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sirr 1. ~iufitfinnntr~~naziido?'mq iio wngcuvo~uuinuo.sua~K~ni5n~zo'n (n) lunr&f/t t ~ ~ n r r i i r ~ ~ ~ i a ~ n ~ c i i ~

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Page 1: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

sirr 1. ~iufitfinnntr~~naziido?'mq iio wngcuvo~uuinuo.sua~K~ni5n~zo'n (n) lunr&f/ t t ~ ~ n r r i i r ~ ~ ~ i a ~ n ~ c i i ~

Page 2: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~
Page 3: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~
Page 4: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~
Page 5: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

kunnurhrw'uaiiilr6uo::n"in~mn'ia'in"mn3iuuo44iud~n'm~inni566nll54n5::n"id6?"~1~~o

w agcuuo.ruuimuo4 w (F) tus-uzm.rd~q in~oud& duniini~n5::o"a (s)

I a

J J d i i i n i n ~ ~ i ~ 8 ~ u d l f l ~ ~ ~ 1 4 0 ~ ~ 4 ~ ~ " 1 ~ M ' f l ~ 1 4 d l L 5 4 n 5 ~ ~ i Iun~d8~1uh&?u

o::f l~4l~~ldp9iun"io' i~~n?i~~~44iudndi2~~iau'74~~&~u1#11?n"~1~~~::6t)4w'0i5~i

~iusin~~r~nrrn~idoa"mf]86 wnrJruuoc~~z4d4umnoonm7uuu2 iffumr~djblq~nifoudtu J 4 4

5 - u : : w i ~ d ~ i ~ innaun miuadn 4.1

. W = (F cos 8)s ........ 4.2

uoI~~m~1iin~iufu~"u8'miu01uni~ 4.2 inQounYUmmr 4.1 I1~n5dd0 lj3ugut.f

o::?&ii~iudnr::iilmu~~z.j F iio Fs fi~un~iufuw"us'miu~~unir 4.1 $&!d64iaunssil

l m u ~ a r c i r ~ d o % ~ ~ n d o ~ ~ I u M ' ~ n i . ~ ~ # u a ~ ~ ~ ~ ~ . ~ n ~ : : v l ' i d2un~iurlirriirkiu~unir 4.2 d 4 fiunrd.n"a!d ~~a"m~m~oud!fluM'floun~u'dM'flv~.~~~r~n~::ii un::6inin 8 du sd d::

!riilur4nniiioi~1qIu~flni.~uo.~ni5nz::<m 74lriiiciun~::ii1mu~~5~u"ueit)~mq riu mr 4 J 4 J oonulr4iiokuoQm q sinnoiunnujldk~nnoiunnu4 dotsin~a.mrrniioIi"lu3flni4

G m~ainn'um~mdoudvo.~7"m~ ur i i iu~sns~i ihazi i~~a"m~~nd~ud~f lu~~u?~::ui~~miu

~ m z 1 ~ i ~ o o n u ~ . ~ a : : ~ n i ~ o u 4 i i ~ n ~ u i i I m n " m i u lunrd&::~u'~~m.rium.~~i~nd~~eidz::niz~m B1lun"la'in'nn?iudins"~~iueijn~i~u"i~~u Itq1fl6iis~diiunr::iilmu~~z.~ F eio

~~Iunrdfieio!d8

I. i~~adoud~mudmrzm s !d~iluqut.f

2. 1~sanr::n"i~o7'~~~udflni.~d7"m~1ndoud !dauqud

Page 6: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

~~u~umiittrn a z t ~ u I ~ i ' i l i i n ~ n t t r ~ n r : : i i i ~ ~ m ~ I r i ~ i u i ~ i i ~ t n d o u d I ~ ~ i n * .& r iittnridi8u 1mud s - o idotm~fiind~ummr 4.1 d o 4.2 azI6wnniubfluguu uuno

