Physics Workbook For Dummies

Physics Workbook For Dummies
by Steven Holzner, PhD
Contents at a Glance
Introduction .1
Part I : Applying Physics .5
Chapter 1: Getting Started with Physics 7
Chapter 2: The Big Three: Acceleration, Distance, and Time 25
Chapter 3: Vectors: Knowing Where You’re Headed .41
Part II: May the Forces Be with You .59
Chapter 4: Applying Force 61
Chapter 5: Working with Inclined Planes .81
Chapter 6: Round and Round: Circular Motion .101
Part III: Being Energetic: Work 121
Chapter 7: Working the Physics Way 123
Chapter 8: Getting Things to Move: Momentum and Kinetic Energy .143
Chapter 9: Winding It Up: Rotational Kinematics 161
Chapter 10: Getting Dizzy with Rotational Dynamics .177
Chapter 11: Potential and Kinetic Energy Together: Simple Harmonic Motion 195
Part IV: Obeying the Laws of Thermodynamics 215
Chapter 12: You’re Getting Warm: Thermodynamics .217
Chapter 13: Under Pressure: From Solid to Liquid to Gas .233
Chapter 14: All about Heat and Work .249
Part V: Zap: Electricity and Magnetism .269
Chapter 15: Static Electricity: Electrons at Rest 271
Chapter 16: Electrons in Motion: Circuits 289
Part VI: The Part of Tens 307
Chapter 17: Ten Common Mistakes People Make When Solving Problems .309
Chapter 18: Ten Top Online Physics Tutorials and Resources .313
Index .315Table of Contents
Introduction .1
About This Book 1
Conventions Used in This Book 1
Foolish Assumptions 1
How This Book Is Organized 2
Part I: Applying Physics 2
Part II: May the Forces Be with You 2
Part III: Being Energetic: Work .2
Part IV: Obeying the Laws of Thermodynamics 2
Part V: Zap: Electricity and Magnetism 2
Part VI: The Part of Tens 3
Icons Used in This Book .3
Where to Go from Here .3
Part I: Applying Physics .5
Chapter 1: Getting Started with Physics .7
Measuring the Universe .7
Putting Scientific Notation to Work 10
Converting between Units .12
Converting Distances .14
Converting Times 16
Counting Significant Figures 17
Coming Prepared with Some Algebra .18
Being Prepared with Trigonometry 20
Answers to Problems about Getting Started with Physics 22
Chapter 2: The Big Three: Acceleration, Distance, and Time .25
From Point A to B: Displacement 25
Reading That Speedometer .27
Putting Pedal to Metal: Acceleration 28
Connecting Acceleration, Time, and Displacement 31
Connecting Speed, Acceleration, and Displacement 34
Answers to Problems about Acceleration, Distance, and Time 36
Chapter 3: Vectors: Knowing Where You’re Headed .41
Creating a Vector .41
Understanding Vector Components .43
Finding a Vector’s Components .45
Finding a Vector’s Magnitude and Direction 47
Adding Vectors Together .49
Handling Motion As a Vector .53
Answers to Problems about Vectors 55
Part II: May the Forces Be with You 59
Chapter 4: Applying Force 61
Newton’s First Law of Motion 61
Newton’s Second Law of Motion .62
Force Is a Vector 65
Calculating Net Force and Acceleration .67
Sorting Out Weight and Mass 69
Newton’s Third Law of Motion 72
Answers to Problems about Force 74
Chapter 5: Working with Inclined Planes .81
Breaking Ramps Up into Vectors .81
Acceleration and Inclined Planes 84
Running Down Ramps: Speed 85
It’s a Drag: The Coefficient of Friction 87
Starting from zero: Static friction 88
Already in motion: Kinetic friction 89
Static Friction along Ramps .90
Kinetic Friction along Ramps 92
Acceleration along Ramps Including Friction .94
Answers to Problems about Inclined Planes .96
Chapter 6: Round and Round: Circular Motion .101
Converting between Angles .101
Period and Frequency 103
Getting into Angular Velocity .104
Whipping Around with Angular Acceleration .107
Connecting Angular Velocity and Angular Acceleration to Angles .109
Connecting Angular Acceleration and Angle to Angular Velocity 111
