Introductory Physics for the Life Sciences

Preface
References
Electronic Supplementary Material
Electronic Supplementary Material
Contents
1 Vectors and Kinematics
1.1 Introduction
1.2 Your Learning Goals for This Chapter
1.3 Vectors
1.3.1 Multiplication of a Vector by a Scalar
1.3.2 Vector Addition and Subtraction
1.3.3 Products of Two Vectors
Scalar Products of Two Vectors
Vector or Cross Product
1.3.4 Example: Tetrahedral Bond Angles
1.3.5 Coordinate Systems
Right-Handed Coordinate Systems and the Right-Hand Rule
Scalar Product in Terms of Components
1.3.6 Example: A Trigonometric Identity
1.3.7 Position Vector and Displacement Vector
1.3.8 Example: Tensegrity Geometry
1.4 Kinematics
1.4.1 Motion in One-Dimension
1.4.2 Motion in Two or Three Dimensions
1.4.3 Example: Motion in a Circle at Constant Angular Velocity
1.4.4 Motion Subject to a Constant Acceleration in One Dimension
1.4.5 Motion Subject to Constant Acceleration in Two and Three Dimensions
1.4.6 Example: Trajectory of Projectile Motion
1.5 Frames of Reference and Relative Velocity
1.5.1 Example: Relative Position
1.6 Chapter Outlook
1.7 Problems
Reference
2 Force and Momentum: Newton's Laws and How to Apply Them
2.1 Introduction
2.2 Your Learning Goals for This Chapter
2.3 Newton's Laws of Motion
2.4 How to Apply Newton's Laws: 7-Step Strategy
2.5 Weight and Normal Forces
2.5.1 Example: Normal Forces Between Objects Sitting on a Table
2.5.2 Example: The Normal Forces Between Three Masses Being Pushed Along
2.6 Newton's Universal Law of Gravitation
2.6.1 Example: Geostationary Orbits
2.7 Tension and Compression
2.7.1 Validity of Hooke's Law
2.7.2 Tensegrity Structures
2.7.3 Example: Prismatic Tensegrity with Three-Fold Rotational Symmetry
2.7.4 Pulleys
2.7.5 Example: Atwood's Machine
2.7.6 Example: Mechanical Advantage
2.8 Frictional Forces Between Solid Surfaces
2.8.1 Example: Two Masses Pulled Along a Surface with Friction
2.8.2 Example: Stationary Block on an Inclined Plane with Friction
2.8.3 Example: Moving Block on an Inclined Plane with Friction
2.8.4 Block on an Inclined Plane with Friction: Visualization of Results
2.9 Fluid Friction
2.9.1 Example: ``DNA Curtains''
2.9.2 Example: Sphere Moving Through a Viscous Fluid
2.9.3 Example: Relaxation Time
2.10 Newton's Second Law in Terms of Total Momentum
2.10.1 Conservation of Momentum
2.10.2 Center of Mass
2.11 Force from a Stream of Particles
2.11.1 General Strategy for Problems Involving a Flow/Stream of Material That Changes Direction
2.11.2 Example: Force on a Wall from a Stream of Particles
2.11.3 Pressure of a Gas
2.11.4 Example: Hurricane-Force Winds and Water Jets
2.12 Chapter Outlook
2.13 Problems
References
3 Energy: Work, Geckos, and ATP
3.1 Introduction
3.2 Your Learning Goals for This Chapter
3.3 Types of Energy
3.3.1 Example: The Most Important Meal of the Day
3.4 Energy Transfers
3.4.1 Examples of Energy Transfers: Heat and Work
3.4.2 Kinetic Energy and the Work-Energy Theorem
3.4.3 Example: The Work-Energy Theorem for the Gravitational Force and Escape Velocity
3.4.4 Example: The Work-Energy Theorem for a Sliding Block with Friction
3.5 Potential Energy and Work Done by Conservative Forces
3.6 Generalized Work-Energy Theorem
3.6.1 Example: Working Out
3.6.2 Example: The Earth-Projectile System Revisited
3.7 Force from Potential Energy
3.7.1 Example: Force from Potential Energy Graphically
3.8 Potential Energy Models to Predict the Force
3.8.1 Example: Energy, Force, and Geckos' Feet
3.8.2 Example: Microtubule Buckling
3.9 Bound States and Binding Energies
3.9.1 Atomic and Molecular Binding
3.9.2 Intermolecular Potentials
