ISBN (No. Jld lengkap) ISBN Harga Eceran Tertinggi (HET) Rp ,-

76

Mudah dan Aktif Belajar Fisika untuk Kelas XI

Contoh 3.9 <e%)s',e$t)0,).'7)"A)"%'LR'90'/et&/)'+&,e$&'%)3)'LR'N5'6e$)7)/).'e"e$%&'7ote"s&)1 7e%)s'A&/)'%)3)'7)+)'7e%)s'te$se,-t'+&A)+&/)"'P8W'/)1&'1&7)tD D$E$&F >&/et).-&M %L'N'LR'NY'"">L''N'LR'90'N'R8L'05 7'N'

FL LR N 'N' 'N'LRR'NZ05 R8L'0 >L

T&/)'%P'N'P8W(%L'N'HP8WIHLR'NI' $ %P'N'PW'N5 >P'N'

FP PW N 'N' 'N'LRR'NZ0'N'R8PW'05 LRR'NZ0 7P

Kata Kunci

L L DC"N' '7>P'N' 'HLRR'NZ0IHR8PW'0IP'N''J8LPW'T5 P P T)+&8',es)$'e"e$%&'7ote"s&)1'e1)st&s'7e%)s')+)1).'J8LPW'T5

Tes Kompetensi Subbab

• energi kinetik • energi potensial

B

K-r6$8$.3$;(d$3$%(&484(3$C7;$.* L5

P5

J5

:e,-).',)t-'/e9&1',e$0)ss)'V'%'+&1e7)s/)"'+)$&'/)t)7e1 se.&"%%)',es)$'e"e$%&'/&"et&/'3)"%'+&0&1&/&"3)')+)1). L\R'Ao-1e5'U&t-"%'/e1)A-)"',)t-'te$se,-t5 Co,&1' ,e$0)ss)' LWR' /%' se+)"%' ,e$%e$)/' +e"%)" /e9e7)t)"'XP'/0ZA)08't&,)4t&,)'+&$e0'+)"',e$.e"t& sete1).'0e"e07-.'A)$)/'PR'05'Fe"t-/)"1).M )5 %)3)'$e0'7)+)'0o,&1Y'+)" ,5 -s).)'3)"%'+&7e$o1e.'+)$&'7e"%e$e0)"5 ?e$et)' 0)&")"' 3)"%' 0)ss)"3)' V' /%' +&1e7)s/)"' +)$& 7-"9)/',&+)"%'0&$&"%'1&9&"'+e"%)"'s-+-t'/e0&$&"%)" JRS'te$.)+)7'.o$&fo"t)15'T&/)'7)"A)"%'1&"t)s)"',&+)"% 0&$&"%'LP'0'+)"'9'N'LR'0ZsP8'te"t-/)"'7e$-,).)"'e"e$%& 7ote"s&)1'+&'='+)"'/e$et)'sete1).'0e"e07-.'A)$)/'LR'05

V5

W5

6e"+)',e$0)ss)'R8P'/%'+&1e7)s/)"'+)$&'/et&"%%&)"'LRR'905 )5 U&t-"%1).'-s).)'3)"%'+&1)/-/)"'%)3)'%$)2&t)s& 7)+)',e"+)'te$se,-t5 ,5 U&t-"%1).',e$/-$)"%"3)'e"e$%&'7ote"s&)1'%$)2&t)s& ,e"+)'te$se,-t5 6e"+)'C',e$0)ss)'L'/%'A)t-.'0e"%%e1&"9&$'+)$&')t)s ,&+)"%'0&$&"%'+e"%)"'s-+-t'/e0&$&"%)"'JXS5'6e"+) te$se,-t'0e"-0,-/'se,-).'7e%)s'3)"%'te$1et)/'L'0 +)$&'1et)/'C'se0-1)5'T&/)'7'N'PRR'NZ0'+)"'7e%)s te$te/)"'0)/s&0-0'seA)-.'LR'908'.&t-"%'/oeB&s&e" %ese/')"t)$)',)1o/'C'+e"%)"',&+)"%'0&$&"%5

C. Gaya Konservatif dan Hukum Kekekalan Energi Mekanik <e$.)t&/)"' #$%&$r' )5NG/$15' :e,-).' 7e%)s' +&1et)//)"' +&' )t)s' 1)"t)& +)"' s)1).' s)t-' -A-"%"3)' +&&/)t/)"' 7)+)' +&"+&"%5' ?e0-+&)"8' se,-).' ,)1o/ ,e$0)ss)'''0e1-"9-$'+e"%)"'/e9e7)t)"'''te7)t'/e')$).'7e%)s5'T&/)'1)"t)& +)t)$'+)"'1&9&"8'se$t)'7e%)s"3)'&+e)18's&ste0')/)"'0e0e"-.&'U-/-0'Uoo/e8 !' N' K7 S8' +e"%)"' !' )+)1).' %)3)' 7)+)' 7e%)s' s))t' -A-"%' ,e,)s"3)' ,e$%ese$ seA)-.' (5' ?e)+))"' 3)"%' +&&"%&"/)"' 7)+)' s&ste0' te$se,-t' )+)1).' e"e$%& /&"et&/'te$7-s)t'7)+)'0)ss)',)1o/'se.&"%%)'e"e$%&'/&"et&/'7e%)s'+&),)&/)"5 =/&,)t"3)8' 0)ss)' 7e%)s' +&)"%%)7' s)"%)t' /e9&1' +)$&7)+)' 0)ss)' ,)1o/5 ?et&/)',)1o/'0e"3e"t-.'7e%)s8'1)A-',)1o/',e$/-$)"%'s)07)&')/.&$"3) ,e$.e"t&' /)$e")' %)3)' 7e%)s' 3)"%' 0e1)G)"' %)3)' +o$o"%)"' +)$&' ,)1o/5 <e$.)t&/)"'#$%&$r')5NG/&15'?e0-+&)"8')$).',)1o/',e$,)1&/')/&,)t'%)3) 7e%)s' ,e/e$A)5' =/&,)t"3)8' ,)1o/' 0e07e$o1e.' e"e$%&' /&"et&/"3)' /e0,)1& se7e$t&' s))t' ,)1o/' 0e"3e"t-.' 7e%)s8' G)1)-7-"' )$)."3)' ,e$,e+)5' 6)1o/

H)I

v k m licin

H,I

x m

H9I

x1

licin v

%x = x2 – x1

m x2

Gambar 3.14

licin

Gaya pada pegas merupakan gaya konservatif.

Usaha, Energi, dan Daya

77

/e.&1)"%)"' e"e$%&' /&"et&/"3)' 7)+)' s)1).' s)t-' )$).' %e$)/"3)8' tet)7& 0e07e$o1e.' e"e$%&' /&"et&/"3)' /e0,)1&' 7)+)' )$).' %e$)/' 3)"%' 1)&"8' 3)&t/et&/)' ,)1o/' ,e$,)1&/' /e' 7os&s&' se0-1)' H#$%&$r' )5NG/R1I5 <)+)' 7e$&st&G)' te$se,-t8' -s).)' 3)"%' +&1)/-/)"' %)3)' 7e%)s' !' N' 7 S t&+)/'0e"%-,).'e"e$%&'0e/)"&/'s&ste0'7e%)s5'^)3)'3)"%'+&1)/-/)"'o1e. 7e%)s'te$se,-t',e$s&B)t'/o"se$2)t&B5'^)3)'%$)2&t)s&'A-%)',e$s&B)t'/o"se$2)t&B8 +)7)t/).'="+)'0e"Ae1)s/)"'0e"%)7)'%)3)'%$)2&t)s&',e$s&B)t'/o"se$2)t&BD >)$&'s-+-t'7)"+)"%'3)"%'1)&"8'%)3)'/o"se$2)t&B'A-%)'0e0&1&/&'9&$&',).G) A-01).'-s).)'3)"%'+&1)/-/)"'%)3)'7)+)'7)$t&/e1'H,e"+)'+&)"%%)7'se,)%)& 7)$t&/e1I')+)1).'"o15'<)+)'/e)+))"'set&0,)"%'H7os&s&'>'N'RI8'%)3)'7e%)s !7' 7)+)' 9o"to.' te$se,-t' +&"3)t)/)"' +e"%)"' 7e$s)0))" !7"#"7S

F).-/).' ="+)' -s).)' 3)"%' +&1)/-/)"' o1e.' %)3)' 7e%)s' te$se,-tD <e$.)t&/)"' /e0,)1&' #$%&$r( )*NG8' /et&/)' ,e"+)' ,e$7&"+).' +)$&' 7os&s&' L 3)"%'0e0&1&/&'s&07)"%)"'>L'/e'7os&s&'P'+e"%)"'s&07)"%)"'>P8',es)$'-s).) 3)"%'+&1)/-/)"'%)3)'7e%)s'te$.)+)7',e"+)'+&"3)t)/)"'+e"%)"'7e$s)0))" !L8P'N'K%C %> """""""""""""""""""""""""!L8P'N'K7> %> ''''''''''''''''''''HiI F)"+)' "e%)t&B' 0e"3)t)/)"' ,).G)' )$).' %)3)' 7e%)s' %C' ,e$1)G)")" +e"%)"' )$).' 7e$7&"+).)"' %> $" M3*C/6" &4'C*69*6" j" 3*C*." 34C2:)12;" 3*:4 641*4":*.*N:*.*"3*:4"&4'C*69*6">L'+)"'>P5 >e"%)"' +e0&/&)"8' 7e$s)0))"' HiI' +)7)t' +&"3)t)/)"' +e"%)" !L8P N'K7> %> *> %> + !L8P N'K7 , P L - # >P ) >L $ . P / 7 !L8P #" ) # >P % >L $# >P ) >L $ P 7 !L8P #" ) >PP ) >LP ' HiiI P 6e$+)s)$/)"' 7e$s)0))"' HiiI8' Ae1)s1).' ,).G)' -s).)' 3)"%' +&1)/-/)" o1e.'7e%)s't&+)/'0e"%-,).'e"e$%&'0e/)"&/'s&ste0'+)"'t&+)/',e$%)"t-"% 7)+)'7os&s&')G)1'+)"'7os&s&')/.&$',e"+)'3)"%'+&/e")&'%)3)'7e%)s'te$se,-t5 <e$.)t&/)"'#$%&$r()*NH*':e,-).'7et&'+&7&"+)./)"'/e'te07)t'1)&" set&"%%&' ;$' Es).)' 3)"%' +&7e$1-/)"' -"t-/' 0e0&"+)./)"' 7et&' )+)1). !L'N'K'9;$'F)"+)'"e%)t&B't&0,-1'/)$e")')$).'%)3)',e$)t'!',e$1)G)")" +e"%)"' )$).' %e$)/' 7et&5 Es).)' /et&/)' 0e0&"+)./)"' 7et&' t&+)/' ,e$%)"t-"%' 7)+)' 7)"A)"% 1&"t)s)"'3)"%'+&1)1-&'7et&8'tet)7&',e$%)"t-"%'7)+)',es)$'7e$-,).)"'t&"%%& 7et&'+)$&'/e+-+-/)"')/.&$'/e'/e+-+-/)"')G)1"3)5'T&/)'7et&'+&7&"+)./)" 1)%&'/e'7os&s&')G)1"3)8'-s).)'3)"%'+&1)/-/)""3)')+)1).'!P'N''9;5':e9)$) 0)te0)t&s8' -s).)' tot)1' 3)"%' +&1)/-/)"' -"t-/' 0e0&"+)./)"' 7et&' +)$& ,)G).' /e' )t)s' H!LI8' 1)1-' +&7&"+)./)"' 1)%&' /e' ,)G).' H!PI' )+)1). !tot N'!P'a"!L N' HK'9;I' a' H'9;I N'R 6es)$' -s).)' 7e0&"+).)"' se,-).' 7et&' +)$&' /e+-+-/)"' )G)1' .&"%%) /e0,)1&' /e' /e+-+-/)"' )/.&$"3)' ,e$"&1)&' "o15' T)+&8' +)7)t' +&s&07-1/)" ,).G)' -s).)' 3)"%' +&1)/-/)"' o1e.' %)3)' /o"se$2)t&B' )/)"' ,e$"&1)&' "o18 A&/)' /e+-+-/)"' )/.&$' ,e"+)' /e0,)1&' /e' /e+-+-/)"' )G)1"3)5

#

Gambar 3.15 Seseorang sedang melakukan usaha memindahkan peti.

Tugas Anda 3.2 Sebutkan contoh-contoh gaya konservatif yang ada di sekitar Anda.

78

HJKPLI

Mudah dan Aktif Belajar Fisika untuk Kelas XI

$

1. Perumusan Hukum Kekekalan Energi Mekanik >)1)0' 0e+)"' %$)2&t)s&8' A-01).' e"e$%&' 7ote"s&)1' +)"' e"e$%&' /&"et&/ s-)t-',e"+)'tet)7'HA&/)'.)"3)')+)'%)3)'%$)2&t)s&I5'<e$"3)t))"'te$se,-t'+&/e")1 se,)%)&' U-/-0' ?e/e/)1)"' !"e$%&' Ce/)"&/5' <e$.)t&/)"( #$%&$r( )*NI5 :e,-).' ,e"+)' ,e$0)ss)' '' A)t-.' ,e,)s5' <)+)' 7os&s&' L8' /et&"%%&)""3)' ;H te$.)+)7' )9-)"' H1)"t)&I5' :es))t' /e0-+&)"8' ,e"+)' ,e$)+)' 7)+)' 7os&s&' P +e"%)"' /et&"%%&)"' ;G' te$.)+)7' )9-)"5' >&/)t)/)"' ,).G)' 7)+)' ,e"+) te$A)+&' 7e"%-$)"%)"' e"e$%&' 7ote"s&)1' 3)"%' ,es)$"3)' s)0)' +e"%)"' -s).) 3)"%' +&1)/-/)"' %)3)' ,e$)t5 HJKPPI !"N"K'HD7P" +"D7LI <)+)' 7os&s&' L8' /e9e7)t)"' ,e"+)' BH8' /e0-+&)"' ,e"+)' t-$-"' .&"%%) 7)+)' 7os&s&' P' +e"%)"' /e9e7)t)"' BG$" <)+)' /e)+))"' te$se,-t8' /e9e7)t)" ,e"+)' ,e$t)0,).' /)$e")' 7e"%)$-.' 7e$9e7)t)"' %$)2&t)s&' se.&"%%)' -s).) 3)"%' +&1)/-/)"' ,e"+)' s)0)' +e"%)"' 7e$-,).)"' e"e$%&' /&"et&/8' 3)&t!"N"D/P" +"D/L

v1

1

v2

2 h1

h2

mg

Gambar 3.16 Balok dijatuhkan dari ketinggian tertentu.

HJKPJI

6e$+)s)$/)"' ,-rs$%$$.' /)0++1' +)"' ,-rs$%$$.( /)0+)1' +&7e$o1e. D7L'K'D7P"N"D/P'K'D/L )t)-

D7L'?'D/L"N"D7P"a'D/P

HJKPVI

Contoh 3.10 :e,-).',o1)',e$0)ss)'''+&1e07)$/)"'2e$t&/)1'/e')t)s'+e"%)"'/e9e7)t)"')G)1'se,es)$''R$ Fe"t-/)"M )5 t&"%%&'0)/s&0-0'3)"%'+&9)7)&Y'+)" ,5 /e9e7)t)"'/et&/)',o1)'0e"9)7)&'t&"%%&'sete"%).'0)/s&0-05 v2 = 0 D$E$&F Ek2 ; Ep2 h2 = h )5 DCL"?"D7L"N"DCP?"D7P '9;L'a' L 'BLP N''9;P'a' L 'BPP P P R'a' L 'BLP #"'9;"a'R h P BRP L P `1e.'/)$e")'BH"'N"BA"0)/)' 'BR 'N''9;" $";''N P9 P T)+&8't&"%%&'0)/s&0-0'3)"%'+&9)7)&')+)1).';"#" ,5

DCL"?"D7L

BRP 5 P9

Ek1 ; Ep1

m

h1 = 0 v1 = v0

N"DCP?"D7P

R''a L 'BRP N''9 L ; '*7& a L 'B P P P P

#

$

P L 'B P N''9 * L BR + a L 'B P , R P . P P9 / P L 'B P N'' L BP a L 'B P P R V R P L 'B P N L 'B P V R P B P #" L BP P R L BP BP N P R T)+&8'/e9e7)t)"',o1)'/et&/)'0e"9)7)&'t&"%%&'sete"%).'t&"%%&'0)/s&0-0')+)1).

B"N'

L BP $ P R

Usaha, Energi, dan Daya

79

Contoh 3.11 :e,-).',)t-',e$0)ss)'''te$%)"t-"%'7)+)'se-t)s't)1&'3)"%'7)"A)"%"3)' ! '+&,e$&'%)3) 0e"+)t)$5'6)t-'0-1)&',e$%e$)/'+e"%)"'/e1)A-)"')G)1'BR'se7e$t&'7)+)'%)0,)$8'/et&/) ,)t-'0e"3&07)"%'+e"%)"'s-+-t' ! 8't&"%%&'3)"%'+&9)7)&',o1)'+)$&'t&t&/'set&0,)"%"3) )+)1).';5'Fe"t-/)"M )5 t&"%%&'0)/s&0-0'3)"%'+&9)7)&',)t-Y'+)" ,5 ,es)$'/e9e7)t)"')G)1',)t-'HBRI5 D$E$&F )5 DC="?"D7="N"DC6?"D76 ! '9;='a' L m B 2A N''9;6'a' L 'BP6 P P ! 2 L R'a' mB0 N''9;6'a'R P h BRP BR'N' P9; ' ' ; #" v0 P9 T)+&8't&"%%&'0)/s&0-0'3)"%'+&9)7)&',)t-'N' ,5

9os ! &

!); !

;"N' ! 'K' ! " 9os ! &

Tugas Anda 3.3 Apakah Anda tahu olahraga bungee jumping? Selidikilah Hukum Kekekalan Energi yang bekerja saat orang melakukan bungee jumping.

BRP P9 $

! 'K' ! ' 9os ! &

BRP P9

BRP P9

BR'N' P 9 ! #L ) 9os ! $

Contoh 3.12 6)1o/'='3)"%',e$0)ss)'W'/%'0e"%%e1&"9&$'+)$&')t)s'se,-).',&+)"%'0&$&"%'3)"%'s-+-t 0&$&"%"3)'JRS5'6)1o/'te$se,-t'/e0-+&)"'0e"-0,-/'7e%)s'3)"%'te$1et)/'\'0'+)$& 7os&s&'se0-1)5'T&/)'/oeB&s&e"'%ese/')"t)$)',)1o/'='+e"%)"',&+)"%'0&$&"%'R8PW8',e$)7) 0ete$'7e%)s'te$te/)"D'>&/et).-&'/o"st)"t)'7e%)s'N'WRR'NZ05 D$E$&F Es).)'3)"%'+&1)/-/)"'%)3)'7e%)s')+)1).'"e%)t&B'/)$e")'7e%)s'0e1)G)"'%)3)'te/)" ,)1o/5'=$t&"3)8'/et&/)'7e%)s'te$te/)"8'7e%)s'0e1)G)"'%)3)'te/)"'se.&"%%)'%)3) 7e%)s'+)"')$).'7e$7&"+).)"',e$1)G)")"')$).5'<e$.)t&/)"'%)0,)$',e$&/-t5 !7e%)s'N' L '7>P'N'K L '78P P P s !%$)2"#"+ % DC"#"+"'9H;9'K';)I A b 'N''9H&"?"8I's&"'JRS ha 'N'R8W''9H&"?"8I B Es).)'o1e.'%ese/)"',e$"&1)&'"e%)t&B hb /)$e")')$).',)1o/',e$1)G)")" hc C 30° +e"%)"')$).'%)3)'%ese/5 !92&27 #"+!5/"H&"?"8I N' ) " k '9"9os'JRS"H&"?"8I N' L J "'9"H&"?"8I " / P

80

Mudah dan Aktif Belajar Fisika untuk Kelas XI

Ce$-A-/'7$&"s&7'e"e$%&'+&/et).-&',).G) !.).*1"#" %D7 se.&"%%)'+&'7e$o1e. !C29*&"?"!9:*B"?"!92&27"#" L '"HB(G"+"B*GI P L L L G K 78 "?" "'9H&"?"8I'K' 3 '9H&"?"8I "k 'N' L '"HRP'K'RPI P P P P

Pembahasan Soal

L * J" k +- 8"+"R8W'&'a'' L 3 " k &'N'R K L 7"8G"?" L "'"9" , R8 W ) P P P P . / ="+)'+)7)t'0e"3e1es)&/)"'7e$s)0))"'/-)+$)t'te$se,-t'+e"%)"'0e"%.&t-"%'8'+)$& '"#"W'/%8'7"#"WRR'NZ08'&"#"\'08' " k 'N'R8PW8'+)"'9"#"LR'0ZsP5 WRR'N/m

#P$#W'/% $ #LR'0ZsP $

+ L L 3 J +- #R8PW$ - 8"+"HR8WIH\'0I'a' HR8PWIH\'0I'N'R P .P / /

* .

# $

8G"0P'K' , R8W ) *,

W'8G0P"+"R8P\PW'8'0K'P8P_\'0'N'R P

8LP N' N' N'

) # )R8 P\PW $ ' H )R8 P\PWI )

a.

3 mv2 2

d.

1 mv2 2

b.

mv 2

e.

1 mv 2 4

c.

3 2 4 mv

Soal UMPTN Tahun 1989

# V $#W$ #)P8 P_P\ $

Pembahasan: hB = 2hA Berarti, EpB = 2 EpA Sesuai dengan Hukum Kekekalan Energi Mekanik maka EpB – EpA = EkA – EkB EkB = 2 EkA

LR R8 P\PW '

Dua buah benda A dan B yang bermassa masing-masing m, jatuh bebas dari ketinggian h meter dan 2h meter. Jika A menyentuh tanah dengan kecepatan v m/s, benda B akan menyentuh tanah dengan energi kinetik sebesar ....

