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Physics, Mechanics, Heat and Molecular Handbook

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Physics, Mechanics, Heat and Molecular Handbook

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What are the tools at the disposal of the physical science that allow it to reign the world?

First of all, physics clearly deals with phenomena in real world, and hence the first step in gaining knowledge about these phenomena involves observations.

However, scientific observation is not a simple problem. Let us watch, for example, falling bodies. It can be easily seen that a body dropped from a small height strikes the ground with a small force, while the impact as a result of a fall from a large height can be much stronger and may even destroy the falling body. The observation of rain drops does not reveal, however, any difference in the impacts of the drops from low and high clouds. Everybody knows that a pilot who falls from an aeroplane is smashed to death, while a pilot who jumps with a parachute even from a larger height lands smoothly. Aircraft bombs, especially heavy ones, hit with a tremendous force that enables them to pierce multi story buildings. Thus, a comparatively simple phenomenon of falling may proceed in different ways. If we want to control this phenomenon, we must find the relationship between its different aspects, viz. establish how certain characteristics of the motion of a body are influenced by the shape and mass of the body, the height from which it falls, etc. and (this is most important) draw general conclusions from these facts, which explain why the body falls in this way and not in another way.

The same problems emerge in studying any other phenomenon. We must establish what affects a phenomenon and learn how to suppress or enhance its individual aspects. For this purpose, we must be the phenomenon, single out its individual elements and, if possible, change the conditions in which it occurs. This means a transition from the simple observation to an experiment. Here it is very important not to limit ourselves to general qualitative impressions about the phenomenon but to find quantitative characteristics of its individual elements in the form of measurable quantities. In other words, we must determine the concepts which may serve as the quantitative characteristics of the phenomenon and find the methods of measurement of relevant quantities. Having determined these quantities, we can establish numerical relations between them, i.e. formulate the laws governing the phenomenon in a quantitative (analytical) form. Thus, in the above example of falling bodies, we introduce the concepts of the velocity of the falling body, its acceleration (i.e. the change in velocity), the height of fall, air resistance, the mass of the body, the force of gravity acting on it, and so on. To find the laws of fall means to establish a relation between these quantities able to analyze.

TOC

Part One. Mechanics 19

Chapter 1. Kinematics 19

1.1. Motion of Bodies (19). 1.2. Kinematics. Relative Nature of Motion and State of Rest (21). 1.3. Trajectory of Motion (22). 1.4. Translatory and Rotary Motion of a Body (24). 1.5. Motion of a Point (25). 1.6. Description of Motion of a Point (26). 1.7. Measurement of Length (29). 1.8. Measurement of Time Intervals (32). 1.9. Uniform Rectilinear Motion and Its Velocity (34). 1.10. The Sign of Velocity in Rectilinear Motion (36). 1.11. Units of Velocity (36). 1.12. Path vs. Time Graph (39). 1.13. Velocity vs. Time Graph (43). 1.14. Nonuniform Rectilinear Motion. Average Velocity (44). 1.15. Instantaneous Velocity (45). 1.16. Acceleration in Rectilinear Motion (47). 1.17. Velocity of Uniformly Accelerated Motion in a Straight Line (49). 1.18. The Sign of Acceleration in Rectilinear Motion (50). 1.19. Velocity Graphs for Uniformly Accelerated Motion in a Straight Line (51). 1.20. Velocity Graph for an Arbitrary Nonuniform Motion (52). 1.21. Calculation of the Path Traversed in Nonuniform Motion with the Help of Velocity Graph (54). 1.22. Distance Covered in a Uniformly Variable Motion (54). 1.23. Vectors (56). 1.24. Decomposition of a Vector into Components (60). 1.25. Curvilinear Motion (63). 1.26. Velocity of Curvilinear Motion (63). 1.27. Acceleration in Curvilinear Motion (65). 1.28. Motion in Different Reference Systems (67). 1.29. Kinematics of Motion in Outer Space (69).

