Preface |
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xiii | |
Acknowledgments |
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xv | |
Contributors |
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xvii | |
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1 | (66) |
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1 Dynamics of Braking Vehicles: From Coulomb Friction to Anti-Lock Braking Systems |
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3 | (14) |
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3 | (2) |
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1.2 The dynamics of braking using Coulomb friction |
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5 | (4) |
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1.2.1 Static friction force |
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6 | (1) |
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1.2.2 Kinetic friction force |
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7 | (1) |
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1.2.3 The two regimes for braking |
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7 | (2) |
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1.3 The advantage of the ABS |
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9 | (2) |
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1.4 Comparison with the model [ 3] and with real data |
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11 | (6) |
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15 | (2) |
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2 Simple Thermodynamics of Jet Engines |
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17 | (18) |
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18 | (1) |
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2.2 Performances of jet engines |
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19 | (1) |
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2.3 The simplest model of a jet engine |
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20 | (2) |
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2.4 Jet engine with an ideal compressor and turbine |
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22 | (3) |
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2.5 Overall efficiency and thrust |
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25 | (3) |
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2.6 Non-ideal compressor and turbine |
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28 | (2) |
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30 | (5) |
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31 | (2) |
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33 | (2) |
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3 Surprises of the Transformer as a Coupled Oscillator System |
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35 | (12) |
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35 | (2) |
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3.2 Natural frequencies of a transformer |
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37 | (2) |
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3.3 Resonant frequencies of a driven transformer |
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39 | (4) |
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42 | (1) |
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42 | (1) |
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43 | (4) |
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44 | (1) |
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45 | (2) |
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4 Maximum Thermodynamic Power Coefficient of a Wind Turbine |
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47 | (20) |
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48 | (1) |
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4.2 Power coefficient of a wind turbine |
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49 | (1) |
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4.3 One-dimensional reversible fluid flows |
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50 | (9) |
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4.3.1 Incompressible flow |
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52 | (1) |
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4.3.2 Isentropic flow of an ideal gas |
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52 | (2) |
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4.3.3 Isothermal flow of an ideal gas |
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54 | (3) |
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4.3.4 Power coefficient calculations |
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57 | (2) |
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59 | (1) |
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59 | (2) |
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4.5 Supplementary material |
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61 | (6) |
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4.5.1 Generalized clausius inequality |
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61 | (1) |
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4.5.2 Linear momentum equation |
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62 | (1) |
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4.5.3 Proof that o∫∫cv pnzdS = 0 for a compressible ideal flow |
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62 | (2) |
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64 | (1) |
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65 | (2) |
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67 | (158) |
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5 Mutual Inductance between Piecewise Linear Loops |
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69 | (20) |
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70 | (1) |
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71 | (2) |
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5.3 Line integral along a straight path |
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73 | (4) |
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73 | (4) |
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77 | (1) |
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5.4 The magnetic flux and mutual inductance |
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77 | (1) |
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5.5 First application: two square wires on the plane |
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78 | (2) |
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5.6 Second application: two square wires stacked |
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80 | (3) |
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83 | (6) |
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83 | (2) |
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85 | (2) |
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87 | (2) |
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6 The Hertz Contact in Chain Elastic Collisions |
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89 | (14) |
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89 | (1) |
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6.2 Independent collisions |
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90 | (1) |
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6.3 Noninstantaneous collisions |
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91 | (7) |
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92 | (1) |
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6.3.2 Dynamical equations |
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93 | (1) |
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6.3.3 Numerical resolution |
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94 | (4) |
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6.4 Discussion and conclusions |
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98 | (5) |
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99 | (2) |
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101 | (2) |
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7 Tilted Boxes on Inclined Planes |
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103 | (22) |
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104 | (1) |
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7.2 Boxes resting evenly on the plane |
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105 | (7) |
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7.2.1 Case 1: no sliding and no tumbling |
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108 | (1) |
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7.2.2 Case 2: no sliding and tumbling forward |
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108 | (1) |
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7.2.3 Case 3: sliding down and no tumbling |
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109 | (1) |
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7.2.4 Case 4: sliding down and tumbling forward |
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110 | (1) |
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110 | (2) |
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7.3 Boxes tilted with respect to the plane |
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112 | (8) |
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7.3.1 The case where 0 < φ ≤ β |
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114 | (1) |
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7.3.2 The case where β < φ < π/2 |
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115 | (1) |
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7.3.2.1 The case of β < φ < π/2 and a = 0 |
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116 | (1) |
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7.3.2.2 The case of β < φ < π/2 and a > 0 |
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117 | (1) |
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7.3.2.3 The case of β < φ < π/2 and a < 0 |
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118 | (1) |
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119 | (1) |
