... THE MOTION OF FALLING OBJECTS The motion of falling objects is the simplest and most common example of motion with changing velocity. The early pioneers of physics had a correct intuition that the way things drop was a message directly from Nature herself about how the universe worked. Other examples seem less likely to have deep significance. A walking person who speeds up is making a conscious choice. If one stretch of a river flows more rapidly than another, it may be only because the channel is narrower there, which is just an accident of the local geography. But there is something impressively consistent, universal, and inexorable about the way things fall. Stand up now and simultaneously drop a coin and a bit of paper side by side. The paper takes much longer to hit the ground. That's why Aristotle wrote that heavy objects fell more rapidly. Europeans believed him for two thousand years. Now repeat the experiment, but make it into a race between the coin and your shoe. My own shoe is about 50 times heavier than the nickel I had handy, but it looks to me like they hit the ground at exactly the same moment. So much for Aristotle! Galileo, who had a flair for the theatrical, did the experiment by dropping a bullet and a heavy cannonball from a tall tower. Aristotle's observations had been incomplete, his interpretation a vast oversimplification. It is inconceivable that Galileo was the first person to observe a discrepancy with Aristotle's predictions....
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...1. The term Zodiac refers to C) a group of constellations lying near the ecliptic. ----------- 2. You have just won 100 million dollars on that hit TV survival show ``Astronomy Midterm No. 1''. How much money is this? A) \$10$^8$ ----------- 3. In current scientific opinion, Stonehenge is considered to have been D) an astronomical observatory. ----------- 4. You have just won $10^4$ dollars on that hit TV survival show ``Astronomy Midterm No. 1''. How much money is this in real money? C) \$10,000 ----------- 9. Most Greek astronomers believed that the Earth is immobile because they did not observe E) parallaxes for the stars. ----------- 14. Sunspots were discovered by C) Galileo. ----------- 15. Aristarchus argues E) for a heliocentric universe. ----------- 16. The higher the frequency of light B) the shorter (smaller) its wavelength. ----------- 17. Aristarchus estimated the relative distances to the Sun and Moon by observing the A) angle between the half Moon and the Sun in the sky. ----------- 18. The smaller the wavelength of light A) the larger its frequency. ----------- 19. The difference in the lengths of shadows simultaneously cast by identical sticks placed vertically in the ground at two different points on a meridian indicates that D) the...
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...Introductory Physics I Elementary Mechanics by Robert G. Brown Duke University Physics Department Durham, NC 27708-0305 rgb@phy.duke.edu Copyright Notice Copyright Robert G. Brown 1993, 2007, 2013 Notice This physics textbook is designed to support my personal teaching activities at Duke University, in particular teaching its Physics 141/142, 151/152, or 161/162 series (Introductory Physics for life science majors, engineers, or potential physics majors, respectively). It is freely available in its entirety in a downloadable PDF form or to be read online at: http://www.phy.duke.edu/∼rgb/Class/intro physics 1.php It is also available in an inexpensive (really!) print version via Lulu press here: http://www.lulu.com/shop/product-21186588.html where readers/users can voluntarily help support or reward the author by purchasing either this paper copy or one of the even more inexpensive electronic copies. By making the book available in these various media at a cost ranging from free to cheap, I enable the text can be used by students all over the world where each student can pay (or not) according to their means. Nevertheless, I am hoping that students who truly find this work useful will purchase a copy through Lulu or a bookseller (when the latter option becomes available), if only to help subsidize me while I continue to write inexpensive textbooks in physics or other subjects. This textbook is organized for ease of presentation and ease of learning. In particular, they are...