Z u r #.I - 1diiciunrzii1muttr kt* niroonttr~whbwodIm q ttdb~uuutslmmi~o~ntmu id $ifloontt~dnrzii$uaruq t ~ u v ~ ~ i u n i u ~ u u o ~ m u ~ d ~ n t ~ i ~ ~ ~ m i u itdni17I6-ikii~iuIm 7

tbn&ainniroon ttr~nr::i~ tJufluni4fland ~~~ i i I i i t f ind i~a inn i r9a i r~~ i~ i4~ iu Iu

n i r d ~ ~ ~ i u ~ ~ u $ ~ ~ t t d o u ' i ~ ' 1 m tdo~ainninfld6fuuou~uiu1flnrziin'anir~if~ q

ttiY muironrziin'eniru"u1ir~d~4'Ifl6miu ttu~ni4d'Ififuui j iuii l6~i~~u~ilri~~n4iu uo~muttnzodimn~~'I~u n~iu4n~iur8uiflunirmo ttnu67u \

chnknrdi(norliimnwnrziioio?"mrlk~~inn"~3mi~d?"fiqtndoud1mu~ e - go* azIfi<i cos go0 = o tdottn~~in~Iu(rumr 4.2 azI6wni'vdi~ugud fiUu 5dIi~'4iu nrzrillmuttr~~u &iJu nnaoonttrc~ob~uo~~~'tndoud'I~n~tiu~k~~inn"~~ttr~nr::ii~~

Y u l l nrii?$idliu uonainu uduttr~m~iii io~~~unir~air~inirtndoudu8~?"m~ni~fl~nd ~dkainn'u~modmrtndo~duo~?"m~te~uo ttrdda~uitdain (N) ~ j d ~ i l m i

ttfi~Iuuncioutiny~tr~1u'uci~~ t i f odain ttr.~~.~~muo.~1n nrrriisio~~d~oduu#urruiu fi ti~mjlfluy.Id 4.2 a z i ~ u ~ i ~ ~ ~ i u l ~ l u u r ~ ~ u i ( R " . ~ a i n t t n z . ~ i u l ~ l u eio?'sl~ariflugud t~odnnttrd&aotnrr~i~~?"sl~~u~flk~inn"unirtndouduod?'m~

un~tdo limn ttr~nr~iioio?'w~~tnun'm~d?"m~ tnd~uda::tflugud

Page 7: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

U. ~ I U ~ ~ ~ = ~ " - ~ ~ ~ U L L ~ J L ~ U ~ ~ I U e

a. aiuqn%dn~ziilmu~~~anawum -4 * asni n. ~ovocqdd 4.3 (n) ttnrilnuriidia q nalurmnir 4.2

Page 8: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

WF = (F cos 8) s = (6oN) (COS 37°) (3 m) I

n. 1~ri=iwi~dd 4.3 (u) r~YCIuji ~ m d j j ~ u i ~ ~ ~ i n N i~nr~=i~lCu(ia~ mg in i r & Y U & fim=iaboun rjlrjii~iumrriiIeru~~=i~n~~a~u muu ~1u~3dnrrr i ida~a~bou~0wn

~auua~wnR"wflufia n. ~ ~ n r U. fif!

Wgr3 " ' W F + W f = 120 J -30 J = 90 J

4.2 siwfiflwfloriaarnai3 oiu~1u~i~1~~1naiufind1au6a~unau~au~eru~n~1rn1~lnai~~uw"~bl~~un1~ 4.2

air ~uu~fiulwrjr&~6

Page 9: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

W = F.s = Fs cos 8

rrnz m ( A . B) = (mA) . B ........ 4.8

Imud m iflufmicumnai5'

-- J Iwnisw'oircu11~n~~loiwiuiinu3n'm~in 3 UQI qr~drznoumjultnu X, y llnz z 1au iil3niaofw$~wci3u (unit vector) 1, i naz E l u u d n z u n u m i u h l e z l d i ~ a ~ w m n i f r h ~ ~ u l ? n l a o f ~ d ~ n ~ i u a ~ t ~ u 3 n ' u K J ~