3.9.3 Example: Energy from ATP Hydrolysis
3.10 Chapter Outlook
3.11 Problems
References
4 Probability Distributions: Mutations, Cancer Rates, and Vision Sensitivity
4.1 Introduction
4.2 Your Learning Goals for This Chapter
4.3 The Rules of Probability
4.3.1 The Sum Rule
4.3.2 The Multiplication Rule
4.3.3 The Addition Rule
4.3.4 Example: Las Vegas Vacation
Die Hard
A Throw of Dice
Queen Margot
Aces High
4.3.5 Example: Anti-HIV Drug Cocktails
4.4 Discrete and Continuous Random Variables
4.5 Discrete Probability Distributions
4.6 Mean and Variance
4.7 Poisson Distribution
4.7.1 Example: Counting Bacterial Colonies
4.7.2 Example: Breast Cancer Susceptibility
4.7.3 Example: The Threshold of Human Vision
4.7.4 Example: Unilateral vs. Bilateral Retinoblastoma
4.8 Binomial Distribution
4.9 Sums of Independent Random Variables
4.10 Continuous Probability Distributions
4.10.1 Example: A Certain Continuous Probability Distribution
4.11 Exponential Distributions: Fluorescence Lifetimes, Radioactive Decay, and Drug Elimination from the Body
4.12 Gaussian Distributions
4.13 The Central Limit Theorem
4.14 Parameter Estimation, Experimental Errors, and Counting Statistics
4.15 Chapter Outlook
4.16 Problems
References
5 Random Walks: Brownian Motion and the Tree of Life
5.1 Introduction
5.2 Your Learning Goals for This Chapter
5.3 Brownian Motion
5.3.1 Brownian Motion and the Atomic Hypothesis
5.3.2 Statistical Properties of Brownian Motion
5.4 Random Walks
5.4.1 One-Dimensional Brownian Motion, Modeled as a 1D Random Walk
5.4.2 Random Walks in the Continuum Limit
5.4.3 Two- and Three-Dimensional Random Walks
5.5 The Einstein Relation and How We Know There Are Atoms
5.6 Actin Polymerization
5.6.1 Actin Polymerization as a Random Walk
5.6.2 Example: Molecular Motors as Random Walkers
5.7 Evolutionary ``Genetic Drift''
5.7.1 Gambler's Ruin
5.7.2 Example: Stacked Odds
5.7.3 The Moran Model
5.7.4 Probability That a Mutation Becomes Fixed in the Population and Phylogenetic Trees
5.8 Chapter Outlook
5.9 Problems
References
6 Diffusion: Membrane Permeability and the Rate of Actin Polymerization
6.1 Introduction
6.2 Your Learning Goals for This Chapter
6.3 The Diffusion Equation
6.3.1 Particle Flux and Fick's Law
6.3.2 Particle Number Conservation and Fick'sSecond Law
6.3.3 The Steady-State, One-Dimensional DiffusionEquation
6.3.4 Diffusion Through a Membrane or a Tube
6.3.5 Diffusion Through a Membrane: More RealisticVersion
6.3.6 Diffusive Conductance and Membrane Permeability
6.3.7 Diffusion Through Multilayer Membranes
6.3.8 Example: Concentration Between the Layers of a Two-Layer Membrane
6.3.9 Example: Diffusion Along a Tube of Varying Cross-Sectional Area
6.3.10 Example: A Different Process for Transmembrane Transport and Conductances ``In Parallel''
6.4 Spherical Cows
6.4.1 The Steady-State, Spherically Symmetric Diffusion Equation
6.4.2 Example: Diffusion Enforces a Fundamental Limit on Cell Size
6.5 The Rate of Actin Polymerization
6.5.1 Diffusion to Capture and Diffusion-Limited Actin Polymerization
6.5.2 Actin Polymerization with Fractional Capture Efficiency
6.5.3 Example: Depletion as a Result of Capture
6.5.4 Diffusion Predictions Compared to Experiments
6.5.5 Actin Monomer Dissociation
6.6 Receptors and Biological Signaling Efficiency
Example 6.6.1: Receptor Real Estate
6.7 Chapter Outlook
6.8 Problems
References
7 Rates of Change: Drugs, Infections, and Weapons of Mass Destruction
7.1 Introduction
7.2 Your Learning Goals for This Chapter
7.3 Rates of Change
7.4 Administering Therapeutics: Continuous Infusion with Elimination
7.4.1 The Same Equations Have the Same Solutions
