3: Conservation Laws & Concept-Based Problem Solving

Activities & Reader (ISBN 0-7872-3931-3, 224 pages)

How to Use this Book    xiii

Acknowledgments    xv

Activities

  • 71 - Investigating Collisions in which Two Objects Stick Together    313
  • 72 - Introducing the Concepts of Impulse and Momentum    317
  • 73 - Using Impulse and Momentum to Solve Constant-Force Problems    321
  • 74 - Analyzing Collisions Using Newton's Third Law    325
  • 75 - Relating Momentum Ideas to One-Body Problem Situations    331
  • 76 - Relating Momentum Ideas to Situations Having Two or More Objects    335
  • 77 - Reasoning with Impulse and Momentum Ideas    339
  • 78 - Solving Problems Using Momentum Principles    343
  • 79 - Summarizing and Structuring Momentum and Impulse Ideas    347
  • 80 - Recording Your Thoughts about Energy    349
  • 81 - Relating Forces to the Motion of Objects    353
  • 82 - Relating Work to Forces and Displacements    357
  • 83 - Recognizing the Presence of Work    361
  • 84 - Comparing the Work Done by Forces    367
  • 85 - Computing the Work Done by Forces    371
  • 86 - Recognizing and Comparing Kinetic Energy    375
  • 87 - Reasoning with Work and Energy Ideas    381
  • 88 - Solving Problems with the Work-Kinetic Energy Theorem    385
  • 89 - Recognizing the Presence of Potential Energy    389
  • 90 - Comparing the Potential Energy    393
  • 91 - Computing the Potential Energy    399
  • 92 - Keeping Track of Energy: The Law of Conservation of Energy    403
  • 93 - Reasoning with Energy Ideas    411
  • 94 - Solving Problems Using Energy Ideas    415
  • 95 - Summarizing and Structuring Energy Ideas    419
  • 96 - Recording Your Ideas about Problem Solutions    421
  • 97 - Recognizing the Appropriate Principle/Law    425
  • 98 - Matching Solution Strategies with Problems    433
  • 99 - Writing and Comparing Solution Strategies    437
  • 100 - Solving One-Principle Problems    441
  • 101 - Solving More Complex Problems    445
  • 102 - Structuring Mechanics    449