Page 10: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

i . i - 3 . 3 - E.E - 1 ...... 4.12

1.1 - I.%- j.ii - o ...... 4.13

Imud A - A J + A J + A ~ ~ ...... 4.14

B - BJ+BJ+B$ ....,. 4.15

od6 A. B - h B x + A+$, +A$, ...,.. 4.16

ttnzlunadd A = B 0~16 A . A - A x P + A y e + A 2 - A2 ,..... 4.17

,

F . s cos 0 = - u (lc + $).(27 + 3J)

Fs 6 f i

Page 11: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

d ss 4.3 si'~'hm~rllas7dols~aIwwpbs~~

t u ~ o u ~ s t : f i s i w i ~ ~ u d n ~ r n ' i ~ m ~ ~ ~ ~ d ~ ~ n ~ ~ ~ d.riiuuimtdduuudn~'Id&~dd 4.6

u c u d i ~ ~ t n d o u ~ ~ u t ~ n u x sinqa&liu xi ' l ~ ~ q m + ~ l i i u XI s11iIuii F GUUIR d8uuuldn~~iaci i l i~u~ x K J ~ U F Ff~iflu$~n'$uuo~ x H'foduu'l6ii F - F(x) lu n ~ ~ 7 ~ t : m l u ' n a a n o i ~ u e n ~ n i ~ 4.2 la 4.6 iio w = (F cos 0)s = F(S cos e) ~ i l o ~ r i n r m n i ~ ~ ~ 6 ~ r r i z n r ~ d F naRi ( ~ c i i h ~ ~ n ~ i ~ u o r a i u h u 4.1)

I I

Area = A A 3 Fx AX

1.r

(n> (u > 4.6 ~doIfimuisn~iu~luvi~iuI~tu11s.j1in.~1~'a~ nriiau'ia#u ~~lio~4nsluiiisa nsziiI17

3mqm8oudhltduxuma1uh~& 7 &yld 4.6 ((n v d u i i F, i i ~ u i n d o u ~ ~ d ' W E 1R'a?l4~?q& 7 u wuu siuInuu,a nsm'i1fi3mq ~nii'ouddiauni~nszo'~~ hr lio F,&

unrtmwiuArm~tIfitin~nnrru~ ~ ,h ~ P O R S Z U Z V I N ~ ~ ~ ~ xi ;a 4 4sii0Xud

I#lhIfhhl~; 4.6 (w) n

n i m 1 ~ i u d n ~ r n ' i 1 m u u ~ ~ ~ d n ~ ~ ~ ~ 1 ~ 6 ~ u ' srlio~fisi~~11~1~nsrn'11~'3'm~~ndoud ' I d h u n i m s ~ q ax &pJd 4.6 (n) i~a&r' I6i i~i~~n~rn' idoimq1wi~1ni~ tnboud x l o F, liuum~iioun~ol'31u(li~~ku q dx ii~mai~nni~id6sinrmmr 4.2 nlo

4.6 ~flufiaiol.nud F, nrr~itlri?'~qmdouhd AX ~ u '

Page 12: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~
Page 13: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

F, is negative x i s positive

I .r = 0

44 0 acni ~ a i 5 o l i ~ d d 4.7 i i n e t i n u r i i n b ~ t l n i ~ 4.20 9 4 6

Page 14: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~
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cog

