Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

1326 Pages·2016·40.63 MB·english

by  Randall D. Knight

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Knight_04_1292157429_Final.indd 1 16/07/16 10:43 AM
Useful Data
Me Mass of the earth 5.98*1024 kg
Re Radius of the earth 6.37*106 m
g Free-fall acceleration on earth 9.80 m/s2
G Gravitational constant 6.67*10-11 N m2/kg2
kB Boltzmann’s constant 1.38*10-23 J/K
R Gas constant 8.31 J/mol K
NA Avogadro’s number 6.02*1023 particles/mol
T0 Absolute zero -273°C
s Stefan-Boltzmann constant 5.67*10-8 W/m2 K4
p Standard atmosphere 101,300 Pa
atm
v Speed of sound in air at 20°C 343 m/s
sound
mp Mass of the proton (and the neutron) 1.67*10-27 kg
me Mass of the electron 9.11*10-31 kg
K Coulomb’s law constant (1/4pP0) 8.99*109 N m2/C2
P0 Permittivity constant 8.85*10-12 C2/N m2
m0 Permeability constant 1.26*10-6 T m/A
e Fundamental unit of charge 1.60*10-19 C
c Speed of light in vacuum 3.00*108 m/s
h Planck’s constant 6.63*10-34 J s 4.14*10-15 eV s

U Planck’s constant 1.05*10-34 J s 6.58*10-16 eV s

aB Bohr radius 5.29*10-11 m
Common Prefixes Conversion Factors
Prefix Meaning Length Time
femto- 10-15 1 in = 2.54 cm 1 day = 86,400 s
pico- 10-12 1 mi = 1.609 km 1 year =3.16*107 s
nano- 10-9 1 m = 39.37 in Pressure
micro- 10-6 1 km = 0.621 mi 1 atm = 101.3 kPa = 760 mm of Hg
milli- 10-3 Velocity 1 atm =14.7 lb/in2
centi- 10-2 1 mph = 0.447 m/s Rotation
kilo- 103 1 m/s = 2.24 mph = 3.28 ft/s 1 rad =180°/p=57.3°
mega- 106 Mass and energy 1 rev =360°=2p rad
giga- 109 1 u = 1.661 *10-27 kg 1 rev/s =60 rpm
terra- 1012 1 cal = 4.19 J
1 eV =1.60*10-19 J
Mathematical Approximations
Binominal approximation: (1+x)n ≈1+nx if xV 1
Small-angle approximation: sin u ≈tan u≈u and cos u≈1 if uV 1 radian
Greek Letters Used in Physics
Alpha a Mu m
Beta b Pi p
Gamma Γ g Rho r
Delta ∆ d Sigma g s
Epsilon P Tau t
Eta h Phi Φ f
Theta ϴ u Psi c
Lambda l Omega Ω v
A00_KNIG7429_04_GE_FEP.indd 1 15/07/16 9:44 pm
Problem-Solving Strategies and Model Boxes
PROBLEM-SOLVING STRATEGY PAGE MODEL PAGE
1.1 Motion diagrams 35 2.1 Uniform motion 57
1.2 General problem-solving strategy 43 2.2 Constant acceleration 68
2.1 Kinematics with constant 4.1 Projectile motion 110
acceleration 69 4.2 Uniform circular motion 119
4.1 Projectile motion problems 110 4.3 Constant angular acceleration 121
6.1 Newtonian mechanics 156 5.1 Ball-and-spring model of solids 136
7.1 Interacting-objects problems 189 6.1 Mechanical equilibrium 154
8.1 Circular-motion problems 217 6.2 Constant force 158
10.1 Energy-conservation problems 265 6.3 Friction 164
11.1 Conservation of momentum 292 8.1 Central force with constant r 208
12.1 Rotational dynamics problems 331 9.1 Basic energy model 231
17.1 Interference of two waves 498 11.1 Collisions 299
19.1 Work in ideal-gas processes 542 12.1 Rigid-body model 317
19.2 Calorimetry problems 552 12.2 Constant torque 332
21.1 Heat-engine problems 601 12.3 Static equilibrium 333
22.1 Electrostatic forces and 14.1 Molecular model of gases and liquids 380
Coulomb’s law 636
14.2 Ideal fluid 395
23.1 The electric field of multiple point
15.1 Simple harmonic motion 428
charges 653
16.1 The wave model 460
23.2 The electric field of a continuous
18.1 Solids, liquids, and gases 513
distribution of charge 659
19.1 Thermodynamic energy model 546
24.1 Gauss’s law 695
22.1 Charge model 626, 628
25.1 Conservation of energy in charge
22.2 Electric field 640
interactions 719
23.1 Four key electric fields 652
25.2 The electric potential of a
continuous distribution of charge 727 26.1 Charge escalator model of a battery 745
28.1 Resistor circuits 802 29.1 Three key magnetic fields 824
29.1 The magnetic field of a current 825 33.1 Wave model of light 971
30.1 Electromagnetic induction 871 34.1 Ray model of light 983
36.1 Relativity 1066 38.1 Photon model of light 1115
40.1 Quantum-mechanics problems 1168 38.2 The Bohr model of the atom 1122
A00_KNIG7429_04_GE_FEP.indd 2 19/07/16 10:07 am
ph y s ic s

for scientists and engineers a strategic approach
fourth edition
with modern physics
global edition
.
