Physics With Illustrative Examples From Medicine and Biology

1 Kinematics.- 1.1 Introduction.- 1.2 Motion in One Dimension: Velocity and Acceleration.- 1.2.A. Velocity.- 1.2.B. Acceleration.- 1.2.C. Examples of Accelerated Motion.- 1.3 Motion in Two and Three Dimensions: Velocity and Acceleration.- 1.3.A. Velocity.- 1.3.B. Acceleration.- 1.3.C. Uniform Circular Motion.- 1.3.D. Projectile Motion.- 1.4 Units and Conversion Factors.- Appendix to Chapter 1: Vectors.- 1.5 References and Supplementary Reading.- 1.6 Problems.- 2 Dynamics.- 2.1 Introduction.- 2.2 Newton’s First Law: The Law of Inertia.- 2.3 Newton’s Second Law of Motion.- 2.4 Newton’s Third Law of Motion: The Law of Action and Reaction.- 2.5 The Fundamental Forces of Physics.- 2.5.A. The Gravitational Force.- 2.5.B. Motion of a Satellite or the Moon Around the Earth.- 2.6 Nonfundamental or Derived Forces.- 2.6.A. Contact Forces.- 2.6.B. Drag Forces in Fluids (Liquids and Gases).- 2.7 Newton’s Laws Applied to Problems in Dynamics.- 2.7.A. Introduction.- 2.7.B. Illustrative Examples.- (i) Freight Train.- (ii) Block on an Inclined Plane.- (iii) Harmonic Oscillation.- (iv) Spring Gun.- (v) Viscous Damping Force. The Exponential Function.- (vi) Air Drag and Terminal Velocity.- (vii) Damped Oscillation of a Pendulum.- (viii) The Centrifugal Pendulum.- 2.8 References and Supplementary Reading.- 2.9 Problems.- 3 Static Equilibrium and the Forces Acting on Muscles and Bone within the Human Body.- 3.1 Introduction.- 3.2 Conditions of Static Equilibrium.- 3.3 Applications of Statics.- 3.3.A. The Board Resting Against a Wall.- 3.3.B. Forces Acting at the Hip Joint.- (i) Elementary Anatomy of the Femur and Hip.- (ii) Calculation of the Force on the Head of the Femur and in the Hip Abductor Muscles.- (iii) Clinical and Anatomical Implications.- (iv) Effect of a Cane on the Forces Acting at the Hip Joint.- 3.3.C. Forces Acting on the Lumbar Vertebrae. Low Back Pain. Disease of Vertebral Discs.- (i) Elementary Anatomy of the Spine, Vertebrae, and Back Muscles.- (ii) Force on the Fifth Lumbar Vertebra on Bending and Lifting.- (iii) Shear Stress in the Lumbo-Sacral Disc with “Sway Back”.- 3.3.D. Further Applications. Comments on the Torque Condition for Static Equilibrium.- 3.4 Static Equilibrium of Deformable Bodies: Stress, Strain, and Fracture.- 3.4.A. Introduction.- 3.4.B. Stress and Strain in Tension and Compression, Hooke’s Law, Young’s Modulus, Failure or Fracture.- 3.4.C. Bending Moment and Curvature of a Beam.- 3.4.D. Differential Equations for Deflection of a Loaded Beam.- 3.4.E. Bending and Breaking of a Beam or a Bone: Application to Fracture of the Tibia.- 3.4.F. Stress and Strain in Shear.- 3.5 Static Equilibrium of Fluids.- 3.5.A. Introduction and Definition of Hydrostatic Pressure.- 3.5.B. Fluid in a Gravitational Field: The Variation of Pressure with Height.- (i) Incompressible Fluid: Pascal’s Law: Pressure Units.- (ii) Compressible Fluid: Ideal Gas.- (iii) Buoyant Force on Bodies Immersed in a Fluid.- 3.5.C. Physiologic Effects of Increased Fluid Pressure, Underwater Diving, Postural Effects on Blood Pressure, and Effect of High Acceleration.- (i) Underwater Diving.- (ii) Postural Effects on Blood Pressure.- (iii) Effect of High Acceleration.- 3.5.D. Physiologic Effects of Decrease of Air Pressure. Mountain Sickness; Balloon Ascensions, Physiology of the Storage and Delivery of Oxygen by the Blood.- (i) Mountain Sickness.- (ii) Balloon Ascensions and the Physiological Effects of Decreased Air Pressure.- (iii) Oxygen Storage and Delivery by the Blood, Mountain Sickness, and High-Altitude Anoxia.- (iv) High Altitude Air Travel: Cabin Pressurization.- 3.5.E. Buoyancy and the Measurement of Molecular Weight of Macromolecules.- 3.6 References and Supplementary Reading.- 3.7 Problems.- 4 Momentum.- 4.1 Introduction.- 4.2 Momentum and the Dynamics of a System of Many Particles.- 4.3 Motion of the Center of Mass of an Extended Body.- (i) Center of Mass of Two Bodies.- (ii) Center of Mass of a Right Triangle.- (iii) Experimental Determination of the Center of Mass.- 4.4 Conservation of Momentum.- 4.4.A. The Boy, the Ball, and the Boat.- 4.4.B. The Oscillator in a Box.- 4.5 Ballistocardiography.- 4.5.A. Introduction.- 4.5.B. Elementary Anatomy and Physiology of the Heart.- 4.5.C. The Ballistocardiogram.- 4.6 Impulse and the Change of Momentum.- 4.6.A. Introduction and Definition of Impulse.- 4.6.B. Forces Acting During Collisions: Illustrative Examples.- (i) The Driven Golf Ball.- (ii) The Falling Elevator and Bone Fracture.- (iii) Jumps or Falls to the Ground from a Height.- (iv) Tolerance Levels for Whole Body Impacts. Survival in Falls from a Great Height.- (v) Deceleration Pulses and the Severity Index: A Criterion for Concussion and Injury to the Brain.- (vi) Safety Considerations in Automobile Accidents.