7.4.2 Solution by Direct Substitution Revisited
7.4.3 Initial Conditions
7.5 Administering Therapeutics: Oral Dosage with Elimination
7.5.1 Eigenvalues, Eigenvectors, Eigenmodes, and Superposition
7.5.2 Example: Tumor Suppressor Genes and Tumorigenesis: The Case of Retinoblastoma
7.5.3 Example: Gene Expression
7.6 Progression of HIV Infection in an Individual Patient
7.6.1 Example: Building a Model of HIV Infection
7.6.2 Numerical Solution of HIV Infection Model
7.6.3 Steady-State Solutions: Living with HIV
7.6.4 HIV Infection Predictions Compared to Experiments
7.7 Nuclear Chain Reactions and Atomic Bombs
7.7.1 Example: Linear Chain Reaction Equations at Early Times
7.8 Chapter Outlook
7.9 Problems
References
8 Statistical Mechanics: Boltzmann Factors, PCR, and Brownian Ratchets
8.1 Introduction
8.2 Your Learning Goals for This Chapter
8.3 The Boltzmann Factor
8.3.1 Example: Ion Channels
8.3.2 Example: Molecular Height Distribution
8.3.3 Protein and Nucleic Acid Folding–Unfolding and Microstate Multiplicity
8.4 DNA Unzipping and Polymerase Chain Reaction
8.4.1 DNA Zipping and Unzipping as a Random Walk
8.4.2 Connection to the Second Law of Thermodynamics
8.5 Brownian Ratchets
8.5.1 Brownian Ratchet Mechanism of Helicase-Catalyzed Unzipping
8.5.2 Helicase Translocation as a Random Walk
8.5.3 Clash of the Titans
8.5.4 Example: Force Generation by Actin Polymerization: Another Brownian Ratchet
8.6 Binding and Reactions
8.6.1 Langmuir Binding Curve
8.6.2 Chemical Equilibrium and the Law of Mass Action
8.7 Entropy, Temperature, and the Ideal Gas Law
8.7.1 Entropy
8.7.2 Temperature
8.7.3 The Ideal Gas Equation of State
8.8 Chapter Outlook
8.9 Problems
References
9 Fluid Mechanics: Laminar Flow, Blushing, and Murray's Law
9.1 Introduction
9.2 Your Learning Goals for This Chapter
9.3 Pressure and Hydrostatic Pressure
9.4 Two Types of Fluid Behavior: Laminar Fluid Flow and Turbulent Fluid Flow
9.5 Viscous Forces and Viscosity
9.6 Reynolds Number
9.7 How to Describe Laminar Fluid Flow
9.7.1 Velocity Profile in a Thin Channel
9.7.2 Flow Rate
9.8 Laminar Fluid Flow in a Cylindrical Tube
9.8.1 Example: Velocity Profile in a Cylindrical Tube
9.8.2 Poiseuille's Law, Blushing, and Atherosclerosis
9.8.3 Steady-State Approximation for the Human Circulatory System
9.9 Flow Conductance and Resistance
9.9.1 Flow Channels ``In Series'' and LiquidIncompressibility
9.9.2 Flow Channels ``In Parallel''
9.9.3 Example: Square Microfluidics
9.10 Power Dissipation in a Viscous Fluid Flow
9.11 Murray's Law and the ``Engineering'' of the Human Circulatory System
9.12 Chapter Outlook
9.13 Problems
References
10 Oscillations and Resonance
10.1 Introduction
10.2 Your Learning Goals for This Chapter
10.3 Simple Harmonic Motion
10.3.1 General Solution That Is the Sum of a Sineand a Cosine
10.3.2 General Solution That Is a Cosine with an Amplitude and a Phase
10.3.3 Energy of an Undamped Simple Harmonic Oscillator
10.4 Primer on the Algebra of Complex Numbers
10.4.1 General Solution That Is the Sum of Imaginary Exponentials
10.5 Damped Simple Harmonic Motion
10.5.1 Example: General Solution for Damped Simple Harmonic Motion: Sum of Complex Exponential Functions
10.5.2 General Solution for Damped Simple Harmonic Motion: Exponentially Decaying (Co)sinusoidal Solutions
10.5.3 Using WolframAlpha
10.5.4 Example: Energy Dissipation of a Damped Harmonic Oscillator
10.6 Forced Damped Simple Harmonic Motion and Resonance
10.6.1 Steady-State Solution at Late Times
10.6.2 Resonance and Power Dissipation
10.7 Superposition Revisited
10.8 Examples of Resonance
10.9 Coupled Harmonic Oscillators