(n) (u 3dd 4.0 (n) rruupn(jYod1~~1udr::nouK3u~nPguuan m ~ri6muin) uu~uhut9onai

sd asm i ~ ~ r ~ 1 1 ~ 1 u p l d 4.9 (n) pnljU~ziiniaA~un~rnrzo"m ~ ~ u i f i r o u q r u o . r ~ ~ n n u ? d

x=(L - h) tan 0 , m h w = I ( F ~ ~ X + F , & ) ...... 4.23 xpo, y=o

1muo1~n~nnmdouduo~i i~~u~'od I+ ~trdnrzil F ~n~il~uudn~uu~mid~I~p~u~afi"u

Fx = T sin 0 ...... 4.24

Page 16: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

x=(L - h) tan 0, y = h w = Jrngtan0dx ...... 4.27

x=o, y=o

iriaairdd 4.0 (n) sz~fluii

tan 0 = dy/dx v3o tan e dx = dy ...... 4.28

unudi 4 . ~ 8 n d u 4 . ~ 7 ael#uii~iudnaeii~mu~~ad P &ndtYu.~7uda Y 1iih &ad

= i m v f e - i m v ? ...... 4.32

k u ~ a ~ ~ 1 a m i i m : ~ ~ ~ d ~ u ~ ~ u a ~ 1 t Y ~ ~ i e r " ~ ~ ~ ~ u o ~ o " m a i d a u ~ ~ i m q i?o nnfi.nutad (Kinetic energy)' &ad I

Page 17: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

a d v Y * o~taunnaiufinir##idmuuai "nqhija~u-mdj.siu (Work-Energy Theorem) dmdiaii u~iulmu tta~nwiid~nazn'i~io?'m~

onduo.s~m~Zu- luns~ka~dtt5~nazn"i9iofo\ oz~0u~dmiunqu~~iu-~&~iut~ut~~~n'u

~ j o z t t n m ~ f i t ~ u o ~ ~ I ~ o i o I ~ G I m u ~ o i ~ w i ~ a a ~ ~ ~ u m n a z ~ i o i o ~ m ~ ~ w ~ ~ n w x 310 Z F ~ tin=

dv dv ' d x P - . dv

a = - dt dx di = v z

uonnnGu 6i~inf~~l67utt1~rnzn"il~n.~~an"~uuimtta::~~ni d ~ o z n ' i l ? ~ ~ ~ tnboufl8uthlfi ci~ChCiilnvia~~Iumoud 4.3 une 4.4 ozidulJmiunqua~iu-wcddiu Xau d~sza~dmiunqv~~iu-wsr"~.ji~~~iii

I. diuhutl~d~n 7 n a ~ i ~ o f ~ ~ o z ~ ~ i n ' . r l f l i ~ ~ d d ~ ~ ~ ~ d n ~ w s r " ~ . ~ i ~ o n u " U o ~ ? ' m ~ ~ ~ 2. ( > q) I t ~ i h ~ m 5 1

Y fiauo.rimprruinuu 3. 6iciuqnltdunu ~ : l ~ 1 6 ~ ~ n ' J ~ ~ 0 n d ~ O d . r " ~ l l ~ ~ ~ ~ d (K, < I$) hh~hli?

Page 18: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

u. ~nrtuifld 4.10 (v) uaslmuriia~lunum5 4.3 uar 4.34 e d 6

wf E -fs = -p mgS = (-0.16)(6 kg)(9.8 m . ~ - ~ ) ( 3 m)

Page 19: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

a4 0 a m 1muoilnpfbdno.auodQq8u anrunudin~~ulurmnis~~9io~du"

fl. a = F = 12N = 2m.s2 - m 6 kg

U. a = - F-f = (12-8.82)N = 0.63 m.s-2 m 6

= O ~iu~meus~TCuciw w = FS = mgh

U€IZ W = Kf-I ( i = f m v , 2 - 0 = mgh

Page 20: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

I

d 4-12 (n) ~m~ldoulnn!duu&8nu~auo"m5~~san~$a

(u) YinqOkm6~ runr:&imqnqnih

Page 21: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~
Page 22: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

w f i ~ p ~ & & h 4 (Kilowatt-hour, kwh)" ~munlnuiitw oj4lun!o4lu~aldiuu1d.;t!61~ llnu 1 $ah4 6auo'An 1 filnikd Buudin'udui~luwriaupn &6