Chapter 2. Dynamics 72

2.1. Problems of Dynamics (72). 2.2. Law of Inertia (72). 2.3. Inertial Reference Systems (74). 2.4. Galileo’s Relativity Principle (75). 2.5. Forces (76). 2.6. Balanced Forces. State of Rest and Inertial Motion (78). 2.7. Force as a Vector. Standard of Force (79). 2.8. Spring Balance (80). 2.9. The Point of Application of a Force (83). 2.10. Resultant Force (84). 2.11. Composition of Forces Acting along a Straight Line (84). 2.12. Composition of Forces Acting at an Angle to Each Other (85). 2.13. Relation between Force and Acceleration (87). 2.14. Mass of a Body (89). 2.15. Newton’s Second Law (91). 2.16. Units of Force and Mass (94). 2.17. Systems of Units (94). 2.18. Newton’s Third Law (95). 2.19. Applications of Newton’s Third Law (98). 2.20. Momentum of a Body (100). 2.21. System of Bodies. Law of Momentum Conservation (101). 2.22. Application of the Law of Momentum Conservation (103). 2.23. Free I all of Bodies (105). 2.24. Free Fall Acceleration (106). 2.25. Falling of a Body with Zero Initial Velocity and Motion of a Body Thrown Vertically Upwards (106). 2.26. Weight of a Body (108). 2.27. Mass and Weight (110). 2.28. Density of Substances (111). 2.29. Emergence of (113). 2.31. Deformations in Stationary Bodies Caused by the Force of Gravity (114). 2.32.
Deformation of a Body Moving with an Acceleration (115). 2.33. Vanishing of Deformations in Free Fall (117). 2.34. Destruction of Moving Bodies (119). 2.35. Frictional Forces (120). 2.36. Rolling Friction (123). 2.37. Role of Friction (124). 2.38. Resistance of Medium (125). 2.39. Falling of Bodies in Air (126).

Chapter 3. Static's 129

3.1. Problems of Static's tl29). 3.2. Perfectly Rigid Body (130). 3.3. Translation of the Point of Application of a Force Acting on a Rigid Body (131). 3.4. Equilibrium of a Body under the Action of Three Forces (133). 3.5. Decomposition of Forces (134). 3.6. Projections of Forces. General Conditions of Equilibrium (137). 3.7. Constraints. Constraining Forces. A Body with a Fixed Axis (139). 3.8. Equilibrium of a Body with a Fixed Axis (141). 3.9. Moment of Force (142). 3.10. Measurement of Torque (145). 3.11. Force Couple (146). 3.12. Composition of Parallel Forces. Center of Gravity (147). 3.13. Determination of the Centrex of Gravity of a Body (150). 3.14. Equilibrium of a Body under the Action of the Force of Gravity (153). 3.15. Conditions of Stable Equilibrium under the Action of the Force of Gravity (155). 3.16. Simple Machines (158). 3.17. Wedge and Screw (164).

Chapter 4. Work and Energy 168

4.1. “Golden Rule” of Mechanics (168). 4.2. Applications of the “Golden Rule” (169). 4.3. Work Done by a Force (170). 4.4. Work Done during a Displacement Normal to the Direction of Force (172). 4.5. Work Done by a Force Acting at an Arbitrary Angle to Displacement (172). 4.6. Positive and Negative Work (173). 4.7. Units of Work (174). 4.8. Motion over a Horizontal Plane (175). 4.9. Work Done by the Force of Gravity in Motion over an Inclined Plane (175). 4.10. Principle of Work Conservation (176). 4.11. Energy (178). 4.12. Potential Energy (179). 4.13. Potential Energy of Elastic Deformation (181). 4.14. Kinetic Energy (183). 4.15. Kinetic Energy in Terms of Mass and Velocity of a Body (183). 4.16. Total Energy of a Body (184). 4.17. The Law of Energy Conservation (186). 4.18. Frictional Forces and the Law of Conservation of Mechanical Energy (189). 4.19. Conversion of Mechanical Energy into Internal Energy (190). 4.20. General Nature of the Law of Energy Conservation (192). 4.21. Power (193). 4.22. Calculation of Power of Machines (194). 4.23. Power, Speed and Dimensions of Machines (195). 4.24. Efficiency of Machines (196).