randall d knight
California Polytechnic State University
San Luis Obispo
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Authorized adaptation from the United States edition, entitled Physics for Scientists and Engineers: A
Strategic Approach with Modern Physics,4/e, ISBN 978-0-13-394265-1, by Randall D. Knight published
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A catalogue record for this book is available from the British Library
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ISBN 10: 1-292-15742-9
ISBN 13: 978-1-292-15742-9
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About the Author
Randy Knight taught introductory physics for 32 years at Ohio State University
and California Polytechnic State University, where he is Professor Emeritus of
Physics. Professor Knight received a Ph.D. in physics from the University of
California, Berkeley and was a post-doctoral fellow at the Harvard-Smithsonian
Center for Astrophysics before joining the faculty at Ohio State University. It was at
Ohio State that he began to learn about the research in physics education that,
many years later, led to Five Easy Lessons: Strategies for Successful Physics
Teaching and this book, as well as College Physics: A Strategic Approach, co-
authored with Brian Jones and Stuart Field. Professor Knight’s research interests
are in the fields of laser spectroscopy and environmental science. When he’s not
in front of a computer, you can find Randy hiking, sea kayaking, playing the piano,
or spending time with his wife Sally and their five cats.
A01_KNIG7429_04_GE_FM.indd 3 18/07/16 2:52 pm
9.1 Energy Overview 207
Energy Overview
9.1
Energy. It’s a word you hear all the time, and everyone has some sense of what energy
means. Moving objects have energy; energy is the ability to make things happen;
energy is associated with heat and with electricity; we’re constantly told to conserve
energy; living organisms need energy; and engineers harness energy to do useful
things. Some scientists consider the law of conservation of energy to be the most
important of all the laws of nature. But all that in due time—first we have to start
with the basic ideas.
Just what is energy? The concept of energy has grown and changed with time, and
it is not easy to define in a general way just what energy is. Rather than starting with
a formal definition, we’re going to let the concept of energy expand slowly over the
course of several chapters. Our goal is to understand the characteristics of energy,
how energy is used, and how energy is transformed from one form into another. It’s a
complex story, so we’ll take it step by step until all the pieces are in place.
Some important forms of energy
Kinetic energy K Potential energy U Thermal energy E
th
46 CHAPTER 2 Kinematics in One Dimension
A research-driven approach,
Built from the ground up on physics education research and
crafted using key ideas from lear1n42 iCnHAgPT ERt 6h Dyenamoics rI: Myo,ti onK Alonng ai gLinhe t has set the
fine-tuned for even greater Exercises and Problems 259
standard for eff ective and accessible pedagogical materials in
Kinetic energy is the energy of motion. Potential energy is stored energy associated Thermal energy is the sum of the micro-
All moving objects have kinetic energy. with an object’s position. The roller coaster’s scopic kinetic and po5t5e.n t||i|a l Pernoetrogniess and neutrons (together called nucleons) are held 61. || The potential energy for a particle that can move along the
The more massive an object or the faster gravitational potential energy depends on of all ethe ataomss ande bontdo-sg ethtohaet rm inafk teh- eu pn uucleuss ofe an a toma byn a fordce ca llesd thte sturong dexn-axis tis U =sAx2u+B scin pcx/Le, whsere As, B, and L are constants. physics. In this fourth edition, Knight continues to refi ne and
it moves, the larger its kinetic energy. its height above the ground. the object. An object has more thermal
force. At very small separations, the strong force between two What is the force on the particle at (a) x=0, (b) x=L/2, and (c)
energy when hot than wnhuecnl ecoonlds .is larger than the repulsive electrical force between two x=L? 1 2 expand the instructional techniques to take students further.
protons—hence its name. But the strong force quickly weakens 62. || A particle that can move along the x-axis experiences an
as the distance between the protons increases. A well-established interaction force Fx= 3x2-5x N, where x is in m. Find an
model for the potential energy of two nucleons interacting via the expression for the system’s potential energy.
The Energy Principle strong force is 63. || An object moving i1n the xy-p2lane is subjected to the force
Fu= 2xy ni +x2 nj N, where x and y are in m.
