University Physics I - Classical Mechanics, 2019

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CONTENTS v 3.3 Extended systems and center of mass . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.3.1 Center of mass motion for an isolated system . . . . . . . . . . . . . . . . . . 59 3.3.2 Recoil and rocket propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.4 In summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.5.1 Reading a collision graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.5.2 Collision in different reference frames, center of mass, and recoil . . . . . . . 65 3.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4 Kinetic Energy 69 4.1 Kinetic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.1.1 Kinetic energy in collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.1.2 Relative velocity and coefficient of restitution . . . . . . . . . . . . . . . . . . 74 4.2 “Convertible” and “translational” kinetic energy . . . . . . . . . . . . . . . . . . . . 76 4.2.1 Kinetic energy and momentum in different reference frames . . . . . . . . . . 79 4.3 In summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.4.1 Collision graph revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.4.2 Inelastic collision and explosive separation . . . . . . . . . . . . . . . . . . . . 83 4.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5 Interactions and energy 89
vi CONTENTS 5.1 Conservative interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.1.1 Potential energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.1.2 Potential energy functions and “energy landscapes” . . . . . . . . . . . . . . 94 5.2 Dissipation of energy and thermal energy . . . . . . . . . . . . . . . . . . . . . . . . 96 5.3 Fundamental interactions, and other forms of energy . . . . . . . . . . . . . . . . . . 98 5.4 Conservation of energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.5 In summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.6 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.6.1 Inelastic collision in the middle of a swing . . . . . . . . . . . . . . . . . . . . 103 5.6.2 Kinetic energy to spring potential energy: block collides with spring . . . . . 104 5.7 Advanced Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.7.1 Two carts colliding and compressing a spring . . . . . . . . . . . . . . . . . . 106 5.7.2 Getting the potential energy function from collision data . . . . . . . . . . . . 107 5.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6 Interactions, part 2: Forces 113 6.1 Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 6.1.1 Forces and systems of particles . . . . . . . . . . . . . . . . . . . . . . . . . . 115 6.2 Forces and potential energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 6.3 Forces not derived from a potential energy . . . . . . . . . . . . . . . . . . . . . . . . 120 6.3.1 Tensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Page 1: University Physics I: Classical Mec
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Page 11 and 12: viii CONTENTS 7.7 Examples . . . .
Page 13 and 14: x CONTENTS 10.4 Examples . . . . .
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Page 17 and 18: xiv CONTENTS they have read. Then,
Page 19 and 20: Chapter 1 Reference frames, displac
Page 21 and 22: 1.2. POSITION, DISPLACEMENT, VELOCI
Page 33 and 34: 1.3. REFERENCE FRAME CHANGES AND RE
Page 35 and 36: 1.3. REFERENCE FRAME CHANGES AND RE
Page 37 and 38: 1.4. IN SUMMARY 19 with a velocity
Page 39 and 40: 1.5. EXAMPLES 21 1.5 Examples 1.5.1
Page 41 and 42: 1.5. EXAMPLES 23 (twice what it was
Page 43 and 44: 1.5. EXAMPLES 25 Note that I have d
Page 45 and 46: 1.6. PROBLEMS 27 1.6 Problems Probl
Page 47 and 48: 1.6. PROBLEMS 29 Problem 5 You are
Page 49 and 50: Chapter 2 Acceleration 2.1 The law
Page 51 and 52: 2.1. THE LAW OF INERTIA 33 This is
Page 53 and 54: 2.2. ACCELERATION 35 2.2 Accelerati
Page 55 and 56: 2.2. ACCELERATION 37 called “conc
Page 57 and 58: 2.2. ACCELERATION 39 2.2.2 Motion w
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2.2. ACCELERATION 41 2.2.3 Accelera
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2.3. FREE FALL 43 proportional to t
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2.4. IN SUMMARY 45 4. Changes in ve
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2.5. EXAMPLES 47 which the rocket r
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2.6. PROBLEMS 49 (a) How far did yo
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Chapter 3 Momentum and Inertia 3.1
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3.1. INERTIA 53 reliable, repeatabl
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3.1. INERTIA 55 3.1.2 Inertial mass
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3.2. MOMENTUM 57 the system is p i
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3.3. EXTENDED SYSTEMS AND CENTER OF
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3.4. IN SUMMARY 61 3.3.2 Recoil and
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3.5. EXAMPLES 63 3.5 Examples 3.5.1
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3.5. EXAMPLES 65 3.5.2 Collision in
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3.6. PROBLEMS 67 3.6 Problems Probl
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Chapter 4 Kinetic Energy 4.1 Kineti
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4.1. KINETIC ENERGY 71 v 2i =0,v 1f
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4.1. KINETIC ENERGY 73 special case
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4.1. KINETIC ENERGY 75 This immedia
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4.2. “CONVERTIBLE” AND “TRANS
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4.2. “CONVERTIBLE” AND “TRANS
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4.3. IN SUMMARY 81 7. Besides the c
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4.4. EXAMPLES 83 On the other hand,
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4.4. EXAMPLES 85 K cm ′ = 1 2 (m
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4.5. PROBLEMS 87 (a) What is the in
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Chapter 5 Interactions and energy 5
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5.1. CONSERVATIVE INTERACTIONS 91 T
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5.1. CONSERVATIVE INTERACTIONS 93 A
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5.1. CONSERVATIVE INTERACTIONS 95 d
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5.2. DISSIPATION OF ENERGY AND THER
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5.4. CONSERVATION OF ENERGY 99 leve
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5.5. IN SUMMARY 101 gravitational p
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5.6. EXAMPLES 103 5.6 Examples 5.6.