VW8 VV

LR

R8 P\PW ' _8 XV LR

#1 $

= 2 2 mv = mv2

8H"#"KR8_W'0'Ht&+)/'te$7)/)&I 8G"#"R8X'0 T)+&8'7e%)s'te$te/)"'seA)-.'R8X'05

2

Jawaban: b

Contoh 3.13 6o1)'+)7)t',e$%e$)/'t)"7)'%ese/)"'7)+)'1&"t)s)"'se7e$t&'%)0,)$',e$&/-t5':))t'+&'t&t&/ =8',o1)',e$/e9e7)t)"'PRR'90Zs5'6e$)7)'1)A-'+&'t&t&/'6'+)"']D A C 80 cm 50 cm B D$E$&F <)+)'s&ste0',e$1)/-'?e/e/)1)"'!"e$%&'Ce/)"&/'se.&"%%)M L L )5 '"9;='a' 'B=P'N''"9;6'a' 'B6P P P L L HLR'0ZsPIHR8\'0I'a' HP'0ZsIP'N'R'a' B6P P P B6'N' PR'0Zs'N'V8VV'0Zs T)+&8'/e1)A-)"',o1)'+&'t&t&/'6')+)1).'V8VV'0Zs5 L L ,5 '"9;='a' 'B=P'N''"9;]'a' 'B]P P P

L L HLR'0ZsPIHR8\'0I'a' *, +- HP'0ZsIP'N'HLR'0ZsPIHR8W'0I'a' B]P P .P/ B]'N' LR '0Zs'N'J8LV'0Zs T)+&8'/e1)A-)"',o1)'+&'t&t&/']')+)1).'J8LV'0Zs5

Usaha, Energi, dan Daya

81

2. Analisis Gerak pada Roller Coaster A lintasan loop B

Sumber: Dokumentasi Penerbit

Gambar 3.17 Lintasan roller coaster.

A C

N c mg

B

Gambar 3.18 Lintasan roller coaster dengan loop berbentuk lingkaran.

U)07&$'se0-)'te/"o1o%&'+&'t)0)"'.&,-$)"'se7e$t&' O4&62<"P*638' O4&62< !):138')t)-'>-"&)'@)"t)s&'s)"%)t'/)3)')/)"'/o"se7'B&s&/)5'>&')"t)$)'seA-01). 7e$0)&")"' 3)"%' )+)8' :)112:" ()*&.2:' )t)-' 3)"%' ,&)s)' +&se,-t' .)1&1&"t)$' +)7)t 0e"+o$o"%'="+)'-"t-/'0e0).)0&'1e,&.'+)1)0'/o"se7'B&s&/)'te"t)"%'%e$)/5 <e$.)t&/)"' #$%&$r( )*NJ5' ?e"+)$))"' t)"7)' 0es&"' 0e"%%-")/)"' ,)" ,e$A)1)"'H()6B2<):"821.I'-"t-/'")&/'/e'7-"9)/',-/&t'='0e1)1-&'1&"t)s)"'3)"% t&+)/' te$1)1-' 9-$)05 <-"9)/' ,-/&t' =' se"%)A)' +&$)"9)"%' 1e,&.' t&"%%&' +)$&7)+)' 7-"9)/ 1oo7' 68' .)1' te$se,-t' 0e0-"%/&"/)"' e"e$%&' 7ote"s&)1' /e"+)$))"' +&' = 3)"%' 1e,&.' ,es)$' se.&"%%)' 0)07-' ,e$A)1)"' 0e1)1-&' 1&"t)s)"' 0e"-A7-"9)/' 6' +e"%)"' ,)&/5' d&"t)s)"' 1oo7' se"%)A)' +&,-)t' se7e$t&' tetes)"' )&$ te$,)1&/5'T&/)'1oo7',e$-7)'1&"%/)$)"'7e"-.8')/)"'+&7e$o1e.',o,ot'7e"-04 7)"%'e")0'/)1&',o,ot'"o$0)1"3)'s))t'/e"+)$))"'+&'7os&s&'te$e"+).8'/o"+&s& &"&' +)7)t' 0e"3e,),/)"' 7-s&"%' 1)1-' 7&"%s)"5' d&"t)s)"' 1oo7' 3)"%' se7e$t& tetes)"' )&$' .)"3)' 0e0,e$&/)"' ,o,ot' 0)/s&0-0' J8X' /)1&' ,o,ot' "o$0)14 "3)8' 7)+)' ,o,ot' te$se,-t' 7e"-07)"%' 0)s&.' 0e$)s)/)"' /e"3)0)")"5 ?et&/)':)112:"()*&.2:',e$)+)'+&'t&t&/'te$t&"%%&'+)$&'1&"t)s)"'1oo78'3)&t+&'t&t&/']'se7e$t&'3)"%'="+)'1&.)t'7)+)'#$%&$r()*NK8'%)3)'se"t$&7et)1"3) )+)1).' $es-1t)"' +)$&' @]' H%)3)' te/)"I' +)"' ,es)$' %)3)' ,e$)t' 7e"-07)"% '9' se.&"%%) BP Q :3)$)t' /e1)A-)"' 0&"&0)1' +&' t&t&/' ]' )+)1).' @(' N' R' se.&"%%)' +&7e$o1e.

"%s'N'@9'a''9'N' '

R"?"'9"#" '

BP( Q

B Cmin 'N' 9: ?et&/)' :)112:" ()*&.2:' ,e$)+)' +&' t&t&/' te$e"+).8' 3)&t-' t&t&/' 68 DC6 #"R D76?"DC6 #"D79"?"DC9

L L 'B P'a''9;6 N' 'B]P'a''9;] P 6 P P ?)1&/)"' /e+-)' $-)s' 7e$s)0))"' te$se,-t' +e"%)"' ' se.&"%%)' +&7e$o1e. '

P"9;6"?"B6G"#"P"9;]"?"B]G `1e.'/)$e")';6"#"R'Y';]"#"PQY'+)"'B]G"#"9Q'0)/) 7e$s)0))"' 0e"A)+& R'a'B6G"#"P"9HPQI'a'9Q B60&" 'N' W9Q

HJKPWI

?et&"%%&)"' )G)1' 0&"&0)1' 1-"9-$)"' +&' t&t&/' =' +)7)t' ="+)' .&t-"% 0e1)1-&' 7e"e$)7)"' U-/-0' ?e/e/)1)"' !"e$%&' Ce/)"&/' +&' t&t&/' =' +)"' ] )%)$' :)112:" ()*&.2:' 0)07-' 0e1eG)t&' 1oo7' +e"%)"' )0)"5

82

Mudah dan Aktif Belajar Fisika untuk Kelas XI

Contoh 3.14 :e7oto"%',)1o/',e$0)ss)'''0e1-"9-$'7)+)'s-)t-'t)1)"%'H1&"%/)$)"'+)1)0I'se7e$t& te$1&.)t'7)+)'%)0,)$5'T&/)'%)3)'%ese/')"t)$)',)1o/'+)"'t)1)"%'+&),)&/)"8 )5 ,e$)7)/).'/et&"%%&)"'0&"&0-0',)1o/'3)"%'.)$-s'+&1e7)s')%)$'%e$)/)""3)'+)7)t 0e"9)7)&'7-"9)/'1&"%/)$)"'Ht&t&/'6IDY'+)" ,5 te"t-/)"1).',es)$'7e$9e7)t)"',)1o/'+&'t&t&/'65 D$E$&F A

B

v

NB mg

hA R

C

)5

^-")/)"'$-0-s'/e1)A-)"'0&"&0-0'7)+)'t&t&/'te$e"+).8',-rs$%$$.(/)0+H15 T)+&8'/e1)A-)"'0&"&0-0'+&'t&t&/']',es)$"3)'B]'0&"'N' W9Q 'se.&"%%)')"t)$)'t&t&/ ='+)"']'+e"%)"'0e"%%-")/)"'.-/-0'/e/e/)1)"'e"e$%&'0e/)"&/5 DC='a'D7='N'DC]'a'D7] ' 9 ;='a'

L L 'B P'N'' 9 ;]'a' 'B]P P = P

' 9 ;='a'R'N'R'a'

,5

L ''HW9QI P

;='N'P8W'Q T)+&8'/et&"%%&)"'0&"&0-0')%)$',)1o/'0e"9)7)&'t&t&/'6')+)1).'P8W'Q5 6es)$'7e$9e7)t)"'+&'t&t&/'6')+)1).'7e$9e7)t)"'se"t$&7et)15'6e$+)s)$/)"'%)0,)$8 +&'t&t&/'6 %s'N'@'a''9 '*&"#"'98'+&'0)")'@'N'R *&'N'9 T)+&8''7e$9e7)t)"',)1o/'+&'t&t&/'L')+)1).'*&'N'95

Tes Kompetensi Subbab

Kata Kunci • • • • •

energi mekanik gaya konservatif gaya sentripetal kelajuan minimal konstanta pegas

C

K-r6$8$.3$;(d$3$%(&484(3$C7;$.* L5 =7)/).'3)"%'="+)'/et).-&'te"t)"%'%)3)'/o"se$2)t&B +)"'%)3)'t&+)/'/o"se$2)t&BD P5 =7)/).'.-/-0'/e/e/)1)"'e"e$%&'0e/)"&/',e$1)/7)+)'se,-).',e"+)8'A&/)'%)3)'/o"se$2)t&B',e/e$A)'7)+) ,e"+)'te$se,-tD J5 >-)',-).',e"+)'='+)"'6'3)"%',e$0)ss)'0)s&"%40)s&"% '8'A)t-.',e,)s'+)$&'/et&"%%&)"';'0ete$'+)"'P;'0ete$5 T&/)'='0e"3e"t-.'t)").'+e"%)"'/e9e7)t)"'Q'0Zs8 te"t-/)"1).' e"e$%&' /&"et&/' ,e"+)' 6' s))t' )/)" 0e"3e"t-.'t)").5

V5

W5 _5

:e,-).',)1o/',e$0)ss)'W'/%'0-1)40-1)'+&)05'6)1o/ te$se,-t'/e0-+&)"'+&A)t-./)"'+)$&'s-)t-'/et&"%%&)" _8W'90'7)+)'se,-).'7e%)s'3)"%'/o"st)"t)'%)3)"3) LRR'NZ05'T&/)'9'N'[8\'0ZsP8'',e$)7)'0ete$'7e%)s'te$te/)"D Fo1e' 0e0&"+)./)"' ,-/-' +)$&' 1)"t)&' /e' )t)s' 0eA)5 6e$)7)'-s).)'tot)1'3)"%'+&te$&0)'o1e.',-/-'te$se,-tD F&%)',)t-',)t)'3)"%'te,)1"3)'\'90'+&1et)//)"'+&')t)s se,-).' 0eA)5' U&t-"%1).' -s).)' -"t-/' 0e"-07-/ /et&%)',)t-',)t)'te$se,-t'+)1)0's)t-'t-07-/)"'A&/) 0)ss)'set&)7',)t-',)t)'N'L8W'/%5

Usaha, Energi, dan Daya

83

X5

\5

:e,-).'/e1)7)'A)t-.',e,)s'+)$&'/et&"%%&)"'_'0ete$5 T&/)' 0)ss)' ,-).' /e1)7)' P8W' /%' +)"' 9' N' LR' 0ZsP8 te"t-/)"1).'/e9e7)t)"',-).'/e1)7)'s))t'0e"9)7)& /et&"%%&)"'P'0ete$'+)$&'t)").'+)"'e"e$%&'/&"et&/',-). /e1)7)'ses))t'se,e1-0'0e"9)7)&'t)").5 :e,-).'/e$et)'0e1eG)t&'1&"t)s)"':)112:"()*&.2:'+e"%)" +&)0ete$'PR'05'=%)$'/e$et)'+)7)t'0e1&"t)s'+e"%)" )0)"8' te"t-/)"1).' /e9e7)t)"' 0&"&0-0' /e$et) te$se,-t5

[5

:e,-).' ,e"+)' ,e$0)ss)' R8XW' /%' A)t-.' ,e,)s' +)$& /et&"%%&)"'\'0ete$'+&')t)s't)").5'T&/)'9'N'LR'0ZsP8 te"t-/)"1).M )5 /e9e7)t)"',e"+)'s))t't&,)'+&'t)").Y'+)" ,5 -s).)'o1e.'%)3)',e$)t'se1)0)'7e$7&"+).)"5 LR5 :e,-).'7e1-$-'+&te0,)//)"'0&$&"%'/e')t)s'+e"%)" s-+-t'e1e2)s&'VWS'+)"'e"e$%&'/&"et&/'se,es)$'LWR'T5 T&/)'9'N'LR'0ZsP8'te"t-/)"1).'e"e$%&'/&"et&/'+)"'e"e$%& 7ote"s&)1',e"+)'7)+)'s))t'0e"9)7)&'t&t&/'te$t&"%%&5

D. Daya

Tugas Anda 3.4

="+)' te1).' ,e1)A)$' te"t)"%' 9)$)' 0e"%.&t-"%' -s).)' +)$&' %)3)' 3)"% +&1)/-/)"5' >&,)"+&"%/)"' 0e"%et).-&' ,es)$' -s).)8' 1e,&.' 0e")$&/' 0e"%e4 t).-&' se,e$)7)' 1)A-' -s).)' te$se,-t' +&/e$A)/)"5' Fe"t-"3)' ,es)$)"' G)/t-' +& +)1)0' ,).)s)"' &"&' 0e"A)+&' s)"%)t' ,e$7e$)"5' :))t' -s).)' 7e$' s)t-)"' G)/t+&+eB&"&s&/)"8' 0-"9-11).' &st&1).' +)3)5 <e$1-'="+)'&"%)t',).G)'+)3)'t&+)/'+&te"t-/)"'o1e.',es)$'e"e$%&'3)"% +&0&1&/&' s-)t-' ,e"+)5' E"t-/' 1e,&.' 0e0).)0&"3)8' 7e$.)t&/)"' 9o"to. ,e$&/-t5' E9o/' +)"' 6-tet' ,e$0)ss)' s)0)8' 3)&t-' WR' /%8' 0e")&/&' 1)"t)&' +-) se/o1)."3)' set&"%%&' J' 0ete$5' ?e+-)"3)' 0e0&1&/&' e"e$%&' s)0)' ,es)$' -"t-/ 0e1)/-/)"'-s).)'L5WRR'Ao-1e5'!"e$%&'7ote"s&)1'3)"%'+&0&1&/&'0e$e/)'s)0)8 G)1)-7-"'/e"3)t))""3)'E9o/'s)07)&'+&'1)"t)&'+-)'1e,&.'9e7)t5'>)$&'-$)&)" 9o"to.' te$se,-t' +&/et).-&' ,).G)' )$t&"3)' -s).)' ,e1-0' +)7)t' 0e0,e$&/)" &"Bo$0)s&'1e,&.'1e"%/)7'te"t)"%'7e$7&"+).)"')/&,)t'7e"%)$-.'%)3)5'>)1)0 7e$&st&G)' &"&8' +)7)t' +&/)t)/)"' ,).G)' E9o/' 0e0&1&/&' +)3)' 1e,&.' ,es)$ +)$&7)+)' 6-tet' G)1)-7-"' /e+-)"3)' 0e0&1&/&' /e0)07-)"' -"t-/' 0e"%4 .)s&1/)"' e"e$%&' 3)"%' s)0)5 T)+&8' +)3)' )+)1).' ,es)$)"' B&s&/)' 3)"%' 0e"3)t)/)"' -s).)' 3)"% +&1)/-/)"'o1e.',e"+)'set&)7'se/o""3)')t)-'1)A-'e"e$%&'3)"%'+&,-t-./)" ,e"+)' set&)7' se/o""3)5 >)3)' H$)t)4$)t)I'N'

Sebutkan contoh alat-alat yang mencantumkan besaran daya yang ada di sekitar Anda.

R&

-s).)' se1)"%'G)/t-

% %& ! ')t)-' & %B R& %. %.

HJKP_I

?ete$)"%)"M ! N' -s).)' 3)"%' +&1)/-/)"' HAo-1eI %. N' G)/t-' 3)"%' +&7e$1-/)"' Hse/o"I B N' /e1)A-)"' $)t)4$)t)' H0ZsI >)1)0's&ste0':e8's)t-)"'+)3)'+&t-$-"/)"'+)$&'s)t-)"'-s).)8'3)&t-'TZs5 :)t-)"' te$se,-t' se$&"%' +&se,-t' G)tt8' +&tet)7/)"' se,)%)&' 7e"%.)$%))" te$.)+)7' &10-G)"' :/ot1)"+&)8' 3)&t-' D$%-s( W$CC' HLXJ_KL\L[I5 :)t-)"' +)3)' +)1)0' /e0)07-)"' se,-).' 0es&"' ,&)s)' 0e"%%-")/)" s)t-)"' ;):&2" C),2:' H;CI' )t)-' +)3)' /-+)5 L'.7'N'XV_'G)tt'N'R8XV_'/k5 L'/k.'N'L'H/kIHL'A)0I'N'J8_'b'LR_'T5

84

Mudah dan Aktif Belajar Fisika untuk Kelas XI

/k.' )+)1).' s)t-)"' -s).)' )t)-' e"e$%&8' ,-/)"' s)t-)"' +)3)5' :)t-)" te$se,-t',)"3)/'+&%-")/)"'-"t-/'0e"3)t)/)"'e"e$%&'1&st$&/5'T&/)'set$&/) 1&st$&/' 0e0&1&/&' +)3)' JRR' G)tt8' e1e0e"' set$&/)' te$se,-t' e"e$%&' 1&st$&/ 0e1)/-/)"' /e$A)' )t)-' -s).)' JRR' Ao-1e' set&)7' se/o""3)5

Contoh 3.15 l&"to'3)"%',e$0)ss)'WR'/%'0e")&/&'t)"%%)'/e'1)"t)&'t&%)'set&"%%&'LP'0'se1)0)'R8W'0e"&t5 6e$)7)/).'+)3)'$)t)4$)t)'3)"%'+&1)/-/)"'l&"toD D$E$&F >&/et).-&M ''N'WR'/% ;'N'LP'0 .'N'R8W'0e"&t R'N' R' &

! %.

&

'9; %.

#WR'/% $ #LR'0ZsP $ #LP'0 $

N'PRR'G)tt JR's T)+&8'l&"to'0e"%e1-)$/)"'+)3)'se,es)$'PRR'G)tt5

Contoh 3.16 :e,-).'0es&"'7o07)'se"t$&B-%)1'+)7)t'0e0&"+)./)"'JRR'/%')&$'/e',)/'3)"%'t&"%%&"3) \'0ete$'se1)0)'P8W'0e"&t5'T&/)'eB&s&e"s&'0es&"'7o07)'te$se,-t'.)"3)'\Rm8',e$)7)/). +)3)'$)t)4$)t)'1&st$&/'3)"%'+&7e$1-/)"D D$E$&F >&/et).-&M ' N'JRR'/% ; N'\'0 . N'P8W'0e"&t'N'LWR's >)3)'3)"%'+&7e$1-/)"'-"t-/'0e0&"+)./)"')&$')+)1). %! '9; & R'N' %. %. ''' &

# JRR /% $ #LR 0ZsP $ #\ 0 $

N'L_R'G)tt LWR s >)3)'3)"%'+&7e$1-/)"'7o07)'-"t-/'0e07e$o1e.'-s).)'se,es)$'L_R'G)tt'+e"%)" eB&s&e"s&'0es&"'\Rm')+)1). R'N'

L_R'G)tt L_R'G)tt & 'N'PRR'G)tt5 \Rm R8\

T)+&8'+)3)'7o07)')%)$'eB&s&e"s&"3)'\Rm'.)$-s'se,es)$'PRR'G)tt5

Usaha, Energi, dan Daya

85

Tes Kompetensi Subbab

D

K-r6$8$.3$;(d$3$%(&484(3$C7;$.* L5

P5

J5

V5

l&"o'0e")&/&'t)"%%)'3)"%'t&"%%&"3)'W'0'+)1)0'G)/t_'+et&/5'U&t-"%1).'+)3)'$)t)4$)t)'l&"o'+)1)0's)t-)" ;C'A&/)'0)ss)"3)'_R'/%5'H9'N'[8\'0ZsPI5 :e,-).'7o07)'0es&"'+&%e$)//)"'o1e.'0oto$'1&st$&/'3)"% 0e0&1&/&'+)3)'J';C5'Ces&"'te$se,-t')/)"'0e")&//)" ,e,)"'PPJ8\'/%'/e'te07)t'3)"%'t&"%%&"3)'LV'05'U&t-"%1). G)/t-' 3)"%' +&,-t-./)"' -"t-/' 0e")&//)"' ,e,)" te$se,-t5 :e,-).'0o,&1'0e"%%-")/)"'0es&"'LR'';C5'6e$)7)'%)3) $)t)4$)t)'3)"%'+&,e$&/)"'0es&"'0o,&1'te$se,-t')%)$'+)7)t ,e$%e$)/'+e"%)"'/e9e7)t)"'/o"st)"'[R'/0ZA)0D :e,-).',)1o/',e$0)ss)'P'/%',e$)+)'+)1)0'/e)+))" +&)0'+&')t)s',&+)"%'0&$&"%5'6)1o/'te$se,-t'0e"+)7)t %)3)'!'se,es)$'L_'N'se)$).',&+)"%'0&$&"%'/e')t)s5

m = 2 kg

F 30°

)5

W5

_5

X5

\5

:e,-).'0es&"'7o07)'+)7)t'0e0&"+)./)"'WRR'/%')&$ /e'se,-).',)/'3)"%'t&"%%&"3)'LP'0'se1)0)'LW'0e"&t5 T&/)'eB&s&e"s&'0es&"'7o07)'&"&'\Rm8',e$)7)/).'+)3) 1&st$&/'3)"%'+&7e$1-/)"D To)"',e$0)&"'7)7)"'1-"9-$'+&'/et&"%%&)"'P'0ete$'+)$& 1)"t)&5'T&/)'/e9e7)t)"'To)"'7)+)')G)1'7e1-"9-$)"'J'0Zs8 ,e$)7)/).'/e9e7)t)""3)'/et&/)'0e"3e"t-.'1)"t)&D >)$&'/et&"%%&)"'JR'08'se,-).'/e1)7)'3)"%'0e0&1&/& 0)ss)' R8W' /%' A)t-.' +)$&' 7o.o"5' 6e$)7)/).' e"e$%& /&"et&/' 3)"%' +&0&1&/&' /e1)7)' 7)+)' s))t' 0e"9)7)& /et&"%%&)"'LR'0'+&')t)s't)").'H9'N'LR'0ZsID :e,-).',e"+)'3)"%'0)ss)"3)'_'/%',e$%e$)/'+e"%)" /e9e7)t)"'tet)7'V'0Zs5'?e0-+&)"8',e"+)'te$se,-t'+&,e$& %)3)' se.&"%%)' ,e"+)' 0e"%)1)0&' 7e$1)0,)t)"8 /e0-+&)"',e$.e"t&'sete1).'0e"e07-.'A)$)/'LP'05 Fe"t-/)"M )5 ,es)$'%)3)'7e"%e$e0)"'3)"%',e/e$A)'7)+)',e"+)Y ,5 -s).)'3)"%'+&1)/-/)"',e"+)'.&"%%)',e$.e"t&5