❮❮ Section 7.1 introduced interaction diagrams and the very important distinction REVISED COVERUA=UG0 E1- Ae-xN/x0 D ORGANIZATIONa. TGhe IpaVrtiEcle mINoveSs frTomR thUe oCrigiTn tOo thRe pSoi nt with coordinates NEW AND UPDATED LEARNING TOOLS PROMOTE DEEPER AND
between the system, those objects whose motion and interactions we wish to a1, b by mov2ing first along the x-axis to a, 0 , then parallel
analyze, and the environment, objects external to the system but exerting forces where x is the dGistaRncEe bAetT3weEenR th eC 4ceHnteOrs oIf CtheE t wAo nNuclDe- FLEXIBILITY BETTER-CONNECTED UNDERSTANDING
osyns ttehme .s yWsthemy?. BTehcea musoes te nimerpgoyr tiasn nt ostt espo mine a dni seenmerbgoyd aienda,l yesthise rise atol sculebastralyn cdee;f iint’es tthhee oUn0s ,= x60 . 0is* a 1c0o-n11s tJa.nt having the value x0 =2.0*10-15 m, and b. tT1oah ,te hb pe2 a ybr-tyaic xmlieso .m vHionovgwe sf mifrrsuotcm ah l towhneog ro ktrh idgeoi nye -stao tx htihese ft oporo c1ien0 t,d wbo2?it, ht hceono rpdainraaltleesl
Quantum effects are essential for a proper understand-
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theB eunte rsgyyst eomf tsh oe fsteynst edmo ,i neittehrearc ti nwcirteha stihnegir i te n(evnierorgnym aedndt.e Td)h oosr ed einctreeraascitnigon ist (cehnaenrggye ETnheregrmy caaln be trCanh Isenfmoitriimcaalelldy the block is1 at rest at2 x=0 m. What is the block’s spee-2d 65.- 2Wc. riI1tse tah ir2se aal icsotincs perrovbatleivme ffoorr cwe?hich the energ1y ba2r chart shown in wniozrek wedh eenx aamndp lheos,w h etolp uinseg rsetucuderrnitnsg t om roedceolgs-, a acceleration changes. ■■    KRoinlleitnigc ffrriiccttiioonn:: OOppppoosseess mmooTtthiieoo nnsl owwpEeiix tteihhsrc vissffe.kr 1==6mmrk n n.. Mto othtieo nsu irsf areclea.tive
when it has been pulled to x=4.0 m? ■  Graphically:
removed). We say that interactions with the environment transfer energy into or Heat 57. || A syWstoermk has potential energy FIGURE P10.65 correctly shows the energy at the beginning and end key critical-thinking skill.
out of the system. Interestingly, there are only two ways to transfer energy. One is Energy removed of the problem.
by mechanical means, using forces to push and pull on the system. A process that Environment U x =x+1Nsie1nw.t6on2 ’s ar saeddco/vmnad lnxawc Fue=dm aut aopppliiecs t oR obojeccts kwehotse Ip mnPr oaPrsbsrol odeobmpelse.u mnFolosst r ci6 hoe6aan ncgtheh .r Toohfu agtth’hse 6se8, yyoouu aarree gtoiven the equation used to solve a fs max = mmksnnf Static KiTfnrheicteti icoobnj erceta cshliepss fws mhaexn. static
as a particle move1s 2over thea rna enx1cg1eell e0n tm ass…um2xpt2…ionp fo rm ba.lls and bicycles, but what abao.u t Wsomriettehi nag r leikael ias rtoicck eptr oblem for which this is the correct equation. Sintcarteica sferisc ttoio mnatch Kasi ntheeti co bfrjeicctti omno ivse cso.nstant
a. Where are the equilibriutmhmaast spl oaosrseeis st oiaol vsneigdsn wiifniitc hta hmntio sam mreaonnutungmte o? rfa tmhears sth aasn iatcs cfeuleerl aitsio bnu. brWn.e ed’lD?l lProaroowkb al ett mhones e ob ifme vfpaoorrryteian-ngat nd-after pictorial representation. the push or pull. 0 Rest Moving Push or pull force
b. For each, is it a point of esxtaambplele .or unstable equilibrium? c. Finish the solution of the problem. 6 Dynamics I: Motion
NEW! ADV58A. N|w| iCtAh E ppDoatre tnictilea l tehnaet rcgayn moveiwn eafalFluIkoGe inUnncRg ceE o dt1m 1hb.py2ea 9 g rxrsiash-ovaoniwxt ytsio so at rh irdesor rcaopkgcae.k tPr eebtt ’reshoi tnafhpg rs aup i srtst oi.y spT seahlt rlieeosm dcmk ba eyyt intnho det ebteehp rh usigsptha colyef rwbeuahrleinrsietni cgg,r bafvuueitt liy gb inuso tvr eninrogyt FraeImGpoUreuRsnEet 1 no1t.fa 2tf9uio enAl. obfe afo rroec-kaentd b-aufrtneirn pg icat somriaalll Along a LineM03_KNIG2651_04_SE_C02.indd 46 9/13/15 8:41 PM
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M11_KNIG2651_04_SE_C09.indd 207 9/28/15 5:35i Pn Mthxe2 end-oxf-chapter problems. SUMMARY
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c. A sprong-loaded toy guTnh e smhaosos otsf thai s 2lit0tl eg p acpkl1eats o2tfi cbu rbnaedll f.u eW1l ish2 tahet mass lCosath bnyad th lielm reocpnk1regot: vmeefu dePl =ur-so2idn1mbg. l eMmastse2ringPhysics® data, strength of gravity. An object in free fall is weightless. B FuG Summary, consolidating and
