Schaum College Physics.pdf

THEORY AND PROBLEMS

OF

COLLEGE PHYSICS

Ninth Edition

FREDERICK J. BUECHE, Ph.D.

EUGENE HECHT, Ph.D.

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SCHAUM'S OUTLINE SERIES

# $% & %! '( )

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0-07-1367497

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DOI: 10.1036/0071367497

abc

Preface

8 0& FF == FF == &! ) & ! ! ! ! !

FF == #! !! #

! ! , ! !! & G

! ! ( & 8 !! 0& # # ! ! # ! ! # ' / & ! : ! ! = GD G

! & 0 ! # & !! # !# ! H ' & !! 0 !!! I' . . ! 8 ! # ! # # - 0& ' & 0& & !!! & ! 0& & : #0 # & !! ! . & G & ! !&0 ! # = ! !

: & ! #( ! FF - ( = #!== 1 ! # FF== #! ! ' = ! ! 8 ! . & ! #! & #! I & 0 !! 8 0- ! ! ' #! G ' I # # ( FF0& & == 0 ! ! ! # ! 0#- & )

& = ! & & #0

#

& #! # * # ' !H &0 ! 8 # ! . !

B '! & !#H # -

& / !

0 3/4 & # & & 3/4

3 4 & # !0 3 4 8 # ! &= & ! & # # !# & & # 8 . . 3 ' 4 #! ! . # !0 ! ! I ! ! : & # & & ! #

!! # ' #! = 0 ! : ! " 12 $$,5%

"0 $ ::1: :" 8

Contents

Chapter

1

_{INTRODUCTION TO VECTORS 1}

9 G J G

3 !4 ! ! 9#

8! "! "! !

!

Chapter

2

_{UNIFORMLY ACCELERATED MOTION} 13

9 J ! !

!

J ! ( #!

Chapter

3

_{NEWTON'S LAWS 27}

9 0! B 1 ' 8 &

1&= B & 1&= 9 & 1&= 8 &

& #& !

& 8 B 1! "K 0

"K ! !

&

Chapter

4

_{EQUILIBRIUM UNDER THE ACTION OF CONCURRENT}

FORCES 47

" #( G#! B G#!

#! ! 3 4 #( 8

B 1!

Chapter

5

_{EQUILIBRIUM OF A RIGID BODY UNDER COPLANAR}

FORCES 56

8G 3 !!4 8& G#! "

' #

Chapter

6

_{WORK, ENERGY, AND POWER} 69

0 &0 : L

0 ! " & L&

Chapter

7

SIMPLE MACHINES 80

! &0 :K

Chapter

8

_{IMPULSE AND MOMENTUM 87}

!!! ! ! !!!

" !!! " '

"K " !

Chapter

9

ANGULAR MOTION IN A PLANE 99

! :G

! ! #&

G " "

Chapter

10

_{RIGID-BODY ROTATION} 111

8G 3 !!4 ! 8G

L "!# 0 &

!!! ! ' !

G

Chapter

11

SIMPLE HARMONIC MOTION AND SPRINGS 126

BG # ! !

9! ! ! 0 ! :

: 9 9 9

9 ! 9! ! 9

Chapter

12

_{DENSITY; ELASTICITY 138}

9 . : 9 9 : !

2= ! /0 ! 9 !

Chapter

13

_{FLUIDS AT REST 146}

9 !

= !=

Chapter

14

_{FLUIDS IN MOTION 157}

B I& :G 9 J

= & 0 # 0 #

/= G 8= ! !#

Chapter

15

_{THERMAL EXPANSION 166}

8! ' ' J!

'

Chapter

16

_{IDEAL GASES 171}

3 4 ; ! # & 9

# H 9 !

3984 = & & #!

Chapter

17

KINETIC THEORY 179

L = !# !

0 ! G # !

Chapter

18

_{HEAT QUANTITIES} 185

8! 9 . 3 4

H #! "! #! #

! ! &

Chapter

19

_{TRANSFER OF HEAT ENERGY 193}

: # " 8! "

Chapter

20

_{FIRST LAW OF THERMODYNAMICS 198}

0 # ! B & 8!!

