crowell. conservation laws

Conservation Laws Benjamin Crowell Book 2 in the Light and Matter series of introductory physics textbooks www.lightandmatter.com Conservation Laws The Light and Matter series of introductory physics textbooks: 1 Newtonian Physics 2 Conservation Laws 3 Vibrations and Waves 4 Electricity and Magnetism 5 Optics 6 The Modern Revolution in Physics Conservation Laws Benjamin Crowell www.lightandmatter.com Light and Matter Fullerton, California www.lightandmatter.com © 1998-2002 by Benjamin Crowell All rights reserved. Edition 2.1 rev. 2002-07-30 ISBN 0-9704670-2-8 To Uri Haber-Schaim, John Dodge, Robert Gardner, and Edward Shore. 9 Brief Contents 1 Conservation of Energy 13 2 Simplifying the Energy Zoo 29 3 Work: The Transfer of Mechanical Energy 41 4 Conservation of Momentum 63 5 Conservation of Angular Momentum 89 Exercises 115 Solutions to Selected Problems 117 Glossary 119 Index 121 Useful Data 132 10 Contents 1 Conservation of Energy 13 1.1 The Search for a Perpetual Motion Machine 13 1.2 Energy 14 1.3 A Numerical Scale of Energy 16 1.4 Kinetic Energy 20 1.5 Power 23 Summary 25 Homework Problems 26 2 Simplifying the Energy Zoo 29 2.1 Heat is Kinetic Energy 30 2.2 Potential Energy: Energy of Distance or Closeness 32 2.3 All Energy is Potential or Kinetic 36 Summary 38 Homework Problems 39 3 Work: The Transfer of Mechanical Energy 41 3.1 Work: The Transfer of Mechanical Energy 41 3.2 Work in Three Dimensions 47 3.3 Varying Force 49 3.4 ∫ Applications of Calculus 51 3.5 Work and Potential Energy 52 3.6* When Does Work Equal Force Times Distance? 54 3.7* The Dot Product 56 Summary 57 Homework Problems 58 [...]...4 Conservation of Momentum 63 4.1 Momentum 64 4.2 Collisions in One Dimension 70 4.3* Relationship of Momentum to the Center of Mass 74 4.4 Momentum Transfer 76 4.5 Momentum in Three Dimensions 79 4.6∫ Applications of Calculus 83 Summary 84 Homework Problems 85 5 Conservation of Angular Momentum 89 5.1 Conservation of Angular Momentum... standard form of it, and then measure other forms by comparison with this standard The flexible and adaptable nature of this procedure is part of what has made conservation laws such a durable basis for the evolution of physics 16 Chapter 1 Conservation of Energy Example: heating a swimming pool Question: If electricity costs 3.9 cents per MJ (1 MJ = 1 megajoule = 106 J), how much does it cost to heat... always conserved That is, it cannot be created or destroyed but only transferred between objects or changed from one form to another Conservation of energy is the most important and broadly applicable of all the laws of physics, more fundamental and general even than Newton’s laws of motion Heating an object requires a certain amount of energy per degree of temperature and per unit mass, which depends on... because of its decreasing height above the earth, and conservation of energy says that it must gain an equal amount of energy of motion (minus a little heat created by friction) The balls lose the same amount of height, so their final speeds must be equal It’s impressive to note the complete impossibility of solving this problem using only Newton’s laws Even if the shape of the track had been given mathematically,... mentioned Einstein’s theory of relativity above, it’s more relevant right now to consider how conservation of energy relates to the simpler Galilean idea, which we’ve already studied, that motion is relative Galileo’s Aristotelian enemies (and it is no exaggeration to call them enemies!) would probably have objected to conservation of energy After all, the Galilean idea that an object in motion will continue... context, the word “conserve” does not have its usual meaning of trying not to waste something In physics, a conserved quantity is something that you wouldn’t be able to get rid of even if you wanted to Conservation laws in physics always refer to a closed system, meaning a region of space with boundaries through which the quantity in question is not passing In our example, the alchemist’s laboratory is a closed... objects that interact via forces The total energy of a closed system always remains constant Energy cannot be created or destroyed, but only transferred into or out of a system The moon rock story violates conservation of energy because the rockcylinder and the ball together constitute a closed system Once the ball has made one revolution around the cylinder, its position relative to the cylinder is exactly... energy of the car’s motion is converted into heat in the brake shoes Discussion Question Hydroelectric power (water flowing over a dam to spin turbines) appears to be completely free Does this violate conservation of energy? If not, then what is the ultimate source of the electrical energy produced by a hydroelectric plant? 1.3 A Numerical Scale of Energy Energy comes in a variety of forms, and physicists... Perpetual Motion Machine 13 engine Generations of inventors have tried to create a machine, called a perpetual motion machine, that would run forever without fuel Such a machine is not forbidden by Newton’s laws of motion, which are built around the concepts of force and inertia Force is free, and can be multiplied indefinitely with pulleys, gears, or levers The principle of inertia seems even to encourage... would be like flicking it with a few tiny energy-drops The human body is tremendously inefficient The calories we “burn” in heavy exercise are almost all dissipated directly as body heat 18 Chapter 1 Conservation of Energy A Example: You take the high road and I’ll take the low road ball #1 track #1 ball #2 track #2 B Forms of Energy Discovered in Recent Times Einstein showed that mass itself could . Conservation Laws Benjamin Crowell Book 2 in the Light and Matter series of introductory physics textbooks www.lightandmatter.com Conservation Laws The Light and. textbooks: 1 Newtonian Physics 2 Conservation Laws 3 Vibrations and Waves 4 Electricity and Magnetism 5 Optics 6 The Modern Revolution in Physics Conservation Laws Benjamin Crowell www.lightandmatter.com Light. Energy 41 4 Conservation of Momentum 63 5 Conservation of Angular Momentum 89 Exercises 115 Solutions to Selected Problems 117 Glossary 119 Index 121 Useful Data 132 10 Contents 1 Conservation