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...PHYSIC AL CONSTANTS CONSTANT Speed of light Elementary charge Electron mass Proton mass Gravitational constant Permeability constant Permittivity constant Boltzmann’s constant Universal gas constant Stefan–Boltzmann constant Planck’s constant Avogadro’s number Bohr radius SYMBOL c e me mp G m0 P0 k R s h 15 2p"2 NA a0 THREE-FIGURE VALUE 3.003108 m/s 1.60310219 C 9.11310231 kg 1.67310227 kg 6.67310211 N # m2/kg 2 1.2631026 N/A2 1H/m2 8.85310212 C 2/N # m2 1F/m2 1.38310223 J/K 8.31 J/K # mol 5.6731028 W/m2 # K4 6.63310234 J # s 6.0231023 mol21 5.29310211 m BEST KNOWN VALUE* 299 792 458 m/s (exact) 1.602 176 4871402 310219 C 9.109 382 151452 310231 kg 1.672 621 6371832 310227 kg 6.674 281672 310211 N # m2/kg 2 4p31027 (exact) 1/m0c2 (exact) 1.380 65041242 310223 J/K 8.314 4721152 J/K # mol 5.670 4001402 31028 W/m2 # K4 6.626 068 961332 310234 J # s 6.022 141 791302 31023 mol21 5.291 772 08591362 310211 m *Parentheses indicate uncertainties in last decimal places. Source: U.S. National Institute of Standards and Technology, 2007 values SI PREFIXES POWER 1024 1021 1018 1015 1012 109 106 103 102 101 100 1021 1022 1023 1026 1029 10212 10215 10218 10221 10224 THE GREEK ALPHABET PREFIX yotta zetta exa peta tera giga mega kilo hecto deca — deci centi milli micro nano pico femto atto zepto yocto SYMBOL Y Z E P T G M k h da — d c m μ n p f a z y Alpha ...
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...LEONARD MLODINOW A Briefer History of Time The Drunkard’s Walk: How Randomness Rules Our Lives Euclid’s Window: The Story of Geometry from Parallel Lines to Hyperspace Feynman’s Rainbow: A Search for Beauty in Physics and in Life FOR CHILDREN The Last Dinosaur (with Matt Costello) Titanic Cat (with Matt Costello) The Grand Design The Grand Design The Grand Design The Grand Design Copyright © 2010 by Stephen W. Hawking and Leonard Mlodinow Original art copyright © 2010 by Peter Bollinger All rights reserved. Published in the United States by Bantam Books, an imprint of The Random House Publishing Group, a division of Random House, Inc., New York. Cartoons by Sidney Harris, copyright © Sciencecartoonsplus.com BANTAM BOOKS and the rooster colophon are registered trademarks of Random House, Inc. eISBN: 978-0-553-90707-0 www.bantamdell.com v3.0 The Grand Design The Grand Design The Grand Design The Grand Design E EACH EXIST FOR BUT A SHORT TIME, and in that time explore but a small part of the whole universe. But humans are a curious species. We wonder, we seek answers. Living in this vast world that is by turns kind and cruel, and gazing at the immense heavens above, people have always asked a multitude of questions: How can we understand the world in which we find ourselves? How does the universe behave? What is the nature of reality? Where did all this come from? Did the universe need a creator? Most of us do not spend most of our...
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...Chapter 2 Galileo’s Great Discovery: How Things Fall Galileo Galilei (1564–1642), the famous Italian mathematician at the leading edge of the scientific revolution that was to sweep Europe, was curious about motion. He was an experimentalist who for the first time had the insight and talent to link theory with experiment. He rolled balls down an inclined plane in order to see how things fell toward the Earth. He discovered in this way that objects of any weight fell toward the Earth at the same rate – that they had a uniform acceleration. He surmised that if they fell in a vacuum, where there was no air resistance to slow some objects more than others, even a feather and a cannon ball would descend at the same rate and reach the ground at the same time. He also explored the motion of pendulums and other phenomena. He is perhaps most famous for his 1610 telescopic discoveries of the moving moons of Jupiter, the phases of Venus, and the craters of the moon, all of which convinced him, against the ages-old wisdom of Aristotle and of the Catholic Church, of the rightness of the Copernican heliocentric view of the solar system. In his investigations of motion, Galileo was the first clearly to understand that the forces acting upon objects could be broken into independent components; that a thrown stone had a force pulling it down as well as the force throwing it horizontally outward. These insights would be of great use to Isaac Newton, born the year Galileo died, in devising the...