Handling Centripetal Acceleration 112
Getting Forceful: Centripetal Force .114
Answers to Problems about Circular Motion 116
Part III: Being Energetic: Work .121
Chapter 7: Working the Physics Way .123
A Different Kind of Work .123
Dealing with the Net Force .126
Getting Energetic: Kinetic Energy .127
Getting Kinetic Energy from Work 129
Storing Your Energy: Potential Energy .131
Powering It Up .133
Answers to Problems about Work 135
Chapter 8: Getting Things to Move: Momentum and Kinetic Energy .143
Acting on Impulse .143
Getting Some Momentum .145
Relating Impulse and Momentum .146
Conserving Momentum 148
Conserving Kinetic Energy — or Not 149
Collisions in Two Dimensions .151
Answers to Problems about Momentum and Kinetic Energy 154
viii Physics Workbook For DummiesChapter 9: Winding It Up: Rotational Kinematics 161
Finding Tangential Speed .161
Targeting Tangential Acceleration 164
Angular Velocity as a Vector 165
Angular Acceleration as a Vector 166
Doing the Twist: Torque .168
The Balancing Act: Rotational Equilibrium .170
Answers to Problems about Rotational Kinematics .173
Chapter 10: Getting Dizzy with Rotational Dynamics 177
Putting Newton on Wheels .177
Moments of Inertia for Everyone 179
Doing Some Rotational Work .182
Round and Round: Rotational Kinetic Energy .183
Getting Working with Ramps Again 185
Can’t Stop This: Angular Momentum .187
Answers to Problems about Rotational Dynamics .189
Chapter 11: Potential and Kinetic Energy Together: Simple Harmonic Motion .195
Hooking into Hooke’s Law 195
Simply Simple Harmonic Motion .197
Getting Periodic .199
Considering Velocity .201
Figuring the Acceleration .203
Bouncing Around with Springs 204
Talking about Energy 206
Following the Ticktock of Pendulums 207
Answers to Problems about Simple Harmonic Motion 209
Part IV: Obeying the Laws of Thermodynamics .215
Chapter 12: You’re Getting Warm: Thermodynamics 217
Converting Between Temperature Scales 217
Getting Bigger: Linear Expansion 219
Plumping It Up: Volume Expansion .221
Getting Specific with Heat Capacity .223
Changes of Phase: Latent Heat 226
Answers to Problems about Thermodynamics .228
Chapter 13: Under Pressure: From Solid to Liquid to Gas 233
How Heat Travels: Convection 233
How Heat Travels: Conduction 234
How Heat Travels: Radiation .237
A Biggie: Avogadro’s Number 239
Ideally Speaking: The Ideal Gas Law .241
Molecules in Motion .243
Answers to Problems about Pressure 244
Chapter 14: All about Heat and Work .249
The First Law of Thermodynamics .249
Constant Pressure: Isobaric Processes 250
Constant Volume: Isochoric Processes 253
Constant Temperature: Isothermal Processes 254
At Constant Heat: Adiabatic 256
Table of Contents ixHeat Moves: The Second Law of Thermodynamics 259
Making Heat Work: Heat Engines 259
Maximum Efficiency: Carnot Heat Engines 262
The Third Law of Thermodynamics .263
Answers to Problems about Heat and Work 264
Part V: Zap: Electricity and Magnetism .269
Chapter 15: Static Electricity: Electrons at Rest 271
Talking about Electric Charges 271
Getting Forceful with Charges .272
Electrical Forces Are Vectors 274
Force at a Distance: Electric Fields .275
Easy Electric Field: Parallel Plate Capacitors 277
Ramping Up Some Voltage .279
Electric Potential from Point Charges 281
Answers to Problems about Static Electricity .283
Chapter 16: Electrons in Motion: Circuits .289
Electrons in a Whirl: Current .289
Giving You Some Resistance: Ohm’s Law .290
Powering It Up .292
One after the Other: Series Circuits 293
All for One: Parallel Circuits 295
The Whole Story: Kirchhoff’s Rules 297
Answers to Problems about Circuits 300
Part VI: The Part of Tens 307
Chapter 17: Ten Common Mistakes People Make When Solving Problems 309