is the launch speed if tMhaet hsempraotincagll yc, tohne smtainnuts siisg n 4te0ll,s0 u0s 0th,a tw thiet hm ass of thee xbupranendd fu etlh (eth er gaansegs)e a nodf physics and math skills TERMS AND NOTATION
the units you found in pthaer tr oack, eat nmdas st haree cshparnogningg iins ocpopomsipter deisrescetdio ns. Phys6isc9ta.ul ly|d|,| ewneA tk snp oewwn itdhlula tl uudmsme6 its0o ,f osromlveed pfrroomb lae msmsa.ll ball of mass m on a string M07_KNIG2651_04_SE_C06.indd 131 equilibrium model weigh9t/13/15 8:09 PM rolling friction drag coefficient, C structuring understanding.
10 cm? Assume the barrseol tihse ferxihcatuisot nglaesesss .have a positive mass. of length L. As FIGURE CP10.69 shows, a peg is height h=L/3 cfloant-setaanrtth-f oarpcper omxoimdealtion ccooeeffffiicciieenntt ooff kstianteitci cf rfircitcitoionn, ,m msk c oefrfifcictiioenn,t mofr rolling terminal speed, vterm
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M13_KNIG2651_04_SE_C11.indd 281 9/28/15 5:23 PM
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9.1 Energy Overview 207
Energy Overview
9.1
Energy. It’s a word you hear all the time, and everyone has some sense of what energy
means. Moving objects have energy; energy is the ability to make things happen;
energy is associated with heat and with electricity; we’re constantly told to conserve
energy; living organisms need energy; and engineers harness energy to do useful
things. Some scientists consider the law of conservation of energy to be the most
important of all the laws of nature. But all that in due time—first we have to start
with the basic ideas.
Just what is energy? The concept of energy has grown and changed with time, and
it is not easy to define in a general way just what energy is. Rather than starting with
a formal definition, we’re going to let the concept of energy expand slowly over the
course of several chapters. Our goal is to understand the characteristics of energy,
how energy is used, and how energy is transformed from one form into another. It’s a
complex story, so we’ll take it step by step until all the pieces are in place.
Some important forms of energy
Kinetic energy K Potential energy U Thermal energy E
th
46 CHAPTER 2 Kinematics in One Dimension
A research-driven approach,
Built from the ground up on physics education research and
crafted using key ideas from lear1n42 iCnHAgPT ERt 6h Dyenamoics rI: Myo,ti onK Alonng ai gLinhe t has set the
fine-tuned for even greater Exercises and Problems 259
standard for eff ective and accessible pedagogical materials in
Kinetic energy is the energy of motion. Potential energy is stored energy associated Thermal energy is the sum of the micro-
All moving objects have kinetic energy. with an object’s position. The roller coaster’s scopic kinetic and po5t5e.n t||i|a l Pernoetrogniess and neutrons (together called nucleons) are held 61. || The potential energy for a particle that can move along the
The more massive an object or the faster gravitational potential energy depends on of all ethe ataomss ande bontdo-sg ethtohaet rm inafk teh- eu pn uucleuss ofe an a toma byn a fordce ca llesd thte sturong dexn-axis tis U =sAx2u+B scin pcx/Le, whsere As, B, and L are constants. physics. In this fourth edition, Knight continues to refi ne and
it moves, the larger its kinetic energy. its height above the ground. the object. An object has more thermal
force. At very small separations, the strong force between two What is the force on the particle at (a) x=0, (b) x=L/2, and (c)
energy when hot than wnhuecnl ecoonlds .is larger than the repulsive electrical force between two x=L? 1 2 expand the instructional techniques to take students further.
protons—hence its name. But the strong force quickly weakens 62. || A particle that can move along the x-axis experiences an
as the distance between the protons increases. A well-established interaction force Fx= 3x2-5x N, where x is in m. Find an
model for the potential energy of two nucleons interacting via the expression for the system’s potential energy.