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...studentNational University of Singapore MW5200 MSC SCIENCE COMMUNICATION PROJECT Project Report Strengthening student engagement in the classroom. Course: Msc (Science Communication) Faculty of Science National University of Singapore Ganeshini D/O Sri kanthan A0075383Y Name: Student ID: Project Supervisor: A/P Helmer Aslaksen ABSTRACT The Ministry of Education (MOE) recognizes the importance of student engagement in the classroom. However, keeping students engaged in the classroom is a challenge for many educators these days. Student engagement is a contested concept, theorized in a variety of different ways within academic literature. This projects aims to define and understand the concept of student engagement. The purpose of this project was also to find out the usage of engagement based approaches in the classroom. The survey results in this project indicate that teachers do use these approaches in the classroom but not frequently enough. Usage of engagement based approaches in the classroom can be increased with changes in attitudes of teachers, sufficient support from schools and changes in modes of assessment. i AKNOWLEDGEMENTS I would like to thank the following people who have helped me in making this Masters Project interesting and a memorable one: Associate Professor Helmer Aslaksen for his guidance and patience. Without his constant assurance and encouragement this would not be possible. Colleagues and friends who contributed...
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...SENIOR SECONDARY COURSE PHYSICS 1 (CORE MODULES) Coordinators Dr. Oum Prakash Sharma Sh. R.S. Dass NATIONAL INSTITUTE OF OPEN SCHOOLING A-25, INSTITUTIONAL AREA, SECTOR-62, NOIDA-201301 (UP) COURSE DESIGN COMMITTEE CHAIRMAN Prof. S.C. Garg Former Pro-Vice Chancellor IGNOU, Maidan Garhi, Delhi MEMBERS Prof. A.R. Verma Former Director, National Physical Laboratory, Delhi, 160, Deepali Enclave Pitampura, Delhi-34 Dr. Naresh Kumar Reader (Rtd.) Deptt. of Physics Hindu College, D.U. Dr. Oum Prakash Sharma Asstt. Director (Academic) NIOS, Delhi Prof. L.S. Kothari Prof. of Physics (Retd.) Delhi University 71, Vaishali, Delhi-11008 Dr. Vajayshree Prof. of Physics IGNOU, Maidan Garhi Delhi Sh. R.S. Dass Vice Principal (Rtd.) BRMVB, Sr. Sec. School Lajpat Nagar, New Delhi-110024 Dr. G.S. Singh Prof. of Physics IIT Roorkee Sh. K.S. Upadhyaya Principal Jawahar Navodaya Vidyalaya Rohilla Mohammadabad (U.P.) Dr. V.B. Bhatia Prof. of Physics (Retd.) Delhi University 215, Sector-21, Faridabad COURSE DEVELOPMENT TEAM CHAIRMAN Prof. S.C. Garg Former Pro-Vice Chancellor IGNOU, Delhi MEMBERS Prof. V.B. Bhatia 215, Sector-21, Faridabad Prof. B.B. Tripathi Prof. of Physics (Retd.), IIT Delhi 9-A, Awadhpuri, Sarvodaya Nagar Lucknow-226016 Sh. K.S. Upadhyaya Principal Navodaya Vidyalaya Rohilla Mohammadabad, (U.P.) Dr. V.P. Shrivastava Reader (Physics) D.E.S.M., NCERT, Delhi EDITORS TEAM CHAIRMAN Prof. S.C. Garg Former Pro-Vice Chancellor IGNOU, Delhi MEMBERS Prof. B.B. Tripathi Prof...
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...Arturo Alcaraz (Philippines) - Instrumental in a team of scientists, who in 1967 were able to harness steam from a volcano resulting in the production of electricity. Diosdado Banatao (Philippines) - Improved computer performance throughthe development of accelerator chips, helping to make the Internet a reality. Marie Curie (Poland) - Winner of two Nobel Prizes in Chemistry and Physicsfor her studies into Radioactivity and her discoveries of Radium and Polonium. Paul Dirac (England) - An important contributor in the fields of QuantumMechanics and Electro Dynamics, Dirac was co-winner of the Nobel Prize inPhysics (1933). Albert Einstein (Germany) - Arguably needing no introduction, the most famous scientist that lived and a name that has become synonymous in popular culture with the highest intelligence. Enrico Fermi (Italy) - Heavily involved in the development of the world's first nuclear reactor and his work in induced radioactivity saw him awarded with the 1938 Nobel Prize in Physics. Vitaly Ginzburg (Russia) - One of three recipients of the 2003 Nobel inPhysics for their pioneering work in the theory of superconductors and superfluids. Christiaan Huygens (Netherlands) - Most well known for his wave theory of light, Huygens is credited with discovering the first of Saturn's moons. Werner Israel (Canada) - In 1990 Israel co-pioneered a study on black hole interiors. Ali Javan (Iran) - Born in Tehran, Ali Javan is listed as one of the top 100 living...