Mixing Units .309
Expressing the Answer in the Wrong Units .309
Swapping Radians and Degrees .309
Getting Sines and Cosines Mixed Up 310
Not Treating Vectors as Vectors 310
Neglecting Latent Heat .310
Getting Refraction Angles Wrong 310
Getting the Signs Wrong in Kirchhoff Loops 311
Adding Resistors Incorrectly .311
Using the Wrong Rays in Ray Diagrams .312
Chapter 18: Ten Top Online Physics Tutorials and Resources 313
The Physics Classroom 313
ThinkQuest 313
HyperPhysics .313
Roman Goc’s Physics Tutorial .313
Physics 24/7 Tutorial 314
University of Guelph’s Tutorial .314
Tutor4Physics 314
Kenneth R. Koehler’s Tutorial Page 314
Fear of Physics’s Problem Solver 314
Vector Resolver .314
Index .315
x Physics Workbook For Dummies
Symbols
α (angular acceleration), 107
β (coefficient of volume expansion), 221
δ (Stefan-Boltzman constant), 238
ε (permittivity of free space), 272
ω (angular velocity), 105
τ (torque), 145
Ω (ohms), 290
• A •
a (linear acceleration), 107
absolute zero
definition, 217
reaching, 263
acceleration
calculating, 67–69
description, 28–30
harmonic motion, springs, 203–204
inclined planes, 84–85, 94–95
relating to displacement, 31–35
relating to speed, 34–35
tangential, 164–165
adiabatic processes, 256–258
adiabats, 256
algebra, 18–20
Ampere (A), 8, 289–290
angles
angular acceleration, 109–111
angular velocity, 109–111
converting between, 101–102
angular acceleration (α), circular motion
angles, 109–111
circular motion, 111
description, 107–108
unit of measure, 107
angular acceleration (α), rotational kinematics, 166–167
angular frequency, harmonic motion,
199–201
angular momentum (L), 187–188
angular speed, harmonic motion, 200
angular velocity, circular motion
angles, 109–111
description, 104–106
angular velocity, rotational kinematics,
165–166
atoms per mole, calculating. See Avogadro’s
Number
Avogadro’s Number (N)
calculating atoms per mole, 239–241
definition, 239
and the ideal gas law, 241
• B •
barye (ba), 8
biot (Bi), 8
Boltzmann’s constant (k), 241
Btu (British Thermal Unit), 223
• C •
C (Coulomb), 8, 271–272
Calorie (C), 223
calories versus Calories, 223
Carnot engines, 262
Celsius (C) scale, 217–218
centigrade scale. See Celsius (C) scale
centimeter (cm), 7
centripetal acceleration, 112–113
centripetal force, 114–115
CGS (centimeter-gram-second) system
conversions, 12–14
description, 7–9
force, measuring, 62
torque, measuring, 168
units of measure, 7–8, 62
work, measuring, 123–125
charge density, 277
circuits. See electric circuits
circular motion. See also frequency;
period (T)
centripetal acceleration, 112–113
centripetal force, 114–115
frequency, 103–104
period, 103–104
circular motion, angles
angular acceleration, 111
angular velocity, 111
degree/radian conversion, 101–102
Indexcircular motion, angular acceleration
angles, 109–111
description, 107–108
unit of measure, 107
circular motion, angular velocity
angles, 109–111
description, 104–106
cm (centimeter), 7
coefficient of friction
definition, 87
description, 87–88
kinetic, 88–89
static, 88–89
coefficient of volume expansion (β), 221
collisions. See also kinetic energy
elastic, 149–150
two-dimensional, 151–163
common mistakes
degree/radian conversion, 309
Kirchhoff’s laws, 311
latent heat, 310
loop rule, 311
normal line, 310
radian/degree conversion, 309
ray diagrams, 312
refraction angles, 310
resistors, 311
sine/cosine mixups, 310
units of measure, 309
vectors, 310
conduction, 234–237
conservation of
energy, 249–250
kinetic energy, 149–150
momentum, 148–150
convection, 233–234
conversions
Btus to Joules, 223
CGS (centimeter-gram-second) system,
12–14
degrees/radians, 101–102
distance units, 14–15
FPI (foot-pound-inch) system, 12–14
measurement systems, 12–14
