FF: Fundamental Forces & Fields
Activities & Reader (ISBN 0-7872-5412-6, 207 pages)
How to Use this Book
xv
Acknowledgments
xvii
Activities
FF·1 - Exploring Models of Electromagnetism
1
FF·2 - Using a Model to Interpret, Explain, and Predict
7
FF·3 - Investigating Electrical Properties of Materials
13
FF·4 - Reasoning with a Model for Electrical Interactions
17
FF·5 - Exploring the Magnetic Interaction
21
FF·6 - Modeling the Magnetic Properties of Materials
25
FF·7 - Modeling the Magnetic Properties of Moving Charges
29
FF·8 - Reasoning with a Model for Magnetic Interactions
35
FF·9 - Exploring the Gravitational Interaction
39
FF·10 - Exploring the Idea of Weight
43
FF·11 - Distinguishing Mass and Weight
47
FF·12 - Modeling Universal Gravitation
51
FF·13 - Using a Mathematical Model for the Electric Force
55
FF·14 - Applying Coulomb's Law to Continuous Distributions of Charge
59
FF·15 - Estimating Electric Forces Using Coulomb's Law
65
FF·16 - Reasoning with Coulomb's Law
69
FF·17 - Developing an Empirical Force Law for Magnets
73
FF·18 - Using the Universal Law of Gravitation
79
FF·19 - Applying Universal Gravitation to Large-Scale Objects
83
FF·20 - Reasoning with Universal Gravitation
87
FF·21 - Mapping Magnetic Fields
91
FF·22 - Representing the Electric Field
97
FF·23 - Representing the Electric Field as a Vector Field
101
FF·24 - Investigating the Gravitational Field
107
FF·25 - Representing Vector Fields Using Field Line Diagrams
111
FF·26 - Applying Newton's Laws
117
FF·27 - Applying Work and Energy Ideas
121
FF·28 - Solving Problems Using Work and Energy Ideas
127
FF·29 - Summarizing and Structuring the Fundamental Forces
131
Reader: Fundamental Forces and Fields
0. Introduction
R1
what is meant by a
fundamental force
R1
a list of the fundamental forces
R1
some examples of what the fundamental forces are responsible for
R1
the organization of the Reader
R1
1. QUALITATIVE DESCRIPTIONS OF FUNDAMENTAL FORCES
R1-20
1.1. Modeling interactions
R2
what is meant by the term
model
R2
goal of a model
R2
graphic representation of modeling
R2
1.2. Electric phenomena
R2,3
examples of electric phenomena
R2
table showing how rubbed objects interact with each other
R3
introducing
electric charge
to explain pattern of electric phenomena
R3
defining which objects are said to be
positive
, which are
negative
, and which are
neutral
R3
1.3. Reasoning about electric interactions
R4
an example showing how we can predict the behavior of something
R4
an example showing the limitations of our current model
R4
1.4. A simplified model of electric interactions
R4-6
goal of our simplified model
R4
assumption 1: All matter is made up of sub-microscopic particles
R5
assumption 2: These particles have mass and charge
R5
assumption 3: "Like" charges repel; "opposite" charges attract; neutral particles do not interact
R5
assumption 4: Everyday objects are neutral
R6
assumption 5: Charges can be transferred
R6
assumption 6: Electric interactions occur when one or both objects have excess charge
R6
assumption 7: Charge is
conserved
R6
assumption 8: The mass of sub-microscopic particles is very small
R6
assumption 9: When styrofoam is rubbed with fur, the fur is defined to be positive, and the styrofoam is defined to be negative
R6
1.5. Applying the simplified model of electric interactions
R7
An example showing how the model can predict the behavior of something
R7
1.6. The atomic model of matter
R7,8
types of charge on the proton, neutron, and electron
R7
how the atomic model will and will not be used
R8
1.7. A model of the electrical properties of materials
R8,9
goal of our model of electrical properties of materials
R8
assertion 1: Only electrons can be transferred by rubbing
R8
assertion 2: Excess electrons on a conductor flow easily
R8
why some electrical demonstrations give inconsistent results
R8
assertion 3: Excess electrons on an insulator do not flow very easily
R9
assertion 4: Some electrons in a conductor are relatively free to move
R9
conductors exchange electrons on contact
R9
assertion 5: Most electrons in an insulator are not relatively free to move
R9
assertion 6: The strength of the electric force depends on charge separation
R9
1.8. Applying the atomic model of electric interactions
R10,11
explaining why neutral objects are attracted to charged objects
R10
predicting the charges on pie plates
R11
1.9. Magnetic phenomena
R11,12
what is meant by a
permanent magnet
R11
what is meant by the
poles
of a magnet
R11
what is meant by the
North
(
N
) and
South
(
S
) poles of a magnet
R11
table showing how different materials interact magnetically
R12
other properties of interacting materials
R12
1.10 Modeling the magnetic interaction
R12-14
what is meant by a
nanomagnet
R13