&edw 4.11 rouud$4wuim:~hnd~fluaa 800 8nn% anrriJsz8nlnivlioun: 14 " U d atm~u1~~1uundi~~1~un15li~1nia~uu~;;%M"~nd~ud6au~~;11~a 27 lua5.%difl-1

rinnissom~.ra~Cud 1 ~ ~ ~ ~ 1 5 N l ~ l ~ ~ l 5 l f i ~ ¶ ~ ~ ~ 4 4 1 ~ M d ~ 6 ~ 1 ~ u " l u " ~ 1 5.5 dl&

Page 23: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

4.7 nqni.rn~&'?uoqvcA'qiod m ~ u d ~ ~ m ~ ~ u m u d 4.5 i i h i i d i d n u ~ i s d l n q ns:iidojkqu:iYiifi'unis

t: :,a I d d ~ u l i d t l d ~ & ~ I w o ~ ~ ' v Q Q ~ " ~ ~ M u UunQ

W = AK ...... 4.45 ' A ' d 1nudw~ciuan~uiuod~~r:l1lluuiu~a"m~indoud6~u~msi~auin~u uarciu~iSnnn

J d J atns:iilfla"mqmdoun rcmuabotn'unisid~uui~da.~wfi.~iuaa~u~~a"m~ udlnukaYd z

ujfiiirtdu 1 nsziido~mpkriol~iSn~iulnuiis.juu 1 ao:wk~iuluaddu 7 3nKau Ai$uustiiugauocafi.~lu$aorii.~ 4.4 i i l ~ ? ~ m ~ m d o u d n ~ u ~ u 9 j i i i i ~ d ~ a u ~ a idu ~~uan'uintlfluriadhKaoriid 4.5 i i~f l~n~uimidd6i i i~doauqa d~fiiifiui(nurnw

ua;rafi;liia:naiu~dudaduod~an l~in'n~iulnuus~&ndiaiiazwa"~~iuiid~dunii "w &diu d rlnt (potential energy, U)" ~azdu i iTmqd~n~nn 'un f i~ iuo~d~n~mauns:&

J u 4 %qnyadc a z ~ u ~ n d o u n n n u n u ~ 6 i ~ i ~ ~ ~ a u q a i 1 ~ f l ~ ~ i l ~ n u u i u m ~ n lcidunir

Page 24: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

naiuifuw'ukiununir 4-48 iio ungm.rn~$auatwfidiu~4dnn (law ofeonserva- v u 4'

' tion of mechanical energy) &I QIQ t d ~ ~ i a ~ ~ ~ f i m m t u

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nYn~~kuol:rioud~.js:ii~n~udiii~nri.jnuQa~uS1] 4.13 (u) 6I?u nfi~iusa6

uot~~$.jnotLdol3ufiuIu~r1 4.13 (n) ~ ~ u ~ u $ . j ~ u n ~ : n m u ~ ~ u ~ ~ . j i u ~ n G linrsrni

a&.jiuaauii'a~u$.jnunsinni~~~nudi~.j1ununi 4.34

AK = (AK), + (AK), = -; (10)(2), - (4)(6), = -70 J

arcu w~.jiu~nSua.j~ruua:i4utu +70 J o inni rd~. jgn<mI~adnf i . j i r r~niuo~ 8 v t : a d nl i rum:dr in~ iuu i~~~ni~~aquu m~uu n~j.jiurinfiuuru-dnlrS~~n<n~tii~imun = 70

3 u. ~ s i s o l i ~ d d 4-13 (v) L i ~ r ~ 6 n u d i ~ ~ n ~ l u ~ u w " ~ ~ d l ~ ~ ~ ~ l u ~ n ~ i i I . j n ' u ~ ~ ~ o ~

nd5.j &'..IuRjo(ii~ 4.4 11~: 4.9 Ro w = i k x 2 d.j1~iin~~nia~jduuii11a.jw<.j.jiuXnSua~