10.9.1 The Forces Acting on Two Masses Connected by a Spring
10.9.2 Example: Weakly Coupled Oscillators and Beats
10.9.3 Example: Three Identical Masses and Four Identical Springs
10.9.4 Example: Coupled, Damped, Driven Oscillators
10.10 Chapter Outlook
10.11 Problems
References
11 Wave Equations: Strings and Wind
11.1 Introduction
11.2 Your Learning Goals for This Chapter
11.3 The Wave Equation and Transverse Waves on a String
11.3.1 General Solutions to the Wave Equation
11.3.2 Example: Only Time Will Tell
11.4 Periodicity in Space and Time for Sinusoidal Traveling Waves
11.5 Sinusoidal Traveling Waves
11.5.1 Example: Writing the Equation for a Harmonic Wave
11.5.2 Example: Making Waves
11.6 Sound Waves
11.6.1 Longitudinal Sound Waves
11.6.2 Example: Loudspeaker Sound Generation and Power Output
11.7 Longitudinal Waves and Transverse Waves: Factsto Get Straight
11.8 Standing Waves
11.8.1 From Initial Conditions to Eigenmode Amplitudes
11.8.2 Example: Plucking a String
11.8.3 Standing Sound Waves in a Clarinet
11.9 Wave Reflection and Transmission
11.9.1 Reflected and Transmitted Waves
11.9.2 Boundary Conditions at the Interface
11.9.3 Calculating Reflection and Transmission Coefficients
11.9.4 Example: Another Boundary Condition, Another Reflected Wave.... or Not
11.9.5 Impedance
11.9.6 Example: Energy Conservation at Wave Reflection
11.9.7 Medical Ultrasound Imaging
11.10 Clarinets, Flutes, and Ears: Resonance Revisited
11.11 Chapter Outlook
11.12 Problems
Reference
12 Gauss's Law: Charges and Electric Fields
12.1 Introduction
12.2 Your Learning Goals for This Chapter
12.3 Force Between Charges: Coulomb's Law
12.4 Electric Field
12.4.1 Electric Field of a Single Point Charge
12.4.2 Facts to Know
12.4.3 Example: Using Superposition to Find the Electric Field of Two Charges
12.4.4 Electric Field Lines
12.5 Gauss's Law
12.5.1 Demonstration of Gauss's Law for a SinglePoint Charge
12.5.2 Using Gauss's Law to Find the E-Field for a Point Charge
12.5.3 Using Gauss's Law to Find the E-Field of Highly Symmetric Extended Objects
12.5.4 Example: Gauss's Law Applied to Uniformly Charged Sphere
12.5.5 Charge Densities for Uniformly Charged Extended Objects
12.5.6 Example: Gauss's Law to Find the E-Field of an Infinite Charged Plane
12.5.7 The Electric Field of a Parallel Plate Capacitor
12.6 Chapter Outlook
12.7 Problems
13 Electric Potential, Capacitors, and Dielectrics
13.1 Introduction
13.2 Your Learning Goals for This Chapter
13.3 Potential Energy Associated with Electrostatic Force
13.4 Electrostatic Potential
13.4.1 Electrostatic Potential of a Capacitor and Capacitance
13.4.2 Example: Capacitance of a Spherical Capacitor
13.4.3 Capacitors ``In Parallel'' and ``In Series''
13.4.4 Example: Funky Capacitors
13.5 Energy Stored on a Capacitor
13.5.1 Example: Electrostatic Energy of a Parallel Plate Capacitor
13.6 Dielectric Materials
13.6.1 Example: Capacitor Filled with a Dielectric Material
13.6.2 Example: Ionic Solubility and MembranePermeability
13.7 Electrostatics in Ionic Solutions
13.7.1 Spherically Symmetric Screening
13.7.2 Example: Energy of a Charge Q in Ionic Solution
13.7.3 Viral Assembly
13.8 Chapter Outlook
13.9 Problems
References
14 Circuits and Dendrites: Charge Conservation, Ohm's Law, Rate Equations, and Other Old Friends
14.1 Introduction
14.2 Your Learning Goals for This Chapter
14.3 Current, Resistance, and Ohm's Law
14.4 Kirchhoff's Current Law: Conservation of Electric Charge
14.5 Kirchhoff's Loop Law: Electrostatic Forces Are Conservative
14.6 Resistors in Series and in Parallel
14.6.1 Example: A Voltage Divider
