1000 Solved Problems in Classical Physics

Transcription

1 1000 Solved Problems in Classical Physics

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3 Ahmad A. Kamal 1000 Solved Problems in Classical Physics An Exercise Book 123

4 Dr. Ahmad A. Kamal Silversprings Lane Murphy Texas USA ISBN e-isbn DOI / Springer Heidelberg Dordrecht London New York Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: estudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (

5 Dedicated to my Parents

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7 Preface This book complements the book 1000 Solved Problems in Modern Physics by the same author and published by Springer-Verlag so that bulk of the courses for undergraduate curriculum are covered. It is targeted mainly at the undergraduate students of USA, UK and other European countries and the M.Sc. students of Asian countries, but will be found useful for the graduate students, students preparing for graduate record examination (GRE), teachers and tutors. This is a by-product of lectures given at the Osmania University, University of Ottawa and University of Tebriz over several years and is intended to assist the students in their assignments and examinations. The book covers a wide spectrum of disciplines in classical physics and is mainly based on the actual examination papers of UK and the Indian universities. The selected problems display a large variety and conform to syllabi which are currently being used in various countries. The book is divided into 15 chapters. Each chapter begins with basic concepts and a set of formulae used for solving problems for quick reference, followed by a number of problems and their solutions. The problems are judiciously selected and are arranged section-wise. The solutions are neither pedantic nor terse. The approach is straightforward and step-by-step solutions are elaborately provided. There are approximately 450 line diagrams, onefourth of them in colour for illustration. A subject index and a problem index are provided at the end of the book. Elementary calculus, vector calculus and algebra are the prerequisites. The areas of mechanics and electromagnetism are emphasized. No book on problems can claim to exhaust the variety in the limited space. An attempt is made to include the important types of problems at the undergraduate level. It is a pleasure to thank Javid, Suraiya and Techastra Solutions (P) Ltd. for typesetting and Maryam for her patience. I am grateful to the universities of UK and India for permitting me to use their question papers; to R.W. Norris and W. Seymour, Mechanics via Calculus, Longmans, Green and Co., 1923; to Robert A. Becker, Introduction to Theoretical Mechanics, McGraw-Hill Book Co. Inc, 1954, for one problem; and Google Images for the cover page. My thanks are to Springer-Verlag, vii

8 viii Preface in particular Claus Ascheron, Adelheid Duhm and Elke Sauer, for constant encouragement. Murphy, Texas November 2010 Ahmad A. Kamal

9 Contents 1 Kinematics and Statics Basic Concepts and Formulae Problems Motion in One Dimension Motion in Resisting Medium Motion in Two Dimensions Force and Torque Centre of Mass Equilibrium Solutions Motion in One Dimension Motion in Resisting Medium Motion in Two Dimensions Force and Torque Centre of Mass Equilibrium Particle Dynamics Basic Concepts and Formulae Problems Motion of Blocks on a Plane Motion on Incline Work, Power, Energy Collisions Variable Mass Solutions Motion of Blocks on a Plane Motion on Incline Work, Power, Energy Collisions Variable Mass ix

10 x Contents 3 Rotational Kinematics Basic Concepts and Formulae Problems Motion in a Horizontal Plane Motion in a Vertical Plane Loop-the-Loop Solutions Motion in a Horizontal Plane Motion in a Vertical Plane Loop-the-Loop Rotational Dynamics Basic Concepts and Formulae Problems Moment of Inertia Rotational Motion Coriolis Acceleration Solutions Moment of Inertia Rotational Motion Coriolis Acceleration Gravitation Basic Concepts and Formulae Problems Field and Potential Rockets and Satellites Solutions Field and Potential Rockets and Satellites Oscillations Basic Concepts and Formulae Problems Simple Harmonic Motion (SHM) Physical Pendulums Coupled Systems of Masses and Springs Damped Vibrations Solutions Simple Harmonic Motion (SHM) Physical Pendulums Coupled Systems of Masses and Springs Damped Vibrations...279

11 Contents xi 7 Lagrangian and Hamiltonian Mechanics Basic Concepts and Formulae Problems Solutions Waves Basic Concepts and Formulae Problems Vibrating Strings Waves in Solids Waves in Liquids Sound Waves Doppler Effect Shock Wave Reverberation Echo Beat Frequency Waves in Pipes Solutions Vibrating Strings Waves in Solids Waves in Liquids Sound Waves Doppler Effect Shock Wave Reverberation Echo Beat Frequency Waves in Pipes Fluid Dynamics Basic Concepts and Formulae Problems Bernoulli s Equation Torricelli s Theorem Viscosity Solutions Bernoulli s Equation Torricelli s Theorem Viscosity Heat and Matter Basic Concepts and Formulae Problems...414

12 xii Contents Kinetic Theory of Gases Thermal Expansion Heat Transfer Specific Heat and Latent Heat Thermodynamics Elasticity Surface Tension Solutions Kinetic Theory of Gases Thermal Expansion Heat Transfer Specific Heat and Latent Heat Thermodynamics Elasticity Surface Tension Electrostatics Basic Concepts and Formulae Problems Electric Field and Potential Gauss Law Capacitors Solutions Electric Field and Potential Gauss Law Capacitors Electric Circuits Basic Concepts and Formulae Problems Resistance, EMF, Current, Power Cells Instruments Kirchhoff s Laws Solutions Resistance, EMF, Current, Power Cells Instruments Kirchhoff s Laws Electromagnetism I Basic Concepts and Formulae Problems...583

13 Contents xiii Motion of Charged Particles in Electric and Magnetic Fields Magnetic Induction Magnetic Force Magnetic Energy, Magnetic Dipole Moment Faraday s Law Hall Effect Solutions Motion of Charged Particles in Electric and Magnetic Fields Magnetic Induction Magnetic Force Magnetic Energy, Magnetic Dipole Moment Faraday s Law Hall Effect Electromagnetism II Basic Concepts and Formulae Problems The RLC Circuits Maxwell s Equations, Electromagnetic Waves, Poynting Vector Phase Velocity and Group Velocity Waveguides Solutions The RLC Circuits Maxwell s Equations and Electromagnetic Waves, Poynting Vector Phase Velocity and Group Velocity Waveguides Optics Basic Concepts and Formulae Problems Geometrical Optics Prisms and Lenses Matrix Methods Interference Diffraction Polarization Solutions Geometrical Optics Prisms and Lenses Matrix Methods...737

14 xiv Contents Interference Diffraction Polarization Subject Index Problem Index...769