ELEMENTARY MECHANICS & THERMODYNAMICS Professor John W. Norbury Physics Department University of Wisconsin-Milwaukee P. Box 413 Milwaukee, WI 53201 November 20, 2000 www.com Contents 1 MOTION ALONG A STRAIGHT LINE 11 1.2 Position and Displacement .3 Average Velocity and Average Speed .4 Instantaneous Velocity and Speed .6 Constant Acceleration: A Special Case .7 Another Look at Constant Acceleration .8 Free-Fall Acceleration .1 Vectors and Scalars .2 Adding Vectors: Graphical Method .3 Vectors and Their Components .1 Review of Trigonometry .2 Components of Vectors .5 Adding Vectors by Components .6 Vectors and the Laws of Physics .1 The Scalar Product (often called dot product) .2 The Vector Product. 46 3 MOTION IN 2 & 3 DIMENSIONS 47 3.1 Moving in Two or Three Dimensions .2 Position and Displacement .3 Velocity and Average Velocity .4 Acceleration and Average Acceleration .6 Projectile Motion Analyzed .7 Uniform Circular Motion .1 What Causes an Acceleration? .2 Newton’s First Law .5 Newton’s Second Law .6 Some Particular Forces .7 Newton’s Third Law .8 Applying Newton’s Laws.
77 5 FORCE & MOTION - II 79 5.2 Properties of Friction .3 Drag Force and Terminal Speed .4 Uniform Circular Motion. 85 6 POTENTIAL ENERGY & CONSERVATION OF ENERGY 89 6.3 Work-Energy Theorem .4 Gravitational Potential Energy .5 Conservation of Energy .6 Spring Potential Energy .7 Appendix: alternative method to obtain potential energy. 105 7 SYSTEMS OF PARTICLES 107 7.2 The Center of Mass .3 Newton’s Second Law for a System of Particles .4 Linear Momentum of a Point Particle .5 Linear Momentum of a System of Particles .6 Conservation of Linear Momentum .1 What is a Collision? .2 Impulse and Linear Momentum .3 Elastic Collisions in 1-dimension .4 Inelastic Collisions in 1-dimension .5 Collisions in 2-dimensions .6 Reactions and Decay Processes .1 Translation and Rotation .2 The Rotational Variables .3 Are Angular Quantities Vectors? .4 Rotation with Constant Angular Acceleration .5 Relating the Linear and Angular Variables .6 Kinetic Energy of Rotation .7 Calculating the Rotational Inertia .9 Newton’s Second Law for Rotation .10 Work and Rotational Kinetic Energy. 142 10 ROLLING, TORQUE & ANGULAR MOMENTUM 145 10.5 Newton’s Second Law in Angular Form .6 Angular Momentum of a System of Particles .7 Angular Momentum of a Rigid Body Rotating About a Fixed Axis .8 Conservation of Angular Momentum .1 The World and the Gravitational Force .2 Newton’s Law of Gravitation .3 Gravitation and Principle of Superposition .4 Gravitation Near Earth’s Surface .5 Gravitation Inside Earth .6 Gravitational Potential Energy .2 Simple Harmonic Motion .3 Force Law for SHM .4 Energy in SHM .5 An Angular Simple Harmonic Oscillator .1 Waves and Particles .2 Types of Waves .3 Transverse and Longitudinal Waves .4 Wavelength and Frequency .5 Speed of a Travelling Wave .6 Wave Speed on a String .7 Energy and Power of a Travelling String Wave .8 Principle of Superposition .9 Interference of Waves .12 Standing Waves and Resonance .2 Speed of Sound .3 Travelling Sound Waves .5 Intensity and Sound Level .6 Sources of Musical Sound.
208 15 TEMPERATURE, HEAT & 1ST LAW OF THERMODY- NAMICS 211 15.2 Zeroth Law of Thermodynamics .4 Celsius, Farenheit and Kelvin Temperature Scales .6 Temperature and Heat .7 The Absorption of Heat by Solids and Liquids .8 A Closer Look at Heat and Work .9 The First Law of Thermodynamics .10 Special Cases of 1st Law of Thermodynamics .11 Heat Transfer Mechanisms. 223 16 KINETIC THEORY OF GASES 225 16.1 A New Way to Look at Gases .4 Pressure, Temperature and RMS Speed .5 Translational Kinetic Energy .6 Mean Free Path .7 Distribution of Molecular Speeds. 233 17 Review of Calculus 235 17.1 Derivative Equals Slope .1 Slope of a Straight Line .2 Slope of a Curve .3 Some Common Derivatives .4 Extremum Value of a Function .1 Integral Equals Antiderivative .2 Integral Equals Area Under Curve .3 Definite and Indefinite Integrals .com 8 CONTENTS PREFACE The reason for writing this book was due to the fact that modern intro- ductory textbooks (not only in physics, but also mathematics, psychology, chemistry) are simply not useful to either students or instructors. The typ- ical freshman textbook in physics, and other fields, is over 1000 pages long, with maybe 40 chapters and over 100 problems per chapter.
This is overkill! A typical semester is 15 weeks long, giving 30 weeks at best for a year long course. At the fastest possible rate, we can ”cover” only one chapter per week. For a year long course that is 30 chapters at best. Thus ten chapters of the typical book are left out! 1500 pages divided by 30 weeks is about 50 pages per week.