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...also be useful as preparation for any undergraduate mathematics course, even if you do not plan to take STEP. The questions are all based on recent STEP questions. I chose the questions either because they are ‘nice’ – in the sense that you should get a lot of pleasure from tackling them – or because I felt I had something interesting to say about them. In this booklet, I have restricted myself (reluctantly) to the syllabus for Papers I and II, which is the A-level core (i.e. C1 to C4) with a few additions. This material should be familiar to you if you are taking the International Baccalaureate, Scottish Advanced Highers or other similar courses. The first two questions (the sample worked questions) are in a ‘stream of consciousness’ format. They are intended to give you an idea how a trained mathematician would think when tackling them. This approach is much too long-winded to sustain, but it should help you to see what sort of questions you should be asking yourself as you work through the later questions. I have given each of the subsequent questions a difficulty rating ranging from (∗) to (∗ ∗ ∗). A question labelled (∗) might be found on STEP I; a question labelled (∗∗) might be found on STEP II; a question labelled (∗ ∗ ∗) might be found on STEP III. But difficulty in mathematics is in the eye of the beholder: you might find a question difficult simply because you overlooked some key step, which on another day you would not have hesitated over. You should not therefore...
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...Cooperative Problem Solving in Physics A User’s Manual Why? What? How? STEP 1 Recognize the Problem What's going on? STEP 2 Describe the problem in terms of the field What does this have to do with ...... ? STEP 3 Plan a solution How do I get out of this? STEP 4 Execute the plan Let's get an answer STEP 5 Evaluate the solution Can this be true? Kenneth Heller Patricia Heller University of Minnesota With support from the National Science Foundation, University of Minnesota, and U.S. Department of Education © Kenneth & Patricia Heller, 2010 Acknowledgments In reaching this stage in this work, we gratefully acknowledge the support of the University of Minnesota, the U.S. Department of Education FIPSE program, and the National Science Foundation. This work would not have existed without the close cooperation of the University of Minnesota School of Physics and Astronomy and Department of Curriculum and Instruction. We have incorporated the suggestions of many faculty members from both Physics and Education at the University of Minnesota and other institutions that have communicated with us at workshops, meetings, and by e-mail. This work has depended on the efforts and feedback of many graduate student teaching assistants in the School of Physics and Astronomy over the years. Much of this development is directly based on the research of the graduate students in the University of Minnesota Physics Education Program: Jennifer...
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...g Easier! Making Everythin ™ heory tring T S Learn: • The basic concepts of this controversial theory • How string theory builds on physics concepts • The different viewpoints in the field • String theory’s physical implications Andrew Zimmerman Jones Physics Guide, About.com with Daniel Robbins, PhD in Physics Get More and Do More at Dummies.com® Start with FREE Cheat Sheets Cheat Sheets include • Checklists • Charts • Common Instructions • And Other Good Stuff! To access the Cheat Sheet created specifically for this book, go to www.dummies.com/cheatsheet/stringtheory Get Smart at Dummies.com Dummies.com makes your life easier with 1,000s of answers on everything from removing wallpaper to using the latest version of Windows. Check out our • Videos • Illustrated Articles • Step-by-Step Instructions Plus, each month you can win valuable prizes by entering our Dummies.com sweepstakes. * Want a weekly dose of Dummies? Sign up for Newsletters on • Digital Photography • Microsoft Windows & Office • Personal Finance & Investing • Health & Wellness • Computing, iPods & Cell Phones • eBay • Internet • Food, Home & Garden Find out “HOW” at Dummies.com *Sweepstakes not currently available in all countries; visit Dummies.com for official rules. String Theory FOR DUMmIES ‰ by Andrew Zimmerman Jones with Daniel Robbins, PhD in Physics String Theory For Dummies® Published by Wiley Publishing, Inc. 111 River St. Hoboken, NJ 07030-5774 www...