Fe"t-/)"'/e9e7)t)"',)1o/'sete1).'0e"e07-. A)$)/'&'N'R8W'0'se7)"A)"%',&+)"%'0&$&"%5 U&t-"%'+)3)'3)"%'+&,e$&/)"'o1e.'%)3)'%$ H&'N'R8W'0Y"9'N'LR'0ZsPY's-+-t',&+)"%'0&$&"%'N'JRSI

,5

Rangkuman L5 Es).)' )+)1).' ,es)$"3)' %)3)' H%I' se)$).' 7e$4 7&"+).)"'HsI'+&/)1&'+e"%)"',es)$"3)'7e$7&"+).)" !'N'%"9os ! "&')t)-'!'N'%&"9os ! +e"%)"' ! ' )+)1).' s-+-t' )"t)$)' %)3)' +)" 7e$7&"+).)"5 Es).)',e$.)$%)'"e%)t&B'0e"-"A-//)"',).G)'%)3) 3)"%',e/e$A)',e$1)G)")"'+e"%)"')$).'7e$7&"+).)"5 P5 <)+)'%$)B&/'%)3)'te$.)+)7'7e$7&"+).)"8',es)$'-s).) 0e$-7)/)"'1-)s'+)e$).'3)"%'+&)$s&$5 F

W1 s Wtotal = W1+W2

W2

J5 !"e$%&' )+)1).' /e0)07-)"' -"t-/' 0e1)/-/)" -s).)5'!"e$%&'/&"et&/')+)1).'e"e$%&'3)"%'+&0&1&/& o1e.'set&)7',e"+)'3)"%',e$%e$)/5

86

Mudah dan Aktif Belajar Fisika untuk Kelas XI

D7'N

L '"B"G P

!"e$%&'7ote"s&)1')+)1).'e"e$%&'3)"%'+&0&1&/&'o1e. set&)7',e"+)'/)$e")'/e+-+-/)""3)5'T&/)'/e)+))" 0e0-"%/&"/)"8'e"e$%&'te$se,-t'+)7)t'+&0-"9-1/)"5 DC"N''9;'-"t-/'e"e$%&'7ote"s&)1'%$)2&t)s& DC"e1)st&s'N'

L P' 7"> -"t-/'e"e$%&'7ote"s&)1'7e%)s P

V5 Es).)' 0e$-7)/)"' 7e$-,).)"' e"e$%&' +)$&' s-)t,e"+)5 !"#"D7P"+"D7L'-"t-/'e"e$%&'/&"et&/ !"#"DCP'+"DCL'-"t-/'e"e$%&'7ote"s&)1 W5 U-/-0' ?e/e/)1)"' !"e$%&' Ce/)"&/M' nT&/)' 7)+) s-)t-' s&ste0' 3)"%' ,e/e$A)' .)"3)' %)3)4%)3) /o"se$2)t&B8'e"e$%&'0e/)"&/'s&ste0'se1)1-'tet)75o DS"#"DC"+"D7"#"/o"st)" DCL"?"D7L'#"DCP'a'D7P

T$ Es).)'tot)1'3)"%'+&1)/-/)"'o1e.'%)3)'/o"se$2)t&B .)"3)'0e07e$.)t&/)"'/e)+))"')G)1'+)"'/e)+))" )/.&$'7os&s&',e"+)8'1&"t)s)"'t&+)/'0e0e"%)$-.&5

X5 >)3)' )+)1).' -s).)' 3)"%' +&1)/-/)"' o1e.' ,e"+) set&)7'se/o"')t)-'1)A-'e"e$%&'3)"%',e$-,).'0e"A)+& e"e$%&',e"t-/'1)&"5

Peta Konsep :s$;$<(=.-r>7<(d$.(@$y$ 0e0,).)s

Es).)

!"e$%&

>)3)

.-,-"%)""3)

Es).)'N'<e$-,).)"'!"e$%& 0e0,).)s

!"e$%&'?&"et&/

!"e$%&'
U-/-0'?e/e/)1)" !"e$%&'Ce/)"&/

0e0,).)s

!"e$%&'
!"e$%&'
Refleksi Setelah mempelajari bab ini, tentu Anda dapat memahami konsep usaha, energi, dan daya. Anda juga tentu dapat mengetahui hubungan antara usaha, energi, dan daya. Nah, dari materi-materi bab ini, bagian manakah yang Anda anggap sulit? Coba diskusikan dengan teman atau guru Fisika Anda.

Dengan mempelajari konsep usaha, Anda dapat menentukan usaha dengan menentukan lintasan yang lebih efisien untuk dilakukan. Hal tersebut adalah salah satu manfaat mempelajari bab ini. Coba Anda sebutkan manfaat lain setelah mempelajari bab ini.

Usaha, Energi, dan Daya

87

Tes Kompetensi Bab 3 A.

Pilihlah salah satu jawaban yang paling tepat dan kerjakanlah pada buku latihan.

L5

:)t-)"4s)t-)"',e$&/-t'&"&'3)"%'.43*7'te$0)s-/'s)t-)" -s).)')+)1).'5555 )5 "eGto"'0ete$ ,5 Ao-1e 95 /%0PZsKP +5 /%0PZsP e5 /%0PZs 6es)$)"4,es)$)"',e$&/-t'&"&'.43*7"0e0&1&/&'s)t-)"'s)0) )+)1).'5555 )5 -s).)4e"e$%& ,5 -s).)4e"e$%&'/&"et&/ 95 e"e$%&'7ote"s&)14e"e$%&'/&"et&/ +5 te")%)4-s).) e5 %)3)4-s).) :e,-).',e"+)'0)ss)"3)'_'/%'+)1)0'/e)+))"'+&)05 ?e0-+&)"8',e"+)'te$se,-t'+&,e$&'%)3)'tet)7'se,es)$ JR' N' se1)0)' V' +et&/5' Es).)' 3)"%' +&1)/-/)"' %)3) te$se,-t')+)1).'5555 )5 L5PRR'T ,5 L5LRR'T 95 L5RRR'T +5 \RR'T e5 _RR'T 6-' C&")' 0e0,)G)' /e$)"A)"%' ,e$0)ss)' PR' /%' +)" ,e$A)1)"'seA)-.'LR'05'T&/)'7e$9e7)t)"'%$)2&t)s&'LR'0ZsP8 ,es)$'-s).)'3)"%'+&1)/-)"'6-'C&")')+)1).'5555 )5 P5RRR'T ,5 L5RRR'T 95 PRR'T +5 LRR'T e5 "o1 Co,&1' 3)"%' 0)ss)"3)' P5RRR' /%' +&$e0' +e"%)"' %)3) VR5RRR'N'se.&"%%)',e$.e"t&'7)+)'A)$)/'P'05'6es)$'-s).) s))t'7e"%e$e0)"'0o,&1'te$se,-t')+)1).'5555 )5 L8_'b'LRW'T ,5 \'b'LRV'T 95 V'b'LRV'T +5 \'b'LRJ'T e5 V'b'LRJ'T 6e"+)',e$0)ss)'LL'/%'te$1et)/'7)+)',&+)"%'+)t)$5'6e"+) te$se,-t'+&,e$&'%)3)'LRR'N'3)"%'0e0,e"t-/'s-+-t'JRS te$.)+)7',&+)"%'+)t)$5'T&/)',e"+)',e$7&"+).'seA)-.'P'08 ,es)$'-s).)'3)"%'+&1)/-/)"',e"+)')+)1).'5555

P5

J5

V5

W5

_5

88

)5

LLR J 'T

,5

LRR J 'T

95

WW J 'T

+5

WR J 'T

e5

PW J 'T

Mudah dan Aktif Belajar Fisika untuk Kelas XI

X5 <)+)',&+)"%'0&$&"%'+)"'1&9&"'=68'+&1e7)s/)"',e"+) t)"7)'/e9e7)t)"')G)1'.&"%%)',e"+)',e$)+)'+&'/)/& ,&+)"%'0&$&"%'seA)-.'W'05'T&/)'s&"! 'N'R8\8'/e9e7)t)" ,e"+)'=6')+)1).'5555 )5

W W '0Zs

,5

V W '0Zs

95

J W '0Zs

+5

P W '0Zs

e5 W '0Zs \5 :e,-).'%)3)'!'N'HP7(a'J6I'N'0e1)/-/)"'-s).)'+e"%)" t&t&/'t)"%/)7"3)',e$7&"+).'0e"-$-t''r'N'HV7'a'*6I'0 +)"'2e/to$'7'+)"'6',e$t-$-t4t-$-t')+)1).'2e/to$'s)t-)" 3)"%' se)$).' +e"%)"' s-0,-4>' +)"' s-0,-4<' 7)+) /oo$+&")t'])$tes&-s5'T&/)'-s).)'te$se,-t',e$"&1)&'P_'T8 "&1)&'*'s)0)'+e"%)"'5555 )5 W ,5 _ 95 X +5 \ e5 LP /:U,VW(NMMN1 [5 ^e$o,)/'+e"%)"'0)ss)'PR'/%'te$1et)/'7)+)',&+)"% 0&$&"%' 3)"%' s-+-t' /e0&$&"%)""3)' JRS' te$.)+)7 ,&+)"%'.o$&fo"t)15'T&/)'+&/et).-&'7e$9e7)t)"'%$)2&t)s& 9'N'LR'0ZsP'+)"'%e$o,)/',e$%ese$'seA)-.'J'0'/e')$). ,)G).8' -s).)' 3)"%' +&1)/-/)"' o1e.' %)3)' ,e$)t )+)1).'5555 )5 _R'T ,5 _R J 'T 95 LWR'T +5 PRR'T e5 JRR'T LR5 :e,-).' ,e"+)' ,e$0)ss)' W' /%' A)t-.' ,e,)s' +)$& /et&"%%&)"'LWR'05'T&/)',es)$'7e$9e7)t)"'%$)2&t)s&'9's)0) +e"%)"' LR' 0ZsP8' /e9e7)t)"' ,e"+)' s))t' ,e$)+)' +& /et&"%%&)"'PW'0'+)$&'t)").')+)1).'5555 )5 PW'0Zs ,5 JW'0Zs 95 VR'0Zs +5 WR'0Zs e5 XW'0Zs LL5 =&$'te$A-"'set&"%%&'\'0'0e"%)1&$/)"'LR'0J')&$'set&)7 se/o"5'C)ss)'Ae"&s')&$'N'L5RRR'/%Z0J'+)"'7e$9e7)t)" %$)2&t)s&'9'N'LR'0ZsP5'T&/)'.)"3)'LRm'e"e$%&'7ote"s&)1 )&$' 3)"%' +)7)t' +&-,).' 0e"A)+&' e"e$%&' 1&st$&/8' ,es)$ e"e$%&'1&st$&/'3)"%'+)7)t'+&.)s&1/)"'set&)7'se/o""3) )+)1).'5555

LP5

LJ5

LV5

LW5

L_5

)5 XR'/T ,5 XW'/T 95 \R'/T +5 [R'/T e5 [W'/T :e,-).'7ot'A)t-.',e,)s'+)$&'te07)t'3)"%'t&"%%&"3)'\R'05 T&/)'e"e$%&'7ote"s&)1')G)1'7ot'se,es)$'V5RRR'Ao-1e'+)"'9'N LR'0ZsP8'te7)t'se,e1-0's)07)&'+&'t)").'/e9e7)t)""3) )+)1).'5555 )5 WR'0Zs ,5 VR'0Zs 95 JW'0Zs +5 PW'0Zs e5 PR'0Zs :e,-).'7)1-',e$0)ss)'P'/%'+)"',e$/e9e7)t)"'PR'0Zs 0e"%.)"t)0'se,-).'7)/-'se.&"%%)'7)/-'0)s-/'/e +)1)0'/)3-'W'905'6es)$'%)3)'t).)")"'3)"%'+&se,),/)" /)3-')+)1).'5555 )5 VRR'N ,5 \RR'N 95 V5RRR'N +5 \5RRR'N e5 VR5RRR'N /2X,=WUYZ:(NMKM1 =&$'te$A-"'set&"%%&'LR'0'+e"%)"'+e,&t'se,es)$'WR'0JZs +&0)"B))t/)"' -"t-/' 0e0-t)$' t-$,&"' 3)"%' 0e"%4 %e$)/)"'%e"e$)to$'1&st$&/5'T&/)'PWm'e"e$%&')&$'te$A-"'+)7)t +&-,).'0e"A)+&'1&st$&/8'+)3)'/e/-)t)"'%e"e$)to$'set&)7 se/o""3)'s)0)'+e"%)"'5555 )5 R8[R'0k ,5 L8LR'0k 95 L8PW'0k +5 L8JR'0k e5 L8WR'0k T&/)'="+)',e$se7e+)'0e"-$-"&',-/&t't)"7)'0e"%)3-. +)"',es)$'/e9e7)t)""3)'tet)78'te$A)+&'7e$-,).)"'e"e$%& +)$&'5555 )5 /&"et&/'0e"A)+&'7ote"s&)1 ,5 7ote"s&)1'0e"A)+&'/&"et&/ 95 7ote"s&)1'0e"A)+&'/)1o$ +5 /)1o$'0e"A)+&'7ote"s&)1 e5 /&"et&/'0e"A)+&'/)1o$ /V-s(XV[(NMJH1 :e,-).' ,o1)' +&%)"t-"%/)"' 7)+)' -A-"%' t)1&' 3)"% 7)"A)"%"3)'L8W'05'6o1)'+&t)$&/'/e's)07&"%'se.&"%%) t)1&'0e0,e"t-/'s-+-t'_RS'te$.)+)7'2e$t&/)15'T&/)',o1) +&1e7)s/)"8'/e1)A-)"',o1)'7)+)'/e+-+-/)"'te$e"+). )+)1).'5555

)5 ,5 95

LW'0Zs PR'0Zs PW'0Zs

+5 LW '0Zs e5 PR '0Zs LX5 :e,-).' ,e"+)' 3)"%' ,e$0)ss)' V' /%' 0-1)40-1)' +&)08 /e0-+&)"',e$%e$)/'1-$-s'+e"%)"'7e$9e7)t)"'J'0ZsP5'Es).) 3)"%'0e"A)+&'e"e$%&'/&"et&/'sete1).'P'+et&/')+)1).'5555 )5 _'Ao-1e ,5 LP'Ao-1e 95 PV'Ao-1e +5 V\'Ao-1e e5 XP'Ao-1e L\5 :e,-).'7e%)s'0e0&1&/&'tet)7)"'7'N'PRR'NZ05'T&/)'7)+) -A-"%' 7e%)s' te$se,-t' +&%)"t-"%/)"' ,e,)"' 3)"% ,e$)t"3)'LR'N8'e"e$%&'7ote"s&)1'3)"%'+&s&07)"'+)1)0 7e%)s'te$se,-t')+)1).'5555 )5 R8RW'T ,5 R8LR'T 95 R8LW'T +5 R8PR'T e5 R8PW'T L[5 >-)',e"+)'='+)"'6'0)s&"%40)s&"%',e$0)ss)'''A)t-. ,e,)s' +)$&' /et&"%%&)"';' 0ete$' +)"' P;' 0ete$5' T&/)' = 0e"3e"t-.'t)").'+e"%)"'/e9e7)t)"'B'0Zs8',e"+)'6')/)" 0e"3e"t-.'t)").'+e"%)"'e"e$%&'/&"et&/'se,es)$'5555 )5 ,5

J P 'B P 'BP

95

J 'BP V

+5

L P 'B P

e5

L 'BP V

PR5 :e,-).' 7e%)s' +&t)$&/' +e"%)"' %)3)' LRR' N' .&"%%) ,e$t)0,).'7)"A)"%'W'905'6es)$'e"e$%&'7ote"s&)1'7e%)s te$se,-t')+)1).'5555 )5 R8W'T ,5 L8R'T 95 L8W'T +5 P8R'T e5 P8W'T

Usaha, Energi, dan Daya

89

[*

D$E$&3$;(5-rC$.y$$.(&-r784C(7.7(d-.>$.(C-5$C*

L5

:e,-).',e"+)'3)"%'0)ss)"3)'P'/%'+)$&'/e)+))"'+&)0 ,e$%e$)/'.&"%%)'/e9e7)t)""3)'0e"A)+&'LR'0Zs'se1)0) P'se/o"'/)$e")'7e"%)$-.'%)3)'#5'6e$)7)/).',es)$ -s).)'3)"%'+&1)/-/)"'o1e.'%)3)'te$se,-tD :e,-).',e"+)'0e0&1&/&'0)ss)'V'/%'+)1)0'/e)+))"'+&)05 ?e0-+&)"8' ,e$%e$)/' 1-$-s' +e"%)"' /e9e7)t)"' J' 0Zs se1)0)'P'+et&/5':)0)/).',es)$'-s).)'+)"'7e$-,).)" e"e$%&'/&"et&/'3)"%'te$A)+&D'Te1)s/)"5 :e,-).'7e1-$-',e$0)ss)'P'/%'+&te0,)//)"'2e$t&/)1'/e )t)s' +e"%)"' /e9e7)t)"' )G)1' WR' 0Zs5' F&"%%&' 3)"% +&9)7)&' 7e1-$-' )+)1).' LRR' 05' 6e$)7)/).' ,es)$"3) 7e$-,).)"'e"e$%&'0e/)"&/'0e"A)+&'e"e$%&'7)")s'7)+) 7e$&st&G)'te$se,-tD'H9'N'LR'0ZsPI :e,-).',e"+)'+&te0,)//)"'2e$t&/)1'/e')t)s'+e"%)" /e9e7)t)"')G)1'BR5'F&"%%&'0)/s&0-0'3)"%'+&9)7)& )+)1).';5'N3)t)/)"'/et&"%%&)"',e"+)'+)1)0';'7)+) s))t' e"e$%&' 7ote"s&)1' ,e"+)' s)0)' +e"%)"' e"e$%& /&"et&/"3)D :e,-).':)112:"()*&.2:'H+&'>-"&)'@)"t)s&'="9o1'+&se,-t .)1&1&"t)$I'0e"+)/&'/e'/et&"%%&)"'0)/s&0-0"3)';= N'WR'0'+&')t)s't)").'+e"%)"'/e1)A-)"'BL'N'R8W'0Zs5 ?e0-+&)"8' :)112:" ()*&.2:' 0e1-"9-$' /e' ,)G).' /e /et&"%%&)"'0&"&0-0"3)';6"N'W'0'se,e1-0'0e"+)/& /e0,)1&'0e"-A-'/et&"%%&)"';]'N'PR'05

P5

J5

V5

W5

A C

hA

lintasan roller coaster

B

hC

hB

T&/)'%)3)'%ese/':)112:"()*&.2:'+)"'1&"t)s)""3)'+&),)&/)"8 te"t-/)"' /e1)A-)"' :)112:" ()*&.2:' 7)+)' /e+-)' t&t&/ te$se,-t5

90

Mudah dan Aktif Belajar Fisika untuk Kelas XI

_5 :e,-).',e"+)',e$0)ss)'J'/%'+&%)"t-"%'+e"%)"'se-t)s t)1&'3)"%'7)"A)"%"3)'P'05'EA-"%'t)1&'3)"%'1)&"'+&&/)t 7)+)'1)"%&t41)"%&t5'6e"+)'+&7-/-1'se.&"%%)',e$%e$)/ +e"%)"'/e9e7)t)"'tet)7' P W '0Zs5'6e$)7)/).',es)$ s-+-t'0)/s&0-0'3)"%'+&,e"t-/'t)1&'te$.)+)7')$). 2e$t&/)1D X5 6o1)'3)"%'0)ss)"3)'R8V'/%'+&1e07)$/)"'/e')$).'.o$&4 fo"t)1'+e"%)"'/e9e7)t)"'LR'0Zs'+)$&'7-"9)/'0e")$) %e+-"%'3)"%'t&"%%&"3)'LPR'05 v0 A 0 120 m

vy

gedung

vx v

B

vx

lantai gedung vy

v

U&t-"%1).M )5 e"e$%&'/&"et&/')G)1Y ,5 e"e$%&'7ote"s&)1')G)1Y 95 e"e$%&'/&"et&/',o1)'/et&/)'0e"-0,-/'t)").Y +5 /e1)A-)"',o1)'/et&/)'0e"-0,-/'t)").5 \5 <)+)'se,-).'7e%)s'te$%)"t-"%',e,)"'3)"%'0)ss)"3) L'/%5'<e%)s'te$se,-t',e$t)0,).'7)"A)"%'W'905'U&t-"%1). e"e$%&'7ote"s&)1'7e%)s'+)"',e$)7)/).',es)$'e"e$%& 7ote"s&)1'7e%)s'A&/)',e,)""3)'+&t)0,).'P'/%D H9'N'LR'0ZsPI [5 :e,-).',)1o/',e$0)ss)'J'/%'0-1)40-1)'+&)05'6)1o/ te$se,-t'/e0-+&)"'+&A)t-./)"'+)$&'/et&"%%&)"'L'0'7)+) se,-).'7e%)s5'Fe$"3)t)8'7e%)s'te$te/)"'0)/s&0-0 se,es)$'VR'905'6e$)7)/).'/o"st)"t)'7e%)s'te$se,-tD H9'N'LR'0ZsPI LR5 =&$'te$A-"'\'0'+e"%)"'+e,&t'WR'0JZs'+&%-")/)"'-"t-/ 0e0-t)$'%e"e$)to$'1&st$&/5'T&/)'+&/et).-&'9'N'LR'0ZsP +)"' .)"3)' LRm' e"e$%&' )&$' 3)"%' ,e$-,).' 0e"A)+& e"e$%&' 1&st$&/8' ,e$)7)' G)tt' +)3)' 3)"%' +&.)s&1/)" %e"e$)to$'te$se,-tD e"e$%& * + , 7et-"A-/ M+)3)N se/o" 8 0e0&1&/&'s)t-)"'G)tt . /

Bab

4 Sumber: www.savannah.com

Petinju secara rutin berlatih meningkatkan kecepatan pukulan dan berusaha mempersingkat interaksi dengan sasarannya. Petinju juga menggunakan sarung tangan ketika bertinju.