Chapter 5. Curvilinear Motion 198

5.1. Emergence of Curvilinear Motion (198). 5.2. Acceleration of a Curvilinear Motion (199). 5.3. Motion of a Body Thrown along the Horizontal (200). 5.4. Motion of a Body Thrown at an Angle to the Horizontal (203). 5.5. Flight of Bullets and Projectiles (206). 5.6. Angular Velocity (207). 5.7. Forces in a Uniform Circular Motion (208). 5.8. Emergence of the Force Acting on a Body Moving in a Circle (210). 5.9. Rupture of Flywheels (212). 5.10. Deformation of a Body Moving in a Circle (213). 5.11. Roller Coaster (215). 5.12. Banking of Tracks (217). 5.13. The Circular Motion of a Suspended Body (218). 5.14. Motion of Planets (219). 5.15. The Law of Universal Gravitation (223). 5.16. Artificial Satellites of the Earth (227).

Chapter6. Motion in Noninertial Reference Systems and Inertial Forces 235

6.1. The Role of a Reference System (235). 6.2. Motion Relative to Different Inertial Systems (236). 6.3. Motion Relative to an Inertial and a Noninertial Reference System (237). 6.4. Noninertial Systems in Translatory Motion (239). 6.5. Inertial Forces (239). 6.6. Equivalence of Inertial Forces and Gravitational Forces (241). 6.7. Weightlessness and Overloads (244). 6.8. Is the Earth an Inertial Reference System? (246). 6.9. Rotating Reference Systems (247). 6.10. Inertial Forces for a Body Moving Relative to a Rotating Reference System (249). 6.11. Proof of the Earth’s Rotation (250). 6.12. Tides (253).

Chapter 7. Hydrostatics 255

7.1. Mobility of Liquids (255). 7.2. Force of Pressure (256). 7.3. Measurement of Compressibility of a Liquid (258). 7.4. “Incompressible” Liquid (259). 7.5. Forces of Pressure Are Transmitted in a Liquid in All Directions (259). 7.6. Direction of Forces of Pressure (260). 7.7. Pressure (260). 7.8. Membrane Manometer (261). 7.9. Independence of Pressure of the Orientation of an Area Element (262). 7.10. Units of Pressure (263). 7.11. Determination of Forces of Pressure from Pressure (263). 7.12. Distribution of Pressure in a Liquid (264). 7.13. Pascal’s Principle (265). 7.14. Hydraulic Press (266). 7.15. Liquid under the Action of the Force of Gravity (268). 7.16. Communicating Vessels (272). 7.17. Liquid Column Manometer (274). 7.18. Water Supply System. Pressure Pump (275). 7.19. Siphon (277). 7.20. Force of Pressure on the Bottom of a Vessel (278). 7.21. Water Pressure in Sea Depths (281). 7.22. The Strength of a Submarine (284). 7.23. Archimedes’ Principle (285). 7.24. Measurement of Density of Bodies on the Basis of Archimedes’ Principle (289). 7.25. Floatation of Bodies (289). 7.26. Floatation of Hollow Bodies (292). 7.27. Stability of Floating Ships (294). 7.28. Rising of Bubbles to the Surface (295). 7.29. Bodies Lying on the Bottom of a Vessel (295).

Chapter 8. Aerostatics 297

8.1. Mechanical Properties of Gases (297). 8.2. Atmosphere (298). 8.3. Atmospheric Pressure (299). 8.4. Other Experiments Confirming the Existence of the Atmospheric Pressure (301). 8.5. Vacuum Pumps (303). 8.6. Effect of the Atmospheric Pressure on the Level of Liquid in a Pipe (304). 8.7. Maximum Height of a Liquid Column (306). 8.8. Torricelli’s Experiment. Mercury Barometer and Aneroid Barometer (308). 8.9. Distribution of Atmospheric Pressure over Altitude (311). 8.10. Physiological Effect of Lowered Air Pressure (314). 8.11. Archimedes’ Principle for Gases (314). 8.12. Balloons and Airships (315). 8.13. Application of Compressed Air in Engineering (317).

