PHYSICS
1 Vectors and Kinematics 1 11 Introduction 2 12 Your Learning Goals for This Chapter 2 13 Vectors 2 131 Multiplication of a Vector by a Scalar 3 132 Vector Addition and Subtraction 4 133 Products of Two Vectors 5 134 Example: Tetrahedral Bond Angles 6 135 Coordinate Systems 8 136 Example: A Trigonometric Identity 10 137 Position Vector and Displacement Vector 11 138 Example: Tensegrity Geometry 12 14 Kinematics 15 141 Motion in One-Dimension 15 142 Motion in Two or Three Dimensions 17 143 Example: Motion in a Circle at Constant Angular Velocity 18 144 Motion Subject to a Constant Acceleration in One Dimension 19 145 Motion Subject to Constant Acceleration in Two and Three Dimensions 20 146 Example: Trajectory of Projectile Motion 21 15 Frames of Reference and Relative Velocity 22 151 Example: Relative Position 24 16 Chapter Outlook 25 17 Problems 26 2 Force and Momentum: Newton’s Laws and How to Apply Them 37 21 Introduction 38 22 Your Learning Goals for This Chapter 40 23 Newton’s Laws of Motion 40 24 How to Apply Newton’s Laws: 7-Step Strategy 41 25 Weight and Normal Forces 42 251 Example: Normal Forces Between Objects Sitting on a Table 42 252 Example: The Normal Forces Between Three Masses Being Pushed Along 44 26 Newton’s Universal Law of Gravitation 47 261 Example: Geostationary Orbits 47 27 Tension and Compression 50 271 Validity of Hooke’s Law 51 272 Tensegrity Structures 52 273 Example: Prismatic Tensegrity with Three-Fold Rotational Symmetry 55 274 Pulleys 60 275 Example: Atwood’s Machine 61 276 Example: Mechanical Advantage 63 28 Frictional Forces Between Solid Surfaces 67 281 Example: Two Masses Pulled Along a Surface with Friction 69 282 Example: Stationary Block on an Inclined Plane with Friction 72 283 Example: Moving Block on an Inclined Plane with Friction 74 284 Block on an Inclined Plane with Friction: Visualization of Results 76 29 Fluid Friction 77 291 Example: “DNA Curtains” 78 292 Example: Sphere Moving Through a Viscous Fluid 81 293 Example: Relaxation Time 85 210 Newton’s Second Law in Terms of Total Momentum 87 2101 Conservation of Momentum 89 2102 Center of Mass 90 211 Force from a Stream of Particles 92 2111 General Strategy for Problems Involving a Flow/Stream of Material That Changes Direction 92 2112 Example: Force on a Wall from a Stream of Particles 92 2113 Pressure of a Gas 94 2114 Example: Hurricane-Force Winds and Water Jets 95 212 Chapter Outlook 97 213 Problems 98 References 130 3 Energy: Work, Geckos, and ATP 131 31 Introduction 132 32 Your Learning Goals for This Chapter 132 33 Types of Energy 133 331 Example: The Most Important Meal of the Day 134 34 Energy Transfers 136 341 Examples of Energy Transfers: Heat and Work 137 342 Kinetic Energy and the Work-Energy Theorem 138 343 Example: The Work-Energy Theorem for the Gravitational Force and Escape Velocity 140 344 Example: The Work-Energy Theorem for a Sliding Block with Friction 142 35 Potential Energy and Work Done by Conservative Forces 144 36 Generalized Work-Energy Theorem 146 361 Example: Working Out 147 362 Example: The Earth-Projectile System Revisited 148 37 Force from Potential Energy 149 371 Example: Force from Potential Energy Graphically 150 38 Potential Energy Models to Predict the Force 151 381 Example: Energy, Force, and Geckos’ Feet 151 382 Example: Microtubule Buckling 155 39 Bound States and Binding Energies 160 391 Atomic and Molecular Binding 160 392 Intermolecular Potentials 162 393 Example: Energy from ATP Hydrolysis 163 310 Chapter Outlook 165 311 Problems 166 References 183 4 Probability Distributions: Mutations, Cancer Rates, and Vision Sensitivity 185 41 Introduction 185 42 Your Learning Goals for This Chapter 186 43 The Rules of Probability 187 431 The Sum Rule 189 432 The Multiplication Rule 