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.
Author(s): P.I.C. Teixeira
Publisher: CRC Press
Year: 2022
Language: English
Pages: 275
City: Boca Raton
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 < ' < ˇ=2 and a > 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