Chapter 9. Fluid Dynamics 320

9.1. Pressure in a Fluid Flow (320). 9.2. Fluid Flow in Pipes. Fluid Friction (322). 9.3. Bernoulli’s Law (325). 9.4. Fluid in Noninertial Reference Systems (327). 9.5. Reaction of a Moving Fluid and Its Application (329). 9.6. Motion over Water Surface (332). 9.7. Rockets (334). 9.8. Jet Engines (335). 9.9. Ballistic Missiles (336). 9.10. Launching a Rocket from the Earth (338). 9.11. Air Resistance. Resistance of Water (338). 9.12. Magnus Effect and Circulation (342). 9.13. Lifting Force of a Wing and the Flight of an Aeroplane (344). 9.14. Turbulence in a Fluid Flow (347). 9.15. Laminar Flow (348).

Part Two. Heat. Molecular Physics 349

Chapter 10. Thermal Expansion of Solids and Liquids 349 10.1. Thermal Expansion of Solids and Liquids (349). 10.2. Thermometers (353). 10.3. Formula of Linear Expansion (355). 10.4. Formula for Volume Expansion (357). 10.5. Relation between Temperature Coefficients of Linear and Volume Expansion (359). 10.6. Measurement of Temperature Coefficient of Volume Expansion for Liquids (360). 10.7. Thermal Expansion of Water (360).

Chapter 11. Work. Heat. Law of Energy Conservation 362

11.1. Change of the State of Bodies (362). 11.2. Heating of Bodies on Which Work is Done (363). 11.3. The Change in the Internal Energy in Heat Transfer (365). 11.4. Units of Heat (366). 11.5. Dependence of Internal Energy of a Body on Its Mass and Substance of Which It is Made Up (367). 11.6. Heat Capacity of a Body (368). 11.7. Specific Heat Capacity (369). 11.8. Calorimeter. Measurement of Heat Capacity (369). 11.9. The Law of Energy Conservation (372). 11.10. Perpetual-Motion Machine (Perpetuum Mobile) (374). 11.11. Types of Processes Involving Heat Transfer (374).

Chapter 12. Molecular Theory 379

12.1. Molecules and Atoms (379). 12.2. Size of Atoms and Molecules (380). 12.3. Microworld (381). 12.4. Internal Energy from the Viewpoint of Molecular Theory (382). 12.5. Molecular Motion (383). 12.6. Molecular Motion in Gases, Liquids and Solids (384). 12.7. Brownian Movement (385). 12.8. Intermolecular Forces (386).

Chapter 13. Properties of Gases 389

13.1. Pressure of a Gas (389). 13.2. Temperature Dependence of Gas Pressure (391). 13.3. Formula Expressing Gay-Lussac’s Law (392). 13.4. Gay-Lussac’s Law from the Point of View of Molecular Theory (393). 13.5. Variation of Gas Temperature with a Change in Its Volume. Adiabatic and Isothermal Processes (394). 13.6. Boyle’s Law (396). 13.7. Formula Expressing Boyle’s Law (398). 13.8. The Graph Representing Boyle’s Law (399). 13.9. Relation between the Gas Density and Pressure (399). 13.10. Molecular Interpretation of Boyle’s Law (400). 13.11. Variation of Gas Volume with Temperature (401). 13.12. Charles’ Law (402). 13.13. Graphs Representing Gay-Lussac’s and Charles’ Laws (403). 13.14. Thermodynamic Temperature (404). 13.15. Gas Thermometer (406). 13.16. Gas Volume and Thermodynamic Temperature (407). 13.17. Temperature Dependence of Gas Density (407). 13.18. Equation of State for a G a s (408). 13.19. Dalton’s Law (409). 13.20. Density of Gases (411). 13.21. Avogadro’s Law (412). 13.22. Mole. Avogadro’s Number (413). 13.23. Velocities of (ias Molecules (414). 13.24. Measurement of Velocities of Gas Molecules (Stern’s Experiment) (418). 13.25. Specific Heat Capacities of Gases (420). 13.26. Molar Heat Capacities (421). 13.27. The Dulong and Petit Law (422).