# ! ! #

9 . 9 . 0

:K

Chapter

21

ENTROPY AND THE SECOND LAW 209

9 & 8!! : : !

##

Chapter

22

_{WAVE MOTION 213}

& ! # 9

& 9 & "

3! 4 &

Chapter

23

_SOUND 223

9 & :G 9

3 4 / )

)

Chapter

24

_{COULOMB'S LAW AND ELECTRIC FIELDS 232}

"!#= & " GH " 8

: . 9 . : .

9

Chapter

25

_{POTENTIAL; CAPACITANCE 243}

) # :

1 : "

" :

Chapter

26

_{CURRENT, RESISTANCE, AND OHM'S LAW 256}

" / ;!= & ! #

!! ! 8! )

& !

Chapter

27

_{ELECTRICAL POWER} 265

: &0 : & & 8!

"

Chapter

28

_{EQUIVALENT RESISTANCE; SIMPLE CIRCUITS 270}

Chapter

29

KIRCHHOFF'S LAWS 283

L)= 3 (4 L)= 3 4 9

G #

Chapter

30

_{FORCES IN MAGNETIC FIELDS 289}

. . " !

! .

. B ! . 8G I

Chapter

31

_{SOURCES OF MAGNETIC FIELDS} 299

. ! . B!

! !! . !

Chapter

32

_{INDUCED EMF; MAGNETIC FLUX 305}

) ! . I' !

B= & ! H= & !

Chapter

33

_{ELECTRIC GENERATORS AND MOTORS 315}

: : !

Chapter

34

_INDUCTANCE;R-C_ANDR-L_{TIME CONSTANTS . . . . 321}

9 : 23!

23! :'

Chapter

35

ALTERNATING CURRENT 329

:! # 8! &

B! ;!= & !

& 8!

Chapter

36

_{REFLECTION OF LIGHT} 338

1 & I ! 9 !

G 9H !

Chapter

37

REFRACTION OF LIGHT 346

9 ' 9= & "

I !

Chapter

38

_{THIN LENSES 353}

8 ;#( ! !0= G &

Chapter

39

_{OPTICAL INSTRUMENTS 359}

"!# 8

8

Chapter

40

_{INTERFERENCE AND DIFFRACTION OF LIGHT 366}

" & ) )

9 ) ! ) G

) M ;

Chapter

41

_{RELATIVITY 374}

! 9 !!!

! 8! 9!

J !

Chapter

42

_{QUANTUM PHYSICS AND WAVE MECHANICS 382}

E ) !! "!

) / & / & EH Chapter

43

_{THE HYDROGEN ATOM 390}

! : # : ! :! 9 ; # Chapter

44

_{MULTIELECTRON ATOMS} 396

1 ! E! !# ' Chapter

45

_{NUCLEI AND RADIOACTIVITY 399}

1 1 ! !# ! ! !# / 1 G Chapter

46

_{APPLIED NUCLEAR PHYSICS} 409

1 # B B ! :) !! Appendix

A

SIGNIFICANT FIGURES 417

Appendix

B

TRIGONOMETRY NEEDED FOR COLLEGE PHYSICS 419

Appendix

C

EXPONENTS 422

Appendix

D

LOGARITHMS 424

Appendix

E

PREFIXES FOR MULTIPLES OF SI UNITS; THE GREEK ALPHABET 427

Appendix

F

FACTORS FOR CONVERSIONS TO SI UNITS 428

Appendix

G

PHYSICAL CONSTANTS 429

Appendix

H

TABLE OF THE ELEMENTS 430

INDEX 433

Chapter 1

Introduction to Vectors

A SCALAR QUANTITY, ! & ! ! ! ! H # 8 !# G ( ! G

9 . # !# # & 8& #'

A VECTOR QUANTITY # . ! & # ! 3H4 !

!!! G B '! "! , ! #

! 6 ! & x !

. '! &

6% & 314 & ; & %66, 3$%% 1ˆ%:66, #4 9!

