CK-12 21st Century Physics: A Compilation of Contemporary and Emerging Technologies Read online

  Tapas Kar, PhD: Author, Utah State University, Utah

  Tapas Kar is an Assistant Professor with the Department of Chemistry and Biochemistry at Utah State University (USU). Prior to working at USU he taught and did research at Southern Illinois University Carbondale (SIUC). Tapas focuses his research and teaching in the area of nanoscience and nanotechnolgy. He introduced nanotechnology courses at USU and currently teaches nanochemistry courses.

  John S. Ochab, Jr., PhD: Author, J. Sargeant Reynolds Community College, Virginia

  John Ochab was born in a suburb of Boston, MA. He attended the University of Massachusetts (at Boston) and obtained a BA in Biology. He worked as a biochemiocal laboratory technician for 3 years (with journal aknowledgements) and as a toxicologist for one year. He then decided to go into physics. After taking courses in advanced mathematics and physics (at M.I.T. and at Boston University), he enetered graduate school at Clark university, (Worcester, MA) where he obtained an MA in physics (nuclear solid state). He then entered the University of Maine (at Orono) were he obtained a PhD in experimental surface physics. Upon graduation, he worked in the industry for such companies as Spectra Physics, GTE Sylvania, as well as smaller companies. He also did research in high temperature superconducting thin films at Brookhaven National Laboratory in Long Island, NY.

  Due to the financial crises of the late 1980s, he moved to California, where he trained process engineers in semiconductor metrology and taught physics part-time at local community colleges. John then moved to West Virginia and taught physics, physical and engineering physics, and after getting married, moved with his wife to Virginia. He has been teaching algebra and calculus-based physics at J. Sargeant Reynolds Community college ever since. He has first-author publications in Journal of Surface Science, and co-authored publications in the Physical Review Letters, Journal of Applied Physics, and Physicsa C. He is a member of the American Association of Physics Teachers, the Virginia Academy of Science, and was a long-standing member of the American Institute of Physics.

  Dr. David A. Slykhuis: Author, James Madison University, Virginia

  Dr. David Slykhuis is Chair of the Physics/Physical Science Academy. Dr. Slykhuis has been at James Madison University since the fall of 2004. His primary responsibilities lie in the preparation of science teachers in the middle and secondary education program. His research interest involves the use of technology in K-16 science classrooms to increase student achievement. Dr. Slykhuis received his PhD in science education from North Carolina State University in May of 2004. He has five years of high school classroom experience, teaching primarily chemistry and physics.

  David P. Stern: Author, Greenbelt, Maryland

  Dr. Stern received his MS in physics from the Hebrew University in Jerusalem, his doctorate from the Israel Institute of Technology, and retired after 40 years of research with NASA Goddard SFC on the Earth's magnetosphere. He has produced extensive education resources on the Web, including "From Stargazers to Starships." He has also written space-related history, poems and a middle-school mathematics enrichment text, Math Squared.

  Jim Batterson: Project Manager, Newport News, Virginia

  Jim Batterson taught high school physics and mathematics, worked as a scientific programmer for LTV Corporation, and, from 1980 until his retirement in 2008, was a research engineer at NASA Langley Research Center. At NASA he was responsible for flight research on the dynamics and control of aerospace vehicles, served as Head of the Dynamics and Control Branch, and later as Deputy Director for Strategic Development. He has also served on a number of community boards including the Newport News (Virginia) School Board and New Horizons Regional Education Center Board. While at NASA, he served on assignments to the Office of Science and Technology Policy, the National Nanotechnology Coordination Office, NASA Headquarters, and, most recently, to the Office of Virginia’s Secretary of Education.

  Chapter 2: Toward Understanding Gravitation.

  Andrew Jackson. "Toward Understanding Gravitation", 21st Century Physics FlexBook.

  Preface—A Note to the Teacher and Student Regarding Background Information and Pedagogy

  Nearly every physics textbook has an adequate section regarding Newton’s universal gravitation, Cavendish’s work and an introduction of Kepler’s laws of planetary motion. Therefore, in this work I will not attempt to teach those topics, but will assume that students have a basic understanding of the physics involved as it pertains to an understanding of gravity. Many textbooks do not contain a treatment on current understanding and development of the ideas regarding gravitation. Those that do often place this material as footnotes to a chapter or as chapters late in the text that a typical class may never cover. This chapter of the Century Physics FlexBook will attempt to address our changing understanding of gravitation and in doing so also introduce the student to a few interesting areas of astronomy and cosmology. This chapter should be an appropriate extension to a study of Newton’s universal law of gravitation. The presentation deals with gravitation from a purely conceptual approach. The appropriate high school level mathematical treatment would pertain to Newton’s universal law of gravitation and it is assumed that the students will study from traditional text or with their teachers.