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dn-~iuuia~nZa~4~~ 0.2 L ~ F ; I T ad 0 aanl imuriindununi~ 4-48 ~ [ I W ~ ~ ~ U O ~ ~ & H U ~ ~ ~ E I Q ~ : ~ ~ ~ ~ E I ~ U ~ ~ ~ E I

A K ~ = 2 (;mvi)2 = 2( i)(8 kg) (3 m.s-l)Z = 72 J

un::rr~j.riur~nSuot~~v01::Md~n~m?d 0.05 turns REI

* Y n. bqnoua~mdamnuu~ 5 ium

u. ~qrnndd&iniin&niln 5 turn3 s4 0 d l Y d d Y aanl n. ~ o l 3 w w < ~ c 1 u ~ n ~ ~ 6 ~ a " m q ~ ~ : ~ 1 ~ ~ ~ u ~ d ~ : n m n ~ 6 ; 1 l U A " i ~ u ~ u t ~ u ~ u u t 0 ~ ~ ~ u

&$u wfiqiutTntdtdduu1~ = 08 ~n

an:: 6'6;1dh~EIt3"rnq = 6.8 t o ~ P l T . ? ~ l f i - ~

Page 27: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

w , + w 2 + .......... +wn = LU( ...... 4.51 t:

i do~o in~ iud i?~o inas~n~~u~o ioo" i ~lunosddil~lu 3 d5:rnn 3o I. ciu~dotoinln~a~~nd(conservativeforces), ~ ~ ~ ~ n u d ~ l u o ~ ~ n & u i u d ~ ~ L s d

ddnr:ii io~~~fi~n86ud5:11iid 2 (PI 1 ~ ~ 1 1 1 ' I ~ R d 1 ~ d d ~ d & n " ~ 1 L ~ ~ ~ l 4 5 Z ~ ~ l 4 ~ R & ~ ~ 4

2. ~iudarainaJjlda~?ni (nonconservative forces), ZwnC kuda~lrjo~r'nd d a nmuiit ar~d.rnsmM"i4o7'slq~fiindoud5::~ii~ 2 QR ~~Tio~fiiTi~aiuaaw~n"~~idu~i.~

t: s:niidpnndaod

3. J l ~ I d ~ d 0 1 f l l l 3 J l ~ ~ ~ 1 1 1 ~ (fri~ti~ll), Wf I R U ~ ~ ~ U ~ % ~ ~ I U B Z ~ ~ R ~ " U J Z H ~ I Q E ~

$uwiruad%quwriniCoud d i ~ f i ~ ~ ~ n ? i u d i u n i u n 1 5 i n ~ ~ u d ~ ~ ~ ~ 1 m ~ d ~ i u n " ~ ~ e ( n i ~

m8ouduo.r~~ 1 e.~~duurrunis 4.51 %&;I

xwc + w, + Zwnc = LU( ...... 4.52 ~ n u ~ u . r ~ o ~ i n b ; l i l u ~ ~ o ~ ~ ~ ~ ~ ~ ~ i u ~ n i ~ j r ~ I ~ ~ e i ~ r u i I u m o u i o I ~ ~m:n?iui%ummu

16u~~oafin3iu~ou ~~o: i i iu l6 i1 i~oi i i~n~1ui%u~n1uo~i~l~i f i~w&~1un~1u~ou~

63u &do ZWc = -ZAU

6LflZ wf = -Q

o:16iinunis 4-52 30 W = AK + ~ A u + Q ...... 4.53

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...... ulu'u~?~ = mgh 4.61

...... FYd¶h F ~ ~ ~ r i ? ~ = -mg 4.62

uonainw<ddiu$nu'a:dn?iudi~y~unirnil~~~oy%d&ndi?a#?~idfiu n1.1

8 n ~ i w kiu$nddd$uu11flu.r:uundd a:i?u~n'~iai~oo~uiun~~~ndoud%odr:uu

¶hl~fl~fJ~l~ fiodldlbu . i : u u % Q n ' u ~ t ~ ~ 1 ~ ~ ~ f l 5 1 d f l ? 1 ~ $ ~ w ' ~ t i ' 5 ~ ~ ~ 1 4 ~ ~ d l ~