assumption 1: All matter is made up of tiny nanomagnets
R13
assumption 2: "Like" poles repel; "opposite" poles attract
R13
assumption 3: Every material's nanomagnets have a characteristic strength
R13
what is meant by
magnetic materials
R13
assumption 4: The interaction of two nanomagnets depends on their strengths
R13
assumption 5: The interaction of two nanomagnets depends on their separation
R13
what is meant by
non-magnetic materials
R13
how these assumptions are applied to different materials
R13
rough depictions of the nanomagnets in non-magnetic materials, magnetic materials, and permanent magnets
R14
what is meant by a
magnetic domain
R14
1.11 Applying our simplified model of magnetic interactions
R14
Examples of how to apply this model of magnetic interactions
R14
1.12 An atomic model of magnetic interactions
R15
reasons we need to go to the atomic model
R15
two moving charges are needed for the magnetic interaction
R15
how to go from moving charges to nanomagnets
R15
1.13 Applying the atomic model of magnetic interactions
R16
one more assumption: the strength of a nanomagnet is due primarily to an atom's orbiting electrons
R16
examples of how to apply the atomic model of magnetic interactions
R16
1.14 "Local" gravitation
R17,18
what is meant by
local gravitation
R17
how we know that gravitation is caused by the Earth
R17
what is meant by "local" gravitation on the Moon
R18
1.15 Weight
R18
how weight might appear to be different for different observers
R18
definition of the term
weight
R18
why a scale sometimes cannot be used to determine weight
R18
why air has weight
R18
1.16 Mass vs. weight
R19
differences between
mass
and
weight
R19
1.17 "Universal" gravitation
R19,20
what is meant by
Universal gravitation
R19
gravitational force as a function of position assuming the Earth has a uniform density
R19
comparison of the gravitational forces exerted by the Earth and the Moon
R20
why the local gravitational constant on the Moon is 1/6 that on the Earth
R20
summary of gravitation
R20
2. MATHEMATICAL DESCRIPTIONS OF FUNDAMENTAL FORCES
R21-33
2.1. Coulomb's law for electric forces
R21,22
what is meant by a
point charge
R21
mathematical description of Coulomb's law
R21
how to find the direction of the electric force
R21
MKS unit of charge (the
Coulomb
, C)
R22
charges of the proton and electron
R22
an example of how to apply Coulomb's law
R22
2.2. The Superposition Principle
R22,23
why we need the Superposition Principle
R22
verbal description of the Superposition Principle
R22
an example showing how to apply the Superposition Principle
R23
2.3. Applying Coulomb's law to non-point objects
R24
force law when objects are far apart
R24
how to treat objects close together
R24
2.4. Reasoning with Coulomb's law
R25,26
a convenient unit of charge is the
microCoulomb
(µC)
R25
3 examples showing how to reason using Coulomb's law
R25,26
2.5. Universal law of gravitation
R27,28
mathematical description of the Universal law of gravitation
R27
how to find the direction of the gravitational force
R27
an example showing how to apply the Universal law of gravitation
R27
an example showing how to apply the Superposition Principle
R28
2.6. Applying Universal gravitation to non-point objects
R28,29
applying Universal gravitation when objects are far apart
R28
applying Universal gravitation when an object is close to a celestial body
R28,29
what is meant by a
shell
R28
force law when object is outside the mass shell
R29
force law when object is inside the mass shell
R29
how to apply these results to celestial bodies such as the Earth and Moon
R29
2.7. Astronomical data
R30
mass, average radius, average density,
g
on its surface, average orbital radius, and orbital period for the Earth, the Moon, and the Sun
R30
an example of how to use astronomical data
R30
2.8. Deciding how to apply the Universal law of gravitation
R30,31
3 general methods for applying the Universal law of gravitation
R30,31
an example showing how these methods apply to 6 situations
R31
2.9. Reasoning with Universal gravitation
R32,33
examples showing how to reason using Universal gravitation
R32,33
2.10 The magnetic interaction
R33
why we cannot provide a mathematical description of the magnetic interaction
R33
some features you should still know about the magnetic interaction
R33
3. FIELDS
R34-45
some of the different ways the term
field
is used
R34
3.1. Scalar vs. vector fields
R34
what is meant by a
scalar field
R34
what is meant by a
vector field
R34
temperature is a good example of a scalar field
R34
velocity of air currents is a good example of a vector field
R34
vector field diagram
for air currents in a certain region of space
R34
3.2. Fields for fundamental forces
R35
why we introduce fields for fundamental forces