! @% 0!7 ! @% 0!79;8

G # # & & 8 & ! G 36 ! 6% 1 @% 0!7 # '! 4 8 & G

! # # F & #

~F !! ! . & # !

#

THE RESULTANT, ! !# 3 '! 4 & ! ) 0

GRAPHICAL ADDITION OF VECTORS (POLYGON METHOD): 8 ! . ~

R 3~A ~B ~C4 # & 3 4 & 8 ! # 0 A ~A_‡~B_‡~C_ˆ~C_‡~A_‡~B_ˆ~R 8 & & B $$

$ Fig. 1-1

8 # & &

~R Rˆ j~R_j H ,

PARALLELOGRAM METHOD & A 8 & ! # # ! 8 & & ! & B $6 8 & ! &

SUBTRACTION OF VECTORS: 8 # ~B ! ~A

~B ~A ~A ~B_ˆ~A_‡ ~B_†:

THE TRIGONOMETRIC FUNCTIONS . B & B $5 # .

ˆ ˆB

C; ˆ

(

ˆA

C; ˆ

(ˆ

B A

!

BˆC AˆC BˆA

A COMPONENT OF A VECTOR ) B '! x

! ! ! x' #

! ! ! # !

,!! "" ! 9! & !

6 18;"8;1 8; J:"8;9 N" $

! # & ! & !

B $@ & ~R x y ! ~R_x ~R_y &

!

j~R_{xj ˆ j}~R_{j j}~R_{yj ˆ j}~R_j

G

RxˆR RyˆR

COMPONENT METHOD FOR ADDING VECTORS: : x y

z! & ! 0 8 x!

Rx ~R # ! x! 8 y z

! ! & ! 0& ! #

Rˆ R6 x‡R6y‡R6z

q

& ! & x' # !

ˆRy

Rx

UNIT VECTORS ! # # !#

& 8 ^i ^j k^ x y z'

5^i _‡x & ,^k .

z ~R x y z! Rx Ry

Rz # & ~RˆRx^i‡Ry^j‡Rzk^

THE DISPLACEMENT: #( ! ! ! ! .

" $O 18;"8;1 8; J:"8;9 5

Solved Problems

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!!# ! ! # & ' & &

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Chapter 2

Uniformly Accelerated Motion

SPEED G #( 0 ! t l

"_ˆ

! 0

vavˆ l t

3 4 8 & = !

VELOCITY G #( !~s !

t

! ˆ !

! 0

~v_avˆ~s t

8 ! ! 8 3 4 # ! !7 0!7

ACCELERATION ! ! A

!ˆ

! 0

~a_{av ˆ}~vf ~vi t

&~v_i ~v_f . t ! &

8 # ! 8 '! 3!747 3

!764 30!747 3 0!74 1 G

~v_f ~v_i !! 0 !

( !#

UNIFORMLY ACCELERATED MOTION ALONG A STRAIGHT LINE !

! !

~v ~a # . & ! &

! # s 3

4 ! # # & 6 5 ! !

A

$5

s_ˆvavt

vavˆ vf ‡vi

6

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t v6f ˆv6i ‡6as

sˆvit‡$6at 6

;s #xy !!vf vi & vv%

DIRECTION IS IMPORTANT, ! # & H ! : ! # ! ! # 0

INSTANTANEOUS VELOCITY !

H 8 #( ! _~s ! t #(

~v_ˆ !

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66 1B;2 ""::8: ;8;1 N" 6

Fig. 2-6

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2.23 8 0 0 0 5<%! @% !

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0 # 0 …v=g_†‰$‡p$‡ …6hg=v6_†

Š:

Chapter 3

Newton's Laws

THE MASS #( ! #(

# ! # ! ! & B 0 ! ! G!

THE STANDARD KILOGRAM #( & ! . # 0! 8

! #( # ! & ! , , G

' %%%$ 0

FORCE ! &

#( B G ! *!

& ! #

THE NET EXTERNAL FORCE #( #( 8 ! #( 3 & 0& ! 9 8 ! ' '! # & # 4

THE NEWTON 9 ; & 3$ 14 & &

$ 0 ! $ !76 _{8 " @@, 1}

NEWTON'S FIRST LAWA )7 #!! , 8 )7 , #!!

