Follows the traditional physics cu
Table of Contents
Preface xv
So we’re all on the same page... xvii
What is science? xviii
To the Student xix
To the Teacher xx
Contact Information xx
Acknowledgments xxi
1 Introduction to SNB 1
Why SNB? 1
The Basics 2
Physics à la mode: Math or Text 8
Creating Mathematical Expressions 8
Evaluate and Evaluate Numerically 11
Scientific Notation 13
Substitution and Endpoint Evaluation 14
Solving Equations 17
Solve Exact 18
Solve Numeric 21
Systems of Equations 24
The Compute Menu 25
Simplify and Expand 25
Factor 26
Rewrite and Combine 28
Check Equality 29
Polynomials 31
Power Series 32
Definitions 35
Other Good Stuff 37
Computing In-place 37
Making Assumptions About Variables 37
Limits 40
A Few Words About Calculus 42
Units 46
Converting Units 47
User-Defined Units 51
Plotting 52
Plot 2D Rectangular 54
Other 2-Dimensional Plots 55
Plot 3D Rectangular 58
Cylindrical and Spherical Plots 60
Plotting Data 63
Fitting a Curve to Data 63
Differential Equations 67
Solve ODE Exact and Laplace 68
Solve ODE Numeric 70
Problems 75
2 One-Dimensional Kinematics 83
Constant Acceleration 83
Displacement and Position 83
Velocity and Acceleration 84
Equations of Motion 86
Signs of the Times 88
Free Fall 89
Varying Acceleration 91
Displacement, Velocity, and Acceleration 91
Equations of Motion 93
Gravity and Air Resistance 96
Resisting Air Resistance is Futile 97
Long-Distance Free Fall 99
Problems 102
3 Vectors 105
Components of a Vector 107
Magnitude and Direction 108
Adding Vectors 111
The Component Method 112
The SNB Method 113
The Graphing Method 115
Unit Vectors 119
Multiplying Vectors 120
Dot Product 121
Cross Product 122
Problems 125
4 Projectile Motion 127
No Air Resistance 127
Trajectory 132
Time of Flight 134
Maximum Height 135
Linear Air Resistance 137
Trajectory 141
Time of Flight and Range 143
Maximum Height 145
Turn Off the Air! 146
Turn Down the Air! 147
Quadratic Air Resistance 151
Height-Dependent Air Resistance 152
Problems 154
5 Newton’s Laws of Motion 157
Newton’s First Law 157
Newton’s Second Law for Constant Forces 158
Newton’s Second Law for Varying Forces 165
Time-Dependent Forces 165
Velocity-Dependent Forces 167
Position-Dependent Forces 170
Newton’s Third Law 173
Problems 175
6 Conservation Laws 179
Definitions 179
Conservation of Energy 181
Work 181
The Work-Energy Theorem 185
Potential Energy 186
Mechanical Energy is Conserved 188
A Complete Bookkeeping 191
Conservation of Momentum 193
Collisions in 1-Dimension 193
Collisions in 2-Dimensions 196
Rockets 199
Deep Space 199
Launch 202
Air Resistance 207
Varying Gravity and Air Resistance 213
Problems 216
7 Circular Motion 221
Uniform Circular Motion 222
The Rotating Umbrella 224
Rotational Kinematics 227
The Compact Disk 229
Newton’s Second Law and Circular Motion 233
Uniform Circular Motion and the 2nd Law 233
Non-Uniform Circular Motion and the 2nd Law 235
Sliding on a Sphere 236
Problems 248
8 Harmonic Motion 251
Simple Harmonic Motion, Simply 251
Energy and SHM 254
Not-Quite-as-Simple Harmonic Motion 255
Energy and SHM, Again 257
Damped Harmonic Motion 259
Underdamped (β2 < ω20) 259
Critically Damped (β2 = ω20) 261
Overdamped (β2 > ω20) 262
Driven Harmonic Motion 263
Constant Driving Force, no Damping 263
Sinusoidal Driving Force, no Damping 264
Constant Driving Force with Damping 265
Sinusoidal Driving Force with Damping 267
Small Oscillations 270
Not-so-Simple Harmonic Motion 272
Problems 275
9 Central Forces 279
Equations of Motion 279
Newtonian Gravitation 285
Kepler’s Laws 286
The Effective Potential 292
Two Special Forces 296
The 3-d Harmonic Oscillator 296
The Inverse-Square Force 299
Numerical Stuff 303
Problems 305
10 Fluids 309
Density and Pressure 309
Static Fluids 311
Buoyancy 312
Fluids in Motion 314
Bernoulli’s Equation 316
Applications of Bernoulli’s Equation 318
A More Realistic Approach 320
Flow in a Pipe 321
Stokes’ Law 330
Problems 331
11 Temperature and Heat 335
Temperature Scales 335
Absolute Temperature 337
Heat and Work 338
Heat Flow 339
Change in Temperature: Specific Heat 339
Change in State: Latent Heat 340
Calorimetry 341
Varying Specific Heat 344
The Specific Heat of Solids 345
Problems 353
12 Special Relativity 359
The Two Postulates 360
The Consequences 361
Time Dilation 363
Length Contraction 364
Addition of Velocities 365
Simultaneity 367
The Lorentz Transformation 367
Space-Time 370
Relativistic Momentum and Energy 375
Relativistic Collisions 378
Relativistic Dynamics 382
Four-Vectors 387
Problems 392
A Topics in Classical Physics 397
Newton’s Nose-Cone Problem 397
Simple Shapes 398
Frusta and Fudges 403
Newton’s Minimizer 409
Indented Tips and the Minimizer 411
The Shape of the Eiffel Tower 414
An Interesting Classical Orbit 417
Fisher’s Crystal 421
Problems 428
B Topics in Modern Physics 435
The Tale of the Traveling Triplets 435
Trip 1: Constance goes to Vega 435
Relativistic Interlude: Constant Acceleration 437
Trip 2: Axel goes to Vega 441
What happens on the way to Vega... 443
Orbits in General Relativity 445
Angular Momentum 447
Precessing Ellipses and Periodic Orbits 451
Be the Ball: Embedding Diagrams 456
Classical Lifetime of a Hydrogen Atom 460
Missed It By That Much 460
Can Special Relativity Save the Day? 462
Quantum Mechanical Bound States 465
Infinite Square Well (“Particle in a Box”) 467
Finite Square Well 470
V-shaped Linear Well 477
Problems 483
References and Suggested Reading 491
Index 495