MKS (meter-kilogram-second)
system, 12–14
time units, 16
vector specification methods, 45–46
coordinate system for vectors, 42–43
Coulomb (C), 8, 271–272
current (I), 7–9, 289–290
• D •
deceleration, 29
degree/radian conversion, 101–102, 309
diameter (d), 103
direction. See vectors, direction
displacement
description, 25–26
relating to acceleration, 31–35
relating to time, 31–33
distance. See displacement
distance units, conversions, 14–15
drag, inclined planes. See inclined planes,
friction
dyne, 7
• E •
elastic collisions, 149–150, 241
electric charge
Coulomb (C), 271–272
negative, 271
positive, 271
unit of measure, 7–9
electric circuits
ampere (A), 289–290
current (I), 7–9, 289–290
junction rule, 298
Kirchhoff’s laws, 297–299, 311
loop rule, 298, 311
ohms (ω), 290
Ohm’s Law, 290–292
parallel, 295–297
resistance (R), 290–292
series, 293–295
electric circuits, resistors
common mistakes, 311
heat production, 292–293
in parallel, 296
in series, 294
electric fields. See also electric circuits
charge density, 277
description, 275–276
parallel plate capacitors, 277–278
point charges, 275, 281–282
voltage, 279–282
electric forces
description, 272–273
permittivity of free space, 272
as vectors, 274–275
electric potential. See voltage
316 Physics Workbook For Dummiesemissivity, 238
energy
conservation of, 249–250
potential, 131–132, 206–207. See also kinetic
energy
units of measure, 7–9
equilibrium, 72–73, 170–172
erg, 8, 123–125
• F •
Fahrenheit (F) scale, 217–218
Fear of Physics’s Problem Solver, 314
first law of thermodynamics, 249–250
foot-pound. See also FPI (foot-pound-inch)
system
torque unit, 168
work unit, 124
force. See also Newton’s Three Laws of
Motion; torque (τ)
acceleration, calculating, 67–69
equilibrium, 72–73
of gravity, 69–72
inertia, 61
mass versus weight, 69–72
net, calculating, 67–69, 126–127
units of measure, 7–9, 62
as a vector, 65–67
work, measuring, 126–127
FPI (foot-pound-inch) system
conversions, 12–14
description, 7
torque, measuring, 168
FPS (foot-pound-second) system
force, measuring, 62
mass, unit of measure, 61
slugs, 61
work, measuring, 124–125
franklin (Fr), 8
frequency
circular motion, 103–104
harmonic motion, 199–201
unit of measure, 200
friction, inclined planes. See inclined planes,
friction
• G •
gases
Boltzmann’s constant (k), 241
elastic collisions, 241
ideal, 241
ideal gas law, 241–242
kinetic energy of molecules, 243
universal gas constant (R), 241
gases, thermodynamic processes
adiabatic, 256–258
adiabats, 256
constant heat, 256–258
constant pressure, 250–252
constant temperature, 254–255
constant volume, 253–254
isobaric, 250–252
isochoric, 253–254
isothermal, 254–255
isotherms, 256
gauss (G), 8
gram (g), 7, 61
graphing vectors, 42–43
gravity (g)
force of, on inclined planes, 82–83
mass versus weight, 69–72
• H •
harmonic motion (springs)
acceleration, 203–204
angular frequency, 199–201
angular speed, 200
example, 197–199
frequency, 199–201
Hooke’s constant, 195, 204–206
Hooke’s Law, 195–197
pendulums, 207–208
period, 199–201, 204–206
potential energy, 206–207
spring constant, 195, 204–206
velocity, 201–202
heat. See thermodynamics
heat engines, 259–261
Hertz (Hz), 200
Hooke’s constant, 195, 204–206
Hooke’s Law, 195–197
HyperPhysics, 313
hypotenuse, 20
• I •
I (current), 7–9, 289–290
ideal gas, 241
ideal gas law, 241–242
impulse. See kinetic energy, impulse
Index 317inclined planes
acceleration, 84–85
breaking into vectors, 81–83
definition, 81
normal force, 82
rotational dynamics, 185–187
work, measuring, 126–127
inclined planes, friction
acceleration, 94–95
coefficient of, 87–88
kinetic, 89–90, 92–93
kinetic coefficient of, 88–89
static, 90–92
static coefficient of, 88–89
inclined planes, sliding objects