flnSn'Yni5ns:a'FI fildCl 4-14 miun?ia~wira%mni.~ 4-69 ~:I6nri~~8~ulihlwi~i1uni dddn?iu<udi~~iis.j~u~a%addfid a-liluii ~ d a ~ ~ n ~ n f .rdQnmrln (X = o) k u F = o 1'.~r:o~d~n~fii~in1ni~~~r~n~:M"i~inniuuon ~d id~ i j ~ i *~n~ : i i do~ f i ~ l n "um

oonIdainsinmridmqa?d~idd x il]uu?n a:16iin?iu<u d u ~ d x fluu-m &#u F flunu 4 a ~ M " i ~ f l ~ m ~ ~ d ~ o u d n < u ? d ~ i i ~ ~ ~ ~ ~ a r u q n ~ a u ~ m ~ i ~ ~ ~ lunicmu&uiu Kirnnfflrs-a~n

6 4-14 (n) nnvlm~ulriuh:wian&.j~uXnu'n"un~~n~::o"m x diwl~zuui~qn'unJiq1u A a s - u Loimqar~mi~nniiIInn"uui~~wii~qwGoun~u awnnm x = + X,

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Page 32: sirr iio - old-book.ru.ac.thold-book.ru.ac.th/e-book/p/PH111(51)/PH111-4.pdf · 4.7 nqni.rn~&'?uoqvcA'qiod m~ud~~m~~umud 4.5 iihiididnu~isdln q ns:iidojkqu:iYiifi'unis t: :,a Idd~ulidtld~

r Y 4.1 A q u q n l o i i lnnfuQnm~uu~u~~uq8~f iau~3~n d ~ ~ u r . r l d u t t Y u l 3 o n 200 iiqcRir

vu d aus-u-nic 3.2 111m.1 ~ i n i i i l l l ~ i ~ f l j b l ~ ~ ~ m ~ 4 6 ~ n p I n s~ni~iudnrri i lmu

(n) ~ r - i a ~ ~ l u ~ # u ~ ~ a n llnr

(U) 1 m u ~ l n ~ n U 6 4 j b l ~

(n) OJHIJIU~M% , d '4' Id

(4) O t ~ l ~ ~ l U ~ ~ U ~ 4 ? f l ~ l ~ 6 U ~ ~ d f l 4 ~ ~ ~ 4 ~ ~ U ~ 4 3 ~ ~ ~ 3.2 IUm5

4.3 5 ' ~ q m ~ ~ u d ~ u 5 : u ~ ~ XY fiqu1134 F = (2 $ + ~ 2 3 C76'u Imud x 11n:: Y i i n i q u

fiU111.4 ~ l f l ~ ~ l j ' ~ 6 0 d ~ f l ~ j 6 1 ~ ~ ~ ~ 4 x = 6 lUR3 unr y = 5. lUm ~ j p ~ d 4.15 94

wi.riu~auuri.r P nr:dil~a'fl~mdoud~11~~#~~14

(n) OAC

(u) OBC

PlBU fl. 126 J U. 60 J n. 66.7 J 4. ~ ~ ~ ~ f ~ d l ~ ~ 4 ~ l f l 4 l ~ ~ 1 j I ~ i l n " ~ ~ ~

d n - [ h i 4 d~.ru~mtiiciu$un"pI ~lfumc

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tiraIuiiuarzuiuuuim 160 i ~ 7 i ~ u n-zzfii~io~mqu?~ 40 films doainlqIduu

~ u ~ ~ r z l ~ i i u ~ z z u i ~ i ~ u r ~ u z n i . j B iumz AjuOYD)zi8?naPi7 a . 1 ~ 1