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120 | (5) |
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121 | (2) |
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123 | (2) |
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8 Magnetic Forces Acting on Rigid Current-Carrying Wires Placed in a Uniform Magnetic Field |
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125 | (8) |
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129 | (2) |
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131 | (2) |
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9 Comparing a Current-Carrying Circular Wire with Polygons of Equal Perimeter: Magnetic Field versus Magnetic Flux |
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133 | (14) |
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134 | (2) |
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9.2 Calculating the vector potential |
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136 | (2) |
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138 | (4) |
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142 | (5) |
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143 | (2) |
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145 | (2) |
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10 The Elastic Bounces of a Sphere between Two Parallel Walls |
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147 | (16) |
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147 | (2) |
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10.2 Collision with a horizontal wall |
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149 | (1) |
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10.3 Successive elastic collisions of a sphere with two parallel planar walls |
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150 | (13) |
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158 | (3) |
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161 | (2) |
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11 How Short and Light Can a Simple Pendulum Be for Classroom Use? |
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163 | (8) |
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163 | (1) |
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11.2 Theoretical background |
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164 | (1) |
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11.3 The calculation of g |
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165 | (2) |
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167 | (4) |
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169 | (2) |
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12 Experiments with a Falling Rod |
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171 | (14) |
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172 | (1) |
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12.2 Theoretical background |
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172 | (2) |
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12.3 Experiments and video analysis |
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174 | (3) |
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12.3.1 Rod released on a steel surface |
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174 | (2) |
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12.3.2 Rod released on the cloth surface of a mouse pad |
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176 | (1) |
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12.3.3 Rod released on a marble stone surface |
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176 | (1) |
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12.4 Comparison to theory |
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177 | (3) |
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180 | (5) |
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183 | (2) |
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13 Oscillations of a Rectangular Plate |
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185 | (14) |
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185 | (1) |
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186 | (1) |
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13.3 Results and Discussion |
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187 | (7) |
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13.3.1 Oscillations along the z-axis |
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187 | (5) |
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13.3.2 Oscillations along the z-axis |
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192 | (2) |
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194 | (5) |
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197 | (2) |
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14 Bullet Block Experiment: Angular Momentum Conservation and Kinetic Energy Dissipation |
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199 | (16) |
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200 | (2) |
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14.2 Plastic collision between a rigid body and a point particle |
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202 | (4) |
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14.2.1 Motion of the center of mass of the system |
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202 | (1) |
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14.2.2 Conservation of angular momentum about the CM |
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203 | (1) |
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14.2.3 Rotational kinetic energy |
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204 | (1) |
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14.2.4 Mechanical energy dissipated in the collision |
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205 | (1) |
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14.3 Dissipated energy and angular momentum conservation |
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206 | (4) |
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207 | (2) |
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14.3.2 Rectangular parallelepiped |
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209 | (1) |
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210 | (5) |
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211 | (2) |
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213 | (2) |
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15 The Continuity Equation in Ampere's Law |
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215 | (10) |
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215 | (1) |
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15.2 The problem and its electrostatic analog |
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216 | (4) |
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15.3 The difference between the Biot-Savart law and Ampere's law |
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220 | (1) |
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221 | (4) |
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221 | (2) |
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223 | (2) |
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225 | (28) |
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16 On the Relation between Angular Momentum and Angular Velocity |
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227 | (10) |
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227 | (1) |
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16.2 Angular momentum of a particle describing circular motion |
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228 | (3) |
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16.2.1 Origin on the rotation axis |
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230 | (1) |
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16.2.2 Origin on the plane of motion |
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230 | (1) |
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16.2.3 Origin on the center of circular motion |
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230 | (1) |
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16.3 Angular momentum of two particles describing circular motion |
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231 | (6) |
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235 | (2) |
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17 A Very Abnormal Normal Force |
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237 | (8) |
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237 | (1) |
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17.2 The first contradiction |
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238 | (2) |
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17.3 The second contradiction |
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240 | (1) |
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17.4 The solution to all problems |
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241 | (1) |
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17.5 The importance of the principle of energy conservation |
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242 | (1) |
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243 | (2) |
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18 Rolling Cylinder on an Inclined Plane |
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245 | (8) |
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245 | (1) |
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18.2 Theoretical background |
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246 | (1) |
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18.3 Rolling without slipping |
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247 | (2) |
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18.4 Rolling and slipping |
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249 | (2) |
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251 | (2) |
References |
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253 | (2) |
Index |
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255 | |