University Physics I - Classical Mechanics, 2019

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186 CHAPTER 8. MOTION IN TWO DIMENSIONS 8.8 Problems Problem 1 A pitcher throws a fastball horizontally at a speed of 42 m/s. Neglecting air resistance, (a) How long does it take for the ball to reach the batter, a distance of 18.4 m away? (b) How much does the ball drop vertically in this time? (c) What is the vertical component of the ball’s velocity as it reaches the batter? (Just to set the record straight, a real fastball would probably not drop that much, because of a lift force, called the Magnus effect, due to the interaction of the air with the backspin of the ball!) Problem 2 Two blocks are connected by a massless string threaded over a massless, frictionless pulley, as shown in the picture. The mass of block 1 is 2 kg and the mass of block 2 is 1.5 kg.The angle of the incline is 30 degrees. There is friction between the block and the inclined surface. 1 2 30º (a) Start by assuming that the coefficient of static friction is strong enough to keep the system from moving, and draw free-body diagrams for the two blocks. Try to get all the forces approximately to scale. (The following questions may be helpful.) (b) If the system is not moving, what is the magnitude of the tension? (c) What is the magnitude of the normal force? (d) How large does the coefficient of static friction have to be to keep the system from moving? (e) Now suppose the system is moving, and the coefficient of sliding (kinetic) friction is 0.2. What is the acceleration of the system? (f) What is the tension now? (g) What is the rate at which energy is dissipated (instantaneous dissipated power) when the system’s velocity is 3 m/s? Problem 3 A 60-kg skier starts sliding from rest from the top of a slope that makes an angle of 30 ◦ with the horizontal. Assume the bottom of the slope is 100 m below the top (measured vertically). (a) What is the change in the gravitational potential energy of the system formed by the skier and the Earth, as the skier slides from the top to the bottom of the slope?
8.8. PROBLEMS 187 (b) What is the work done by gravity on the skier for the process described above? (Thinking now of the skier only as the system.) (c) If you could neglect the friction between the skis and the snow, what would be the speed of the skier at the bottom of the slope? Why? (d) If the speed of the skier is only 30 m/s as she reaches the bottom of the slope, how much energy was dissipated by friction? (e) Draw a free-body diagram of the skier as she is sliding down the slope. Make sure you include friction, and indicate the direction of the acceleration. Use your diagram to answer the next couple of questions. (f) What is the magnitude of the normal force exerted by the ground on the skier? (g) Under the same assumptions as in part (d) above, what is the coefficient of friction between the skis and the snow? (h) Again under the assumption that her final speed is 30 m/s, what is the acceleration of the skier along the slope? Problem 4 A child is dragging a 2 kg sled through a flat patch of snow (coefficient of kinetic friction: 0.1) with a constant force, by pulling on a rope at an angle of 25 ◦ to the horizontal. The sled is moving at a constant speed. (a) Draw a free body diagram for the sled as it is being pulled. (b) Find the magnitude of all the forces acting on the sled. (c) If the child were to suddenly release the rope, what would be the new value of the friction force? What would be the sled’s acceleration? (Take the initial direction of motion to be positive.) Problem 5 A man is swinging an object, attached to a string, in a circle over his head (see the sketches). v Top view Side view (a) Draw a free-body diagram for the object. Notice the string is not drawn horizontal in the “side view” diagram above. Why is that? (b) If the mass of the object is 1 kg, what is the vertical component of the tension? (c) If the object makes 3 turns per second, and the radius of the circle (as seen in the top view) is 0.8 m, what is the centripetal acceleration of the object?
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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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2.2. ACCELERATION 35 2.2 Accelerati
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2.2. ACCELERATION 37 called “conc
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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 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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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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