R35
how a fundamental field is defined: in terms of the force exerted on an object
R35
what creates what types of fields
R35
3.3. The electric field
R36
force on point charge
q
due to electric field
E
R36
definition of the electric field
R36
using Coulomb's law to find the electric field created by a point charge
R36
finding the direction of the electric field
R36
how the mutual forces can be the same even though the fields are different
R36
3.4. Electric field for multiple point charges
R37
an example of how to find the electric field for two point charges
R37
vector field diagrams for the "dipole" and "dicharge" distributions of charge
R37
3.5. Electric field for a spherical shell of charge
R38
electric field inside a shell of charge
R38
electric field outside a shell of charge
R38
finding the direction of the electric field outside a shell of charge
R38
an example showing how to find the electric field on a rubber ball
R38
3.6. The gravitational field
R39
why we use the same symbol for "local" and "Universal" gravitation
R39
definition of the gravitational field
R39
gravitational field created by a point mass
R39
how to find the direction of the gravitational field
R39
3.7. Gravitational field for non-point masses
R39,40
using shells to find the gravitational field for a celestial body
R39
sketch of gravitational field strength
g
vs. distance from the center of the Earth
R40
finding and verifying the location between the Earth and the Moon where the gravitational field is zero
R40
3.8. The magnetic field
R41
why we use a compass needle to determine the direction of the magnetic field
R41
magnetic field for a long, straight wire
R41
magnetic field for a loop of wire
R41
3.9. Finding the magnetic field for other arrangements of current-carrying wire
R42
magnetic field for two parallel wires, with currents moving in opposite directions
R42
magnetic field for a coil of wire
R42
3.10 Force on a point charge moving through a magnetic field
R42,43
diagram showing the orientations of the velocity
v
, magnetic field
B
, and magnetic force
F
m
R42
2 mathematical expressions for the magnetic force on charge
q
R43
finding the direction of the magnetic force
R43
why we cannot write an expression for the magnetic field
B
created by a moving point charge
R43
3.11 Limitations of vector field diagrams
R43
many reasons why vector field diagrams are sometimes not the best way to represent fields
R43
an example using the "dipole" arrangement of charges
R43
3.12 Field line diagrams
R44
what is meant by a
field line
R44
how to find the direction of the vector field using a field line
R44
field line diagrams are 3 dimensional
R44
drawing showing the field lines near a positive point charge
R44
how to find the comparative strength of the vector field using the density of field lines
R44
why we usually draw field line diagrams in only 2 dimensions
R44
limitations of the 2-dimensional field line diagram
R44
3.13 Interpreting field line diagrams
R44,45
an example using a pair of point charges
R44,45
description of the field line diagram
R44
analysis of the field line diagram
R44,45
actual charge distribution used in this example
R45
3.14 Reasoning with field line diagrams
R45
3 conclusions that can be reached through reasoning
R45
- Field lines do not cross each other
R45
- Field lines are not the paths of objects
R45
- The field is not strongest near field lines
R45
4. REASONING AND SOLVING PROBLEMS USING PHYSICAL LAWS
R46-53
a list of the useful concepts, principles, and models presented so far
R46
4.1. Reasoning with Newton's laws
R46-48
how this part of the Reader will be different from earlier parts involving forces
R46
an example involving Newton's 2nd and 3rd laws, as well as momentum conservation
R47
an example involving our model of materials
R47
an example showing how diagrams can be useful
R48
4.2. Solving problems using Newton's laws
R48,49
an example involving the magnetic interaction
R48,49
4.3. Reasoning with energy ideas
R49-51
table showing the major energy principles, with related concepts and their definitions
R49
an example involving the Work-Energy Theorem
R50
an example involving the Work-Kinetic Energy Theorem
R50
4.4. Solving problems using energy ideas
R51-53
the procedure for determining potential energy
R51
some common reference points
R51
finding the potential energy stored in the field of two point charges
R51
choosing the reference point for two point charges
R51
mathematical expression for the potential energy for two point charges
R51
mathematical expression for the potential energy for two point masses
R52
an example showing how to apply gravitational and electric potential energy
R52,53
5 common steps needed to solve problems using energy ideas
R53