  The chapter is set up in dialogue style. This technique has a wonderful heritage in physics going back to Galileo’s Dialogue Concerning the Two Chief World Systems published in 1632. Bold Print statements represent questions asked by a student with the appropriate answers following. It is my practice and suggestion that a treatment of universal gravitation in a high school physics class be approached in a historical manner starting with Aristotle and extending to as near the present understanding as possible.

  Toward an Understanding of Gravitation (With a Few Interesting Side Trips)

  Figure 2.1

  Aristotle Contemplating the Bust of Homer - painted by Rembrandt in 1653 at a time when scientists understood the planets to orbit the sun, but had no concept that a force called caused their motion and were only beginning to abandon Aristotelian beliefs of motion.

  What is Gravity?

  If we begin our view of gravity from an Aristotelian view, you may find that it is not far from your own initial thoughts on gravity. Aristotle taught that the heavenly bodies moved in perfect circular orbits around the Earth. The more mundane things here on Earth tended to move toward their natural place. For some objects, like rocks and people, that natural place was to be drawn toward the center of the Earth. For other objects like fire, smoke, and steam that natural place was to the heavens.

  It was quite a long time after Aristotle that the English language included the word gravity in the sense that you think of it in your science class. The Latin word gravis means heavy, but it was not until the mid that the term gravity was used to describe a force that gives objects their weight. Here is a formal definition from the Online Etymology Dictionary, http://www.etymonline.com/index.php?search=gravity.

  Common to Aristotle's and all earlier "theories" of the motion of heavenly bodies is the belief [dogma] that the Earth is at the center of the center of the universe and that they orbit in the perfect geometric form, namely a circle.

  Aristotle’s description of how and why things fell or orbited was attacked often and by many. Many Arabic mathematicians and physicists tackled the issues in the middle ages, which lead to some of the same statements eventually made and published by Galileo and Newton. These ideas published by Newton and Galileo are the ideas you are likely to find in your physics text.

  So Aristotle had it wrong, but now we know the truth about gravity—right?

  Well, in a word—no. Physicists have answered many questions about gravity, but they have created many more questions, too.

  What Do We Know About Gravity Now?

  The modern era of astronomy begins with Copernicus. The Aristotelian astronomy [developed largely by Ptolemy] had use a hierarchy of circles to accurately describe the motion of heavenly body. Copernicus found that the
description is simplified if the sun is placed at the center and the Earth and the other planets revolve around it; in particular, it leads to a simple explanation of retrograde motion.

  Kepler’s, Galileo’s, and Newton’s work with regard to gravity is well supported in your physics book, I am sure. This is the traditional material of introductory physics. I will just touch on a couple of important points to support ideas I wish to develop in this chapter. You will need to use other resources to pick up on the "traditional details" like solving mathematics-based physics problems. In this chapter, I hope to help you understand how our current knowledge about gravity has developed. I hope you will understand how ideas were built on top of one another, how questions got answered, and how new questions came to be while some old questions still remain. I hope you will also get a sense for how technology and data collection played a roll in answering and developing important questions about gravity.

  So, what we know about gravity starts with Kepler? What did he figure out?

  Johannes Kepler was a gifted mathematician. Around 1600 he began working with one of the world’s most gifted astronomers, Tycho Brahe. It is important for you to know that at this time Kepler and his contemporary Galileo understood and believed Copernicus’ theory of a sun-centered solar system. Kepler applied his gifts of geometry to more than three decades of precision data regarding the position of Mars in the sky. By 1619 Kepler had published his three laws of planetary motion.

  All planets move in elliptical orbits with the Sun at one focus.

  A line connecting a planet to the Sun sweeps out equal areas of space in equal amounts of time.

  The period of a planet's orbit squared is directly proportional to the cube of its orbital radius.

  It is so easy to state and learn these laws that it may lead you to think they were easy to figure out. If you would like to gain a little understanding of Kepler’s accomplishments you should look over the details of how he came to these three conclusions at http://www-groups.dcs.st-and.ac.uk/~history/Extras/Keplers_laws.html

  Figure 2.2

  Johannes Kepler as painted in 1610 by an unknown artist. He would soon hear of a revolutionary new tool for astronomythe telescope.

  It is also very useful for you to have a good understanding of these laws and the nature of ellipses, so here is a little project for you to do.

  Elliptical Homework

  Get a scrap piece of cardboard, two push-pins, a loop of string, and a pencil.

  Push the two pins into the cardboard.

  Place the loop of string on the cardboard with the two pins in the loop.

  Use a pencil to pull the loop away from the pens to make the loop tight against the pencil and the two pins.

  Move the pencil around in a circle (it’s an ellipse) keeping the loop tight as you draw.

  Figure 2.3

  Creating an Ellipse

  The shape you have is an ellipse. The two pin holes are the two foci. Mark one as "Sun.” The drawn curve is the path of a planet around the Sun. See if you can sketch in the idea of Kepler’s Second Law of Planetary Motion.