Momentum, Impuls, dan Tumbukan Hasil yang harus Anda capai: menganalisis gejala alam dan keteraturan dalam cakupan mekanika benda titik. Setelah mempelajari bab ini, Anda harus mampu: menunjukkan hubungan antara konsep impuls dan momentum untuk menyelesaikan masalah tumbukan.

!"#$%&'%& )$*% +"$,$-,$ ."#-%$*/$0%$ -/$12 */ 345 3/$12 +"#2.%'%$ 6%7%& 6%-2 ,7%&#%0% 8%$0 92'2. */0"+%#/: ;"<%0%/ <"'%7 6%%<"#-%$*/$0= 6",#%$0 ."-/$12 +"7%-/& .2'27%$$8% 6"9%#% -"#%-2# *%$ /$-"$6/>: ;"."#-/ 8%$0 )$*% 7/&%- .%*% 0%+<%# */ %-%6= 6",#%$0 ."-/$12 +"7%-/& .2'27%$$8% .%*% 62%-2 6%6%#%$ *"$0%$ +"+%'%/ 6%#2$0 -/$12: !"-/$12 <"#7%-/& 6"9%#% /$-"$6/> %0%# #">7"'6 *%$ '"9".%-%$ .2'27%$ 6"+%'/$ +"$/$0'%-: ;"+%'/$ 6/$0'%- /$-"#%'6/ .2'27%$ *"$0%$ 6%6%#%$= 6"+%'/$ <%/' '2%7/-%6 .2'27%$: !"#$%&'%& )$*% <"#./'/#= +"$0%.% ."-/$12 &%#26 +"$002$%'%$ 6%#2$0 -/$125 ).%'%& ."$0%#2& 8%$0 */#%6%'%$ ."-/$12 '"-/'% 7%?%$$8% +"+2'27 *"$0%$ 6%#2$0 -/$125 @"$0%.% ."-/$12 */-2$-2- +"+/7/'/ .2'27%$ 6"9".%- +2$0'/$5 !"#-%$8%%$A."#-%$8%%$ -"#6"<2- *%.%- )$*% 1%?%< 1/'% )$*% *%.%- +"+%&%+/ /6/ <%< /$/:

A. B. C. D.

Momentum Linear Tumbukan Jenis Tumbukan Tumbukan Lenting Sebagian pada Benda Jatuh Bebas E. Ayunan Balistik F. Gaya Dorong Roket

91

Tes Kompetensi Awal 1%2%34)0)%)"%3(5(&6078*'%"098)%*:4);0<)"43';0=(*0>4)247(*;07%&5(7(*3(?0'8(3@'8(302%&674:0=(3()02474 3(:6?(*A G: P: Q:

).%'%& 6"-/%. <"$*% 8%$0 +"+/7/'/ +,+"$-2+ 120% +"+/7/'/ "$"#0/5 T/'% *2% <2%& <"$*% +"+/7/'/ "$"#0/ '/$"-/' 6%+% <"6%#= -"-%./ +%66%$8% <"#<"*%= <"$*% +%$% 8%$0 +"+/7/'/ +,+"$-2+ 7"/6/"$ #"6-/-26/5

E:

B,7% ) <"#+%66% P '0 <"#0"#%' *"$0%$ '"9".%-%$ P +K6: B,7% B <"#+%66% G '0 <"#0"#%' <"#7%?%$%$ %#%& -"#&%*%. <"$*% ) *"$0%$ '"9".%-%$ V +K6: ;"-"7%& <"#-2+<2'%$= '"9".%-%$ <,7% B +"$1%*/ Q +K6: B"#%.%'%& '"9".%-%$ %'&/# <,7% )5

A. Momentum Linear ;"-/%. <"$*% 8%$0 <"#0"#%' *"$0%$ '"9".%-%$ -"#-"$-2 */.%6-/'%$ +"+/7/'/ +,+"$-2+: B"6%#$8% +,+"$-2+ 6%$0%- <"#0%$-2$0 .%*% +%66% *%$ '"9".%-%$ <"$*% -"#6"<2-: @,+"$-2+ 8%$0 */+/7/'/ 62%-2 <"$*% %*%7%& &%6/7 ."#'%7/%$ %$-%#% +%66% *%$ '"9".%-%$ <"$*% .%*% 6%%- -"#-"$-2: !"#6%+%%$ +,+"$-2+ 62%-2 <"$*% 8%$0 <"#+%66% ! *%$ <"#0"#%' *"$0%$ '"9".%-%$ ! 6"9%#% +%-"+%-/6 */#2+26'%$ 6"<%0%/ <"#/'2-:

Tugas Anda 4.1 Jika Anda bersepeda dengan kecepatan tinggi, manakah yang memiliki momentum lebih besar, sepeda atau Anda? Apakah hal tersebut dapat memberikan penjelasan, mengapa Anda akan terpelanting ke depan ketika sepeda berhenti mendadak?

" C !! DEFGH I"-"#%$0%$J " C +,+"$-2+ <"$*% D'0 +K6H ! C +%66% <"$*% D'0H ! C '"9".%-%$ <"$*% D+K6H @,+"$-2+ %*%7%& 6"<2%& <"6%#%$ L"'-,# 8%$0 %#%&$8% 6%+% *"$0%$ %#%& '"9".%-%$ <"$*%: "#$$% '()t+n +"$0"+2'%'%$ &2'2+ 0"#%' 8%$0 '"*2% */'%/-'%$ *"$0%$ +,+"$-2+: M% +"$0%-%'%$ +,+"$-2+ 6"<%0%/ '2%$-/-%6 0"#%': N2'2+ MM O"?-,$ +"$0%-%'%$ <%&?%= ."#2<%&%$ +,A +"$-2+ <"$*% -/%. 6%-2%$ ?%'-2 6"<%$*/$0 *"$0%$ 0%8% #"627-%$ 8%$0 <"'"#1% .%*% <"$*% *%$ <"#%#%& 6%+% *"$0%$ %#%& 0%8% -"#6"<2-: ;"9%#% +%-"+%-/6= *%.%- */-27/6 6"<%0%/ <"#/'2-:

-" DEFPH -t $%&'()((* +,-./ 6"-%#% *"$0%$ <"$-2' F C ! ( 2$-2' 6"<2%& .%#-/'"7 -2$00%7 *"$0%$ +%66% ! D',$6-%$H: !"#&%-/'%$ &2<2$0%$$8% *%7%+ <"$-2' <"#/'2- /$/: #C

FC

Ingatlah Kecepatan yang berada pada kerangka satu-dimensi, penulisan notasi vektornya dapat diganti dengan notasi skalar.

-" -D !!H -! C C ! -t C !( -t -t

DEFQH

!%*% -",#/ #"7%-/L/-%6 D)$*% %'%$ +"+."7%1%#/$8% */ I"7%6 RMM *%7%+ <%&%6%$ S/6/'% @,*"#$H= N2'2+ MM O"?-,$ 2$-2' .%#-/'"7 -2$00%7 <"$-2' # C !( -/*%' <"#7%'2= -"-%./ N2'2+ MM O"?-,$ <"$-2' # C

-" -"-%. <"#7%'2: -t

1. Hukum Kekekalan Momentum Linear T/'% .%#-/'"7 +"$0%7%+/ -,-%7 0%8% 72%# # $,7= $%&'()((*0+,-./ *%.%*/-27/6 6"<%0%/ <"#/'2-: -" CU %-%2 " C -"-%. -t

92

Mudah dan Aktif Belajar Fisika untuk Kelas XI

DEFEH

$%&'()((*0 +,-,/ +"$8%-%'%$ <%&?% 1/'% 0%8% 72%# -,-%7 .%*% 6"<2%& .%#-/'"7 %*%7%& $,7= +,+"$-2+ 7/$"%# -,-%7 p *%#/ 6/6-"+ %*%7%& -"-%.: !"#$8%-%%$ -"#6"<2- */'"$%7 *"$0%$ ./0/! 1(0(0$2$n 3+!(nt/! 4in($6 8%$0 */$8%-%'%$ *"$0%$ "%?%7 C "%'&/#

DEFWH

$%&'()((*0 +,-B/ +"$0%$*2$0 ."$0"#-/%$ <%&?% +,+"$-2+ 7/$"%# -,-%7 .%*% ?%'-2 %?%7 6%+% *"$0%$ +,+"$-2+ 7/$"%# -,-%7 .%*% ?%'-2 %'&/#: M$0%-= $%&'()((*0 +,-B/ %*%7%& <"$-2' L"'-,#: X7"& '%#"$% /-2= %#%& +,+"$-2+ 7/$"%#$8% <"#0%$-2$0 .%*% %#%&:

2. Momentum Linear dan Impuls !"#&%-/'%$ C()2(&0 ,AD: ;"<2%& +,
DEFVH

DEFZH

Y%#/ $%&'()((*0 +,-E/ *%$ $%&'()((*0 +,-F/ */*%.%-'%$ D! " ! H DEF[H #C! P G !t @"$2#2- N2'2+ MM O"?-,$ 8%$0 */'%/-'%$ *"$0%$ +,+"$-2+ 7/$"%# +"$8%-%'%$ <%&?% 0%8% D#H 8%$0 */<"#/'%$ .%*% <"$*% <"6%#$8% 6%+% *"$0%$ ."#2<%&%$ +,+"$-2+ D"H <"$*% ."# 6%-2%$ ?%'-2 DtH: \/&%-" $%&'()((*0+,-./= 8%/-2 # C : B"#%#-/= $%&'()((*0+,-G/ 6"62%/ *"$0%$ -t $%&'()((*0 +,-./: X7"& '%#"$% /-2= 0%8% #%-%A#%-%$8% %*%7%& !" #= !t " " "G = P !t 6"&/$00%

#!t = !! 8 " !!G

< C # !t

Gambar 4.1 Sebuah mobil yang mengalami percepatan sehingga kecepatannya berubah dari v1 menjadi v2.

Tokoh Werner Heisenberg (1901–1976)

DEF]H

B"#*%6%#'%$ $%&'()((*0 +,-H/= )$*% +"$0"-%&2/ <%&?% &%6/7 '%7/ 0%8% D#H *%$ 6"7%$0 ?%'-2 7%+%$8% 0%8% <"'"#1% D !t H 6%+% *"$0%$ ."#2<%&%$ +,+"$-2+ %-%2 6"7/6/& %$-%#% +,+"$-2+ %'&/# D!!PH *%$ +,+"$-2+ %?%7 D!!GH <"$*% 2$-2' 0%8% # 8%$0 -"-%.: O/7%/ # !t */'"$%7 6"<%0%/ /+.276 8%$0 */7%+<%$0'%$ *"$0%$ <: Y"$0%$ *"+/'/%$= *%.%- */6/+.27'%$ <%&?% /+.276 8%$0 <"'"#1% .%*% 62%-2 <"$*% 6%+% *"$0%$ ."#2<%&%$ +,+"$-2+ 8%$0 -"#1%*/ .%*% <"$*% -"#6"<2-: I"-"#%$0%$J < C /+.276 DO6H # C 0%8% DOH !t 7 6"7%$0 ?%'-2 D6H

v2

v1

DEFGUH

Sumber: Conceptual Physics,1998

Ia dilahirkan di Duisberg, Jerman. Ia mempelajari fisika teoritis di Munich, di tempat ini pun ia menjadi penggemar ski dan pendaki gunung. Hasil pemikirannya yang terkenal ialah prinsip ketidakpastian Heisenberg yang didasarkan pada konsep momentum, yaitu foton yang digunakan untuk mengamati posisi elektron memiliki momentum yang relatif sama. Oleh karena itu, ketika terjadi tumbukan antara foton dan elektron akan mengubah posisi elektron.

Momentum, Impuls, dan Tumbukan

93

Contoh 4.1

Ingatlah

;"<2%& <,7% <"#+%66% WU 0 1%-2& *%#/ '"-/$00/%$ Z=P +"-"#: ;"-"7%& +"$2+<2' 7%$-%/= <,7% +"+%$-27 '"+<%7/ D<"#7%?%$%$ *"$0%$ %#%& 6"+27%H *"$0%$ '"-/$00/%$ Q=P +: N/-2$07%&J %: +,+"$-2+ <,7% 6"<"72+ *%$ 6"62*%& +"$2+<2' 7%$-%/^ h1 <: 0%8% 8%$0 */<"#/'%$ 7%$-%/ .%*% <,7% '"-/'% <,7% h2 +"$8"$-2& 7%$-%/ 6"7%+% U=UP 6: I(J(2K Y/'"-%&2/J ! C WU 0 C W _ GUFP '0 9G C Z=P + 9P C Q=P + !t C U=UP 6 `$-2' 0"#%' 1%-2& <"<%6= <"#7%'2 ."#6%+%%$ 6"<%0%/ <"#/'2-:

Impuls sebanding dengan perubahan momentum.

Kata Kunci • impuls • momentum linear

:1 = " P;9G =" %:

<:

Tes Kompetensi Subbab

:2 =

(P)(GU )(Z=P) = –GP m/s

=$

P;9P

(P)DGUH(Q=P)

= [ m/s

%#%& '" <%?%& DFH %#%& '" %-%6DaH FP
A

L%&5(7(*3(?0=(3()0247403(:6?(*A G:

;"<2%& <,7% 6".%' <"#+%66% U=E '0 */-"$*%$0 &,#/c,$A -%7 ,7"& ."$1%0% 0%?%$0 *"$0%$ '"9".%-%$ GUU +K6: 3"$-2'%$ 0%8% 8%$0 */<"#/'%$ ,7"& '%'/ ."$1%0% 0%?%$0 -"#&%*%. <,7% 1/'% 6"7%$0 ?%'-2 '%'/ +"$8"$-2& <,7%J %: E _ GUFP 6 ^ <: P _ GUFQ 6:

P:

;",#%$0 6/6?% +"$00"$00%+ <,7% <"#+%66% U=W '0 *%$ +"7"+.%#'%$$8% 6"9%#% &,#/c,$-%7 *"$0%$ '"9".%-%$ %?%7 PU +K6: B,7% -"#6"<2- +"+<"$-2# -/%$0 6"7%+% P _ GUFP 6 6"&/$00% <"#<%7/' %#%& *"$0%$ '"9".%-%$ GW +K6: 3"$-2'%$J %: /+.276 8%$0 */<"#/'%$ -/%$0 .%*% <,7%^ <: 0%8% 8%$0 */<"#/'%$ -/%$0 .%*% <,7%^ *%$ 9: ."#9".%-%$ <,7% D."+2'27H 6"7%+% <"#6"$-2&%$:

B. Tumbukan Ingatlah Jika berlaku Hukum Kekekalan Momentum Linear, momentum linear awal sama dengan momentum linear akhir.

94

!"#/6-/?% -2+<2'%$ *%.%- )$*% -"+2/ .%*% *2% <"$*% 8%$0 6%7/$0 <"#-%<#%'%$ 6%-2 6%+% 7%/$: !"#+%/$%$ 8%$0 +"+%$>%%-'%$ 6"9%#% 7%$062$0 ."#/6-/?% -2+<2'%$ %*%7%& ."#+%/$%$
Mudah dan Aktif Belajar Fisika untuk Kelas XI

@/6%7$8%= %*% *2% <2%& <"$*% 8%$0 6%7/$0 <"#-2+<2'%$= 6"."#-/ .%*% C()2(&0 ,A. <"#/'2-: vA

vA

vB

vB

Gambar 4.2

ketika tumbukan

sebelum tumbukan vA

Hukum Kekekalan Momentum Linear berlaku pada dua benda yang bertumbukan.

vB FA

setelah tumbukan

I"#"-% ) *%$ '"#"-% B 6"<"72+ <"#-2+<2'%$ +%6/$0A+%6/$0 +"+/7/'/ +%66% !) *%$ !B= *%$ '"9".%-%$ v) *%$ vB: I"*2% '"#"-% -"#6"<2- <"#%*% .%*% 6%-2 "B %?%7 C ") %'&/#a "B %'&/# !)!) > !B!B 7 !)!)d> !B!Bd

DEFGGH

I"-"#%$0%$J !)!)> !B!B C 12+7%& +,+"$-2+ 6"<"72+ -2+<2'%$ !)!)d> !B!Bd C 12+7%& +,+"$-2+ 6"62*%& -2+<2'%$ e,$-,& 7%/$ *%#/ ."#/6-/?% -2+<2'%$ 8%$0 *%.%- */7%'2'%$ ."$*"'%-%$ *"$0%$ N2'2+ I"'"'%7%$ @,+"$-2+ \/$"%# %*%7%& .%*% ."#+%/$%$ ?+!@ ?+! %$6: Y/ <"<"#%.% ',-% <"6%#= ."#+%/$%$ /$/ */6"<2- 120% +,"' 02$9%$0%$ 8%$0 .%7/$0 '"#%6 %'%$ */-"#/+% ,7"& +,
Tes Kompetensi Subbab

Sumber: Dokumentasi Penerbit

Gambar 4.3 Hukum kekekalan momentum terjadi pada bom-bom car yang bertumbukan.

