Offbeat Physics: Machines, Meditations and Misconceptions

Description

Offbeat Physics: Machines, Meditations and Misconceptions is a collection of articles on various topics in classical physics that have intrigued the author and their students throughout the years. The book is divided into three parts. Part I -- Machines, comprises chapters that explain or model the workings of a number of machines (understood in a broad sense) on the basis of physical principles. These machines can be as simple as a rolling wheel or as complex as a jet engine. Then in Part II -- Meditations, the authors go beyond the standard examples, experiments and approximations discussed ad nauseam in most physics textbooks, but which are not always very exciting or realistic. For example, what happens when colliding bodies are not perfectly rigid -- as we know real bodies are not? Finally, Part III -- Misconceptions aims to correct misconceptions that students may have about physical phenomena or clarify issues that are often presented misleadingly, confusingly or imprecisely in textbooks, such as the relationship between angular momentum and angular velocity in rotational motion. This is a book for all those who wish to learn physics beyond the textbooks and from more realistic problems, often occurring in engineering contexts. It will be useful to instructors at all levels, as well as highly motivated students taking General Physics courses in higher education. Cover Half Title Title Page Copyright Page Dedication Contents Preface Acknowledgments Contributors I. Machines 1. Dynamics of Braking Vehicles: From Coulomb Friction to Anti-Lock Braking Systems 1.1. Introduction 1.2. The dynamics of braking using Coulomb friction 1.2.1. Static friction force 1.2.2. Kinetic friction force 1.2.3. The two regimes for braking 1.3. The advantage of the ABS 1.4. Comparison with the model [3] and with real data References 2. Simple Thermodynamics of Jet Engines 2.1. Introduction 2.2. Performances of jet engines 2.3. The simplest model of a jet engine 2.4. Jet engine with an ideal compressor and turbine 2.5. Overall efficiency and thrust 2.6. Non-ideal compressor and turbine 2.7. Conclusion Acknowledgments References 3. Surprises of the Transformer as a Coupled Oscillator System 3.1. Introduction 3.2. Natural frequencies of a transformer 3.3. Resonant frequencies of a driven transformer 3.3.1. Decoupled circuits 3.3.2. Maximum coupling 3.4. Conclusions Acknowledgments References 4. Maximum Thermodynamic Power Coefficient of a Wind Turbine 4.1. Introduction 4.2. Power coefficient of a wind turbine 4.3. One-dimensional reversible fluid flows 4.3.1. Incompressible flow 4.3.2. Isentropic flow of an ideal gas 4.3.3. Isothermal flow of an ideal gas 4.3.4. Power coefficient calculations 4.3.5. Analysis 4.4. Conclusion 4.5. Supplementary material 4.5.1. Generalized clausius inequality 4.5.2. Linear momentum equation 4.5.3. Proof that CV p^nzdS = 0 for a compressible ideal flow Acknowledgments References II. Meditations 5. Mutual Inductance between Piecewise Linear Loops 5.1. Introduction 5.2. The vector potential 5.3. Line integral along a straight path 5.3.1. General case 5.3.2. Planar wires 5.4. The magnetic flux and mutual inductance 5.5. First application: two square wires on the plane 5.6. Second application: two square wires stacked 5.7. Conclusions Appendix Acknowledgments References 6. The Hertz Contact in Chain Elastic Collisions 6.1. Introduction 6.2. Independent collisions 6.3. Noninstantaneous collisions 6.3.1. The Hertz contact 6.3.2. Dynamical equations 6.3.3. Numerical resolution 6.4. Discussion and conclusions Acknowledgments References 7. Tilted Boxes on Inclined Planes 7.1. Introduction 7.2. Boxes resting evenly on the plane 7.2.1. Case 1: no sliding and no tumbling 7.2.2. Case 2: no sliding and tumbling forward 7.2.3. Case 3: sliding down and no tumbling 7.2.4. Case 4: sliding down and tumbling forward 7.2.5. Summary 7.3. Boxes tilted with respect to the plane 7.3.1. The case where 0 < ' 7.3.2. The case where < ' < ˇ=2 7.3.2.1. The case of < ' < ˇ=2 and a = 0 7.3.2.2. The case of < ' 0 7.3.2.3. The case of < ' < ˇ=2 and a < 0 7.3.2.4. Summary 7.4. Conclusions Acknowledgments References 8. Magnetic Forces Acting on Rigid Current-Carrying Wires Placed in a Uniform Magnetic Field Acknowledgments References 9. Comparing a Current-Carrying Circular Wire with Polygons of Equal Perimeter: Magnetic Field versus Magnetic Flux 9.1. Introduction 9.2. Calculating the vector potential 9.3. Calculating the flux 9.4. Conclusions Acknowledgments References 10. The Elastic Bounces of a Sphere between Two Parallel Walls 10.1. Introduction 10.2. Collision with a horizontal wall 10.3. Successive elastic collisions of a sphere with two parallel planar walls Acknowledgments References 11. How Short and Light Can a Simple Pendulum Be for Classroom Use? 11.1. Introduction 11.2. Theoretical background 11.3. The calculation of g 11.4. Conclusions References 12. Experiments with a Falling Rod 12.1. Introduction 12.2. Theoretical background 12.3. Experiments and video analysis 12.3.1. Rod released on a steel surface 12.3.2. Rod released on the cloth surface of a mouse pad 12.3.3. Rod released on a marble stone surface 12.4. Comparison to theory 12.5. Conclusions References 13. Oscillations of a Rectangular Plate 13.1. Introduction 13.2. Experimental setup 13.3. Results and Discussion 13.3.1. Oscillations along the z-axis 13.3.2. Oscillations along the x-axis 13.4. Conclusions References 14. Bullet Block Experiment: Angular Momentum Conservation and Kinetic Energy Dissipation 14.1. Introduction 14.2. Plastic collision between a rigid body and a point particle 14.2.1. Motion of the center of mass of the system 14.2.2. Conservation of angular momentum about the CM 14.2.3. Rotational kinetic energy 14.2.4. Mechanical energy dissipated in the collision 14.3. Dissipated energy and angular momentum conservation 14.3.1. Thin rod 14.3.2. Rectangular parallelepiped 14.4. Conclusions Acknowledgments References 15. The Continuity Equation in Ampere's Law 15.1. Introduction 15.2. The problem and its electrostatic analog 15.3. The difference between the Biot-Savart law and Ampere's law 15.4. Conclusions Acknowledgments References III. Misconceptions 16. On the Relation between Angular Momentum and Angular Velocity 16.1. Introduction 16.2. Angular momentum of a particle describing circular motion 16.2.1. Origin on the rotation axis 16.2.2. Origin on the plane of motion 16.2.3. Origin on the center of circular motion 16.3. Angular momentum of two particles describing circular motion Reference 17. A Very Abnormal Normal Force 17.1. Introduction 17.2. The first contradiction 17.3. The second contradiction 17.4. The solution to all problems 17.5. The importance of the principle of energy conservation 17.6. Conclusion 18. Rolling Cylinder on an Inclined Plane 18.1. Introduction 18.2. Theoretical background 18.3. Rolling without slipping 18.4. Rolling and slipping 18.5. Conclusions References Index