(n) .jidmuura 160 Q3Ku

u?a 4 filans'u uu~uru'7Cunfiai11iii1iinfiaiimoon 2.6 ~ V U ~ L I J P ~ ~ ~

(n) 6ilninld"iu-~a 1.6 fi~an~uiiiu?uitnu arii%flnfiaiimooniuii~m

01811 n. 0.~38 cm. u. 1.26 J

"Y - (n) awi~n8?uoamum~db~1na~uwu~inn"~m

(n) ~ i m d d o u 6 ~ o n u o l z d ~ ~ o ~ ~ " i ~ u 30 oamCuiiu?da w~.jsindniimiawiu

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I 4.9 ~nu~nuan 0.3 ZlnnQ mdoud6i?u~n8a lo o~s.iuiCi-1

(n) oaniw&.nuonu'uoapnuon

(PI) ~ ~ C ~ ~ i G a f l u ~ ~ a ~ Y i i ~ z ~ w Eiiaiuo~GiYj~lur

mall fl. 33.8 J PI. 136 J

4 4.10 aiunun6at4u~ouuban 2600 Z~nnflloonsinnaourio ounrr~a~oflo'~.1111? v

I ~ u m i i r n u 6000 pn fi8iiiuru1alauurniulur q

(n) eani4118a v Iu~~uqurfi iu

(PI) oani~t~an~~iid~~ouu~;17ui~ua~:uiu

mav n. 2 m.s-I PI. 200 N

I U 4 4.1 i nio&*ldaijuaa 40 8nnFu~n w a d 5 MI ain(i tmria~a~~nunuuw'u~zuiu

uqva Aiuwns:~incCa~uu~ua~ruiuuuiur 130 Qa(RYU fii~dr:an$naiulauur u 4' niu'~oa~a8u~~~rniiann'~anuwu~~u 0.3 oani

(n) aiu~urutnans:ii 130 Q3Cu

(PI) aiulurutt~a~~uurniu

(n) wfiaiuonG~tdE(uuYduoann'~a ilnr

(a) &nl7~qnfiiuuoancioa

mav n. 660 J PI. -688 J n. 62 J a. 1.76 m.s-l

4.12 1ouu6uan 1600 f ih l fu Q f l d a n a l ~ ~ a O ~ l a ~ f i i H u 6 0 ~ n n i I u " ~ i n d ~ ~ ~ ~ f l ~ l f l L d u iitiwriany urda aun5znaua.nda lo tumr.iuiCi-1 nib 3 ju~Ci oam

(n) aiun~zrii6o~ouukiulu~aniu"u (PI) ~ / I & ~ T ~ ~ ~ ~ E ( ~ U O ~ ~ R ~ Q ~ ~ ~ ~ ~ ~ 3 ?ul~iltIfl$

(n) riifiaiuIuucuzdtani w7uY1.J 2 3uiB

mav fl. 7.6 x lo4 J U. 2.6 x lo4 W (=3.36 hp) fl. 3.33~ 104W (= 44.7 hp)

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4.14 u?n 3 fihniuim: 6 iilnnfu i ~ u ? u c r ? u i ~ a n i u i n ~ o c i u ' ~ n ' ~ ~ n ~ a n i u ~ ~ ~ ~ i d n ? ~ ~ 2 l " .4

6 a ~ F l Y l l ~ FhIdd 4.16 id~dd~~lfllJ?fl 6 ~ R ~ ~ U R ~ R ~ U I U I ~ ~ R M ~ ~ ~ ~ Y M k~ a i P T u n g n i ~ n ~ ~ ~ u o . ~ w ~ . ~ . ~ i u W ~ I

(n) &n8?ua.ru?a 3 filnn% urudtl?n 6 ?ilnn~umnnsnuddu (u) *rC~~4~mdu?n 3 8 n n i t 1 0 n ~ n ~ a n Y u I ~

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