The Energy Principle strong force is 63. || An object moving i1n the xy-p2lane is subjected to the force
Fu= 2xy ni +x2 nj N, where x and y are in m.
❮❮ Section 7.1 introduced interaction diagrams and the very important distinction REVISED COVERUA=UG0 E1- Ae-xN/x0 D ORGANIZATIONa. TGhe IpaVrtiEcle mINoveSs frTomR thUe oCrigiTn tOo thRe pSoi nt with coordinates NEW AND UPDATED LEARNING TOOLS PROMOTE DEEPER AND
between the system, those objects whose motion and interactions we wish to a1, b by mov2ing first along the x-axis to a, 0 , then parallel
analyze, and the environment, objects external to the system but exerting forces where x is the dGistaRncEe bAetT3weEenR th eC 4ceHnteOrs oIf CtheE t wAo nNuclDe- FLEXIBILITY BETTER-CONNECTED UNDERSTANDING
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Quantum effects are essential for a proper understand-
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theB eunte rsgyyst eomf tsh oe fsteynst edmo ,i neittehrearc ti nwcirteha stihnegir i te n(evnierorgnym aedndt.e Td)h oosr ed einctreeraascitnigon ist (cehnaenrggye ETnheregrmy caaln be trCanh Isenfmoitriimcaalelldy the block is1 at rest at2 x=0 m. What is the block’s spee-2d 65.- 2Wc. riI1tse tah ir2se aal icsotincs perrovbatleivme ffoorr cwe?hich the energ1y ba2r chart shown in wniozrek wedh eenx aamndp lheos,w h etolp uinseg rsetucuderrnitnsg t om roedceolgs-, a acceleration changes. ■■    KRoinlleitnigc ffrriiccttiioonn:: OOppppoosseess mmooTtthiieoo nnsl owwpEeiix tteihhsrc vissffe.kr 1==6mmrk n n.. Mto othtieo nsu irsf areclea.tive
when it has been pulled to x=4.0 m? ■  Graphically:
removed). We say that interactions with the environment transfer energy into or Heat 57. || A syWstoermk has potential energy FIGURE P10.65 correctly shows the energy at the beginning and end key critical-thinking skill.
out of the system. Interestingly, there are only two ways to transfer energy. One is Energy removed of the problem.
by mechanical means, using forces to push and pull on the system. A process that Environment U x =x+1Nsie1nw.t6on2 ’s ar saeddco/vmnad lnxawc Fue=dm aut aopppliiecs t oR obojeccts kwehotse Ip mnPr oaPrsbsrol odeobmpelse.u mnFolosst r ci6 hoe6aan ncgtheh .r Toohfu agtth’hse 6se8, yyoouu aarree gtoiven the equation used to solve a fs max = mmksnnf Static KiTfnrheicteti icoobnj erceta cshliepss fws mhaexn. static
as a particle move1s 2over thea rna enx1cg1eell e0n tm ass…um2xpt2…ionp fo rm ba.lls and bicycles, but what abao.u t Wsomriettehi nag r leikael ias rtoicck eptr oblem for which this is the correct equation. Sintcarteica sferisc ttoio mnatch Kasi ntheeti co bfrjeicctti omno ivse cso.nstant
a. Where are the equilibriutmhmaast spl oaosrseeis st oiaol vsneigdsn wiifniitc hta hmntio sam mreaonnutungmte o? rfa tmhears sth aasn iatcs cfeuleerl aitsio bnu. brWn.e ed’lD?l lProaroowkb al ett mhones e ob ifme vfpaoorrryteian-ngat nd-after pictorial representation. the push or pull. 0 Rest Moving Push or pull force
b. For each, is it a point of esxtaambplele .or unstable equilibrium? c. Finish the solution of the problem. 6 Dynamics I: Motion
NEW! ADV58A. N|w| iCtAh E ppDoatre tnictilea l tehnaet rcgayn moveiwn eafalFluIkoGe inUnncRg ceE o dt1m 1hb.py2ea 9 g rxrsiash-ovaoniwxt ytsio so at rh irdesor rcaopkgcae.k tPr eebtt ’reshoi tnafhpg rs aup i srtst oi.y spT seahlt rlieeosm dcmk ba eyyt intnho det ebteehp rh usigsptha colyef rwbeuahrleinrsietni cgg,r bafvuueitt liy gb inuso tvr eninrogyt FraeImGpoUreuRsnEet 1 no1t.fa 2tf9uio enAl. obfe afo rroec-kaentd b-aufrtneirn pg icat somriaalll Along a LineM03_KNIG2651_04_SE_C02.indd 46 9/13/15 8:41 PM
TadOd PevICenS m aso roep ftiloexniabli slietcyt ions U x gm=raatvhAietym a-altliocBws sto uos ctoo munpdliecrastteadn.d R tohcek eests penrotipaulsls oiof nro wckiteht gprraovpiutyls iios na wCihthaloluent gmea Pkrionbgl tehme E (J)Before: m vx 1Tasa5p chm2ceee ei llpdeeCo .roHawftA eeorPsvf TeuthErl iRt1sh 5e6r0n u oDsmtry mponhfoa tmuinhs ei lcp esjles aIstn: eteMh ntaogonit n ai oe sn Along a Line