The typical text is quite densed mathematics and physics and it’s simply impossible for a student to read all of this in the detail re- quired. Also with 100 problems per chapter, it’s not possible for a student to do 100 problems each week. Thus it is impossible for a student to fully read and do all the problems in the standard introductory books. Thus these books are not useful to students or instructors teaching the typical course! In defense of the typical introductory textbook, I will say that their content is usually excellent and very well writtten.
They are certainly very fine reference books, but I believe they are poor text books. Now I know what publishers and authors say of these books. Students and instructors are supposed to only cover a selection of the material. The books are written so that an instructor can pick and choose the topics that are deemed best for the course, and the same goes for the problems.
However I object to this. At the end of the typical course, students and instructors are left with a feeling of incompleteness, having usually covered only about half of the book and only about ten percent of the problems. I want a textbook that is self contained. As an instructor, I want to be able to comfortably cover one short chapter each week, and to have each student read the entire chapter and do every problem.
I want to say to the students at the beginning of the course that they should read the entire book from cover to cover and do every problem. If they have done that, they will have a good knowledge of introductory physics. This is why I have written this book. Actually it is based on the in- troductory physics textbook by Halliday, Resnick and Walker [Fundamental of Physics, 5th ed., by Halliday, Resnick and Walker, (Wiley, New York, 1997)], which is an outstanding introductory physics reference book.
I had been using that book in my course, but could not cover it all due to the reasons listed above.com CONTENTS 9 Availability of this eBook At the moment this book is freely available on the world wide web and can be downloaded as a pdf file. The book is still in progress and will be updated and improved from time to time.com 10 CONTENTS INTRODUCTION - What is Physics? A good way to define physics is to use what philosophers call an ostensive definition, i. a way of defining something by pointing out examples. Physics studies the following general topics, such as: Motion (this semester) Thermodynamics (this semester) Electricity and Magnetism Optics and Lasers Relativity Quantum mechanics Astronomy, Astrophysics and Cosmology Nuclear Physics Condensed Matter Physics Atoms and Molecules Biophysics Solids, Liquids, Gases Electronics Geophysics Acoustics Elementary particles Materials science Thus physics is a very fundamental science which explores nature from the scale of the tiniest particles to the behaviour of the universe and many things in between.
Most of the other sciences such as biology, chemistry, geology, medicine rely heavily on techniques and ideas from physics. For example, many of the diagnostic instruments used in medicine (MRI, x-ray) were developed by physicists. All fields of technology and engineering are very strongly based on physics principles. Much of the electronics and com- puter industry is based on physics principles.
Much of the communication today occurs via fiber optical cables which were developed from studies in physics. Also the World Wide Web was invented at the famous physics laboratory called the European Center for Nuclear Research (CERN). Thus anyone who plans to work in any sort of technical area needs to know the basics of physics. This is what an introductory physics course is all about, namely getting to know the basic principles upon which most of our modern technological society is based.com Chapter 1 MOTION ALONG A STRAIGHT LINE SUGGESTED HOME EXPERIMENT: Design a simple experiment which shows that objects of different weight fall at the same rate if the effect of air resistance is eliminated.
DRIVING YOUR CAR. DROPPING AN OBJECT. MOTION ALONG A STRAIGHT LINE INTRODUCTION: There are two themes we will deal with in this chapter. They concern DRIVING YOUR CAR and DROPPING AN OBJECT.
When you drive you car and go on a journey there are several things you are interested in. Typically these are distance travelled and the speed with which you travel. Often you want to know how long a journey will take if you drive at a certain speed over a certain distance. Also you are often interested in the acceleration of your car, especially for a very short journey such as a little speed race with you and your friend.
You want to be able to accelerate quickly. In this chapter we will spend a lot of time studying the concepts of distance, speed and acceleration. LECTURE DEMONSTRATION: 1) Drop a ball and hold at different heights; it goes faster at bottom if released from different heights 2) Drop a ball and a pen (different weights - weigh on balance and show they are different weight); both hit the ground at the same time Another item of interest is what happens when an object is dropped from a certain height. If you drop a ball you know it starts off with zero speed and ends up hitting the ground with a large speed.
Actually, if you think about it, that’s a pretty amazing phenomenom. WHY did the speed of the ball increase ? You might say gravity. But what’s that ? The speed of the ball increased, and therefore gravity provided an acceleration. But how ? Why ? When ? We shall address all of these deep questions in this chapter.2 Position and Displacement In 1-dimension, positions are measured along the x-axis with respect to some origin.
It is up to us to define where to put the origin, because the x-axis is just something we invented to put on top of, say a real landscape. POSITION AND DISPLACEMENT 13 Example Chicago is 100 miles south of Milwaukee and Glendale is 10 miles north of Milwaukee. If we define the origin of the x-axis to be at Glendale what is the position of someone in Chicago, Milwaukee and Glendale ? B. If we define the origin of x-axis to be at Milwaukee, what is the position of someone in Chicago, Milwaukee and Glendale ? Solution A.
For someone in Chicago, x = 110 miles. For someone in Milwaukee, x = 10 miles. For someone in Glendale, x = 0 miles. For someone in Chicago, x = 100 miles.
For someone in Milwaukee, x = 0 miles. For someone in Glendale, x = −10 miles. Displacement is defined as a change in position.1) Note: We always write ∆anything ≡ anthing2 −anything1 where anything2 is the final value and anything1 is the initial value. Sometimes you will instead see it written as ∆anything ≡ anthingf − anythingi where sub- scripts f and i are used for the final and initial values instead of the 2 and 1 subscripts.
Example What is the displacement for someone driving from Milwaukee to Chicago ? What is the distance ?