University Physics I - Classical Mechanics, 2019

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62 CHAPTER 3. MOMENTUM AND INERTIA 5. The momentum of an object of inertial mass m movingwithavelocity⃗v is defined as ⃗p = m⃗v. The total momentum of a system of objects is defined as the (vector) sum of all the individual momenta. 6. (Conservation of momentum) The momentum of an isolated system remains always constant, regardless of how the parts that make up the system may interact with one another. 7. In one dimension, the center of mass of a system of particles is a mathematical point whose x coordinate is given by Equation (3.8) above. (In more dimensions, just change the x’s in Eq. (3.8) toy and z to get y cm and z cm .) 8. The center of mass of a system always moves with a velocity ⃗v cm = ⃗p sys M where ⃗p sys is the total momentum of the system, and M its total mass. 9. It follows from 8 and 6 above that for an isolated system, the center of mass must always be at rest or moving with constant velocity. This result generalizes the law of inertia to extended objects, or systems of particles.
3.5. EXAMPLES 63 3.5 Examples 3.5.1 Reading a collision graph The graph shows a collision between two carts (possibly equipped with magnets so that they repel each other before they actually touch) on an air track. The inertia (mass) of cart 1 is 1 kg. Note: this is a position vs. time graph! (a) What are the initial velocities of the carts? (b) What are the final velocities of the carts? (c) What is the mass of the second cart? (d) Does the air track appear to be level? Why? (Hint: does the graph show any evidence of acceleration, for either cart, outside of the collision region?) (e) At the collision time, is the acceleration of the first cart positive or negative? How about the second cart? (Justify your answers.) (f) For the system consisting of the two carts, what is its initial (total) momentum? What is its final momentum? (g) Imagine now that one of the magnets is reversed, so when the carts collide they stick to each other. What would then be the final momentum of the system? What would be its final velocity? x (m) cart 1 cart 2 t (s) Figure 3.5: A collision between two carts. Solution (a) All the velocities are to be calculated by picking an easy straight part of each curve and calculating v = Δx Δt
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University Physics I: Classical Mec
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ii
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iv CONTENTS 1.6 Problems . . . . .
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vi CONTENTS 5.1 Conservative intera
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viii CONTENTS 7.7 Examples . . . .
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x CONTENTS 10.4 Examples . . . . .
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xii CONTENTS 13.2.1 Temperature and
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xiv CONTENTS they have read. Then,
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Chapter 1 Reference frames, displac
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1.2. POSITION, DISPLACEMENT, VELOCI
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Page 37 and 38: 1.4. IN SUMMARY 19 with a velocity
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Page 49 and 50: Chapter 2 Acceleration 2.1 The law
Page 51 and 52: 2.1. THE LAW OF INERTIA 33 This is
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Page 57 and 58: 2.2. ACCELERATION 39 2.2.2 Motion w
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Page 63 and 64: 2.4. IN SUMMARY 45 4. Changes in ve
Page 65 and 66: 2.5. EXAMPLES 47 which the rocket r
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Page 69 and 70: Chapter 3 Momentum and Inertia 3.1
Page 71 and 72: 3.1. INERTIA 53 reliable, repeatabl
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Page 75 and 76: 3.2. MOMENTUM 57 the system is p i
Page 77 and 78: 3.3. EXTENDED SYSTEMS AND CENTER OF
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Page 89 and 90: 4.1. KINETIC ENERGY 71 v 2i =0,v 1f
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Page 99 and 100: 4.3. IN SUMMARY 81 7. Besides the c
Page 101 and 102: 4.4. EXAMPLES 83 On the other hand,
Page 103 and 104: 4.4. EXAMPLES 85 K cm ′ = 1 2 (m
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Page 107 and 108: Chapter 5 Interactions and energy 5
Page 109 and 110: 5.1. CONSERVATIVE INTERACTIONS 91 T
Page 111 and 112: 5.1. CONSERVATIVE INTERACTIONS 93 A
Page 113 and 114: 5.1. CONSERVATIVE INTERACTIONS 95 d
Page 115 and 116: 5.2. DISSIPATION OF ENERGY AND THER
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Page 119 and 120: 5.5. IN SUMMARY 101 gravitational p
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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 129 6.6 Examples 6.6.
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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 153 7.7 Examples 7.7.
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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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University Physics I - Classical Mechanics, 2019

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