M11_KNIG2651_04_SE_C09.indd 207 9/28/15 5:35i Pn Mthxe2 end-oxf-chapter problems. SUMMARY
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c. A sprong-loaded toy guTnh e smhaosos otsf thai s 2lit0tl eg p acpkl1eats o2tfi cbu rbnaedll f.u eW1l ish2 tahet mass lCosath bnyad th lielm reocpnk1regot: vmeefu dePl =ur-so2idn1mbg. l eMmastse2ringPhysics® data, strength of gravity. An object in free fall is weightless. B FuG Summary, consolidating and
is the launch speed if tMhaet hsempraotincagll yc, tohne smtainnuts siisg n 4te0ll,s0 u0s 0th,a tw thiet hm ass of thee xbupranendd fu etlh (eth er gaansegs)e a nodf physics and math skills TERMS AND NOTATION
the units you found in pthaer tr oack, eat nmdas st haree cshparnogningg iins ocpopomsipter deisrescetdio ns. Phys6isc9ta.ul ly|d|,| ewneA tk snp oewwn itdhlula tl uudmsme6 its0o ,f osromlveed pfrroomb lae msmsa.ll ball of mass m on a string M07_KNIG2651_04_SE_C06.indd 131 equilibrium model weigh9t/13/15 8:09 PM rolling friction drag coefficient, C structuring understanding.
10 cm? Assume the barrseol tihse ferxihcatuisot nglaesesss .have a positive mass. of length L. As FIGURE CP10.69 shows, a peg is height h=L/3 cfloant-setaanrtth-f oarpcper omxoimdealtion ccooeeffffiicciieenntt ooff kstianteitci cf rfircitcitoionn, ,m msk c oefrfifcictiioenn,t mofr rolling terminal speed, vterm
M07_KNIG2651_04_SE_C06.indd 152 9/13/15 8:12 PM
M13_KNIG2651_04_SE_C11.indd 281 9/28/15 5:23 PM
A01_KNIG7429_04_GE_FM.indd 5 18/07/16 2:52 pm
M12_KNIG2651_04_SE_C10.indd 259 9/28/15 5:29 PM
10.4 Conservation of Energy 243
A STRUCTURED AND CONSISTENT APPROACH BUILDS MasteringPhysics THE ULTIMATE RESOURCE
PROBLEM-SOLVING SKILLS AND CONFIDENCE BEFORE, DURING, AND AFTER CLASS
With a research-based 4-step problem-solving BEFORE CLASS
PROBLEM-SOLVING STRATEGY 10.1
framework used throughout the text, students
learn the importance of making assumptions
Energy-conservation problems
(in the MODEL step) and gathering informa- NEW! INTERACTIVE PRELECTURE VIDEOS NEW! DYNAMIC STUDY MODULES (DSMs) con-
tion and making sketches (in the VISUALIZE MODEL Define the system so that there are no external forces or so that any address the rapidly growing movement toward pre-lecture tinuously assess students’ performance in real time to provide
external forces do no work on the system. If there’s friction, bring both surfaces
step) before treating the problem mathemati- into the system. Model objects as particles and springs as ideal. teaching and flipped classrooms. These whiteboard-style personalized question and explanation content until students
cally (SOLVE) and then analyzing their results VISUALIZE Draw a before-and-after pictorial representation and an energy bar animations provide an introduction to key topics with master the module with confidence. The DSMs cover basic
(ASSESS). chart. A free-body diagram may be needed to visualize forces. embedded assessment to help students prepare and profes- math skills and key definitions and relationships for topics
sors identify student misconceptions before lecture. across all of mechanics and electricity and magnetism.
SOLVE If the system is both isolated and nondissipative, then the mechanical
energy is conserved:
Detailed PROBLEM-SOLVING Ki+Ui=Kf+Uf
STRATEGIES for different topics and where K is the total kinetic energy of all moving objects and U is the total
categories of problems (circular-motion potential energy of all interactions within the system. If there’s friction, then
problems, calorimetry problems, etc.) Ki+Ui=Kf+Uf+ ∆Eth
are developed throughout, each one built
on the 4-step framework and carefully where the thermal energy increase due to friction is ∆Eth=fk ∆s.
illustrated in worked examples. ASSESS Check that your result has correct units and significant figures, is
reasonable, and answers the question.
