University Physics I - Classical Mechanics, 2019

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86 CHAPTER 4. KINETIC ENERGY 4.5 Problems Problem 1 A 71-kg man can throw a 1-kg ball with a maximum speed of 6 m/s relative to himself. Imagine that one day he decides to try to do that on roller skates. Starting from rest, he throws the ball as hard as he can, so it ends up moving at 6 m/s relative to him, but he himself is recoiling as a result of the throw. (a) Assuming conservation of momentum, find the velocities of the man and the ball relative to the ground. (b) What is the kinetic energy of the system right after the throw? (By the system here we mean the man and the ball throughout.) Where did this kinetic energy come from? (c) Is the man’s reference frame inertial throughout this process? Why or why not? (d) Does the center of mass of the system move at all throughout this process? Problem 2 Analyze Problem 1 from Chapter 3 from the point of view of the system’s kinetic energy. In particular, answer the following questions: (a) What is the total kinetic energy of the system before and after the collision? How much of this energy is translational (that is, center-of-mass kinetic energy), and how much is convertible? (b) What kind of collision is this? (Elastic, inelastic, etc.) What is the coefficient of restitution? Problem 3 Analyze Problem 2 from Chapter 3 from the point of view of the system’s kinetic energy. In particular, answer the following questions: (a) What is the coefficient of restitution for the collision described in part (a) of the problem, and how much kinetic energy is “lost” in that collision? (b) What is the coefficient of restitution for the collision described in part (b) of the problem, and how much kinetic energy is “lost” in that collision? Problem 4 A0.012-kg bullet, traveling at 850 m/s, hits a 2-kg block of wood that is initially at rest, and goes straight through it. Assume that the final velocity of the bullet relative to the block is 400 m/s, and that the system is isolated. (a) What is the coefficient of restitution for this collision? (b) How much kinetic energy is “lost” in the collision? (c) What is the final velocity of the block? Problem 5 A 2-kg object, moving at 1 m/s, collides with a 1-kg object that is initially at rest. Assume they form an isolated system.
4.5. PROBLEMS 87 (a) What is the initial kinetic energy of the system? How much of this is center of mass energy, and how much is convertible? (b) What is the maximum amount of kinetic energy that could be “lost” (converted to other forms of energy) in this collision? (c) If 60% of the amount you calculated in part (b) is in fact converted into other forms of energy in the collision, what are the final velocities of the two objects?
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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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1.3. REFERENCE FRAME CHANGES AND RE
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1.3. REFERENCE FRAME CHANGES AND RE
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1.4. IN SUMMARY 19 with a velocity
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1.5. EXAMPLES 21 1.5 Examples 1.5.1
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1.5. EXAMPLES 23 (twice what it was
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1.5. EXAMPLES 25 Note that I have d
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1.6. PROBLEMS 27 1.6 Problems Probl
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1.6. PROBLEMS 29 Problem 5 You are
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Chapter 2 Acceleration 2.1 The law
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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 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
Page 79 and 80: 3.4. IN SUMMARY 61 3.3.2 Recoil and
Page 81 and 82: 3.5. EXAMPLES 63 3.5 Examples 3.5.1
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Page 87 and 88: Chapter 4 Kinetic Energy 4.1 Kineti
Page 89 and 90: 4.1. KINETIC ENERGY 71 v 2i =0,v 1f
Page 91 and 92: 4.1. KINETIC ENERGY 73 special case
Page 93 and 94: 4.1. KINETIC ENERGY 75 This immedia
Page 95 and 96: 4.2. “CONVERTIBLE” AND “TRANS
Page 97 and 98: 4.2. “CONVERTIBLE” AND “TRANS
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,
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Page 109 and 110: 5.1. CONSERVATIVE INTERACTIONS 91 T
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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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Page 125 and 126: 5.7. ADVANCED TOPICS 107 where the
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Page 139 and 140: 6.3. FORCES NOT DERIVED FROM A POTE
Page 145 and 146: 6.5. IN SUMMARY 127 F s,1 n a F s,1
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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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