acceleration, 94–95
coefficient of friction, 87–88
kinetic coefficient of friction, 88–89
kinetic friction, 89–90, 92–93
speed of, 85–86
static coefficient of friction, 88–89
static friction, 90–92
inertia, 61
isobaric processes, 250–252
isochoric processes, 253–254
isothermal processes, 254–255
isotherms, 256
• J •
Joules (J)
converting to Btus, 223
measuring work, 123–125
unit of measure, 8
junction rule, 298
• K •
k (Boltzmann’s constant), 241
Kelvin (K) scale, 217–218
Kenneth R. Koehler’s Tutorial Page, 314
kilogram (kg), 8, 61
kilogram meters2 (kg-m2), 178
kilogram-meters/second (kg-m/sec), 145
kinetic coefficient of friction, 88–89
kinetic energy. See also potential energy;
work
conserving, 149–150
description, 127–130
elastic collisions, 149–150
of molecules, 243
rotational dynamics, 183–184
two-dimensional collisions, 151–163
kinetic energy, impulse
definition, 143
description, 144–145
momentum, 146–147
unit of measure, 143
kinetic energy, momentum
conserving, 148–150
definition, 145
impulse, 146–147
unit of measure, 145
kinetic friction, 89–90, 92–93
Kirchhoff’s laws, 297–299, 311
• L •
L (angular momentum), 187–188
latent heat, 226–227, 310
Laws of Motion. See Newton’s Three Laws of
Motion
length, units of measure, 7–9
linear acceleration (a), 107
linear expansion, 219–221
liquid-to-gas change, 226–227
loop rule, 298, 311
• M •
magnetism, units of measure, 7–9
mass
definition, 61
units of measure, 7–9, 61
versus weight, 69–72
measurement units. See units of measure
meter (m), 8
MKS (meter-kilogram-second) system
conversions, 12–14
description, 7–9
force, measuring, 62
moment of inertia, measuring, 178
momentum, measuring, 145
torque, measuring, 168
units of measure, 8, 62
work, measuring, 123–125
mole, 239
moment of inertia, 178–181
momentum (p). See also kinetic energy,
momentum
angular momentum (L), 187–188
conservation of, 148–150
318 Physics Workbook For Dummieskinetic energy, impulse, 146–147
measuring, 145
motion as vector, 53–54
• N •
N (Avogadro’s Number)
calculating atoms per mole, 239–241
definition, 239
and the ideal gas law, 241
negative electric charge, 271
net force, calculating, 67–69, 126–127. See
also force
Newton (N), 8
Newton’s Three Laws of Motion. See also
force
First Law, 61–62
Second Law, 62–65
Third Law, 72–73
Newton-second, 143–144
normal force, 82
normal line, 310
numbers
rounding, 17–18
scientific notation, 10–11
significant figures, 17–18
• O •
ohms (Ω), 290
Ohm’s Law, 290–292
online resources, 313–314
origins of vectors, 42
• P •
p (momentum). See momentum (p)
parallel circuits, 295–297
parallel plate capacitors, 277–278
Pascal (P), 8
pendulums, 207–208
period (T)
circular motion, 103–104
harmonic motion, 199–201, 204–206
permittivity of free space (ε), 272
phase changes, 226–227
physical work. See work
The Physics Classroom, 313
Physics 24/7 Tutorial, 314
point charges, 275, 281–282
positive electric charge, 271
potential energy, 131–132, 206–207. See also
kinetic energy
power, 133–134
pressure, units of measure, 7–9
• R •
R (universal gas constant), 241
radian/degree conversion, 101–102, 309
radiation, 237–239
radius (r), 103
ramps. See inclined planes
ray diagrams, 312
refraction angles, 310
resistance (R), 290–292
resistors
common mistakes, 311
heat production, 292–293
in parallel, 296
in series, 294
resources, online, 313–314
right triangles, 20–21
Roman Goc’s Physics Tutorial, 313
rotational dynamics. See also torque (τ)
angular momentum, 187–188
inclined planes, 185–187
kinetic energy, 183–184
moment of inertia, 178–181
work, 182–183
rotational kinematics
angular acceleration, as a vector, 166–167
angular velocity, as a vector, 165–166
equilibrium, 170–172
tangential acceleration, 164–165
tangential speed, 161–163