Reader: Chapter 3 — Conservation Laws

  • 3.0 Introduction    R61
    • What is meant by a conservation law?    R61
    • Why use a conservation law instead of dynamics?    R61
  • 3.1 SYSTEMS    R61
    • What is a system?    R61
    • Sizes of systems    R61
  • 3.2 MOMENTUM AND IMPULSE    R62-65
    • Impulse    R62,63
      • definition of impulse for constant force    R62
      • units for impulse: N-s    R62
      • how to calculate impulse for a given force and time interval    R62,63
      • definition of net impulse for constant net force    R63
      • how to calculate net impulse for constant net force    R63
    • Momentum    R64,65
      • definition of momentum for single bodies    R64
      • how to calculate the momentum    R64
      • units for momentum: kg-m/s    R64
      • what momentum means in some common situations    R64
      • how to find the change in momentum    R64,65
  • 3.3 TWO PRINCIPLES FOR DESCRIBING PHYSICAL SYSTEMS AND SOLVING PROBLEMS    R66-70
    • Impulse-Momentum Theorem    R66,67
      • comparing the net impulse and the change in momentum    R66
      • equivalence of the units for impulse and the units for momentum    R66
      • statement of the Impulse-Momentum Theorem for single bodies    R66
    • Conservation of Momentum for two-body systems    R68-70
      • using Newton's third law to understand collisions    R68
      • using the Impulse-Momentum Theorem to understand collisions    R69
      • statement of Conservation of Momentum for no net force on system    R69
      • definition of total momentum    R69
      • situations in which total momentum is only approximately conserved    R69,70
  • 3.4 USING MOMENTUM IDEAS AND PRINCIPLES TO ANALYZE SITUATIONS AND SOLVE PROBLEMS    R70-79
    • Reasoning with momentum ideas    R70-74
      • situations involving a net impulse    R70-73
        • using the Impulse-Momentum Theorem when there is a net impulse    R71
        • looking at the change in momentum    R71
        • making reasonable assumptions before making comparisons    R72
        • using limiting cases to make comparisons    R72
        • effect of mass on an object's response to an interaction    R73
      • situations in which the net impulse is zero or very close to zero    R73,74
        • using Conservation of Momentum when the impulse is small    R74
        • Conservation of Momentum is a vector equation    R74
    • Solving problems with momentum ideas    R75-78
      • using the Impulse-Momentum Theorem to solve problems    R75,76
        • two different ways of using the Impulse-Momentum Theorem    R75
        • Impulse-Momentum Theorem for constant net force    R75
        • four types of quantities: forces, time intervals, masses, velocities    R75
        • representation of problem solving using the Impulse-Momentum Theorem    R76
      • using Conservation of Momentum to solve problems    R76-78
        • four common steps for solving Conservation of Momentum problems    R76
        • Conservation of Momentum is a vector equation    R77,78
        • representation of problem solving using Conservation of Momentum    R78
    • Summary of momentum ideas and principles    R79
      • one new state quantity: momentum p    R79
      • two new process quantities: impulse J, and change in momentum Dp    R79
      • two new physical principles: the Impulse-Momentum Theorem and Conservation of Momentum    R79
      • new energy ideas: work, kinetic energy, potential energy    R79
      • limitations of momentum ideas    R79
  • 3.5 WORK AND KINETIC ENERGY    R80-90
    • Definition of work    R80-84
      • What factors affect the way a force changes the speed of something?    R80
      • definition of work for a constant force using the component of the force parallel to the displacement    R80
      • work is a scalar quantity    R81
      • units for work: J (joule)    R81
      • calculating the work done by a constant force    R81
      • how the work done can be negative    R81
      • What happens when the force is perpendicular to the displacement?    R81
      • circumstances when a different definition of work is needed    R82
      • definition of work for a constant force using the component of the displacement parallel to the force    R82
      • definition of total work    R83,84
    • Calculating the work done by common forces    R84-89
      • work done by the gravitational force    R84
        • depends on the mass, the gravitational constant (g), and the change in height    R84
        • why there is a minus sign in the expression    R84
      • work done by the normal force    R85,86
        • why the normal force often does no work on an object    R85
        • situations in which the normal force does work on an object    R85
        • the total work done by the normal force is always zero    R85
        • how the normal force can do no work even when it delivers an impulse    R86
      • work done by the tension force    R86,87
        • why the tension force often does no work on an object    R86
        • situations in which the tension force does work    R86,87
        • the total work done by the tension force is always zero    R87
      • work done by the friction force (static and kinetic)    R88
        • the static friction force can do work on isolated objects    R88
        • the static friction force can do no total work    R88
        • why we cannot calculate the work done by kinetic friction    R88
      • work done by the spring force    R89
        • using a graph of force vs. displacement to find the work done    R89
        • the graph of force vs. displacement is often a straight line    R89
    • Kinetic energy    R90,91
      • What changes when total work is done on an object?    R90
      • definition of kinetic energy    R90
      • circumstances under which the kinetic energy changes    R91
      • definition of total kinetic energy    R91
  • 3.6 TWO MORE PRINCIPLES FOR DESCRIBING PHYSICAL SYSTEMS AND SOLVING PROBLEMS    R92-99
    • Work-Kinetic Energy Theorem    R92-94
      • Statement of the Work-Kinetic Energy Theorem    R92
      • depends on the total work and the change in kinetic energy    R92
      • statement of the Work-Kinetic Energy Theorem for a system of objects    R92
      • depends on the total work and the change in total kinetic energy    R92
      • this is a scalar equation    R92
      • using the Work-Kinetic Energy Theorem to find the speed of something    R92,93
      • sometimes the forces doing work are hard to determine    R94
      • more reasons why we cannot calculate the work done by kinetic friction    R94
    • Conservation of Energy    R95-99
      • statement of the Law of Conservation of Energy    R95
      • why we need two new kinds of energy: potential energy and microscopic energy    R95
    • Potential energy    R95-98
      • change in gravitational potential energy    R95
      • gravitational potential energy for objects near the surface of celestial bodies    R95
      • using a reference height to determine the gravitational potential energy    R95
      • gravitational potential energy does not depend upon motion    R96
      • gravitational potential energy can be negative    R96
      • finding the potential energy stored in a spring    R97
      • factors affecting the spring potential energy    R97,98
      • the spring potential energy is always positive    R98
    • Microscopic vs. macroscopic energy    R98,99
      • definitions of the microscopic and macroscopic realms    R98
      • how energy is contained in the microscopic realm    R98,99
      • definition of total energy    R99
      • Law of Conservation of Energy    R99
  • 3.7 USING ENERGY IDEAS AND PRINCIPLES TO ANALYZE SITUATIONS    R100-105
    • Analyzing situations using the Work-Kinetic Energy Theorem    R100,101
      • whenever the kinetic energy of something changes, work is done    R100
      • difficulties in identifying the forces actually doing work    R100,101
      • similarities and differences between momentum and kinetic energy    R101
    • Analyzing situations using Conservation of Energy    R102-106
      • why the law is not particularly useful without modification    R102
      • Work-Energy Theorem (for a system of objects)    R102
      • definition of external work    R102
      • different ways of looking at the same situation    R102-104
      • using dynamics and kinematics to analyze a situation before applying Conservation of Energy    R104
      • where the energy goes during a collision    R104,105
      • change in microscopic energy due to friction    R105
      • different situations that may be used to derive the change in microscopic energy due to friction    R105
      • change in microscopic energy due to air resistance    R106
  • 3.8 USING ENERGY IDEAS AND PRINCIPLES TO SOLVE PROBLEMS    R106-113
    • Solving problems using the Work-Kinetic Energy Theorem    R106-109
      • two procedures for solving problems    R106-108
      • representation of problem solving using the Work-Kinetic Energy Theorem    R108,109
    • Solving problems using Conservation of Energy    R109-113
      • similarities and differences between the Work-Kinetic Energy Theorem and the Work-Energy Theorem    R109
      • problems in which the total work done by external forces is zero or negligibly small    R110,111
      • problem in which the total work done by external forces in non-zero    R112
      • why the Work-Energy Theorem is how we apply Conservation of Energy to a system of objects    R113
      • representation of problem solving using Conservation of Energy    R113
    • Summary of energy ideas and principles    R113
      • many new state quantities: kinetic, potential, and microscopic energy    R113
      • many new process quantities: work, changes in state quantities    R113
      • one new physical law: Conservation of Energy    R113
      • two new problem-solving principles: the Work-Kinetic Energy Theorem and the Work-Energy Theorem    R113
    • Summary of conservation laws    R113-114
      • reasons for using conservation laws    R113
      • how scientists apply conservation laws to new situations    R114
      • what we will do as we study new areas of physics    R114