Exercise 14
716 CHAPTER 26 Potential and Field
TACTICS BOX 26.1
DURING CLASS
Finding the potential from the electric field
●1 Draw a picture and identify the point at which you wish to find the potential.
Call this position f.
●2 Choose the zero point of the potential, often at infinity. Call this position i. NEW! LEARNING CATALYTICS™ is an interactive
●3 Establish a coordinate axis from i to f along which you already know or can 30-8 chapter 30 • Electromagnetic Induction classroom tool that uses students’ devices to engage them in
●4 eCaasrirlyy doeutte trhmei innet ethgera etiloecnt roifc Efiqeulda tcioonm 2p6o.n3e tnot fEins.d the potential. 1P30S8.S1. Tao fhr etehc getar cnaupgrhur lesanhrt o liwono stp hh eoo fwl ow otihpree a mws aait ghfnu renetcsictiis oftianen locdfe c tRihma. nDeg.r eLaswe tt h aar og uragphh menoarbel esso pinhsitsrtuiccatoterds ttoa sgkesn aenradt eth cilnaksisnrogo. mLe dairsnciunsgs iCoant aalnydt ics
counterclockwise current be positive, a clockwise
Exercise 1 current be negative. promote peer-to-peer learning to help students develop
TACTICS BOXES give step-by-step procedures for critical-thinking skills. Instructors can take advantage of
developing specific skills (drawing free-body diagrams, a. What is the magnetic flux through the loop at t=0? real-time analytics to find out where students are struggling
b. Does this flux change between t=0 and t=t1? and adjust their instructional strategy.
using ray tracing, etc.).
c. Is there an induced current in the loop between t=0 and t=t1?
d. What is the magnetic flux through the loop at t=t2?
e. What is the change in flux through the loop between t1 and t2?
f. What is the time interval between t1 and t2?
g. What is the magnitude of the induced emf between t1 and t2?
h. What is the magnitude of the induced current between t1 and t2?
AFTER CLASS
i. Does the magnetic field point out of or into the loop?
j. Between t1 and t2, is the magnetic flux increasing or decreasing?
k. To oppose the change in the flux between t1 and t2, should the magnetic
field of the induced current point out of or into the loop?
The REVISED STUDENT WORKBOOK l. Is the induced current between t1 and t2 positive or negative? NEW! ENHANCED ADAPTIVE FOLLOW-UPS
is tightly integrated with the main text–allowing m. Does the flux through the loop change after t2? END-OF-CHAPTER are personalized assignments
students to practice skM1il2l_sK NfIGro26m51_ t0h4_eS Et_eCx10t.’insd dT a24c3tics no.. IUs steh earlel tahnis i nindfuocremda ctiuornre tnot dinra twhe a l goroapp ahf otefr tth2e? induced current. Add appropriate labels on the QUES1T0/6I/1O5 N9:28S A Moffer stu- that pair Mastering’s powerful
Boxes, work through the steps of Problem-Solv- vertical axis. dents instructional support content with Knewton’s adaptive
ing Strategies, and assess the applicability of the when and where they need learning engine to provide
Models. The workbook is referenced throughout it, including links to the individualized help to students
the text with the icon . © 2017 Pearson Education. eafoTnred xh wto, mrmoenawgth-oa rrnkes mawseesdrig ifanetmeiodenbn,a tcsk. bTtaosehpsfeioigcsresne e samdtdu iahdspocetmonivntesecw esftpoorltrulikoog,wn gisln-e uctdaplu kswd eaii tndhhgdo olrcdeno.s rse
prerequisite topics.
M30_KNIG3162_04_SE_C30.indd 8 09/25/15 4:07 PM
A01_KNIG7429_04_GE_FM.indd 6 18/07/16 2:52 pm
M32_KNIG2651_04_SE_C26.indd 716 10/6/15 9:29 AM
10.4 Conservation of Energy 243
A STRUCTURED AND CONSISTENT APPROACH BUILDS MasteringPhysics THE ULTIMATE RESOURCE
PROBLEM-SOLVING SKILLS AND CONFIDENCE BEFORE, DURING, AND AFTER CLASS
With a research-based 4-step problem-solving BEFORE CLASS
PROBLEM-SOLVING STRATEGY 10.1
framework used throughout the text, students
learn the importance of making assumptions
Energy-conservation problems
(in the MODEL step) and gathering informa- NEW! INTERACTIVE PRELECTURE VIDEOS NEW! DYNAMIC STUDY MODULES (DSMs) con-
tion and making sketches (in the VISUALIZE MODEL Define the system so that there are no external forces or so that any address the rapidly growing movement toward pre-lecture tinuously assess students’ performance in real time to provide
external forces do no work on the system. If there’s friction, bring both surfaces
step) before treating the problem mathemati- into the system. Model objects as particles and springs as ideal. teaching and flipped classrooms. These whiteboard-style personalized question and explanation content until students
cally (SOLVE) and then analyzing their results VISUALIZE Draw a before-and-after pictorial representation and an energy bar animations provide an introduction to key topics with master the module with confidence. The DSMs cover basic
(ASSESS). chart. A free-body diagram may be needed to visualize forces. embedded assessment to help students prepare and profes- math skills and key definitions and relationships for topics
sors identify student misconceptions before lecture. across all of mechanics and electricity and magnetism.
