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
D
p
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