B

L%&5(7(*3(?0=(3()0247403(:6?(*A G: ;",#%$0 $"7%8%$ <"#+%66% EU '0 <"#%*% */ %-%6 ."#%&2 VU '0: !"#%&2 <"#0"#%' *"$0%$ '"7%12%$ GU +K6: 3"$-2'%$ '"9".%-%$ ."#%&2 1/'% $"7%8%$ +"7,+.%*"$0%$ '"9".%-%$ GW +K6 *"$0%$ %#%&J %: '" *".%$= 6"%#%& *"$0%$ %#%& 0"#%' ."#%&2^ <: '" <"7%'%$0= <"#7%?%$%$ *"$0%$ %#%& 0"#%' ."#%&2^ *%$ 9: '" 6%+./$0= -"0%' 72#26 *"$0%$ %#%& 0"#%' ."#%&2:

P:

Y2% <2%& '"7"#"$0 ) *%$ B +%6/$0A+%6/$0 <"#+%66% U=[ '0 *%$ U=V '0= <"#0"#%' 6"%#%& *"$0%$ '"9".%-%$ QU +K6 *%$ WU +K6: !,6/6/ '"7"#"$0 */<2%- 6"*"+/'/%$ 6"&/$00% '"7"#"$0 B +"$2+<2' '"7"#"$0 ) *%#/ <"7%'%$0: ;"-"7%& -2+<2'%$= '"*2%$8% <"#0"#%' <"#6%+%%$: 3"$-2'%$ '"9".%-%$ '"*2% '"7"#"$0 -"#6"<2-: A

vA

B

vB

A

Momentum, Impuls, dan Tumbukan

B

vAB

95

C. Jenis Tumbukan )*% -/0% +%9%+ -2+<2'%$ 8%$0 */."7%1%#/ .%*% .,',' <%&%6%$ -2+<2'%$= 8%/-2 -2+<2'%$ 7"$-/$0 6"+.2#$%= -2+<2'%$ 7"$-/$0 6"<%0/%$= *%$ -2+<2'%$ -/*%' 7"$-/$0 6%+% 6"'%7/: ;2<<%< /$/ &%$8% +"+<%&%6 -2+<2'%$ %$-%#% *2% <"$*% 8%$0 7/$-%6%$ '"*2%$8% <"#%*% .%*% 6%-2 0%#/6 72#26:

1. Tumbukan Lenting Sempurna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f$"#0/ '/$"-/' -,-%7 8%$0 */+/7/'/ <"$*% 6"<"72+ *%$ 6"62*%& -2+<2'%$ %*%7%& -"-%.: f$"#0/ .,-"$6/%7 <"$*% -/*%' */."#&/-2$0'%$ '%#"$% '"*2% <"$*% <"#0"#%' *%7%+ 6%-2
m1

Tumbukan lenting sempurna.

v1 v2

m2

sebelum tumbukan

Tugas Anda 4.2 Anggota polisi sering menggunakan rompi anti peluru dalam melaksanakan tugasnya. Dalam beberapa kejadian, rompi tersebut bisa tembus oleh peluru. Mengapa hal tersebut bisa terjadi?

m1 m2 saat tumbukan

v1'

m1

m2

v2'

setelah tumbukan

!"#&%-/'%$ C()2(&0,A,: Y2% <2%& <"$*% .%*% !P!P C !G!Gd > !P!Pd !GD!G A !GdH C !PD!Pd A !PH

DEFGPH

@"$2#2- N2'2+ I"'"'%7%$ f$"#0/ I/$"-/'= */*%.%-'%$ ."#6%+%%$ <"#/'2-: B0G a B0P C B0Gd a B0Pd G G G G ! : P > !P:PP C !G:Gd P > !P:Pd P P G G P P P

DEFGQH

Y%#/ $%&'()((*0 +,-DM/ %'%$ */."#,7"& ."#6%+%%$ 6"<%0%/ <"#/'2-: !G:GP > !P:PP C !G:Gd P > !P:Pd P !GD:GP A :Gd PH C !PD:Pd P A vPPH !GD:G > :GdHD:G A :GdH C !PD:Pd > :PHD:Pd A :PH

DEFGEH

T/'% #2%6 '%$%$ $%&'()((* +,-D,/ */<%0/ *"$0%$ #2%6 '%$%$ $%&'()((* +,-D./= *%$ #2%6 '/#/ $%&'()((* +,-D,H */<%0/ *"$0%$ #2%6 '/#/ $%&'()((* +,-D./= %'%$ */&%6/7'%$ D:G > :GdH C D:P > :PdH D:GdF :PdH C F D:G A :PH %-%2

96

Mudah dan Aktif Belajar Fisika untuk Kelas XI

# : d " :P d $ "% G & =G ' :G " :P (

DEFGWH

N%#0% G .%*% $%&'()((*0 +,-DG/ +"$8%-%'%$ 0+(Ei#i(n 6(#tit/#i 2$-2' -2+<2'%$ 7"$-/$0 6"+.2#$%: ;"9%#% 2+2+= $%&'()((*0 +,-DG/ */-27/6

# : d " :P d $ "% G &=( ' :G " :P (

DEFG]H

Y%7%+ &%7 /$/= ( %*%7%& ',">/6/"$ #"6-/-26/: $%&'()((*0+,-DH/ <"#7%'2 2$-2' 6"+2% 1"$/6 -2+<2'%$:

2. Tumbukan Lenting Sebagian dan Tumbukan Tidak Lenting Sama Sekali N2'2+ '"'"'%7%$ +,+"$-2+ <"#7%'2 2$-2' 6"+2% 1"$/6 -2+<2'%$: )'%$ -"-%./= &2'2+ '"'"'%7%$ "$"#0/ '/$"-/' &%$8% <"#7%'2 .%*% -2+<2'%$ 7"$-/$0 6"+.2#$%: !%*% -2+<2'%$ 7"$-/$0 6"<%0/%$= 6"<%0/%$ "$"#0/ '/$"-/' 6"-"7%& -2+<2'%$ %'%$ <"#2<%& <"$-2' +"$1%*/ "$"#0/ 7%/$ 6"&/$00% 12+7%& "$"#0/ '/$"-/' 6"-"7%& -2+<2'%$ %'%$ 7"/6/"$ #"6-/-26/ D(H .%*% $%&'()((*0 +,-DE/ <"#%*% .%*% /$-"#A L%7 U h ( h G: !%*% -2+<2'%$ -/*%' 7"$-/$0 6%+% 6"'%7/= 6"<%0/%$ <"6%# "$"#0/ '/$"-/'$8% <"#2<%& <"$-2' 6"&/$00% 12+7%& "$"#0/ '/$"-/' 6"<"72+ -2+<2'%$ 7"
Contoh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a ! B :B C ! ) :) d a ! B : B d DP '0HDV +K6H a DE '0HDFE +K6H C DP '0H :)d > DE '0H :Bd GP +K6 F GV +K6 C P :)d > E :Bd FP +K6 C D:)d > P :BdH +K6 DgH !%*% -2+<2'%$ 7"$-/$0 6"+.2#$%= ( C G +%'% : A ’" : B ’ # : ’" :B ’$ "% A & C G ) F V " ( "E) C G " : : ' A B ( A :)d > :Bd 7 GU +K6 Y%#/ "7/+/$%6/ ."#6%+%%$ DgH *%$ DggH= */."#,7"& FP C :)d > P :Bd ) :)d C FP F P :B +%'% F:)d a :Bd C GU +K6 :Bd C GU +K6 a:)d :Bd C GU +K6 F P +K6 F P:Bd [ :Bd 7 +K6 Q

DggH

Ingatlah •

•

Pada tumbukan lenting sempurna, koefisien restitusinya adalah e = 1. Pada tumbukan lenting sebagian, koefisien restitusinya 0 < e < 1, sedangkan pada tumbukan tidak lenting sama sekali, koefisien restitusinya adalah e = 0.

Momentum, Impuls, dan Tumbukan

97

Tugas Anda 4.3 Jika Anda sedang menggunakan sepatu, cobalah tendang sebuah bola sepak. Kemudian, bukalah sepatu dan tendang kembali bola tersebut. Jika diasumsikan gaya yang Anda berikan selama menyentuh sama besar, selidikilah tendangan mana yang membuat bola terlempar jauh? Apa hubungan kejadian ini dengan konsep impuls?

Y%#/ ."#6%+%%$ DggH= */."#,7"& A:CF > :DF 7 GU +K6 A:CF a [ +K6 C GU +K6 Q PP +K6 C F Z G +K6 :C F C F Q Q T%*/= '"9".%-%$ '"*2% <"$*% 6"-"7%& -2+<2'%$ 7"$-/$0 6"+.2#$% %*%7%& [ :)d C F Z G +K6 *%$ vBd C +K6: Q Q I"*2% '"9".%-%$ +"$0%7%+/ ."#2<%&%$ -%$*%: )#-/$8%= '"*2% <"$*% -"#6"<2+"$0%7%+/ ."#2<%&%$ %#%& 0"#%': T/'% )$*% +"$*%.%-'%$ $/7%/ '"9".%-%$ -/*%' <"#2<%& %#%& 6"-"7%& -2+<2'%$= <"#%#-/ ."#&/-2$0%$ )$*% <"72+ <"$%#: !%*% -2+<2'%$ 7"$-/$0 6"<%0/%$= ( C U=E 6"&/$00% ( : C d " :D d ) " C U=E V +K6 " ( "E +K6 ) F :)d a :Bd C E +K6 DgggH G GU Y%#/ "7/+/$%6/ ."#6%+%%$ DgH *%$ DgggH= */*%.%- :Bd C +K6^ :)d C +K6: Q Q T%*/= 2$-2' -2+<2'%$ 7"$-/$0 6"<%0/%$= '"9".%-%$ <"$*% ) 6"-"7%& -2+<2'%$ %*%7%& GU G +K6 *%$ '"9".%-%$ <"$*% B %*%7%& +K6: Q Q

Contoh 4.3

Tantangan untuk Anda Apakah Anda pernah menonton balapan? Mengapa di beberapa bagian sirkuit diberi pagar dari ban (tyre wall)?

Y2% <2%& <"$*% -"#7"-%' .%*% 6%-2 ! P:8 C ! G: Gd > ! P:Pd D[ '0HDPU +K6H > DGP '0H DFGU +K6H C [ '0 :Gd > GP '0 :Pd GU '0+K6 C P '0 :Gd a Q '0 :Pd DgH `$-2' -2+<2'%$ 7"$-/$0 6"+.2#$%= ( C G= $%&'()((*0+,-DE/ +"$1%*/ # $ :1 ’" :2 ’ F% CG % PU +K6 " ( "GU +K6 ) && ' ( QU C F :Gda:Pd DggH @"$62<6-/-26/'%$ $%&'()((*0+N/ '" $%&'()((*0+NN/ +"$0&%6/7'%$ :Gd C F GV +K6: :Pd C GE +K6: !"#2<%&%$ "$"#0/ '/$"-/' f$"#0/ '/$"-/' 6"<"72+ -2+<2'%$J G G G G B0G > B0P 7 !G:GP > !P:PP C D[ '0HDPU +K6HP a DGP '0HDGU +K6HP C P:PUU T: P P P P f$"#0/ '/$"-/' 6"-"7%& -2+<2'%$J G G G G B0Gd > B08d C !G:Gd P > !P:Pd P C D[ '0HDFGV +K6HP a DGP'0HDGE +K6HP C P:PUU T: P P P P

98

Mudah dan Aktif Belajar Fisika untuk Kelas XI

<:

T%*/= .%*% -2+<2'%$ 7"$-/$0 6"+.2#$%= "$"#0/ '/$"-/' 6"<"72+ *%$ 6"62*%& -2+<2'%$ %*%7%& -"-%.: `$-2' -2+<2'%$ 7"$-/$0 6"<%0/%$= ( C U=PWJ m1 = 8 kg m1

v 1 v2

m2 = 12 kg m2

sebelum tumbukan

9:

v1 '

m1

m2

v2'

setelah tumbukan

Y%#/ N2'2+ I"'"'%7%$ @,+"$-2+= */*%.%- &%6/7 6"."#-/ $%&'()((*0DgH: !%*% -2+<2'%$ 7"$-/$0 6"<%0/%$= ( C U=PW= $%&'()((*0+,-H/ +"$1%*/ Z=W +K6 C F vGd a :Pd DGGGH ;2<6-/-26/'%$ $%&'()((*0+N/ '" *%7%+ $%&'()((*0+NNN/ 6"&/$00% */."#,7"& &%6/7 :Gd C FP=W +K6 :Pd C W +K6 f$"#0/ '/$"-/' 6"-"7%& -2+<2'%$ G G B0Gd > B0Pd C !G:Gd P > !P:Pd P P P G G C D[ '0HDFP=W +K6HP a DGP '0HDW +K6HP P P C PW a GWU C GZW 1,27" T%*/= "$"#0/ '/$"-/' 8%$0 <"#2<%& +"$1%*/ .%$%6 %*%7%& (n(6;i 0in(ti0 #(?(2/! t/!?/0$n A (n(6;i 0in(ti0 #(t(2$9 t/!?/0$n C P:PUU 1,27" F GZW 1,27" C P:UPW 1,27": `$-2' -2+<2'%$ -/*%' 7"$-/$0 6%+% 6"'%7/= ( C UJ m1 = 8 kg m1

v 1 v2

m1

sebelum tumbukan

m2

v'

setelah tumbukan

Tantangan untuk Anda

$3(*%:

X7"& '%#"$% ( 7 U +%'% :Gd C :Pd C :d 6"&/$00% $%&'()((*0+N/ %'%$ +"$1%*/ GU C W :Gd C W :Pd C W :d :d C P +K6: f$"#0/ '/$"-/' 6"-"7%& -2+<2'%$ G G B0Gd > B0Pd C D !G > !P H :dP C DGU '0H DP +K6HP C EU 1,27": P P T%*/= <%$8%'$8% "$"#0/ '/$"-/' 8%$0 <"#2<%& +"$1%*/ .%$%6 %*%7%& DP:PUU F EUH 1,27" C P:GVU 1,27":

Tes Kompetensi Subbab

• tumbukan lenting sebagian • tumbukan lenting sempurna • tumbukan tidak lenting sama sekali

Berikut ini ukuran diameter, massa jenis, dan periode rotasi dari planet-planet.

m2 = 12 kg m2

Kata Kunci

d+7)/

B2+/ GP:VZW @%#6 V:Z]U i2./-"# GEP:][U ;%-2#$26 GPU:WEU

T W=WP Q=]W Q=QQ U=V]

PQ 1%+ WVd PE 1%+ QZd ] 1%+ QWd GU 1%+ EUd

Dari data tersebut, berapakah momentum yang dimiliki setiap planet? Apakah ada hubungan antara momentum dan periode rotasi planet tersebut?

C

L%&5(7(*3(?0=(3()0247403(:6?(*A G:

P:

Q:

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

E:

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b2$%'%$ J E'# C !:PH P

Momentum, Impuls, dan Tumbukan

99

W:

;"<2%& <"$*% ) <"#+%66% P '0 8%$0 <"#0"#%' *"$0%$ '"7%12%$ V +K6 <"#-2+<2'%$ *"$0%$ <"$*% B <"#+%66% E '0 8%$0 */%+: ;"-"7%& -2+<2'%$= <"$*% ) <"#0"#%' +2$*2# *"$0%$ '"7%12%$ G +K6: 3"$-2'%$J %: '"9".%-%$ <"$*% B 6"-"7%& -2+<2'%$^ <: "$"#0/ 8%$0 <"#2<%& %'/<%- -2+<2'%$^ *%$ 9: ',">/6/"$ #"6-/-26/ 2$-2' -2+<2'%$ -"#6"<2-: V: ;"<2%& -#2' <"#/6/ +2%-%$ *"$0%$ +%66% QU -,$ 8%$0 <"#0"#%' *"$0%$ '"9".%-%$ GU +K6 +"$%<#%' 6"<2%& +,
[: 3,$, 8%$0 <"#+%66% QW '0 +"7,$9%- *"$0%$ '"9".%-%$ Q +K6 *%#/ 6"<2%& ."#%&2 '"9/7 8%$0 */%+: @%66% ."#%&2 %*%7%& QU '0: B"#%.%'%& '"9".%-%$ ."#%&2 6"-"7%& 3,$, +"7,+.%-5 ]: Y2% +,
D. Tumbukan Lenting Sebagian pada Benda Jatuh Bebas

v1

h1

v2

32+<2'%$ 7"$-/$0 6"<%0/%$ <"#7%'2 120% .%*% 6"<2%& <"$*% 8%$0 <"#0"#%' 1%-2& <"<%6: Y%7%+ '%626 /$/= 8%$0 <"#-/$*%' 6"<%0%/ <"$*% '"*2% %*%7%& 7%$-%/: !"#&%-/'%$ C()2(&0,AB: Y"$0%$ *"+/'/%$= '"9".%-%$ <"$*% '"*2% 6"<"72+ *%$ 6"62*%& -2+<2'%$ %*%7%& $,7: ;"<2%& <,7% 1%-2& <"<%6 *%#/ '"-/$00/%$ 9 -"#&%*%. 7%$-%/: I"9".%-%$ <,7% 6"6%%- 6"<"72+ *%$ 6"62*%& +"$2+<2' 7%$-%/ +"+"$2&/ ."#6%+%%$

h2

Gambar 4.5 Tumbukan lenting sebagian pada benda jatuh bebas.

: C P;9

DEFGZH

I"9".%-%$ <,7% 6"<"72+ *%$ 6"62*%& +"$2+<2' 7%$-%/ +"+"$2&/ ."#6%+%%$ :G C " P;9G *%$ :Gd C a P ;9G d

DEFG[H

3%$*% $"0%-/> .%*% :G +"$%$*%'%$ %#%& <,7% '" <%?%& *%$ -%$*% .,6/-/> .%*% :Gd +"$%$*%'%$ %#%& <,7% '" %-%6: I,">/6/"$ #"6-/-26/ %$-%#% <,7% *%$ 7%$-%/ *%.%- */."#,7"& *%#/ ."#6%+%%$ (=

# P;9G d " U $ ( = "% & % " P;9 " U & G ' (

m m m h1

h2

h3

m

Tinggi pantulan bola yang mengalami tumbukan lenting sebagian.

100

( = 9d 9

h4

Gambar 4.6

( :G d" :P d ) ( :G " :P )

DEFG]H

$%&'()((*0+,-DH/ *%.%- */02$%'%$ .%*% <"$*% 1%-2& '" 7%$-%/ *%$ '"+2*/%$ +"+%$-27 <"<"#%.% '%7/: ;"<%0%/ 9,$-,&= ."#&%-/'%$ '%626 .%*% C()2(&0 ,AE: !%*% '%626 -"#6"<2-= ."#6%+%%$ ',">/6/"$ #"6-/-26/ +"$1%*/

Mudah dan Aktif Belajar Fisika untuk Kelas XI

(C

9P 9G C

9Q 9P C

9E 9Q

DEFPUH

Contoh 4.4 ;"<2%& <,7% ) */1%-2&'%$ D1%-2& <"<%6H *%#/ 62%-2 -/-/' !: \,'%6/ -/-/' ! */-2$12''%$ .%*% 0%+<%#: B,7% <"#0"#%' <"<%6 6".%$1%$0 -%7%$0 7/9/$ D1%#/A1%#/ -%7%$0 HH: Y/ 212$0 -%7%$0 -"#*%.%- <,7% B 8%$0 +%66%$8% P '%7/ +%66% ): I"*2%$8% <"#-2+<2'%$ 6"9%#% "7%6-/6 6"+.2#$%: %: N/-2$0 '"9".%-%$ <,7% ) 6"6%%- 6"<"72+ +"$2+<2' <,7% B: P A <: N/-2$0 '"9".%-%$ <,7% B 6"6%%- 6"-"7%& x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a ! B : B C ! ) :) d a ! B :B d !:) a U C !:)d a P !:Bd : ) C :)d a :Bd

P;H -%$0 C :)d a :Bd ::::::::::DgH N2'2+ I"'"'%7%$ f$"#0/ @"'%$/'J G G G G ! : P a !B:BPC !):)dP a !B:BdP P ) ) P P P G G !: P C !:)dP a !:BdP P ) P G !;H -%$ 0 C !:)dP a !:BdP P G ;H -%$ 0 C :)dP a :BdP ::::::::DggH P Y%#/ ."#6%+%%$ DgH *%$ DggH= %'%$ */."#,7"& G ;H-%$ 0 C D P ;H -%$ 0 F P :BdHP a :BdP P G ;H-%$ 0 C DP ;H -%$ 0 F E :Bd P ;H -%$ 0 a E :BdPH a :BdP P

Pembahasan Soal Perhatikan gambar berikut.

M h

H

m Sebuah ayunan yang bandulnya bermassa M dinaikkan pada ketinggian H dan dilepaskan. Pada bagian terendah dari lintasannya, bandul membentur suatu balok bermassa m yang mula-mula diam di atas permukaan dataran yang licin. Jika setelah tumbukan kedua benda saling menempel, ketinggian h yang dapat dicapai keduanya adalah .... 2

a.

* m + H ., m + M /-

b.

* m + H ., m + M /-

c.

* M + ,. m + M -/ H

d.

* M + 2 ,. m + M -/ H

e.

* M + 2 H ., m + M /-

2

2

Soal UMPTN Tahun 2001 Pembahasan: Mv = (M + m)v' M 2g H = (M + m)

2g H

M2 2gH = (M + m)2 2gh h=

2 M 2H * M + 2 = H , m + M m + M ( ) . /

Jawaban: c

;H-%$0 C ;H-%$0 F P:Bd P ;H -%$ 0 a Q :BdP

Momentum, Impuls, dan Tumbukan

101

P P ;H -%$ 0 Q I"9".%-%$ <,7% ) 6"62*%& -2+<2'%$ %*%7%& [ G G P ;H -%$ 0 C :)dP a D P ;H -%$ 0 HP C :)dP a ;H -%$ 0 ] P P Q

Kata Kunci

:B d C

• koefisien restitusi

:)dC

P ;H -%$ 0 +K6: ]

P ;H -%$ 0 +K6: ] 3/$00/ +%'6/+2+ 8%$0 */9%.%/ <,7% B 6"-"7%& -2+<2'%$ */."#,7"& +"7%72/ ."#6%+%%$ "$"#0/ +"'%$/' */ .,6/6/ E *%$ W: B!BE a BIBE C B!BW a BIBW G U a !B:BdP C !B;K a U P P G L MDP !HD P ;H -%$ 0 HP C P !;K P Q E ! D ] P;H -%$ 0 H C P !;K E E K C H D ] -%$ 0 H%-%2 K C H DG a ] -%$ 0 H *%#/ *%6%# -%7%$0: E T%*/= -/$00/ +%'6/+2+ <,7% B 6"-"7%& -2+<2'%$ %*%7%& K C H DG a ] -%$ 0 H *%#/ *%6%# -%7%$0: T%*/= '"9".%-%$ <,7% ) 6"-"7%& -2+<2'%$ %*%7%& :)dC

9:

Tes Kompetensi Subbab

D

L%&5(7(*3(?0=(3()0247403(:6?(*A G: ;"<2%& <,7% */7".%6'%$ *%#/ '"-/$00/%$ GU +"-"# */ %-%6 7%$-%/: B,7% +"$2+<2' 7%$-%/ *%$ */.%$-27'%$ '"+<%7/: T/'% ',">/6/"$ #"6-/-26/ -2+<2'%$$8% U=V= <"#%.%'%& -/$00/ <,7% 8%$0 */.%$-27'%$: P: ;"<2%& <"$*% */7".%6'%$ *%#/ 62%-2 -"+.%- 6"1%2& GPW + */ %-%6 7%$-%/: ;"-"7%& +"$0"$%/ 7%$-%/= <,7% +"+%$-27 '"+<%7/ *%$ <"$*% $%/' 7%0/ 6"-/$00/ EW +: N/-2$0 ',">/6/"$ #"6-/-26/ -2+<2'%$ <"$*% -"#6"<2-:

Q:

;"<2%& <,7% */7".%6'%$ *%#/ 0"*2$0 8%$0 -/$00/$8% WU +: ;"-"7%& +"$0"$%/ 7%$-%/= <,7% -"#6"<2- */.%$A -27'%$ '"+<%7/: !%*% .%$-27%$ ."#-%+%= <,7% +"$9%.%/ '"-/$00/%$ 9 +"-"# */ %-%6 7%$-%/ *%$ .%*% .%$-27%$ '"*2% +"$9%.%/ '"-/$00/%$ W +"-"#: N/-2$07%& 9:

E. Ayunan Balistik 2

! vmp

hmaks

vp mp

mp + mb

Gambar 4.7 Ayunan balistik mencapai tinggi maksimum hmaks = ! (1 – cos 2 ).