Chapter 14. Properties of Liquids 424

14.1. Structure of Liquids (424). 14.2. Surface Energy (425). 14.3. Surface Tension (429). 14.4. Liquid Films (432). 14.5. Temperature Dependence of Surface Tension (434). 14.6. Wetting and Nonwetting (434). 14.7. Arrangement of Molecules at the Surface of Bodies (437). 14.8. The Role of the Curvature of the Free Surface of a Liquid (438). 14.9. Capillary Phenomena (442). 14.10. The Height to Which a Liquid Rises in Capillary Tubes (444). 14.11. Adsorption (446). 14.12. Floatation (447). 14.13. Dissolution of Gases (449). 14.14. Mutual Solubility of Liquids (451). 14.15. Dissolution of Solids in Liquids (452).

Chapter 15. Properties of Solids. Transition from Solid to Liquid State 454

Crystal Lattice (459). 15.5. Crystallisation (462). 15.6. Melting and Solidification (463). 15.7. Specific Latent Heat of Fusion (464). 15.8. Supercooling (466). 15.9. The Change in the Density of a Substance during Fusion (467). 15.10. Polymers (468). 15.11. Alloys (471). 15.12. Solidification of Solutions (473). 15.13. Cooling Mixtures (473). 15.14. Variation of Properties of a Solid (474).

Chapter 16. Elasticity and Strength 476

16.1. Introduction (476). 16.2. Elastic and Plastic Deformations (476). 16.3. Hooke’s Law (477). 16.4. Extension and Compression (478). 16.5. Shear (480). 16.6. Torsion (481). 16.7. Bending (483). 16.8. Strength (485). 16.9. Hardness (486). 16.10. What Occurs during Deformations of Bodies? (487). 16.11. Energy Variation during Deformations of Bodies (487).

Chapter 17. Properties of Vapours 489

17.1. Introduction (489). 17.2. Saturated and Unsaturated Vapour (489). 17.3. Variation of Volume of Liquid and Saturated Vapour (491). 17.4. Dalton’s Law for Vapours (493). 17.5. Molecular Pattern of Evaporation (494). 17.6. Temperature Dependence of Saturated Vapour Pressure (495). 17.7. Boiling (496). 17.8. Specific Latent Heat of Vaporisation (500). 17.9. Cooling during Evaporation (503). 17.10. The Change in the Internal Energy during a Transition of a Substance from the Liquid State to Vapour (504). 17.11. Evaporation from Curved Surfaces of Liquids (505). 17.12. Superheating of a Liquid (506). 17.13. Supersaturation of Vapours (507). 17.14. Vapour Saturation in Sublimation (508). 17.15. Liquefaction of Gases (509). 17.16. Critical Temperature (510). 17.17. Liquefaction of Gases in Engineering (513). 17.18. Vacuum Technology (516). 17.19. Water Vapour in the Atmosphere (517).

Chapter 18. Physics of the Atmosphere 521

18.1. The Atmosphere (521). 18.2. Heat Balance of the Earth (522). 18.3. Adiabatic Processes in the Atmosphere (523). 18.4. Clouds (524). 18.5. Artificial Precipitation (526). 18.6. Wind (526). 18.7. Weather Forecasting (528).

Chapter 19. Heat Engines 530

19.1. Necessary Conditions for the Operation of Heat Engines (530). 19.2. Steam Power Plant (531). 19.3. Steam Boiler (532). 19.4. Steam Turbine (533). 19.5. Steam Piston Engine (535). 19.6. Condenser (536). 19.7. Efficiency of Heat Engines (537). 19.8. Efficiency of a Steam Power Plant (537). 19.9. Petrol Internal Combustion Engine (539). 19.10. Efficiency of Internal Combustion Engines (543). 19.11. Diesel Engine (544). 19.12. Jet Engines (545). 19.13. Heat Transfer from a Cold to a Hot Body (546).

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