Reader: Chapter 4 — Concept-Based Problem Solving

  • 4.0 Introduction    R115
    • Some questions you might ask yourself before solving a problem    R115
    • Why a conceptual analysis should precede equation manipulation    R115
  • 4.1 A PHYSICIST'S VIEW OF MECHANICS    R116-121
    • Explanation    R116
      • What is meant by a "view of mechanics"    R116
      • what is meant by an "organizational structure"    R116
      • what motivates a physicist's organizational structure    R116
    • Prioritizing ideas in mechanics    R116-120
      • chronological list of many of the physics concepts learned so far    R116
      • physical principles, the most widely useful ideas in physics    R117
      • concepts, the ideas needed to understand principles    R117
      • equations, the relationships needed to apply concepts and principles (physical laws, definitions, empirical laws, and derived relations)    R117,118
      • a priority scheme for physics ideas, with examples    R118,119
      • other ideas relevant for solving problems (mathematical principles, operations, and problem-solving techniques)    R119,120
    • Interconnecting ideas in mechanics    R121
      • using concepts to organize knowledge    R121
  • 4.2 CONCEPT-BASED PROBLEM SOLVING    R121-126
    • How to start solving a problem    R121-123
      • the first three steps of concept-based problem solving    R121,122
        • step 1: sort the principles    R121,122
        • step 2: choose a principle    R122
        • step 3: apply the chosen principle and solve for the unknown    R122
      • solution to the sample problem    R122,123
    • How to finish solving a problem    R124-126
      • four suggestions for efficient and effective problem solving    R124,125
        • create sketches and diagrams    R124
        • count the number of equations and unknowns    R124
        • challenge your assumptions    R124,125
        • check your answer    R125,126
    • Conclusion    R126
      • representation of the concept-based problem-solving approach    R126