, # ! 0 * " " ) *! B

!

NEWTON'S SECOND LAWA # 1& 9 & & ! ! !!! 8 ! & # " <

& ! # 3 4 ~F

#( ! m H #( 8

~a ! #(

~F & m 0! ~a !76 _{# &}

~a_ˆ~F

m ~Fˆm~a

8 ~a ! ~F:

8 G~F_ˆm~a # & ! !

Fxˆmax Fyˆmay Fzˆmaz

& ! ' #(

6?

NEWTON'S THIRD LAW: & ! Q ! * )0 5!0 ) ""! 0 , )

# & 8 # 2 1

& ) #(

THE LAW OF UNIVERSAL GRAVITATION: & ! m m0

& G ! B ! 3

!! #4 FG #

FGˆG mm0

r6

& r #& ! & Gˆ+:+?$% $$1!6=06 & FG

&mm0 0! r !

THE WEIGHT #( FW† && #( ; : ' #( # & 3 94 3 / !4 / : ! ! # = & ! # & # ) ! . #

RELATION BETWEEN MASS AND WEIGHT: #( ! m &

: #( D & & & FW

#( 8 #(= FW g 8 ~Fˆm~a

& #& F ˆFW aˆg m- FW ˆmg /

gˆ*:<$ !76 _{: $%% 0 #( & *<$ 1 :=}

THE TENSILE FORCE …~FT†

8 ! FT†

THE FRICTION FORCE ~F† #( #( ( & & 8 ! ! ! ; & ' !'!! & #( #

THE NORMAL FORCE …~FN† #( # # !

THE COEFFICIENT OF KINETIC FRICTION …k† . &

kˆ_! ˆ

F FN

THE COEFFICIENT OF STATIC FRICTION s† . & (

sˆ

!'!!

! ˆ

F…!'† FN

& !'!! & #( ( #

DIMENSIONAL ANALYSIS: ! G #

' ! ! !A L ! M ! T B '!

3 4 # 3!46_{- & , L=T}6 _&

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s_ˆv_it _‡$ 6at

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‰MLT 6_Š# ! _‰LT $_Š- ! ! !

MATHEMATICAL OPERATIONS WITH UNITS: !!

! 3 '! # ! 5 _{!7 !7}6_{4 ! # & !# !}

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3.14 "! & & @,0 &! &

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3.16 9 & B 5< ?%0 #' # @%%1 5%8

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1& &Fxˆmax #'

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! &axˆ$:, !76:

" 5O 1:8;1=9 9 5,

Fig. 3-7

3.17 ! 6% !7 H #0 ! & # K #& %*%P ! & #0 #0 = 0

8 & & $

F_$ˆsFN$ˆFW$

&FW$ & # & $ # Ff # !

&A

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# 3& & 4 F_ˆma

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m ˆ

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m ˆ sgˆ … %:*%†…*:<$ !=

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t ˆ

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1& & &Fxˆmax &axˆaˆ%:,% !76 B! B 5* G #!

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B! B 5*

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5+ 1:8;1=9 9 N" 5

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3.20 6%0 #' & B 5$$ 8 K 0 #&

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F 5%8ˆ%:<++

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" 5O 1:8;1=9 9 5?

Fig. 3-10

!

Fxˆmax &

F %:,%mg_ˆma_x ,$ 1 …%:,%†…6%†…*:<$†1ˆ …6% 0†…a_x†

! &axˆ 6:5, !76 8 #' & 6@ !76

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%?, !76 B K 0 #& #'

8 ! & B 5$6 1 & x y' 0

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5<5 1 F …%:+@†…6,†…*:<$†1ˆ …6, 0†…%:?, !=6†

! &F ˆ6%? 1

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0ˆ

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5< 1:8;1=9 9 N" 5

Fig. 3-11

3.22 8& #0 !m$m6 # F & B 5$5 8 K

#& #0 # %@% 3a4 ! # F #0

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m$ˆ5%% m6ˆ,%% !!# &0 9

8 #0 F$ˆ%:@m$g F6ˆ%:@m6g 0 & #0

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3a4 9 F # 0& & .