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d 6"&/$00% <%7,' <"#%82$ *%$ +"$9%.%/ '"-/$00/%$ 9: @"$2#2- N2'2+ I"'"'%7%$ @,+"$-2+ \/$"%#= */*%.%- ."#6%+%%$ !!:. C D!! a !BH:d :. C

102

Mudah dan Aktif Belajar Fisika untuk Kelas XI

( !J $ !D ) : d !J

DEFPGH

@"$2#2- N2'2+ I"'"'%7%$ f$"#0/ @"'%$/'= "$"#0/ '/$"-/' 8%$0 */+/7/'/ ."72#2 *%$ <%7,' .%*% .,6/6/ J 6%+% *"$0%$ "$"#0/ .,-"$6/%7 8%$0 */+/7/'/ ."72#2 *%$ <%7,' '"-/'% +"$9%.%/ '"-/$00/%$ +%'6/+2+: ;"9%#% +%-"+%-/6= '"%*%%$ -"#6"<2- *%.%- */-27/6'%$ 6"<%0%/ <"#/'2-: G D! a ! H: P C D! a ! H;9 B d ! B P ! DEFPPH :d C P;9 Y%#/ $%&'()((*0 +,-.D/ *%$ $%&'()((*0 +,-../= */."#,7"& :J =

D !J $ !D H !J

(

P;9

)

DEFPQH

I"-"#%$0%$J ! ! C +%66% ."72#2 D'0H ! B C +%66% <%7,' D'0H :! C '"9".%-%$ ."72#2 D+K6H :d C '"9".%-%$ 6"-"7%& ."72#2 *%$ <%7,' <"#-2+<2'%$ D+K6H

;".,-,$0 <%7,' '%82 <"#+%66% E=]W '0 -"#0%$-2$0 .%*% 6"2-%6 -%7/: ;"<2%& ."72#2 8%$0 +%66%$8% WU 0 */-"+<%''%$ *%#/ 6"<2%& 6"$%.%$ '" %#%& <%7,' 6"&/$00% ."72#2 -"#6"<2- <"#6%#%$0 */ *%7%+$8%: B%7,' -"#6"<2- <"#%82$ *%$ $%/' 6"-/$00/ [U 9+ *%#/ '"*2*2'%$ 6"+27%: T/'% ."#9".%-%$ 0#%L/-%6/ */ -"+.%- -"#6"<2- GU +K6P= -"$-2'%$ '"9".%-%$ ."72#2 6"<"72+ +"$0"$%/ <%7,':

C

(U=UW)( E=]W) '0 U=UW '0

untuk Anda Gaya dorong pada roket dihasilkan akibat semburan gas panas dengan kecepatan tinggi. Gas panas tersebut dihasilkan dari proses pembakaran hidrogen cair dan oksigen cair. Untuk mengatasi pengaruh gravitasi Bumi, roket memiliki percepatan 3 kali percepatan gravitasi Bumi. Oleh karena itu, gaya dorong yang harus diberikan oleh roket harus lebih dari 3 × 107 N.

Information for You

Contoh 4.5

I(J(2K Y/'"-%&2/J !! C WU 0 C U=UW '0^ !B C E=]W '0^ D !J $ !D H P;9 :J C !J

Informasi

Rocket propulsion is produced by hot gas expelled from the rear of the rocket at high velocity. The hot gas made from burning of liquid hydrogen and liquid oxygen. To abandon the earth’s gravitational force, rocket have to get acceleration three times faster than earth’s gravitational acceleration. So, rocket propulsion should be more 3 × 107 N.

; C GU +K6P 9 C [U 9+ C U=[ +

(P) (GU +K6P ) (U=[) + C EUU +K6

T%*/= '"9".%-%$ ."72#2 6"<"72+ +"$0"$%/ <%7,' %*%7%& EUU +K6:

Tes Kompetensi Subbab

E

L%&5(7(*3(?0=(3()0247403(:6?(*A G:

P:

;"<2%& <%7,' <%1% <"#+%66% P '0 -"#0%$-2$0 .%*% 6"2-%6 -%7/ .%$1%$0: B%7,' -"#6"<2- */-"+<%' ,7"& 6"<2-/# ."72#2 <"#+%66% PU 0 *"$0%$ '"9".%-%$ +"$*%-%# WUU +K6: T/'% -2+<2'%$$8% "7%6-/6 6"<%0/%$ D( C U=VGVUH= &/-2$0 '"-/$00/%$ +%'6/+2+ 8%$0 *%.%*/9%.%/ <%7,' -"#6"<2-: Y2% <,7% '"9/7 8%$0 +%6/$0A+%6/$0 <"#+%66% G '0 *%$ P '0 */0%$-2$0'%$ .%*% 6"2-%6 -%7/ U=P +: ;"-/%. <,7% +27%A +27% */<"#/ %82$%$ 6"<"6%# ]Uj -"#&%*%. 0%#/6 L"#-/'%7 6"."#-/ .%*% 0%+<%#: I"+2*/%$= '"*2% <,7%

Q:

*/7".%6 .%*% 6%%- 8%$0 <"#6%+%%$ *%$ '"*2%$8% <"#-2+<2'%$ 6"9%#% "7%6-/6 6"+.2#$%: N/-2$07%& '"$%/'%$ '"*2% <,7% -"#6"<2- 6"-"7%& -2+<2'%$: ;"<2%& <"$*% -"#0%$-2$0 .%*% 6"2-%6 -%7/ 8%$0 .%$1%$0$8% PU 9+: B"$*% -"#6"<2- */-2+<2' ,7"& <"$*% 7%/$ 8%$0 +%66%$8% E '%7/ +%66% <"$*% 6"+27%: T/'% -2+<2'%$$8% "7%6-/6 6"<%0/%$= *"$0%$ $/7%/ ( C U=ZW= <"#%.%'%& '"9".%-%$ <"$*% 8%$0 +"$2+<2' %0%# <"$*% 8%$0 -"#0%$-2$0 -"#6"<2- +"$9%.%/ -/-/' -"#-/$00/ *%#/ 7/$-%6%$$8%5

Momentum, Impuls, dan Tumbukan

103

E:

B,7% ) 8%$0 +%66%$8% Q '0 <"#%*% .%*% .,6/6/ 6"."#-/ -"#7/&%- .%*% 0%+<%#:

B,7% -"#6"<2- %'%$ +"$2+<2' <,7% B 8%$0 <"#+%66% P '0: T/'% ',">/6/"$ #"6-/-26/ -2+<2'%$ U=W= <"#%.% +"-"#'%& <,7% B %'%$ $%/'5 D.%$1%$0 -%7/ U=P +H:

A

B

F. Gaya Dorong Roket )+
Gambar 4.8 Gaya dorong pada balon.

Tes Kompetensi Subbab

F

L%&5(7(*3(?0=(3()0247403(:6?(*A G: Y/'"-%&2/ 0%6 .%$%6 8%$0 '"72%# *%#/ #,'"- +"+/7/'/ '"7%12%$ PUU +K6: 3"$-2'%$ <"6%# 0%8% *,#,$0 6"<2%& #,'"- 8%$0 +"6/$$8% *%.%- +"$8"+<2#'%$ 0%6 .%$%6 &%6/7 *%#/ ."+<%'%#%$ *"$0%$ '"7%12%$ .%$9%#%$ 0%6 WU '0K6:

104

Mudah dan Aktif Belajar Fisika untuk Kelas XI

P:

@%66% -,-%7 6"<2%& #,'"- -"#+%62' <%&%$ <%'%#$8% %*%7%& G:PUU '0: ;"+<2#%$ 0%8% .%$%6 8%$0 '"72%# *%#/ #,'"- +"+/7/7'/ '"7%12%$ PWU +K6: T/'% */&%#%.'%$ #,'"*%.%- +"7%12 *"$0%$ ."#9".%-%$ P=W +K6P= -"$-2'%$7%& '"7%12%$ ."#2<%&%$ +%66% 0%6 */ *%7%+ #,'"- -"#6"<2-:

Rangkuman G:

P:

Q:

E:

W:

@,+"$-2+ 8%$0 */+/7/'/ 62%-2 <"$*% %*%7%& &%6/7 ."#'%7/%$ %$-%#% +%66% *%$ '"9".%-%$ .%*% 6%%-"#-"$-2: @,+"$-2+ +"#2.%'%$ <"6%#%$ L"'-,# 8%$0 %#%&$8% 6%+% *"$0%$ %#%& '"9".%-%$$8%: "7!! M+.276 %*%7%& &%6/7 '%7/ 0%8% *%$ 6"7%$0 ?%'-2 6"7%+% 0%8% <"'"#1%: < 7 # !t M+.276 8%$0 <"'"#1% .%*% 62%-2 <"$*% <"6%#$8% 6%+% *"$0%$ ."#2<%&%$ +,+"$-2+ 8%$0 */%7%+/ <"$*%: <07 ! !! 0C !!P F !!G N2'2+ I"'"'%7%$ @,+"$-2+ +"$8%-%'%$ <%&?% 12+7%& +,+"$-2+ 6"<"72+ *%$ 6"62*%& -2+<2'%$ %*%7%& 6%+%= 8%/-2 !C !C a !D !D C !C!Cda !D !Dd N2'2+ MM O"?-,$ +"$8%-%'%$ <%&?% 0%8% 8%$0 */<"#/'%$ .%*% 62%-2 <"$*%= <"6%#$8% 6%+% *"$0%$ ."#2<%&%$ +,+"$-2+ <"$*% 6"-/%. 6%-2 6%-2%$ ?%'-2: !" ! ! P " ! ! G = #= !t !t I,">/6/"$ #"6-/-26/ %*%7%& 2'2#%$ '"7"$-/$0%$ D"7%6-/6/-%6H 6"<2%& -2+<2'%$: # : d " :P d $ ( = "% G & ' :G " :P ( N2'2+ I"'"'%7%$ @,+"$-2+ <"#7%'2 .%*% 6"+2% 1"$/6 -2+<2'%$: !%*% -2+<2'%$ 7"$-/$0 6"+.2#$%= <"#7%'2

!G :G a !P :P C !G :Gd a !P :Pd= :Pd F :Gd C FD:P F :GHd %-%2 ',">/6/"$ #"6-/-26/ ( C G: !%*% -2+<2'%$ -/*%' 7"$-/$0 6%+% 6"'%7/= '"*2% <"$*% 8%$0 <"#-2+<2'%$ %'%$ <"#6%-2 *%$ <"#0"#%' <"#6%+% 6"-"7%& -2+<2'%$: !%*% 1"$/6 -2+<2'%$ /$/= N2'2+ I"'"'%7%$ f$"#0/ I/$"-/' -/*%' <"#7%'2= "$"#0/ 6"<%0/%$ &/7%$0 +"$1%*/ "$"#0/ '%7,#= "$"#0/ <2$8/= *%$ +"$8"<%<'%$ ."#2<%&%$ ?212* .%*% <"$*%: !G :G a !P :P C D!G a !PH :d !%*% -2+<2'%$ 7"$-/$0 6"<%0/%$= <"#7%'2 ."#6%+%%$ !G :G a !P :P C !G :Gd a !P :Pd

V:

Z:

# : d " :P d $ ( = "% G &=Uh(hG ' :G " :P ( B"$*% 8%$0 <"#0"#%' 1%-2& <"<%6 +"#2.%'%$ 1"$/6 -2+<2'%$ 7"$-/$0 6"<%0/%$: I,">/6/"$ #"6-/-26/$8% %*%7%& 9E 9P 9Q ( = 9 d %-%2 ( C 9G C 9P C 9Q 9 I"9".%-%$ ."72#2 *%.%- */2'2# *"$0%$ %82$%$ <%7/6-/' *"$0%$ +"+%$>%%-'%$ .#/$6/. -2+<2'%$ -/*%' 7"$-/$0 6%+% 6"'%7/: D ! $ !D H :J = J P;9 !J

(

)

Momentum, Impuls, dan Tumbukan

105

Peta Konsep 98)%*:4);0<)"43';0=(*0>4)247(* +"+<%&%6

N2'2+ I"'"'%7%$ @,+"$-2+

<"#7%'2

@,+"$-2+

M+.276

*/02$%'%$ 2$-2' +"$0%$%7/6/6

<"#7%'2 .%*%

32+<2'%$ 1"$/6$8%

32+<2'%$ \"$-/$0 ;"+.2#

%$32+<2'%$ \"$-/$0 ;"<%0/%$

32+<2'%$ 3/*%' \"$-/$0 ;%+% ;"'%7/

Refleksi Setelah mempelajari bab ini, tentu Anda dapat memahami konsep momentum, impuls, dan tumbukan. Anda juga tentu dapat menjelaskan jenis-jenis tumbukan yang mungkin terjadi dan hukum apa saja yang berlaku di dalamnya. Dari keseluruhan materi yang telah Anda pelajari, bagian manakah yang menurut Anda sulit? Coba Anda diskusikan dengan teman atau guru Fisika Anda.

106

Mudah dan Aktif Belajar Fisika untuk Kelas XI

Dengan mempelajari bab ini, Anda dapat mengetahui bahwa untuk mengukur kecepatan peluru tidak harus memasang alat ukur pada peluru. Anda cukup menghitung jejak yang ditinggalkannya, seperti pada bandul balistik. Nah, coba sebutkan manfaat lain mempelajari bab ini.

Tes Kompetensi Bab 4 OA $636?3(?0'(3(?0'(:405(J(2(*0P(*Q0"(36*Q0:%"(:0=(*07%&5(7(*3(?0"(=(0247403(:6?(*A G:

P:

Q:

E:

W:

Y/+"$6/ /+.276 %*%7%& :::: %: k@lk\lk3lFG <: k@lk\lk3lFP 9: k@lk\lFGk3lFG *: k@lk\lFPk3l ": k@lk\lPk3lP Y2% <"$*% +"+/7/'/ +%66% 8%$0 6%+%= 6"*%$0'%$ +,+"$-2+ <"$*% ."#-%+% *2% '%7/ +,+"$-2+ <"$*% '"*2%: !"#<%$*/$0%$ "$"#0/ '/$"-/' <"$*% ."#-%+% *%$ <"$*% '"*2% -"#6"<2- %*%7%& :::: %: G J G <: G J P 9: G J E *: P J G ": E J G b%+<%# <"#/'2- +"$2$12''%$ 0#%>/' D# A tH *%#/ 0"#%' 6"<2%& <"$*% 8%$0 +%66%$8% W '0: @,+"$-2+ <"$*% s (m) -"#6"<2- %*%7%& :::: %: PG '0+K6 24 <: PU '0+K6 9: G[ '0+K6 *: GW '0+K6 t (s) ": GU '0+K6 8 ;"<2%& <,7% /' +,+"$-2+ D
t

<:

p

t

9:

p

t

*:

p

t

":

p

t

V:

;"<2%& <,7% *%#/ '"%*%%$ */%+ */.2'27 *"$0%$ 0%8% VUU $"?-,$ &/$00% +"7"6%- *"$0%$ '"9".%-%$ VU +K6: T/'% +%66% <,7% U=W '0= ."+2'27 %'%$ +"$8"$-2& <,7% 6"7%+% :::: %: E _ GUFP 6 <: W _ GUFP 6 9: V _ GUFP 6 *: Z _ GUFP 6 ": [ _ GUFP 6 Z: b%8% 8%$0 */."#72'%$ 2$-2' +"$0&"$-/'%$ <"$*% <"#A +%66% QW '0 8%$0 <"#0"#%' *"$0%$ '"9".%-%$ GPU +K6 &/$00% <"#&"$-/ 6"-"7%& W 6"',$ %*%7%& :::: %: Z[U $"?-,$ <: [UU $"?-,$ 9: [PU $"?-,$ *: [EU $"?-,$ ": [VU $"?-,$ [: B"$*% <"#+%66% ! +"+/7/'/ +,+"$-2+ < *%$ "$"#0/ '/$"-/' B: T/'% "$"#0/ '/$"-/' <"#2<%& +"$1%*/ EB= +,+"$-2+$8% +"$1%*/ :::: %: < <: Q< 9: W< *: P< ": E< ]: B,7% ) *%$ B +"+/7/'/ +,+"$-2+ 8%$0 6%+% *%$ +%66% ) mB +%'% :::: %: '"9".%-%$ ) m '"9".%-%$ B <: "$"#0/ '/$"-/' ) C "$"#0/ '/$"-/' B 9: "$"#0/ '/$"-/' ) m "$"#0/ '/$"-/' B *: "$"#0/ '/$"-/' ) h "$"#0/ '/$"-/' B ": '"9".%-%$ ) C '"9".%-%$ B

Momentum, Impuls, dan Tumbukan

107

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

GZ:

G[:

( P;9

<: 9: *:

P;9 ;9( (P9 P;9 ": ( GE: ;"<2%& <,7% 1%-2& <"<%6 *%#/ '"-/$00/%$ PU + */ %-%6 7%$-%/: T/'% -2+<2'%$ *"$0%$ 7%$-%/ "7%6-/6 6"<%0/%$ *"$0%$ ',">/6/"$ #"6-/-26/$8% U=E= '"9".%-%$ .%$-27 <,7% 6"-"7%& +"$2+<2' 7%$-%/ %*%7%& :::: %: E +K6 <: V +K6 9: [ +K6 *: ] +K6 ": GU +K6

GW: ;"<2%& <,7% 1%-2& <"<%6 *%#/ '"-/$00/%$ GUU + */ %-%6 7%$-%/: T/'% ',">/6/"$ #"6-/-26/ %$-%#% <,7% *"$0%$ 7%$-%/ U=W= -/$00/ .%$-27%$ <,7% %*%7%& :::: %: [U + <: ZW + 9: WU + *: PW + ": PU + GV: T/'% */'"-%&2/ <"$*%A<"$*% <"#/'2- */&"$-/'%$ ,7"& */$*/$0 *%7%+ 6"7%$0 ?%'-2 8%$0 6%+%= */ %$-%#% <"$*%A

108

Mudah dan Aktif Belajar Fisika untuk Kelas XI

G]:

PU:

<"$*% -"#6"<2- 8%$0 +"$0%7%+/ 0%8% -"#<"6%# .%*% ?%'-2 <"#-2+<2'%$ *"$0%$ */$*/$0 <%-2 %*%7%& :::: %: <"$*% 8%$0 <"#+%66% GWU '0 <"#0"#%' *"$0%$ 7%12 Z +K6 <: <"$*% 8%$0 <"#+%66% GUU '0 <"#0"#%' *"$0%$ 7%12 GP +K6 9: <"$*% 8%$0 <"#+%66% WU '0 <"#0"#%' *"$0%$ 7%12 GW +K6 *: <"$*% 8%$0 <"#+%66% EU '0 <"#0"#%' *"$0%$ 7%12 PW +K6 ": <"$*% 8%$0 <"#+%66% PW '0 <"#0"#%' *"$0%$ 7%12 WU +K6 ;"<2%& <"$*% <"#+%66% G '0 <"#0"#%' '" '%$%$ *"$0%$ '"9".%-%$ V +K6 *%$ +"$2+<2' <"$*% 7%/$ 8%$0 <"#A +%66% P '0 *%$ <"#0"#%' '" '/#/ *"$0%$ <"6%# '"9".%-%$ Q +K6: T/'% '"*2% <"$*% 6%7/$0 +"7"'%- 6"-"7%& -2+<2'%$= '"9".%-%$ '"*2% <"$*% -"#6"<2- %*%7%& :::: %: E +K6 '" '%$%$ <: E +K6 '" '/#/ 9: P +K6 '" '%$%$ *: P +K6 '" '/#/ ": $,7 !"72#2 <"#+%66% GU 0 <"#0"#%' *"$0%$ '"9".%-%$ 6"<"6%# G:UUU +K6 *%$ +"$"+<26 6"<2%& <%7,' <"#+%66% GUU '0 8%$0 */%+ */ %-%6
RA

I(J(23(?0"%&:(*P((*02%&674:06*60=%*Q(*0:%"(:A

G:

;"<2%& <"$*% <"#+%66% E '0 */1%-2&'%$ -%$.% '"9".%-%$ %?%7 *%#/ '"-/$00/%$ VP=W +: T/'% ."#9".%-%$ 0#%L/-%6/ B2+/ ; C ]=[ +K6P= -"$-2'%$7%& +,+"$-2+ <"$*% 6%%- +"$2+<2' -%$%&: ;"<2%& +,/6/"$ #"6-/-26/ -2+<2'%$ <"$*% -"#6"<2- D(H: <: 3"$-2'%$ <"6%#$8% ."#2<%&%$ +,+"$-2+ <"$*% -"#6"<2-:

P:

Q:

E:

W:

V:

Z: ;"<2%& <%7,' <"#+%66% P '0 -"#7"-%' */ %-%6 7%$-%/ 7/9/$: !"72#2 <"#+%66% GW 0#%+ */-"+<%''%$ &,#/c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

P 1m 1m B

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

Momentum, Impuls, dan Tumbukan

109

Proyek Semester 1 !%*% 6"+"6-"# /$/ )$*% -"7%& <"7%1%# ',$6". -"$-%$0 b"#%' *%$ b%8%: `$-2' 7"
Kereta Dinamika >454(*0L%Q6(:(* @"+."7%1%#/ N2'2+ O"?-,$ O3(:0=(*0R(?(* G: I"#"-% */$%+/'% P: !%.%$ 7%$*%6%$ DPEU 9+ _ QU 9+ _ P 9+H *%$ '%-#,7 +"1% <"#*/%+"-"# E 9+ Q: Ni%0(6 ti!(6 D9"7%& ./-% G=W 9+H *%$ <+)(6 #/<<2KA$8% E: B"<%$ 0%$-2$0 PWU 0 DL%#/%6/ W= GU= PU= *%$ WU 0H W: I"#-%6 '%#<,$ *%$ <"$%$0 $/7,$ $&8'%=4&0$%&S82((* G: `'2# +%66% '"#"-% */$%+/'% *%$ <"<%$ 0%$-2$0: T2+7%& +%66% '"*2%$8% */%$00%. 6"<%0%/ +%66% 6/6-"+: P: ;262$ %7%-A%7%- 6"."#-/ .%*% 0%+<%# <"#/'2-: benang nilon

katrol

sisa beban kereta dinamika ticker timer pita

beban gantung

papan landasan

Q:

E:

b2$%'%$ 6"<%0/%$ <"<%$ 0%$-2$0 2$-2' +"$00"#%''%$ '"#"-% */$%+/'% *%$ 6/6%$8% 6/+.%$ */ %-%6 '"#"-% */$%+/'%: b"#%''%$ '"#"-% */$%+/'% <"#6%+%%$ *"$0%$ */&/*2.'%$$8% ti%0(6 ti!(6: N"$-/'%$ '"#"-% */$%+/'% .%*% 6%%- <"<%$ 0%$-2$0 -".%- %'%$ -/<% */ 7%$-%/ *%$ 6"0"#% +%-/'%$ ti%0(6 ti!(6: 3"7/-/ 1"1%' '"-/'%$ ti%0(6 ti!(6 .%*% ./-% '"#-%6: T/'% 62*%& <%026 &%6/7$8%= 7%$12-'%$ 7%$0'%& <"#/'2-$8%: \%'2'%$ 7%$0'%& '"*2% *%$ '"-/0% */ %-%6 GU '%7/ *"$0%$ <"<%$ 0%$-2$0 D."$00"#%'H 8%$0 <"#<"*% $%+2$ *"$0%$ +%66% 6/6-"+ -"-%.:

$%*Q83(?(*0T(:( G: Y"$0%$ '"#-%6 ./-% 8%$0 */."#,7"& *%#/ ."#9,<%%$ '"#"-% */$%+/'%= <2%-7%& 0#%>/' : C EDtH 2$-2' 6"-/%. ."#9,<%%$: 3"$-2'%$ ."#9".%-%$ 6/6-"+ *%#/ 6"-/%. ."#9,<%%$ <"#*%6%#'%$ 0#%>/' 8%$0 )$*% <2%- -"#6"<2-: P: B2%-7%& 0#%>/' &2<2$0%$ %$-%#% #"627-%$ 0%8% *"$0%$ ."#9".%-%$ 6/6-"+: ).%'%& &%6/7$8% 6"62%/ *"$0%$ N2'2+ MM O"?-,$5 B"#/'%$ ."$1"7%6%$: Q: 3"$-2'%$ <"6%# 0%8% 0"6"' 8%$0 -"#1%*/ *%7%+ ."#9,<%%$ -"#6"<2-:

110

Mudah dan Aktif Belajar Fisika untuk Kelas XI

Tes Kompetensi Fisika Semester 1

OA $636?3(?0'(3(?0'(:405(J(2(*0P(*Q0"(36*Q0:%"(:0=(*07%&5(7(*3(?0"(=(0247403(:6?(*A G:

P:

Q:

E:

W:

!"#9".%-%$ 6"<2%& .%#-/'"7 .%*% 6%%- t %*%7%& Vt 6 F E5: @27%A+27% .%#-/'"7 <"#0"#%' *"$0%$ '"9".%-%$ P6: 4"'-,# '"9".%-%$ .%#-/'"7 .%*% 6%%- t %*%7%& :::: %: DP a QtH6 F Et 5 <: DP F QtPH6 a Et 5 9: DP a QtPH6 F Et 5 *: DQ F PtPH6 a Et 5 ": DQ a PtPH6 F Et 5 ;"<2%& .%#-/'"7 <"#0"#%' 6"62%/ *"$0%$ ."#6%+%%$ .,6/6/ 6 C DtP F EtH/ a DPtP F PtH1= 6 *%7%+ +"-"# *%$ t *%7%+ *"-/': B"6%# '"9".%-%$ <"$*% .%*% 6%%- t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tP F Et: !"#6%+%%$ '"9"A .%-%$ 6"$-#/."-%7$8% %*%7%& ::::: %: EtQ F EtP <: GPtP F [t 9: ]tV F GPtW a EtE *: EtV F VtW a EtE ": QVtE F PEtQ F GVtP ;"<2%& +,/6/"$ 0"6"' '/$"-/' %$-%#% #,*% *%$ 1%7%$ U=P '"+2*/%$ <"#&"$-/ 6"-"7%& E *"-/'= <"6%# 0%8% ."$0"#"+%$ = %*%7%& :::: %: W:UUU O <: E:WUU O 9: Q:WUU O *: Q:UUU O ": E:UUU O

V:

!"#&%-/'%$ 0%+<%# <"#/'2-= 1/'% <"<%$ B */7".%6'%$= <%7,' ) -".%- %'%$ <"#0"#%': 2 kg A

B

Z:

1 kg

T/'% ."#9".%-%$ 0#%L/-%6/ GU +K6P= ',">/6/"$ 0"6"' 6-%-/6 %$-%#% <%7,' *%$ +"1% %*%7%& :::: %: U=W *: U=P <: U=E ": U=G 9: U=Q !"#&%-/'%$ 6262$%$ <"$*%A<"$*% .%*% 0%+<%# <"#/'2-: 4 kg A

B

[:

1 kg

I,">/6/"$ 0"6"' '/$"-/' %$-%#% <%7,' ) *%$ +"1% %*%7%& U=GPW: T/'% <"<%$ B */7".%6'%$= ."#9".%-%$ <"$*% ) %*%7%& :::: D; C GU +K6PH %: P=PW +K6P *: G=ZW +K6P <: P=UU +K6P ": G=WU +K6P 9: G=UU +K6P !"#&%-/'%$ 0%+<%# <"#/'2- /$/: m F

30°

I,">/6/"$ 0"6"' '/$"-/' %$-%#% <"$*% *"$0%$
111

]: ;"<2%& <"$*% *"$0%$ +%66% ! */<"#/ 0%8% = &/$00% <"#0"#%': T/'% 0%8% 0"6"' %$-%#% <"$*% *%$ 7%$-%/ 6%+% *"$0%$ E0= ."#9".%-%$ 0"#%' <"$*% %*%7%& :::: = " E0 %: $ C ! = $ E0 <: $ C ! ! 9: $ C = " E0 *:

$C

= ! $ E0

= ! " E0 GU: ;",#%$0 $"7%8%$ +"$8"<"#%$0/ 62$0%/ +"$002$%'%$ ."#%&2 *%82$0: !"#%&2 *%82$0 -"#6"<2- 6"7%72 */%#%&A '%$ -"0%' 72#26 -"#&%*%. %#%& %#26 %/# *"$0%$ '"9".%-A %$ Q +K6= 6"*%$0'%$ '"9".%-%$ %7/#%$ %/# C Q +K6: I"9"A .%-%$ -,-%7 ."#%&2 *%$ %#%&$8% *%7%+ +"7/$-%6/ 62$0%/ %*%7%& :::: %: Q +K6 *%$ EWj

":

$C

<: 9: *: ":

Q P +K6 *%$ EWj Q P +K6 *%$ ]Uj Q Q +K6 *%$ EWj V +K6 *%$ ]Uj

GG: !"72#2 */-"+<%''%$ *"$0%$ 62*2- "7"L%6/ EWj *%$ '"9".%-%$ %?%7 C GUU +K6: T/'% ."#9".%-%$ 0#%L/-%6/ ; C GU +K6 P = '"*2*2'%$ ."72#2 6%%- t C Q 6"',$ %*%7%& :::: %: I C QUU +^ K C PGU + <: I C WU P +^ K C WU P 9: I C WU P +^ K C PGU + *: I C PGU +^ K C GVZ=GQ + ": I C QUU +^ K C ]U + GP: ;"<2%& ."72#2 */-"+<%''%$ *"$0%$ '"9".%-%$ %?%7 GUU +K6 *%$ 62*2- "7"L%6/$8% WQj: !"#<%$*/$0%$ -/$00/ +%'6/+2+ *%$ -/-/' 1%2& +%'6/+2+ 8%$0 */9%.%/ ,7"& ."72#2 -"#6"<2- %*%7%& :::: %: G J E *: P J G <: G J Q ": Q J G 9: G J P GQ: !%*% ."#+%/$%$ 6".%' <,7%= <,7% 8%$0 */-"$*%$0 +"7%8%$0 */ 2*%#% 6"7%+% E *"-/' *"$0%$ 62*2"7"L%6/ QUj: T/'% 0"6"'%$ *"$0%$ 2*%#% */%<%/'%$ *%$ ; C GU +K6P= <,7% +"$9%.%/ 1%#%' 6"1%2& :::: %: GPU + <: GQ[ + 9: PUU + *: QUU + ": E[U +

112

Mudah dan Aktif Belajar Fisika untuk Kelas XI

GE: ;"<2%& 6"."*% +,-,# +"+<"7,' .%*% -/'2$0%$ <"#<"$-2' <262# 7/$0'%#%$ *"$0%$ 1%#/A1%#/ GU +: T/'% ',">/6/"$ 0"6"'%$ %$-%#% #,*% *%$ 1%7%$ U=PW *%$ ; C GU +K6P= '"9".%-%$ +,-,# -"#<"6%# %0%# 6"."*% +,A -,# -/*%' 67/. %*%7%& :::: %: W +K6 <: P=W +K6 9: P=U +K6 *: G=W +K6 ": G=P +K6 GW: ;"<2%& +,/6/"$ 0"6"' %$-%#% <%$ +,/6/"$ 0"6"' '/$"-/' G Q: B%7,' */<"#/ 0%8% PU O *%$ <"#62*2- QUj -"#&%*%. E
PU: @%66% 1%#/A1%#/ .7%$"- R 6%+% *"$0%$ $ '%7/ +%66% B2+/ *%$ <"#1%#/A1%#/ ? '%7/ 1%#/A1%#/ B2+/: B"#%- <"$*% */ .7%$"- R */<%$*/$0'%$ *"$0%$ <"#%-$8% */ B2+/ +"$1%*/ :::: %: $? '%7/ <: $?8 '%7/ a 9: '%7/ b $ '%7/ *: ?P G '%7/ ": $? PG: ;"<2%& 6%-"7/- <"#%*% .%*% '"-/$00/%$ 9 */ %-%6 ."#+2'%%$ B2+/: T/'% */'"-%&2/ 1%#/A1%#/ B2+/ %*%7%& H= ."#/,*" 6%-"7/- -"#6"<2- +"$0"7/7/$0/ B2+/ %*%7%& :::: D,#
D H $ 9H P3 ;

PW: ;",#%$0 $"7%8%$ +"$%#/' ."#%&2$8% *"$0%$ 62*2- EWj -"#&%*%. %#%& &,#/c,$-%7 *%$ ."#%&2 <"#./$*%& 6"1%2& GU +: T/'% $"7%8%$ -"#6"<2- +"$%#/' ."#%&2 *"$0%$ 0%8% G[U O= <"6%# 26%&% 8%$0 */7%'2'%$ $"7%8%$ -"#6"<2- %*%7%& :::: %: ]UU T *: [WU T <: PV:

PZ:

P3 H $ 9

3 H$9 DH $ 9H E3 P ;

": E3 D H $ 9 H P; PP: ;"<2%& <"$*% 8%$0 <"#%*% */ B27%$ <"#0"#%' *"$0%$ ."#9".%-%$ $ '%#"$% +"$*%.%- 0%8% = : T/'% <"$*% -"#6"<2- */<%?% '" B2+/ 8%$0 0%8% 0#%L/-%6/$8% "$%+ '%7/ +%66% B27%$ *%$ <"$*% -"#6"<2- */<"#/ 0%8% = 120%= ."#9".%-%$ %*%7%& :::: %: V$

P[:

P

$ V $ $ *: V $ ": V PQ: @"$2#2- N2'2+ MMM I".7"#= '2%*#%- ."#/,*" 62%-2 .7%$"- +"$0"7/7/$0/ @%-%&%#/ 6"<%$*/$0 *"$0%$ :::: %: +%66% .7%$"<: 1%#%' .7%$"- '" @%-%&%#/ 9: .%$0'%- -/0% +%66% .7%$"*: .%$0'%- -/0% 1%#%' .7%$"- '" @%-%&%#/ ": '2%*#%- 1%#%' @%-%&%#/ '" .7%$"PE: T/'% ."#/,*" 6%-"7/- 8%$0 +"$0,#
P]:

<: 9:

QU:

]UU 2 T

":

[ZW T

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n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b%6 .%$%6 8%$0 */&%6/7'%$ ,7"& 6"<2%& #,'"- +"+/7/'/ '"7%12%$ EUU +K6 *%$ -"#1%*/ ."+<%'%#%$ 0%6 6"<%$8%' [U '0 *%7%+ ?%'-2 6%-2 6"',$: B"6%#$8% 0%8% *,#,$0 #,'"- -"#6"<2- %*%7%& :::: %: P:UUU O *: PE:UUU O <: GP:UUU O ": QP:UUU O 9: GV:UUU O

Tes Kompetensi Fisika Semester 1

113

RA

I(J(23(?0"%&:(*P((*02%&674:06*60=%*Q(*0:%"(:A

G:

!%*% 6262$%$ <"$*%A<"$*% 6"."#-/ .%*% 0%+<%#= +%66% <"$*% ) *%$ B 6%+%= 8%/-2 W '0: A

B

0

P:

T/'% ',">/6/"$ 0"6"'%$ '/$"-/' %$-%#% <"$*% ) *%$
8k

g

B = 2 kg

0

Q:

T/'% '"*2% <"$*% */7".%6'%$= -%7/ +"+/7/'/ -"0%$0%$ Q PE O: T/'% 6/$ 0 C = <"#%.%'%& ',">/6/"$ 0"6"' %$-%#% W <"$*% ) *%$
B

E:

114

@%66% ) C E '0 *%$ +%66% B C [ '0 D; C GU +K6PH: 3"$-2'%$ <"6%# ."#9".%-%$ <"$*% B *%$ -"0%$0%$ -%7/$8%= 1/'% ',">/6/"$ 0"6"'%$ 6-%-/6 %$-%#%
Mudah dan Aktif Belajar Fisika untuk Kelas XI

W: @%66% .7%$"- i2./-"# %*%7%& G=] _ GUPZ '0 *%$ +%66% @%-%&%#/ C P=U _ GUQU '0: T/'% 1%#%' %$-%#% @%-%&%#/ *%$ .7%$"- i2./-"# %*%7%& Z=[ _ GUGG + *%$ O 6"<"6%# V=VZ _ GUFGG O +PK'0= -"$-2'%$J %: 0%8% 0#%L/-%6/ @%-%&%#/ .%*% .7%$"- i2./-"#^ *%$ <: 7%12 7/$"%# ,#/6/"$ 0"6"' <%7,' *%$
Bab

5 Sumber: Contemporary College Physics, 1993

Peloncat indah menekuk tubuhnya ketika mulai berputar dan merentangkan tubuhnya ketika hendak mendekati air.

Gerak Rotasi dan Kesetimbangan Benda Tegar Hasil yang harus Anda capai: menerapkan konsep dan prinsip mekanika klasik sistem kontinu dalam menyelesaikan masalah. Setelah mempelajari bab ini, Anda harus mampu: memformulasikan hubungan antara konsep torsi, momentum sudut, dan momen inersia berdasarkan Hukum II Newton, serta penerapannya dalam masalah benda tegar.

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

A. Kinematika Gerak Rotasi B. Dinamika Gerak Rotasi C. Kesetimbangan Benda Tegar

115

Tes Kompetensi Awal S"#"$%&'&"&("$a*a+i'k./s"('1"+ak'2.tasi'4a/'5"s"ti&#a/6a/'7"/4a'8"6a+9'k"+*aka/$a:'s.a$;s.a$'#"+ik%t 4a$a&'#%k%'$ati:a/< B; )4%(8%$/(*-+%'20*(*"$/%$(+3+"$(/%8%:(+3+"$ F; D"10.'%$(="$-2-="$-2('"2".-+1%$/%$;(G",%2'%$ '34",:(*%$(+3+"$(-$"#2-%6 *"$/%$(1%&%2%()$*%(2"$*-#-; C; )4%(&010$/%$(%$.%#%(<0'0+(9"'"'%,%$(73+"$H; )4%(4"$/"#.-%$(*%#-(.-.-'(1"#%.(1"$*%6 .0+(D0*0.(*%$(<0'0+(EE(9"4,"#6

A. Kinematika Gerak Rotasi

Gambar 5.1 Baling-baling kipas berotasi pada porosnya.

y P r

s x

! O

G-'%()$*%(+"+4"#&%.-'%$(2"10%&(4-#-$/%$(&-.%+(8%$/(2"*%$/(1"#40.%# %.%0( 1%,-$/-1%,-$/( '-4%2( %$/-$( 8%$/( 2"*%$/( 1"#40.%#:( )$*%( %'%$( +",-&%. 1%&A%( 4-#-$/%$( &-.%+( *%$( 1%,-$/-1%,-$/( '-4%2( %$/-$( ."#2"10.( +",%'0'%$ /"#%'( #3.%2-( 4%*%( 2"10%&( 20+10( 2.%2-3$"#( (.".%4)( *%,%+( '"#%$/'%( %50%$ -$"#2-%(."#."$.0;(K3$.3&(,%-$(*%#-(1"$*%(."/%#(8%$/(2"*%$/(1"#3.%2-(%*%,%& 1%$( 2"4"*%( 8%$/( 2"*%$/( 1"#40.%#( *%$( '3+-*-( 40.%#;

1. Posisi Sudut dalam Gerak Rotasi

!"#&%.-'%$( 1a&#a+' =<>' 8%$/( +"$*"2'#-42-'%$( 2"10%&( 1"$*%( ."/%# 1"#1"$.0'(,-$/'%#%$(8%$/(1"#3.%2-(4%*%(20+10(.".%4(!"*%$(."/%'(,0#02(."#&%*%4 1-*%$/( #$%" L-.-'( !( ."#,".%'( 4%*%( 1"$*%( 2"&-$//%( /%#-2( M!( 1"#3.%2-( 1"#2%+% 1"$*%( ."#2"10.;( D0*0.( ! ( 8%$/( *-1"$.0'( 3,"&( /%#-2( M!( *%$( 20+10-# +"$*"2'#-42-'%$( 432-2-( 1"$*%( 2%%.( 1"$*%( 1"#3.%2-; D0*0.( ! (*-1"$.0'(3,"&(2"10%&(1020#(s"4%*%(,-$/'%#%$(1"#=%#--=%#-('% N-,%-( 20*0.( ! ( (*%,%+( #%*-%$)( *-$8%.%'%$( *"$/%$( 4"#2%+%%$

s (OPB) ' 933#*-$%.( ! (+"$"$.0'%$(432-2-(#3.%2-(*%#-(1"$*%(."/%#(4%*%(20%.0 A%'.0:( ! =( ! (t);(G-'%(4%*%(2%%.(t(432-2-(20*0.(1"$*%( ! (+%'%(4%*%(2%%. t) " t:(432-2-(20*0.$8%( ! " "! ;

! !

Gambar 5.2 Sebuah benda tegar berbentuk lingkaran berotasi pada sumbu koordinat O.

D%+%(&%,$8%(*"$/%$(/"#%'(,-$"%#:(*%,%+(/"#%'(#3.%2-:('"5"4%.%$(20*0. #%.%-#%.%( *-*"@-$-2-'%$( 2"1%/%-( 4"#1%$*-$/%$( %$.%#%( 4"#01%&%$( 20*0.( "! ."#&%*%4(4"#01%&%$(A%'.0(( "t );(!"#&%.-'%$(1a&#a+'=
y P,t2

"!

!C !B

2. Kecepatan Sudut Rata-Rata dalam Gerak Rotasi

P,t1 x

O

1"$*%( ."/%#( 1"#1"$.0'( ,-$/'%#%$( 8%$/( 1"#3.%2-( +"+1"$.0'( 20*0.( !B ."#&%*%4( 20+10-#( 4%*%( A%'.0( tB;( 9"+0*-%$:( 4%*%( 2%%.( tC:( 20*0.( 8%$/ *-1"$.0'$8%( 1"#01%&( +"$=%*-( ! C %" >"$/%$( *"+-'-%$:( '"5"4%.%$( 20*0. #%.%-#%.%$8%( %*%,%&

##%.%-#%.% ! Gambar 5.3 Perpindahan sudut sebesar "! ( dari sebuah benda tegar yang berotasi pada saat t1 dan t2.

116

! C $!B "! ! t C $ tB "t

(OPC)

M,"&( '%#"$%( ! +"+-,-'-( 2%.0%$( *"#%=%.:( #%*-%$:( %.%0( 40.%#%$: '"5"4%.%$( 20*0.( #%.%-#%.%( *%4%.( ( *-$8%.%'%$( *"$/%$( 2%.0%$( *"#%=%.S 2"'3$:( #%*-%$S2"'3$:( %.%0( 40.%#%$S2"'3$;

Mudah dan Aktif Belajar Fisika untuk Kelas XI

3. Kecepatan Sudut Sesaat dalam Gerak Rotasi

! # #%* $

T%/%-+%$%'%&( 5%#%( +"$/0'0#( '"5"4%.%$( 20*0.( 2"2%%.( *%#-( 2"10%& 1"$*%(."/%#(8%$/(1"#/"#%'(#3.%2-6(D%+%(&%,$8%(*"$/%$(/"#%'(,-$"%#:(*%,%+ /"#%'(#3.%2-:('"5"4%.%$(20*0.(2"2%%.(( # )(*-."$.0'%$(*%,%+(2",%$/(A%'.0 ( "t )( 8%$/( 2%$/%.( 2-$/'%.( ( "t % U )( 2"&-$//%( 4"#01%&%$( '"5"4%.%$$8% 2%$/%.( '"5-,;( M,"&( '%#"$%( -.0:( '"5"4%.%$( 20*0.( 2"2%%.( 4%*%( /"#%'( #3.%2*-$8%.%'%$( *"$/%$( 4"#2%+%%$ "! # ! ,-+ # ! ,-+ "t % U "t % U "t %.%0

*! #! *t

!C

0

(OPF)

>"$/%$( *"+-'-%$:( '"5"4%.%$( 20*0.( 2"2%%.( +"#04%'%$( .0#0$%$ 4"#.%+%( *%#-( 4"#2%+%%$( 432-2-( 20*0.( 2"1%/%-( @0$/2-( A%'.0;( !"#&%.-'%$ /#%@-'( ! ( ."#&%*%4( t( 4%*%( 1a&#a+' =<@;

Q

!B

&

P

t1

t(s)

t1

Gambar 5.4 Kecepatan sudut sesaat ( # ) dapat ditentukan dari gradien grafik ! terhadap t pada sebuah titik.