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5.6. EXAMPLES 105 problem involves
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5.7. ADVANCED TOPICS 107 where the
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5.8. PROBLEMS 109 5.8 Problems Prob
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5.8. PROBLEMS 111 here? Explain. (f
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Chapter 6 Interactions, part 2: For
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6.1. FORCE 115 however, somewhat mo
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6.2. FORCES AND POTENTIAL ENERGY 11
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6.2. FORCES AND POTENTIAL ENERGY 11
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6.3. FORCES NOT DERIVED FROM A POTE
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6.5. IN SUMMARY 127 F s,1 n a F s,1
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6.6. EXAMPLES 131 pushes on the bra
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6.6. EXAMPLES 133 This is a huge di
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6.7. PROBLEMS 135 Problem 6 Draw a
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Chapter 7 Impulse, Work and Power 7
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7.2. WORK ON A SINGLE PARTICLE 139
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7.3. THE “CENTER OF MASS WORK”
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7.4. WORK DONE ON A SYSTEM BY ALL T
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7.6. IN SUMMARY 151 which is equal
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7.7. EXAMPLES 155 To plot all this
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7.7. EXAMPLES 157 (a) The external
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7.8. PROBLEMS 159 Problem 5 A block
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Chapter 8 Motion in two dimensions
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8.1. DEALING WITH FORCES IN TWO DIM
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8.2. PROJECTILE MOTION 165 The over
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8.3. INCLINED PLANES 167 8.3 Inclin
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8.4. MOTION ON A CIRCLE (OR PART OF
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8.5. IN SUMMARY 175 As we shall see
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8.6. EXAMPLES 177 8.6 Examples You
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8.7. ADVANCED TOPICS 179 8.7 Advanc
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8.7. ADVANCED TOPICS 181 Now we jus
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8.7. ADVANCED TOPICS 183 Note that
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8.7. ADVANCED TOPICS 185 The cyan a
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8.8. PROBLEMS 187 (b) What is the w
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8.8. PROBLEMS 189 (e) The power is
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Chapter 9 Rotational dynamics Rotat
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9.2. ANGULAR MOMENTUM 193 9.2 Angul
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9.2. ANGULAR MOMENTUM 195 thing is
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9.3. THE CROSS PRODUCT AND ROTATION
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9.3. THE CROSS PRODUCT AND ROTATION
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9.4. TORQUE 201 momentum involves t
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9.4. TORQUE 203 wrenches). It is al
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9.5. STATICS 205 important in engin
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9.6. ROLLING MOTION 207 9.6 Rolling
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9.6. ROLLING MOTION 209 contact wit
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9.7. IN SUMMARY 211 (Note how I hav
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9.8. EXAMPLES 213 9.8 Examples This
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9.8. EXAMPLES 215 Solution The figu
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9.9. PROBLEMS 217 9.9 Problems Prob
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9.9. PROBLEMS 219 A 20-kg plank of
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Chapter 10 Gravity 10.1 The inverse
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10.1. THE INVERSE-SQUARE LAW 223 ne
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10.1. THE INVERSE-SQUARE LAW 225 it
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10.1. THE INVERSE-SQUARE LAW 227 in
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10.1. THE INVERSE-SQUARE LAW 229 an
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10.1. THE INVERSE-SQUARE LAW 231 el
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10.1. THE INVERSE-SQUARE LAW 233 10
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10.1. THE INVERSE-SQUARE LAW 235 Fr
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10.2. WEIGHT, ACCELERATION, AND THE
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10.2. WEIGHT, ACCELERATION, AND THE
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10.3. IN SUMMARY 241 shifted and/or
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10.4. EXAMPLES 243 10.4 Examples 10
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10.4. EXAMPLES 245 The diagram of t
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10.5. ADVANCED TOPICS 247 10.5 Adva
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10.6. PROBLEMS 249 10.6 Problems Pr
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10.6. PROBLEMS 251 an orbit around
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Chapter 11 Simple harmonic motion 1
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11.2. SIMPLE HARMONIC MOTION 255 is
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11.2. SIMPLE HARMONIC MOTION 257 Th
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11.2. SIMPLE HARMONIC MOTION 259 If
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11.2. SIMPLE HARMONIC MOTION 261 Th
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11.3. PENDULUMS 263 o θ l F t F G
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11.3. PENDULUMS 265 11.3.2 The “p
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11.4. IN SUMMARY 267 9. A simple pe
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11.5. EXAMPLES 269 (b) The amplitud
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11.5. EXAMPLES 271 AsshowninSection
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11.6. ADVANCED TOPICS 273 Figure 11
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11.6. ADVANCED TOPICS 275 the oscil
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11.7. PROBLEMS 277 (that is, with r
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Chapter 12 Waves in one dimension 1
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12.1. TRAVELING WAVES 281 Perhaps t
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12.1. TRAVELING WAVES 283 ξ 1 0.5
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12.1. TRAVELING WAVES 285 Comparing
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12.1. TRAVELING WAVES 287 waves, th
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12.2. STANDING WAVES AND RESONANCE
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12.2. STANDING WAVES AND RESONANCE
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12.3. CONCLUSION, AND FURTHER RESOU
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12.5. EXAMPLES 297 However, if you
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12.6. ADVANCED TOPICS 299 12.6 Adva
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12.6. ADVANCED TOPICS 301 In the lo
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Chapter 13 Thermodynamics 13.1 Intr
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13.2. INTRODUCING TEMPERATURE 305 a
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13.2. INTRODUCING TEMPERATURE 307 m
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13.3. HEAT AND THE FIRST LAW 309 th
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13.3. HEAT AND THE FIRST LAW 311 ca
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13.4. THE SECOND LAW AND ENTROPY 31
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13.5. IN SUMMARY 319 13.5 In summar
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13.7. PROBLEMS 323 13.7 Problems Pr
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