Introductory Physics I - Duke University

1 Introductory Physics IElementary MechanicsbyRobert G. BrownDuke University Physics DepartmentDurham, NC NoticeCopyright Robert G. Brown 1993, 2007, 2013 NoticeThis Physics textbook is designed to support my personal teaching activities at DukeUniversity, in particular teaching its Physics 141/142, 151/152,or 161/162 series (Introduc-tory Physics for life science majors, engineers, or potential Physics majors, respectively).It is freely available in its entirety in a downloadable PDF form orto be read online at: rgb/ is also available in aninexpensive(really!) print version via Lulu press here: readers/users can voluntarily help support or reward theauthor by purchasingeither this paper copy or one of the even more inexpensive electronic making the book available in these various media at a cost ranging from free tocheap, I enable the text can be used by students all over the world where each student canpay (or not) according to their , I am hoping that students who truly find this work useful willpurchasea copy through Lulu or a bookseller(when the latter option becomes available), if onlyto help subsidize me while I continue to write inexpensive textbooks in Physics or textbook is organized for ease of presentation and ease of learning.

2 In partic-ular, they are hierarchically organized in a way that directly supports efficient are also remarkablycompletein their presentation and contain moderately detailedderivations of many of the important equations and relations from first principles while notskimping on simpler heuristic or conceptual explanations as a live document (one I actively use and frequently change, adding or deletingmaterial or altering the presentation in some way), this textbook mayhave errors greatand small, stub sections where I intend to add content at some later time but haven t yetfinished it, and they cover and omit topics according tomy ownview of what is or isn timportant to cover in a one-semester course. Expect them to changewith little warning orannouncement as I add content or correct of the paper version should be aware of its probableimperfection and beprepared to either live with it or mark up their copy with corrections or additions as needbe. The latest (and hopefully most complete and correct) versionis always available forfree online anyway, and people who have paid for a paper copy areespeciallywelcometo access and retrieve cherish good-hearted communication from students or other instructors pointing outerrors or suggesting new content (and have in the past done my best to implement manysuch corrections or suggestions).

3 Books by Robert G. BrownPhysics Textbooks Introductory Physics I and IIA lecture note style textbook series intended to support the teaching of introductoryphysics, with calculus, at a level suitable for Duke undergraduates. Classical ElectrodynamicsA lecture note style textbook intended to support the second semester (primarilythe dynamical portion, little statics covered) of a two semester course of graduateClassical Books How to Engineer a Beowulf ClusterAn online classic for years, this is the print version of the famous free online book oncluster engineering. It too is being actively rewritten and developed, no guarantees,but it is probably still useful in its current The Book of LilithISBN: 978-1-4303-2245-0 Web: rgb/ is thefirstperson to be given a soul by God, and is given the job of giving allthe things in the world souls by loving them, beginning with Adam. Adam is given thejob of making up rules and the definitions of sin so that humans mayone day live inan ethical society.

4 Unfortunately Adam is weak, jealous, and greedy, and insists onbeing ontopduring sex to be closer to God .Lilith, however, refuses to be second to Adam or anyone Book of Lilithisa funny, sad, satirical, uplifting tale of her spiritual journey through the ancient worldsoulgiving and judging to find at the end of that journey Who Shall Sing, When Man is GoneOriginal poetry, including the epic-length poem about an imagined end of the worldbrought about by a nuclear war that gives the collection its many longand short works on love and life, pain and roaring, whipped by stormin damned defiance, hating hellwith every wave and every swell,every shark and every shelland shoreline. Hot Tea!More original poetry with a distinctly Zen cast to it. Works range from funny andsatirical to inspiring and uplifting, with a few erotic poems water, carrywood. Ice all around,fire is dying. Winter Zen?All of these books can be found on the online Lulu store here: Book of Lilithis available on Amazon, Barnes and Noble and other online book-seller Layout and Design.

5 XivI: Getting Ready to Learn Physics3 Preliminaries3 See, Do,Teach.. 3 Other Conditions for Learning .. 9 Your Brain and Learning .. 15 How to Do Your Homework Effectively ..22 The Method of Three Passes .. 26 Mathematics .. 28 Summary .. 33 Homework for Week 0 .. 34II: Elementary Mechanics37 Week 1: Newton s Laws39 Summary .. : Introduction: A Bit of History and Philosophy .. : Dynamics .. : Coordinates .. : Newton s Laws .. : Forces .. : The Forces of Nature .. : Force Rules .. : Force Balance Static Equilibrium .. 63 Example : Spring and Mass in Static Force Equilibrium .. : Simple Motion in One Dimension ..65 Example : A Mass Falling from HeightH.. 66 Example : A Constant Force in One Dimension .. : Solving Problems with More Than One Object .. 74 Example : Atwood s Machine .. 75 Example : Braking for Bikes, or Just Breaking Bikes? .. : Motion in Two Dimensions .. : Free Flight Trajectories Projectile Motion.