14.6.2 Example: An Infinite Resistance Ladder
14.7 Power Dissipation in a Resistor
14.8 Circuits with Resistors and Capacitors
14.8.1 Example: Capacitor in Series with a Resistor
14.8.2 Example: Switched RC Circuit
14.9 Dendritic Conduction
14.9.1 Example: A Current Ladder
14.10 Chapter Outlook
14.11 Problems
15 Optics: Refraction, Eyes, Lenses,Microscopes, and Telescopes
15.1 Introduction
15.2 Your Learning Goals for This Chapter
15.3 Refraction and Snell's Law
15.3.1 Total Internal Reflection
15.4 Image Formation by a Spherical Surface and the Human Eye
15.4.1 Real and Virtual Images
15.5 Image Formation by a Lens
15.6 Optical Applications of Lenses
15.6.1 Magnification by a Lens
15.6.2 Corrective Lenses
15.6.3 Example: Magnification with Two Tandem Lenses and Infinity-Corrected Microscopes
15.6.4 Two Tandem Lenses as a Telescope: MagnifyingAngles
15.6.5 Example: Telescope as a Beam Expander
15.6.6 Example: Beam Steering
15.6.7 Example: Effective Focal Length of Two Lenses
15.6.8 Kohler Illumination for Microscopy
15.7 Microscopy Beyond Lenses
15.7.1 Fluorescence Microscopy
15.7.2 Optical Resolution
15.8 Chapter Outlook
15.9 Problems
16 Biologic: Genetic Circuits and Feedback
16.1 Introduction
16.2 Your Learning Goals for This Chapter
16.3 Binary Biologic
16.4 The Genetic Toggle Switch
16.4.1 Chemical Rate Equations for the Genetic ToggleSwitch
16.4.2 Steady-State Solutions for the Genetic Toggle Switch
16.4.3 Stable or Unstable?
Stability of the Bistable Solution
Stability of the Non-bistable Solution
16.5 Repressilator
16.5.1 Steady State for the Repressilator
16.5.2 Stability?
16.6 Chapter Outlook
16.7 Problems
References
17 Magnetic Fields and Ampere's Law
17.1 Introduction
17.2 Your Learning Goals for This Chapter
17.3 Magnetic Fields: Sources and Magnetic Field Lines
17.3.1 Earth's Magnetic Field and Tesla
17.3.2 Magnetic Field Lines
17.3.3 ``Gauss's Law'' for Magnetic Fields and the Impossibility of Having Magnetic Monopoles
17.3.4 The Magnetic Field of a Wire Carrying Current
17.4 Ampere's Law
17.4.1 The Right-Hand Rule and Counting Currents Threading a Loop
17.4.2 How to Apply Ampere's Law
17.4.3 Example: The Magnetic Field of a Current-Carrying Wire
17.5 Magnetic Field of a Coil
17.5.1 Example: The Magnetic Field of a Long Solenoid
17.5.2 Example: The Magnetic Field of a Toroidal Solenoid
17.6 Force on a Moving Charge and Another Version of the Right-Hand Rule
17.6.1 Example: The Force Between Two Parallel Wires Carrying Current
17.6.2 Force Between Two Coils
17.7 Magnetic Materials
17.8 Chapter Outlook
17.9 Problems
18 Faraday's Law and Electromagnetic Induction
18.1 Introduction
18.2 Your Learning Goals for This Chapter
18.3 Faraday's Law
18.3.1 Example: Changing the Magnetic Flux by Changing Area
18.4 Inductance and Inductors
18.4.1 Example: Inductance of a Long Solenoid
18.4.2 Example: Inductance of a Coaxial Cable
18.4.3 Inductors in Circuits
18.4.4 Example: An Inductor in Series with a Resistor Gives Rise to a Familiar Equation
18.4.5 Example: Inductors and Eigenvalues
18.4.6 RLC Circuits: Another Familiar Equation
18.5 Magnetic Field Energy
18.6 Chapter Outlook
18.7 Problems
19 Maxwell's Equations and Then There Was Light
19.1 Introduction
19.2 Your Learning Goals for This Chapter
19.3 Ampere's Law Revisited: The Displacement Current
19.4 An Electromagnetic Wavefront
19.4.1 Gauss's Law at the Wavefront
19.4.2 Gauss's Law for Magnetic Fields at the Wavefront
19.4.3 Faraday's Law at the Wavefront
19.4.4 Ampere's Law at the Wavefront
19.5 The Speed of Light
19.6 Wave Equation for Electromagnetic Waves
19.7 Chapter Outlook
19.8 Problem
Index