189 433 The Addition Rule 190 434 Example: Las Vegas Vacation 190 435 Example: Anti-HIV Drug Cocktails 192 44 Discrete and Continuous Random Variables 194 45 Discrete Probability Distributions 196 46 Mean and Variance 196 47 Poisson Distribution 197 471 Example: Counting Bacterial Colonies 199 472 Example: Breast Cancer Susceptibility 199 473 Example: The Threshold of Human Vision 201 474 Example: Unilateral vs Bilateral Retinoblastoma 203 48 Binomial Distribution 205 49 Sums of Independent Random Variables 207 410 Continuous Probability Distributions 209 4101 Example: A Certain Continuous Probability Distribution 211 411 Exponential Distributions: Fluorescence Lifetimes, Radioactive Decay, and Drug Elimination from the Body 212 412 Gaussian Distributions 213 413 The Central Limit Theorem 214 414 Parameter Estimation, Experimental Errors, and Counting Statistics 215 415 Chapter Outlook 217 416 Problems 218 References 236 5 Random Walks: Brownian Motion and the Tree of Life 237 51 Introduction 238 52 Your Learning Goals for This Chapter 239 53 Brownian Motion 240 531 Brownian Motion and the Atomic Hypothesis 240 532 Statistical Properties of Brownian Motion 242 54 Random Walks 244 541 One-Dimensional Brownian Motion, Modeled as a 1D Random Walk 245 542 Random Walks in the Continuum Limit 247 543 Two- and Three-Dimensional Random Walks 248 55 The Einstein Relation and How We Know There Are Atoms 249 56 Actin Polymerization 251 561 Actin Polymerization as a Random Walk 253 562 Example: Molecular Motors as Random Walkers 257 57 Evolutionary “Genetic Drift” 258 571 Gambler’s Ruin 260 572 Example: Stacked Odds 262 573 The Moran Model 262 574 Probability That a Mutation Becomes Fixed in the Population and Phylogenetic Trees 264 58 Chapter Outlook 266 59 Problems 267 References 282 6 Diffusion: Membrane Permeability and the Rate of Actin Polymerization 285 61 Introduction 285 62 Your Learning Goals for This Chapter 286 63 The Diffusion Equation 287 631 Particle Flux and Fick’s Law 287 632 Particle Number Conservation and Fick’s Second Law 289 633 The Steady-State, One-Dimensional Diffusion Equation 290 634 Diffusion Through a Membrane or a Tube 290 635 Diffusion Through a Membrane: More Realistic Version 293 636 Diffusive Conductance and Membrane Permeability 295 637 Diffusion Through Multilayer Membranes 295 638 Example: Concentration Between the Layers of a Two-Layer Membrane 297 639 Example: Diffusion Along a Tube of Varying Cross-Sectional Area 298 6310 Example: A Different Process for Transmembrane Transport and Conductances “In Parallel” 300 64 Spherical Cows 302 641 The Steady-State, Spherically Symmetric Diffusion Equation 304 642 Example: Diffusion Enforces a Fundamental Limit on Cell Size 307 65 The Rate of Actin Polymerization 308 651 Diffusion to Capture and Diffusion-Limited Actin Polymerization 309 652 Actin Polymerization with Fractional Capture Efficiency 310 653 Example: Depletion as a Result of Capture 311 654 Diffusion Predictions Compared to Experiments 312 655 Actin Monomer Dissociation 312 66 Receptors and Biological Signaling Efficiency 313 67 Chapter Outlook 317 68 Problems 318 References 336 7 Rates of Change: Drugs, Infections, and Weapons of Mass Destruction 337 71 Introduction 338 72 Your Learning Goals for This Chapter 339 73 Rates of Change 339 74 Administering Therapeutics: Continuous Infusion with Elimination 340 741 The Same Equations Have the Same Solutions 340 742 Solution by Direct Substitution Revisited 341 743 Initial Conditions 343 75 Administering Therapeutics: Oral Dosage with Elimination 344 751 Eigenvalues, Eigenvectors, Eigenmodes, and Superposition 345 752 Example: Tumor Suppressor Genes and Tumorigenesis: The Case of Retinoblastoma 350 753 Example: Gene Expression 357 76 Progression