- 4.7 Flow of Mass and Momentum. Transport in Fluids.- 4.7.A. Current Density.- 4.7.B. Pressure Exerted by a Stream of Fluid.- 4.7.C. Pressure on the Walls of a Curved Hose: The Fire Hose and the Aorta.- 4.8 References and Supplementary Reading.- 4.9 Problems.- 5 Work and Energy.- 5.1 Introduction.- 5.2 Work, Kinetic Energy, and Power in One-Dimensional Motion.- 5.2.A. A First Integration of Newton’s Equation. The Work-Kinetic Energy Formula.- 5.2.B. Power and the Rate of Change of Kinetic Energy.- 5.2.C. Determination of x(t) Using Work-Energy Considerations.- 5.2.D. Conservative and Nonconservative Forces.- 5.2.E. Examples of One-Dimensional Motion in Simple Force Fields.- (i) Constant Force of Gravity.- (ii) Linear Restoring Force. The Harmonic Oscillator.- (iii) Motion in a Nonuniform Gravitational Field.- 5.2.F. Conservative Forces and the Conservation of Mechanical Energy.- 5.2.G. Nonconservative Forces; Power, and the Law of Conservation of Energy and Heat.- (i) Motion of a Body Falling Through a Viscous Liquid.- 5.2.H. Units and Conversion Factors.- 5.3 Work, Energy, and Power in Three Dimensions.- 5.3.A. The Work—Kinetic Energy Formula.- 5.3.B. Conservative and Constraint Forces and the Conservation of Mechanical Energy.- 5.3.C. Mechanical Examples. The Recoiling Block and Springboard Diving.- (i) The Recoiling Block.- (ii) Springboard Diving.- 5.3.D. Relation Between Force and Potential Energy— A Mathematical Note.- 5.3.E. Energy Diagrams and Mechanical Stability.- 5.4 The First Law of Thermodynamics.- 5.4.A. The Conservation of Mechanical Energy, External Work and Heat.- 5.4.B. Heat, Work, and Energy Changes in an Electrical Water Heater.- 5.4.C. Elements in the Historical Development of the Law of Conservation of Energy.- 5.4.D. Animal Metabolism, Work, and the First Law of Thermodynamics.- (i) Catabolic Rate, Heat and Power Production.- (ii) “Calorific Equivalent” of Oxygen.- (iii) Oxygen Consumption and Catabolic Rate for Various Activities—Basal Catabolism.- (iv) Mechanical Body Output, and Mechanical Efficiency of the Human Body.- 5.4.E. Basal Metabolism.- (i) Basal Metabolic Rate of Mammals: From the Mouse to the Elephant.- (ii) Energy Requirements of Various Body Organs.- 5.5 Rotational Motion.- (i) Kinetic Energy of the Rotating Body.- (ii) Work Done on the Rotating Body.- (iii) The Physical Pendulum.- 5.6 References and Supplementary Reading.- 5.7 Problems.- 6 Feedback, Control, and Stability in Physical and Biological Systems.- 6.1 Introduction.- 6.1.A. Heat Engines, Power Production, and Automatic Control.- 6.1.B. Brief History of the Field of Automatic Control.- 6.1.C. Mechanics and Feedback and Control Theory.- 6.2 A Mechanical System Under Automatic Control.- 6.2.A. Description of the Overall Operation of the Steam Engine.- 6.2.B. Mathematical Model for the Operation of the Steam Engine—Without Automatic Control.- (i) Equation of Motion for the Engine Output Shaft.- (ii) Steady State Operating Speeds of the Engine. Effect of Changes in Pressure and Load.- (iii) Temporal Response of the Steam Engine to Changes in Steam Pressure and Load Torque.- 6.2.C. Quantitative Analysis of the Operation of the Steam Engine with Feedback Control from a Centrifugal Pendulum.- (i) Differential Equation of the Steam Engine— With the Centrifugal Governor Included.- (ii) Steady State Changes in Engine Output Angular Velocity Produced by Changes in Steam Pressure or Load Torque: The “Open Loop Gain”.- (iii) Temporal Response of the Steam Engine Under Proportional Feedback Control to Changes in Steam Pressure.- 6.2.D. Instability in the Feedback and Control System of the Steam Engine.- (i) Response Time of the Centrifugal Pendulum (tg) and the Characteristic Time for Engine Speed Changes.- (ii) Qualitative Discussion of the Origin of Instability.- (iii) Quantitative Analysis of Instability in a Feedback-Control System.- 6.3 Temperature Control Using Feedback.- 6.3.A. Temperature of a Heated (or Cooled) System without Feedback (Open Loop Operation).- (i) Equation for Temperature of a System as a Function of Time.- (ii) Steady State Operating Temperature.- (iii) Transient Response to Changes in Ambient Temperature or Input Power.- 6.3.B. Temperature of a Heated (or Cooled) System with Feedback.- (i) On-Off Control System.- (ii) Proportional Control System.- (iii) Integral Control System.- 6.4 Control of Body Temperature.- 6.4.A. Body Temperature in Illness and in Health.- 6.4.B. Thermal Properties of the Human Body.- 6.4.C. The Control Elements for the Regulation of Body Temperature.- 6.5 Control of Blood Glucose Level.- 6.5.A. Introduction: Glucose Tolerance Test.- 6.5.B. Control Equation for Blood Glucose Concentration.- 6.5.C. Comparison Between Theory and the Experimentally Observed Glucose Tolerance Curve.- 6.6 References and Supplementary Reading.- 6.7 Problems.