SOLVE If the system is both isolated and nondissipative, then the mechanical
energy is conserved:
Detailed PROBLEM-SOLVING Ki+Ui=Kf+Uf
STRATEGIES for different topics and where K is the total kinetic energy of all moving objects and U is the total
categories of problems (circular-motion potential energy of all interactions within the system. If there’s friction, then
problems, calorimetry problems, etc.) Ki+Ui=Kf+Uf+ ∆Eth
are developed throughout, each one built
on the 4-step framework and carefully where the thermal energy increase due to friction is ∆Eth=fk ∆s.
illustrated in worked examples. ASSESS Check that your result has correct units and significant figures, is
reasonable, and answers the question.
Exercise 14
716 CHAPTER 26 Potential and Field
TACTICS BOX 26.1
DURING CLASS
Finding the potential from the electric field
●1 Draw a picture and identify the point at which you wish to find the potential.
Call this position f.
●2 Choose the zero point of the potential, often at infinity. Call this position i. NEW! LEARNING CATALYTICS™ is an interactive
●3 Establish a coordinate axis from i to f along which you already know or can 30-8 chapter 30 • Electromagnetic Induction classroom tool that uses students’ devices to engage them in
●4 eCaasrirlyy doeutte trhmei innet ethgera etiloecnt roifc Efiqeulda tcioonm 2p6o.n3e tnot fEins.d the potential. 1P30S8.S1. Tao fhr etehc getar cnaupgrhur lesanhrt o liwono stp hh eoo fwl ow otihpree a mws aait ghfnu renetcsictiis oftianen locdfe c tRihma. nDeg.r eLaswe tt h aar og uragphh menoarbel esso pinhsitsrtuiccatoterds ttoa sgkesn aenradt eth cilnaksisnrogo. mLe dairsnciunsgs iCoant aalnydt ics
counterclockwise current be positive, a clockwise
Exercise 1 current be negative. promote peer-to-peer learning to help students develop
TACTICS BOXES give step-by-step procedures for critical-thinking skills. Instructors can take advantage of
developing specific skills (drawing free-body diagrams, a. What is the magnetic flux through the loop at t=0? real-time analytics to find out where students are struggling
b. Does this flux change between t=0 and t=t1? and adjust their instructional strategy.
using ray tracing, etc.).
c. Is there an induced current in the loop between t=0 and t=t1?
d. What is the magnetic flux through the loop at t=t2?
e. What is the change in flux through the loop between t1 and t2?
f. What is the time interval between t1 and t2?
g. What is the magnitude of the induced emf between t1 and t2?
h. What is the magnitude of the induced current between t1 and t2?
AFTER CLASS
i. Does the magnetic field point out of or into the loop?
j. Between t1 and t2, is the magnetic flux increasing or decreasing?
k. To oppose the change in the flux between t1 and t2, should the magnetic
field of the induced current point out of or into the loop?
The REVISED STUDENT WORKBOOK l. Is the induced current between t1 and t2 positive or negative? NEW! ENHANCED ADAPTIVE FOLLOW-UPS
is tightly integrated with the main text–allowing m. Does the flux through the loop change after t2? END-OF-CHAPTER are personalized assignments
students to practice skM1il2l_sK NfIGro26m51_ t0h4_eS Et_eCx10t.’insd dT a24c3tics on.. UIss teh earlle tahnis i nindfuocremda ctiuornre tnot dinra twhe a l goroapp ahf otefr tth2e? induced current. Add appropriate labels on the QUES1T0/6I/1O5 N9:28S A Moffer stu- that pair Mastering’s powerful
Boxes, work through the steps of Problem-Solv- vertical axis. dents instructional support content with Knewton’s adaptive
ing Strategies, and assess the applicability of the when and where they need learning engine to provide
Models. The workbook is referenced throughout it, including links to the individualized help to students
the text with the icon . © 2017 Pearson Education. eafoTnred xh wto, mrmoenawgth-oa rrnkes mawseesdrig ifanetmeiodenbn,a tcsk. bTtaosehpsfeioigcsresne e samdtdu iahdspocetmonivntesecw esftpoorltrulikoog,wn gisln-e uctdaplu kswd eaii tndhhgdo olrcdeno.s rse
prerequisite topics.
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