6 81 Example : Trajectory of a Cannonball .. : The Inclined Plane .. 84 Example : The Inclined Plane .. : Circular Motion .. : Tangential Velocity .. : A Note on Notation .. : Centripetal Acceleration .. 90 Example : Ball on a String .. 92 Example : Tether Ball/Conic Pendulum .. : Tangential Acceleration .. : Conclusion: Rubric for Newton s Second Law Problems .. 94 Homework for Week 1 .. 96 Week 2: Newton s Laws: Continued117 Summary .. : Friction .. 120 Example : Inclined Plane of LengthLwith Friction .. 121 Example : Block Hanging off of a Table ..123 Example : Find The Minimum No-Skid Braking Distance for a Car .. 125 Example : Car Rounding a Banked Curve with Friction .. : Drag Forces .. : Stokes, or Laminar Drag .. : Rayleigh, or Turbulent Drag .. : Terminal velocity .. 135 CONTENTSiiiExample : Falling From a Plane and Surviving .. 136 Example : Solution to Equations of Motion for Stokes Drag .. : Advanced: Solution to Equations of Motion for Turbulent Drag.

7 139 Example : Dropping the Ram .. : Inertial Reference Frames the Galilean Transformation .. : Time .. : Space .. : Non-Inertial Reference Frames Pseudoforces .. : Identifying Inertial Frames .. 148 Example : Weight in an Elevator .. 150 Example : Pendulum in a Boxcar .. : Advanced: General Relativity and Accelerating Frames .. : Just For Fun: Hurricanes .. 156 Homework for Week 2 .. 160 Week 3: Work and Energy169 Summary .. : Work and Kinetic Energy .. : Units of Work and Energy .. : Kinetic Energy .. : The Work-Kinetic Energy Theorem .. : Derivation I: Rectangle Approximation Summation .. : Derivation II: Calculus-y (Chain Rule) Derivation .. 177 Example : Pulling a Block .. 179 Example : Range of a Spring Gun .. : Conservative Forces: Potential Energy .. : Force from Potential Energy .. : Potential Energy Function for Near-Earth Gravity .. : Springs .. : Conservation of Mechanical Energy .. : Force, Potential Energy, and Total Mechanical Energy.

8 188 Example : Falling Ball Reprise .. 189 Example : Block Sliding Down Frictionless Incline Reprise.. 189 Example : A Simple Pendulum .. 189ivCONTENTSE xample : Looping the Loop .. : Generalized Work-Mechanical Energy Theorem .. 192 Example : Block Sliding Down a Rough Incline .. 193 Example : A Spring and Rough Incline .. : Heat and Conservation of Energy .. : Power .. 196 Example : Rocket Power .. : Equilibrium .. : Energy Diagrams: Turning Points and Forbidden Regions .. 201 Homework for Week 3 .. 204 Week 4: Systems of Particles, Momentum and Collisions215 Summary .. : Systems of Particles .. : Newton s Laws for a System of Particles Center of Mass .. 222 Example : Center of Mass of a Few Discrete Particles .. : Coarse Graining: Continuous Mass Distributions .. 225 Example : Center of Mass of a Continuous Rod .. 227 Example : Center of mass of a circular wedge .. 228 Example : Breakup of Projectile in Midflight .. : Momentum .. : The Law of Conservation of Momentum.

9 : Impulse .. 233 Example : Average Force Driving a Golf Ball .. 235 Example : Force, Impulse and Momentum for Windshield and Bug .. : The Impulse Approximation .. : Impulse, Fluids, and Pressure .. : Center of Mass Reference Frame .. : Collisions .. : Momentum Conservation in the Impulse Approximation .. : Elastic Collisions .. : Fully Inelastic Collisions .. : Partially Inelastic Collisions .. : Dimension of Scattering and Sufficient Information .. : 1-D Elastic Collisions .. : The Relative Velocity Approach .. : 1D Elastic Collision in the Center of Mass Frame .. : The BB/bb or Pool Ball Limits .. : Elastic Collisions in 2-3 Dimensions .. : Inelastic Collisions .. 255 Example : One-dimensional Fully Inelastic Collision (only) .. 256 Example : Ballistic Pendulum .. 257 Example : Partially Inelastic Collision .. : Kinetic Energy in the CM Frame ..260 Homework for Week 4 .. 262 Week 5: Torque and Rotation in One Dimension275 Summary.

10 : Rotational Coordinates in One Dimension .. : Newton s Second Law for 1D Rotations .. : Ther-dependence of Torque .. : Summing the Moment of Inertia .. : The Moment of Inertia .. 284 Example : The Moment of Inertia of a Rod Pivoted at One End .. : Moment of Inertia of a General Rigid Body .. 285 Example : Moment of Inertia of a Ring .. 286 Example : Moment of Inertia of a Disk .. : Table of Useful Moments of Inertia .. : Torque as a Cross Product .. 287 Example : Rolling the Spool .. : Torque and the Center of Gravity .. 290 Example : The Angular Acceleration of a Hanging Rod .. : Solving Newton s Second Law Problems Involving Rolling .. 292 Example : A Disk Rolling Down an Incline ..292 Example : Atwood s Machine with a Massive Pulley .. : Rotational Work and Energy .. : Work Done on a Rigid Object .. : The Rolling Constraint and Work .. 297viCONTENTSE xample : Work and Energy in Atwood s Machine .. 299 Example : Unrolling Spool .. 300 Example : A Rolling Ball Loops-the-Loop.