  The eccentricity of an elliptical orbit is found by measuring the two distances shown and dividing the difference between them by the larger. Therefore, the eccentricity of a circle is equal to zero.

  Figure 2.4

  This ellipse has an eccentricity of . The sun would be at one focus.

  The eccentricity for Mars is about , which is much larger than Earth’s. What does that tell you about how elliptical the orbits of the planets are? Can you use a string, pin, and pencil to create an ellipse with ?

  If you make the loop of string a bit shorter and draw another ellipse it will represent the path of another planet. See if you can apply an understanding of Kepler’s third law of planetary motion to the two ellipses. This would be an excellent thing to talk through with another student or teacher once you have given it some thought on your own.

  OK—I drew a couple of ellipses and I think I understand Kepler’s laws of planetary motion. But if they are laws, he got it all figured out, right?

  It is so important to understand the scientific meaning of the words: law, theory, and hypothesis. Before we go on with more physics about gravity, let’s take an important aside.

  An Important Aside

  What is a scientific law? How does it differ from a hypothesis or a theory? How does a theory become a law? These are all great questions that you really need to be able to answer. The earlier in your science studies you understand these differences and relationships the better. A scientific hypothesis is not just a "best guess." It’s an idea of how something works or an explanation based on the evidence available. It is a statement limited to a specific situation and must be testable. In other words, it should be something that could be proven wrong.

  A scientific law is a statement of fact that is believed to be always true, but offers no explanation. The law of inertia is a wonderful example. It is understood that objects at rest will stay at rest unless a force causes them to move. Scientists do not have an explanation for WHY objects cannot begin moving from a state of rest without a force acting on them, but such a thing has never been observed and we believe it to be universally true. Kepler’s laws of planetary motion fit the description of scientific laws well when they were initially stated. In the early we did not understand that the Sun and planets were exerting forces on each other through gravitation. Kepler put together decades of data and found that for the six known planets, all of them behaved as described by his three statements. His laws offer no explanation for WHY the planets behave this way, thus they are planetary laws. Newton’s universal law of gravitation fits this description as well. It does not tell us HOW two different masses exert forces on each other, it simply describes it and names it. The question “How does a theory become a law?” is a trick question. The answer is—it cannot! Scientific theories EXPLAIN things. A theory in science provides a big picture understanding and view that helps to explain many different phenomena. For example, the atomic theory says that matter is made of discrete units of matter that maintain their "identity" through physical and chemical change. This atomic theory is very useful in understanding chemical reactions and much more.

  Therefore, in science, the theory of evolution is not less certain than the law of universal gravitation. They do very different jobs. The theory of evolution EXPLAINS HOW speciation occurs through natural selection and Newton’s law of universal gravitation states what we observe without explanation. We are still in search of a THEORY of gravitation. There are a few promising hypotheses, however.

  Theories and laws. I’ll try to remember the difference. What about this universal law of gravitation?

  I will leave the majority of the teaching of Newton’s universal law of gravitation to your traditional textbook or Internet sources. Go read up on it and do a few problems and come back. One place you can do this is the Physics Classroom at http://www.physicsclassroom.com/Class/circles/u6l3a.cfm

  OK. I solved some problems and I’m back. Seems like Newton got it all figured out.

  Figure 2.5

  Sir Isaac Newton (16431727) as painted in 1689 by Godfrey Kneller.

  In Newton’s life (1643-1727) he came to understand that all masses attracted each other with a force that was directly proportional to the product of the masses and inversely proportional to the distance between them squared. BUT, neither he nor his contemporaries were able to turn this proportionality into an equality. It is not terribly difficult to think up an experiment to try to measure the constant of proportionality in this equation where is some constant that turns the mathematics from a proportionality to an equation. With equations you can solve problems.

  First, you might think of taking two objects of mass and and placing them apart. Now all you need to do is measure the force of attraction and solve for . While this is simple to think of, it is far beyond the ability of simple force scales to measure the incredibly small force of attraction betw
een the two masses, even if the masses are huge. The best scales of Newton’s era were not up to the task. Another simple experiment you may think of is to take a known mass and find out how much it weighs. This would be the force of attraction to the mass of the Earth when separated by a distance equal to the Earth’s radius. During Newton’s time the radius of the Earth was well known, but the value of its mass was not known. One equation with two unknowns, the mass of the Earth and the value of , makes for an unsolvable problem.

  Newton died with two major aspects of universal gravitation left unexplained: the value of the universal gravitation constant , and an explanation for HOW gravity reached out through space and exerted a force. After all, if you want to exert a force on a friend you have to physically touch him or throw something at him. For example, it wasn't obvious that the Earth and the Moon were doing either to each other. So how were the Earth and the Moon pulling on each other with gravity?

  My physics textbook has a value for , so somebody figured that part out. Cavendish, right?

  Figure 2.6

  In 1798 Cavendish finds a way to measure the incredibly small forces that lead to a determination of the Universal Gravitation Constant.