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3b4 1& #0m6 8 x #0m$

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Fxˆmax #! Fb F6ˆm6ax

0& axˆ6:% !76

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3.23 3 # ! 4

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3.24 B 5$, K 0 #& #0 A # %6%

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F_{N ˆ}m_Ag_ˆ6, 0†…*:<$ !=6† ˆ6@, 1

F _ˆ0FNˆ …%:6%†…6@, 1† ˆ@* 1

! . . ! & # !

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3.27 B 5$+ & #' ! @% 0 / '

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3.28 ! & B 5$?3a4 F #0m$ B

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F _6ˆ0m6g #! m$ & ! …m$‡m6†g

F0ˆ0…m$‡m6†g & &Fxˆmax #0 0 ! A

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!FT # & G #

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3.29 ! B 5$< ! # # B

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G

Fˆ …@m$‡m6†…a† aˆ

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6

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Fig. 3-17

3.30 B 5$* & #( 6%% 1 5%% 1 8

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FT$ FT6 #

B& !A& 2 # P6

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#( ! 4 8& & B A

a# && A 8a=6 & B 3P4 &

&Fyˆmay ! 0 !

FT$ 5%% 1ˆ …mB†…$6a† 6%% 1 FT6ˆma

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3.31 "! ! : ! # +5?% 0! &

. .

M# ! : m ! #( := 8 &

#( G mg G GMm_†=r6 &r :=

mg_ˆGMm r6

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6

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+:+?$% $$ _1!6₌₀6 ˆ,:*?$% 6@ ₀

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Supplementary Problems

3.32 ; ! 0 ! ' $% 1 ?<%

# 0 $%%0 ! !

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3.33 8 # @,# 3,% #4 6+6 !7 0 $ !

# ! ' # $+6 # &

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3.35 #( ! 5%% 3a4 & :P 3b4 ! P 3c4

& # & %,%% 1 P & 3a4 6*@

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3.36 H # 6%%0 H 0 8 # ,%% 1 9

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P & 3a4 56 - 3b4 $5 !

3.37 *%%0 6% !7 & G

5% !P 3A B . 4 & +% 01

3.38 $6% # ! ?%% !7 6%% ! # !

# & & P 3' ! 4

& $@? 01

3.39 6%0 B 3! 4 &

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3.40 ,%0 ! B !

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3.41 ?%%1 ! I 8 ' &

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3.61 8 #0 & ! +% 0 *% 0 $% 0 & B 565 8 K

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& 3a4 %5* !76- 3b4 +$ 1 <, 1

3.62 8 := # +5?% 0! #( ! 6% 0 0 $+% 0!

# := 3a4 #(= ! P 3b4 & ! #( &

3 & ' 4 P & 3a4 6% 0- 3b4 %$* 01

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Fig. 3-21 Fig. 3-22

Chapter 4

Equilibrium Under the Action of Concurrent Forces

CONCURRENT FORCES & !! 8 #( # ! #(

AN OBJECT IS IN EQUILIBRIUM

THE FIRST CONDITION FOR EQUILIBRIUM G! ~F_ˆ% ! !

_{FxˆFy ˆFzˆ%}

8 ' #( ! # H 8 K G#! & ' ! # . #( # G#! - " ,

PROBLEM SOLUTION METHOD (CONCURRENT FORCES):

3$4 #(

364 9& #( ! 33) ,4

354 B !

3@4 . G#! G ! 3,4 9 G G

THE WEIGHT OF AN OBJECT …~FW† & & &&

THE TENSILE FORCE …~FT† # 3 !!#4 8 !

FT†

THE FRICTION FORCE ~F† #( #( ( & & 8 ! ! !

THE NORMAL FORCE …~FN† #( # # !

@?

Solved Problems

4.1 B @$3a4 H 5% 1 & B & #(

8 $ G & #( ! 8FT$ˆFW &

& .F_T$F_W

1 0& FT$ 0& 5% 1 # 0 P

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‡

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