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...NATURE OF MAN HISTORY AND PHILOSOPHY OF SCIENCE IN 10 MODULES E. Kolawole Ogundowole, Ph.D., D.Sc. Professor & Head of Philosophy Department University of Lagos. Akoka, Lagos. Nigeria Correct Counsels Limited Research. Counselling. Publishing. Book Supply First published 2003 Correct Counsels Ltd. P. O. Box 53 Akoka, Lagos. C E. Kolawole Ogundowole, 2003 ISBN: 978 -37004 - 0 – 5 This book is copyright. All rights reserved under the Copyright La Enquiries should be addressed to the Publishers. Printed in Nigeria by: Mustard Press Enterprises 16, Ogundola Street Sungas-BAriga. PREFACE A few words about the overall objectives of the course is appropriate as a starting point. Historically, philosophy was the first form of theoretical knowledge. As a rational theoretical tool of comprehending the world, philosophy arose in ancient Greece in stiff battle with mythology and religious consciousness. It came out to lay the foundation for the evolvement of scientific consciousness and the emergence and development of the sciences - Mathematics, Astronomy, Physics, Chemistry, Biology, etc. In an environment rife with various and varying superstitions and myths, the study of the History of Science and Philosophy of Science becomes crucial, lest science itself falls within the ambit of mythology and superstition and becomes another form of myth even in the hands of the tutored. The study of the History of Science...
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...THE UNIVERSE When we look up in the night sky we can see the stars and the moon. And because it is natural to be curious, we ask questions and we want answers. When our view was limited by what our eyes could see, the sky was our Universe. Then the telescopes deepened our view, photography enhanced it, and spectroscopy broadened it. The universe grew from a sky of stars to a realm of galaxies, to an expanding universe of galaxies. Many people believe that nature, the sun and moon, the star, even human beings never had a beginning. There is an endless, external cycle of birth, life and death that constantly repeats itself and it never began and will never end. In the Book of Genesis in the Bible, it was written that at first the world did not exist and that God is the only one who existed. So He created the world. The universe is the totality of everything that has ever existed. It is so large that it contains billions of stars, and all of the planets, galaxies and all of space. The study of the universe is called Cosmology. Traditional Views about the Universe 1. Geocentric Universe Greeks believed that the earth was a sphere that stayed motionless at the center of the universe or the geocentric (Earth-centered) view. Orbiting the earth were seven wanderers (planetai in Greek) including the sun, the moon and the known planets, Mercury, Venus, Mars, Jupiter and Saturn. Greece was centered as the “Golden Age” of early astronomy. Claudius Ptolemy created the book Almagest...
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...Lecture 2. Lecture 3. Lecture 4. Lecture 5. Lecture 6. Lecture 7. Lecture 8. Lecture 9. Lecture 10. Lecture 11. Lecture 12. Lecture 13. Lecture 14. Lecture 15. Lecture 16. Lecture 17. Lecture 18. Lecture 19. Lecture 20. Lecture 21. Lecture 22. Lecture 23. Three-Dimensional Coordinate Systems . . . . . . . . . . . . . . . . . . . . . iii 1 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Lines and Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Vector Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Space Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Multivariable Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Partial Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Directional Derivatives and Gradients . . . . . . . . . . . . . . . . . . . . . . . 77 Tangent Planes and Normal Vectors . . . . . . . . . . . . . . . . . . . . . . . 81 Extremal Values of Multivariable Functions . . . . . . . . . . . . . . . . . . . 91 Lagrange Multipliers* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Double Integrals over Rectangles . . . . . . . . . . . . . . . . . . . . . . . . 105 Double Integrals over General Regions . . . . . . . . . . . . . . . . . . . . . 111 Double Integrals in Polar Coordinates...
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