consists primarily…
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Do Lone Atoms or Molecules Assume States of Matter?

Physics
Search the Internet for the definition of states of matter and much comes up. Perhaps you are the sort of reader who peeks first at Wikipedia to get some ideas what other sites you will visit to obtain answers to your questions. At any rate, you will note basic descriptions for the states of matter you experience every day. Take the following discussion for what it is: a hypothetical discussion on the nature of matter. If you can demonstrate its veracity or illegitimacy, please do that in the Comments section, below. States of Matter Solid: “Atoms or molecules fixed in location and locked in place.” How are these particles locked into place? They bond to each other and do not readily move around, much like the assembled pieces in a…
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Is Our Concept of Matter Merely an Incorrect Perception?

philosophy, Physics
Picture a large polished stainless steel bearing. Now visualize dropping it onto a concrete floor from a height of, say, h. It impacts the concrete and bounces back to a somewhat lesser height h′. What actually was the physics at the time of collision? Our concept of matter provides one answer. Our Concept of Matter The rock-solid steel bearing is not thrown, but “dropped”. It falls with a force equal to its mass times its acceleration due to gravity. That is, F = mg. Upon striking the concrete floor, the bearing experiences an equal yet opposite reaction forcing it to bounce back. Even so, due to internal and external factors, the bearing does not attain its original elevation. Is the Bearing Truly Solid? If the bearing were of solid and…
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