torque, 168–170
rounding numbers, 17–18
• S •
scalar equations, 53
scalar values, 145
scientific notation, 10–11
second (s), 7, 8
second law of thermodynamics, 259
series circuits, 293–295
significant figures, 17–18
sine/cosine mixups, 310
slug, 61
solid-to-gas change, 226–227
solid-to-liquid change, 226–227
Index 319specific heat capacity, 223–226
speed. See also acceleration; velocity
description, 27–28
on inclined planes, 85–86
relating to acceleration, 34–35
tangential, 161–163
spring constant, 195, 204–206
spring motion. See harmonic motion
(springs)
static coefficient of friction, 88–89
static friction, 90–92
Stefan-Boltzman constant (δ), 238
storing energy. See potential energy
• T •
T (period)
circular motion, 103–104
harmonic motion, 199–201, 204–206
tangential acceleration, 164–165
tangential speed, 161–163
temperature scales, converting, 217–218
Tesla (T), 8
thermal expansion, 219–223
thermodynamics. See also gases, thermodynamic processes
absolute zero, definition, 217
absolute zero, reaching, 263
Btu (British Thermal Unit), 223
calories versus Calories, 223
Celsius (C) scale, 217–218
coefficient of volume expansion, 221
conservation of energy, 249–250
definition, 217–218
Fahrenheit (F) scale, 217–218
first law, 249–250
Kelvin (K) scale, 217–218
latent heat, 226–227, 310
linear expansion, 219–221
liquid-to-gas change, 226–227
phase changes, 226–227
second law, 259
solid-to-gas change, 226–227
solid-to-liquid change, 226–227
specific heat capacity, 223–226
temperature scales, converting, 217–218
thermal expansion, 219–223
third law, 263
volume expansion, 221–223
thermodynamics, heat transfer
Carnot engines, 262
conduction, 234–237
convection, 233–234
direction of flow, 259
emissivity, 238
heat engines, 259–261
maximum efficiency, 262
radiation, 237–239
Stefan-Boltzman constant (δ), 238
ThinkQuest, 313
third law of thermodynamics, 263
time
relating to displacement, 31–33
unit conversion, 16
unit of measure, 7–9
torque (τ). See also force; rotational
dynamics
definition, 168
rotational kinematics, 168–170
unit of measure, 168
trigonometry, 20–21
Tutor4Physics, 314
tutorials, 313–314
two-dimensional collisions, 151–163
• U •
units of measure. See also CGS
(centimeter-gram-second) system;
FPI (foot-pound-inch) system;
FPS (foot-pound-second) system;
MKS (meter-kilogram-second) system
angular acceleration, 107
common mistakes, 309
force, 62
frequency, 200
Hertz (Hz), 200
impulse, 143
kilogram-meters/second (kg-m/sec), 145
moment of inertia, 178
momentum, 145
Newton-second, 143–144
torque, 168
work, 123–125
units of measure, conversions
distance, 14–15
multiple, 14–15
between systems, 12–14
time, 16
universal gas constant (R), 241
University of Guelph’s Tutorial, 314
320 Physics Workbook For Dummies• V •
Vector Resolver, 314
vectors
adding, 49–52
angular acceleration as, 166–167
angular velocity as, 165–166
breaking inclined planes into, 81–83
common mistakes, 310
components, 43–46
coordinate system for, 42–43
definition, 41
force as, 65–67
graphing, 42–43
motion as, 53–54
origins, 42
vectors, direction
converting to coordinate system, 45–46
definition, 41
finding, 47–49
specifying a vector, 41–43
vectors, magnitude
converting to coordinate system, 45–46
definition, 41
finding, 47–49
specifying a vector, 41–43
vectors, specifying
converting between methods, 45–46
coordinates from the origin, 43–46
magnitude and direction, 43–46
velocity, 201–202. See also speed
voltage, 279–282
volume expansion, 221–223
• W •
weight
definition, 61
versus mass, 69–72
work. See also kinetic energy; potential
energy; power
definition, 123
measuring, 123–125
potential energy, 131–132
power, 133–134
rotational dynamics, 182–183
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