of HIV Infection in an Individual Patient 361 761 Example: Building a Model of HIV Infection 362 762 Numerical Solution of HIV Infection Model 363 763 Steady-State Solutions: Living with HIV 364 764 HIV Infection Predictions Compared to Experiments 365 77 Nuclear Chain Reactions and Atomic Bombs 365 771 Example: Linear Chain Reaction Equations at Early Times 368 78 Chapter Outlook 372 79 Problems 373 References 386 8 Statistical Mechanics: Boltzmann Factors, PCR, and Brownian Ratchets 389 81 Introduction 390 82 Your Learning Goals for This Chapter 391 83 The Boltzmann Factor 391 831 Example: Ion Channels 392 832 Example: Molecular Height Distribution 395 833 Protein and Nucleic Acid Folding–Unfolding and Microstate Multiplicity 396 84 DNA Unzipping and Polymerase Chain Reaction 400 841 DNA Zipping and Unzipping as a Random Walk 403 842 Connection to the Second Law of Thermodynamics 404 85 Brownian Ratchets 404 851 Brownian Ratchet Mechanism of Helicase-Catalyzed Unzipping 404 852 Helicase Translocation as a Random Walk 405 853 Clash of the Titans 406 854 Example: Force Generation by Actin Polymerization: Another Brownian Ratchet 410 86 Binding and Reactions 415 861 Langmuir Binding Curve 415 862 Chemical Equilibrium and the Law of Mass Action 418 87 Entropy, Temperature, and the Ideal Gas Law 419 871 Entropy 419 872 Temperature 420 873 The Ideal Gas Equation of State 422 88 Chapter Outlook 422 89 Problems 423 References 445 9 Fluid Mechanics: Laminar Flow, Blushing, and Murray’s Law 447 91 Introduction 448 92 Your Learning Goals for This Chapter 449 93 Pressure and Hydrostatic Pressure 450 94 Two Types of Fluid Behavior: Laminar Fluid Flow and Turbulent Fluid Flow 452 95 Viscous Forces and Viscosity 452 96 Reynolds Number 458 97 How to Describe Laminar Fluid Flow 460 971 Velocity Profile in a Thin Channel 460 972 Flow Rate 463 98 Laminar Fluid Flow in a Cylindrical Tube 464 981 Example: Velocity Profile in a Cylindrical Tube 464 982 Poiseuille’s Law, Blushing, and Atherosclerosis 467 983 Steady-State Approximation for the Human Circulatory System 468 99 Flow Conductance and Resistance 469 991 Flow Channels “In Series” and Liquid Incompressibility 470 992 Flow Channels “In Parallel” 472 993 Example: Square Microfluidics 473 910 Power Dissipation in a Viscous Fluid Flow 476 911 Murray’s Law and the “Engineering” of the Human Circulatory System 477 912 Chapter Outlook 481 913 Problems 482 References 497 10 Oscillations and Resonance 499 101 Introduction 500 102 Your Learning Goals for This Chapter 501 103 Simple Harmonic Motion 502 1031 General Solution That Is the Sum of a Sine and a Cosine 503 1032 General Solution That Is a Cosine with an Amplitude and a Phase 504 1033 Energy of an Undamped Simple Harmonic Oscillator 505 104 Primer on the Algebra of Complex Numbers 506 1041 General Solution That Is the Sum of Imaginary Exponentials 509 105 Damped Simple Harmonic Motion 509 1051 Example: General Solution for Damped Simple Harmonic Motion: Sum of Complex Exponential Functions 511 1052 General Solution for Damped Simple Harmonic Motion: Exponentially Decaying (Co)sinusoidal Solutions 512 1053 Using WolframAlpha 513 1054 Example: Energy Dissipation of a Damped Harmonic Oscillator 513 106 Forced Damped Simple Harmonic Motion and Resonance 514 1061 Steady-State Solution at Late Times 515 1062 Resonance and Power Dissipation 517 107 Superposition Revisited 518 108 Examples of Resonance 519 109 Coupled Harmonic Oscillators 520 1091 The Forces Acting on Two Masses Connected by a Spring 522 1092 Example: Weakly Coupled Oscillators and Beats 524 1093 Example: Three Identical Masses and Four Identical Springs 529 1094 Example: Coupled, Damped, Driven Oscillators 532 1010 Chapter Outlook 533 1011 Problems 535 References 542