G-'% "t ! t2 $ t1 2%$/%.( '"5-,( %.%0( +"$*"'%.-( $3,:( .-.-'( V( %'%$( 2%$/%. *"'%.( *"$/%$( !:( %.%0( 1%&'%$( 1"#-+4-.( 2"&-$//%( '"+-#-$/%$( (/#%*-"$) /#%@-' ! ."#&%*%4( t( *-( .-.-'( !( +"#04%'%$( '"5"4%.%$( 20*0.( 2"2%%.;( M,"& '%#"$%( -.0:( '"5"4%.%$( 20*0.( 2"2%%.( *%4%.( 40,%( *-$8%.%'%$( *"$/%$ 4"#2%+%%$( 1"#-'0.;

(# !

*! ! .%$ & *t

(OPH)

4. Percepatan Sudut dalam Gerak Rotasi D"10%&(4%#.-'",(8%$/(1"#/"#%'(#3.%2-(%'%$(+"+-,-'-(4"#5"4%.%$(20*0. =-'%( 4%#.-'",( ."#2"10.( +"$/%,%+-( 4"#01%&%$( '"5"4%.%$( 20*0.;( >"$/%$ *"+-'-%$:( 4"#5"4%.%$( 20*0.( %*%,%&( 4"#01%&%$( '"5"4%.%$( 20*0.( 2".-%4 2%.0%$( A%'.0( 2"&-$//%( 2%.0%$$8%( %*%,%&( #%*S2C; a. Percepatan Sudut Rata-Rata !"#5"4%.%$( 20*0.( #%.%-#%.%( *-$8%.%'%$( *"$/%$( ,%+1%$/( ' ;( G-'% 2"10%&( 4%#.-'",( 1"#/"#%'( +",-$/'%#( *"$/%$( '"5"4%.%$( 20*0.( #1 ( 4%*% 2%%.( tB:( '"+0*-%$( 1"#01%&( +"$=%*-( #2 " 4%*%( 2%%.( tC:( 4"#5"4%.%$( 20*0. #%.%-#%.%(( ' )(4%#.-'",(."#2"10.(*%,%+(2",%$/(A%'.0(Dt(*-$8%.%'%$(*"$/%$ 4"#2%+%%$( 1"#-'0.; # $# (' ! C B t C $ tB %.%0

'!

"# "t

(OPO)

b. Percepatan Sudut Sesaat )$*%(.",%&(+"$/".%&0-(1%&A%('"5"4%.%$(20*0.(2"2%%.(( # )(*-."$.0'%$ *%,%+( 2",%$/( A%'.0( 8%$/( 2%$/%.( 2-$/'%.( ( "t % U )( 2"&-$//%( 4"#01%&%$ '"5"4%.%$$8%( 2%$/%.( '"5-,;( D%+%( &%,$8%( *"$/%$( '"5"4%.%$( 20*0.( 2"2%%. ( # ):(4"#5"4%.%$(20*0.(2"2%%.(( ' )(=0/%(+"#04%'%$(4"#5"4%.%$(20*0.(#%.%#%.%( 8%$/( ."#=%*-( *%,%+( 2",%$/( A%'.0( ( "t )( 8%$/( 2%$/%.( 2-$/'%.:( %.%0 "t % U; ( >"$/%$( *"+-'-%$:( 4"#5"4%.%$( 20*0.( 2"2%%.( *-$8%.%'%$( *"$/%$ 4"#2%+%%$( 1"#-'0.;

Gerak Rotasi dan Kesetimbangan Benda Tegar

117

' ! ,-+ ' "t % U

' ! ,-+

"t % U

# #2

'1

#1

*# *t

'!

(rad/s1)

B

'!

t (s)

t1

(OPW)

>"$/%$( +"$2012.-.02-'%$( A"+sa&aa/' B=C?D( '"( *%,%+( A"+sa&aa/' B=CED: *-4"#3,"&( 4"#2%+%%$( 4"#5"4%.%$( 20*0.( 2"1%/%-( 1"#-'0.;

'2

A

t1

"# "t

Gambar 5.5 Percepatan sudut sesaat berdasarkan gradien garis singgung # = # (t) di titik t.

*# * ( *! ! * *t *t , *t

C ) *! ! + C - *t

(OPX)

>"$/%$( *"+-'-%$:( )$*%( .",%&( +"$/".%&0-( 1%&A%( 4"#5"4%.%$( 20*0. 2"2%%.( +"#04%'%$( .0#0$%$( 4"#.%+%( *%#-( '"5"4%.%$( 20*0.( 2"2%%.( %.%0 .0#0$%$( '"*0%( *%#-( 4"#2%+%%$( 432-2-( 20*0.( 2"1%/%-( @0$/2-( A%'.0;( D",%-$ -.0:( 4"#5"4%.%$( 20*0.( 2"2%%.( *%4%.( 40,%( *-."$.0'%$( 1"#*%2%#'%$( /#%*-"$ /%#-2(2"&-$//%(/#%@-'( # (."#&%*%4(t(*-(20%.0(.-.-';(!"#&%.-'%$(/#%@-'( # (=( # (t) 4%*%( 1a&#a+' =<=;( !"#5"4%.%$( 20*0.( 2"2%%.( *-( .-.-'( )( %*%,%&( .%$ '1 , 2"*%$/'%$( 4"#5"4%.%$( 20*0.( 2"2%%.( *-( .-.-'( T( %*%,%&( .%$ ' 2 .

5. Gerak Rotasi dengan Kecepatan Sudut Konstan G-'%( 2"10%&( 1"$*%( ."/%#( 1"#/"#%'( #3.%2-( *"$/%$( '"5"4%.%$( 20*0. ( # )( '3$2.%$:( 4"#2%+%%$( /"#%'( *%#-( 1"$*%( ."/%#( ."#2"10.( *-$8%.%'%$ *"$/%$( 4"#2%+%%$ *! # ! *t *! ! # (*t !

t

U

U t

. *! ! . # (*t

! #t $ $ ! U ! # . (*t U

! #t $ $ !U ! #t

! #t $ ! ! U " #t

(OPY)

*"$/%$( !0 (%*%,%&(20*0.(8%$/(*-."+40&(4%*%(2%%.(t(=(U; )'%$(.".%4-:(=-'%(4%#.-'",(."#2"10.(+"$/%,%+-(4"#01%&%$('"5"4%.%$ 20*0.( 2"&-$//%( +"$/&%2-,'%$( 4"#5"4%.%$( 20*0.:( 4"#2%+%%$( /"#%'( #3.%2*%#-( 1"$*%( ."/%#( ."#2"10.( *%4%.( *-.0#0$'%$( *%#-( A"+sa&aa/' B=CFD: *"$/%$( $-,%- ' .".%4; *# ' ! *t *# ! ' *t #

t

. *# ! . ' *t

#U

U

t

Kata Kunci • posisi sudut • kecepatan sudut • percepatan sudut

118

Mudah dan Aktif Belajar Fisika untuk Kelas XI

# #t $ $ #U ! ' . *t U

# #t $ $ #U ! ' t # #t $ ! #U " ' t

(OPZ)

T"#*%2%#'%$( A"+sa&aa/' B=CGD( *%$' A"+sa&aa/' B=CHD:( *-4"#3,"& 4"#2%+%%$(432-2-(20*0.(0$.0'(/"#%'(+",-$/'%#(1"#%.0#%$(2"1%/%-(1"#-'0.; t

!

. *! ! . (# #t $ *t U t

!U

! . ##U " ' t $ *t

Tugas Anda 5.1 Buatlah perbandingan antara persamaan posisi, kecepatan, dan percepatan untuk gerak lurus berubah beraturan dan gerak rotasi benda tegar.

U

B C 't C B ! #t $ ! !U " #U t " ' t C C

! $ !U ! #Ut "

Tes Kompetensi Subbab

(OPBU)

A

5"+*aka/$a:'4a$a&'#%k%'$ati:a/< B; D"10%&( #3*%( 1"#=%#--=%#-( FU( 5+( 1"#3.%2-( *"$/%$ 20*0.(#3.%2-(8%$/(*-$8%.%'%$(*"$/%$(4"#2%+%%$ ! (=((H((#%*S2 C)t C;(L"$.0'%$,%& %; 1"2%#(20*0.( ! (4%*%(A%'.0(tB(=(C(2(*%$(tC(=(H:UO *%,%+(2%.0%$(#%*-%$(*%$(*"#%=%.[ 1; =%#%'( ."+40&( 4%#.-'",( 4%*%( ."4-( #3*%( 2",%+% -$."#\%,(A%'.0(tB(*%$(tC[ 5; '"5"4%.%$( 20*0.( #%.%-#%.%( *%,%+( 2%.0%$( #%*S2 %$.%#%(tB(*%$(tC[(*%$ *; '"5"4%.%$(20*.(2"2%%.(4%*%(.(=(F(2;

C;

F;

D"10%&(#3*%(2"4"*%(8%$/(2"*%$/(1"#40.%#(+"+-,-'*-%+"."#( FY( 5+;( G-'%( 2"10%&( .-.-'( 4%*%( ."4-( #3*% +"$"+4",(OW:O('%,-(4%*%(.%$%&:(1"#%4%'%&(4%$=%$/ ,-$.%2%$(8%$/(*-,%,0-(3,"&(#3*%(2"4"*%(."#2"10.6 D"10%&(4-#-$/%$(+,-(1"#3.%2-(*"$/%$('"5"4%.%$ 20*0.( # 8%$/(*-$8%.%'%$(*"$/%$(4"#2%+%%$( # = (Y(#%*S2F)tC;(L"$.0'%$,%&(4"#5"4%.%$(20*0.(#%.%-#%.% %$.%#%(tB(=(B(2(*%$(tC(=(C(2(*%$(1"2%#(4"#5"4%.%$ 20*0.(2"2%%.(4%*%(2%%.(t(=(O(2;

B. Dinamika Gerak Rotasi

r

1. Momen Gaya (Torsi)

M/012"3a$a(%.%0(.3#2-(+"#04%'%$(1"2%#%$(8%$/(+"$8"1%1'%$(2"10%& 1"$*%( ."/%#( (1"$*%( 8%$/( .-*%'( *%4%.( 1"#01%&( 1"$.0')( 5"$*"#0$/( 0$.0' 1"#3.%2-(."#&%*%4(43#32$8%;(73+"$(/%8%(."#+%20'(1"2%#%$(\"'.3#(*%$(*-1"#,%+1%$/( / ( (.%0); T%/%-+%$%'%&(5%#%(+"$"$.0'%$(.3#2-(%.%0(+3+"$(/%8%(8%$/(1"'"#=% 4%*%( 1"$*%( 8%$/( 1"#3.%2-6( !"#&%.-'%$( '"+1%,-( 1a&#a+' =<E' BaD;( 90$5+0#(8%$/(+"+-,-'-(4%$=%$/('(*-/0$%'%$(0$.0'(+"+0.%#(+0#(4%*%(#3*% +31-,;( 9".-'%( +0#( 1"#40.%#( %'-1%.( /%8%( 8%$/( *-1"#-'%$( 4%*%( '0$5-( +0#: +0#( 1"#4"#%$( 2"1%/%-( "$/2",( %.%0( 402%.( 20+10( 40.%#;( 73+"$( /%8% *-#0+02'%$( *"$/%$( 4"#2%+%%$ (OPBB) / (=(!(](" T"#*%2%#'%$(A"+sa&aa/'B=CIID:(*-'".%&0-(1%&A%(.3#2-(%.%0(+3+"$(/%8% +"+-,-'-( 2%.0%$( $"A.3$( +"."#( (N+); !"#&%.-'%$(1a&#a+' =<EB#D(8%$/(+"$0$=0''%$(*-%/#%+(+3+"$(/%8% 8%$/(1"'"#=%(4%*%(2%%.(+"+10'%(+0#(#3*%(+31-,;(93+43$"$(/%8%(J(8%$/ 1"'"#=%( 4%*%( 1%.%$/( !( +"+1"$.0'( 20*0.( ! :( %#%&( 4"#40.%#%$$8%( 2"%#%& *"$/%$( %#%&( 40.%#%$( =%#0+( =%+;( 93+43$"$( /%8%( J( 8%$/( +"$8"1%1'%$ +0#(1"#3.%2-(%*%,%&(^(2-$(! :(8%-.0('3+43$"$(/%8%(8%$/(."/%'(,0#02(."#&%*%4 !;(M,"&('%#"$%(-.0:(1"2%#(+3+"$(/%8%(8%$/(*-&%2-,'%$(%*%,%& / (=('5(2-$( ! (=(5*

F

(%) y

F sin !

! r

F

/ O

Gambar 5.6

x

d

(1)

(a) Gaya F dibutuhkan untuk membuka mur pada roda mobil. (b) Diagram momen gaya atau torsi yang bekerja saat membuka mur pada roda mobil.

(OPBC)

Gerak Rotasi dan Kesetimbangan Benda Tegar

119

9"."#%$/%$_ / =(1"2%#(+3+"$(/%8%((N+) ' =( =%#%'( 20+10( #3.%2-( '"( .-.-'( .%$/'%4( (+) 5 =( 1"2%#( /%8%( 8%$/( *-'"#=%'%$( (N) * =('(2-$( ! (=(,"$/%$(+3+"$((+) !"#&%.-'%$( 4"#2%+%%$( +3+"$( /%8%( 4%*%( A"+sa&aa/' B=CIID;( T"2%# +3+"$( /%8%( *-&%2-,'%$( *%#-( 4"#'%,-%$( \"'.3#;( G-'%( 20*0.( %$.%#%( '" *%$ /%8%(5"."/%'(,0#02((! (=(ZU`):(%'%$(*-4"#3,"&(1"2%#(+3+"$(/%8%(/ (2"1"2%# / (=('5

(OPBF)

)#%&(*%#-(+3+"$(/%8%((/ )(*%4%.(*-."$.0'%$(1"#*%2%#'%$('3$\"$2-(%.%0 '"2"4%'%.%$( 1"#-'0.( -$-;( G-'%( %#%&( 40.%#%$( .3#2-( 2"%#%&( *"$/%$( %#%& 40.%#%$( =%#0+( =%+:( +3+"$( /%8%( (/ )( 1"#$-,%-( 432-.-@;( G-'%( %#%&( 40.%#%$ .3#2-(1"#,%A%$%$(%#%&(*"$/%$(%#%&(40.%#%$(=%#0+(=%+:(+3+"$(/%8%((/ ) 1"#$-,%-( $"/%.-@;

2. Momen Inersia

)$*%(."$.0(+"$/".%&0-(1%&A%(2".-%4(1"$*%(+"+-,-'-('"5"$*"#0$/%$ 0$.0'( +"+4"#.%&%$'%$( '"%*%%$( /"#%'$8%;( >%,%+( /"#%'( ,-$"%#:( 2".-%4 1"$*%(8%$/(*-%+(%'%$(.".%4(*-%+;()*%40$(1"$*%(8%$/(2"*%$/(1"#/"#%' ,0#02( 1"#%.0#%$( +"+-,-'-( '"5"$*"#0$/%$( 0$.0'( .".%4( 1"#/"#%'( ,0#02 1"#%.0#%$:('"50%,-(%*%(#"20,.%$(/%8%(8%$/(+"+"$/%#0&-$8%;(<%,(."#2"10. 2"20%-( *"$/%$( <0'0+( E( N"A.3$;( 9"5"$*"#0$/%$( 1"$*%( 0$.0'( +"+4"#.%&%$'%$( '"%*%%$$8%( *-2"10.( 621's6a" %.%0( 0assa; >"+-'-%$( 40,%( &%,$8%( *"$/%$( *-$%+-'%( /"#%'( #3.%2-;( T"$*%( 8%$/ 2"*%$/( 1"#3.%2-( +"+-,-'-( '"5"$*"#0$/%$( 0$.0'( .".%4( +"+4"#.%&%$'%$ /"#%'( #3.%2-$8%;( 9"5"$*"#0$/%$( ."#2"10.( *-$%+%'%$( 0/012" 621's6a; 73+"$(-$"#2-%(8%$/(1"#3.%2-(*-4"$/%#0&-(3,"&(+%22%(*%$(43,%(*-2.#-102+%22%( ."#&%*%4( 20+10( 40.%#;

m r

# v

Gambar 5.7 Partikel bermassa m berputar mengelilingi sebuah sumbu putar yang berjarak r dari partikel tersebut.

a. Momen Inersia Benda Diskrit (Partikel) G-'%( 2"10%&( 4%#.-'",( 8%$/( 1"#+%22%( 0( 1"#40.%#( +"$/",-,-$/-( 20+10 40.%#( 8%$/( 1"#=%#%'( '( *%#-( 4%#.-'",( ."#2"10.:( *%4%.'%&( )$*%( +"$/&-.0$/ 1"2%#$8%( "$"#/-( '-$".-'( *%#-( 4%#.-'",( ."#2"10.6( !"#&%.-'%$( 1a&#a+' =%,%+( /"#%'( +",-$/'%#:( '"5"4%.%$( ,-$"%#( *-$8%.%'%$( *"$/%$( 7( =( # #: *"$/%$( # ( '"5"4%.%$( 20*0.;( M,"&( '%#"$%( -.0:( 1"2%#( "$"#/-( '-$".-'( #3.%2*%#-( 4%#.-'",( *%4%.( *-$8%.%'%$( *"$/%$

B 98(#3.%2- ! 0' C 7C C

(OPBH)

>%#-( A"+sa&aa/' B=CI@D:( *-4"#3,"&( $-,%-( 0'C( 8%$/( +"$8%.%'%$( +3+"$ -$"#2-%(*%#-(4%#.-'",(8%$/(1"#/"#%'(+",-$/'%#;(73+"$(-$"#2-%(*-,%+1%$/'%$ *"$/%$( :; :(=(0'C (OPBO) >"$/%$(*"+-'-%$:(+3+"$(-$"#2-%(2"10%&(4%#.-'",(2"1%$*-$/(*"$/%$(+%22% 4%#.-'",( *%$( '0%*#%.( =%#%'( %$.%#%( 4%#.-'",( *%$( 20+10( 40.%#$8%;( 73+"$ -$"#2-%( +"#04%'%$( 1"2%#%$( 2'%,%#( 8%$/( +"+-,-'-( 2%.0%$( '/+C;

120

Mudah dan Aktif Belajar Fisika untuk Kelas XI

b. Momen Inersia Benda Tegar D"10%&(1"$*%(."/%#(."#*-#-(%.%2(2"=0+,%&(4%#.-'",(8%$/(."#4-2%&(2%.0 *"$/%$(8%$/(,%-$$8%(2"#.%(=%#%'$8%(.".%4;(73+"$(-$"#2-%$8%(+"#04%'%$ =0+,%&( *%#-( +3+"$( -$"#2-%( 2"+0%( 4%#.-'",( -.0:( 8%'$-( :" = 0 0'C;( )'%$ .".%4-:(0$.0'(2"10%&(1"$*%(8%$/(+"+-,-'-(*-2.#-102-(+%22%(8%$/('3$.-$0: %.%0( .-*%'( *%4%.( *-4-2%&'%$( 2"4"#.-( 1a&#a+' =
:(=( . ' *0

(OPBW)

y dm r

o

sumbu rotasi

D"10%&( 1"$*%( 1"#+%22%( 0" 8%$/( 1"#1"$.0'( 1%.%$/( *"$/%$( 4%$=%$/ ;" .%+4%'( 2"4"#.-( 1a&#a+' =%#-( A"+sa&aa/( B=CIED:( *-'".%&01%&A%('"=(#"*%$(*0"=( M *M (2"#.%(1%.%2-1%.%2(-$."/#%,$8%(%*%,%&(#B(*%$ ; #C:( %'%$( *-4"#3,"&

Gambar 5.8

#C ( M) : ! . # C * + *# #B ,;-

Gambar 5.9

(OPBX)

x

Momen inersia benda pejal dihitung dengan metode integral terhadap r2 dm. y L 0

x x1

x2

dm

x

Sebuah batang homogen memiliki massa m dengan panjang batang L.

a$.0'( 20+10( 40.%#( 8%$/( ."#,".%'( 4%*%( 0=0$/( 1%.%$/( 2"4"#.-( 1a&#a+ =
y

;

; F : ! M . #C *# (=( M 13 B # F 24 (=( M 13 B ; 24 (=( B M;C ; 5F 6 F ; U ; 5 F 6U

(OPBY)

a$.0'( 20+10( 40.%#( 8%$/( ."#,".%'( 4%*%( 4"#."$/%&%$( 1%.%$/:( 2"4"#.B B .%+4%'(4%*%(1a&#a+'=
:! M. ;

L

Gambar 5.10 Momen inersia untuk sumbu putar yang terletak pada ujung batang 1 adalah I = ML2. 3 y

B; C

# C *# ! M 13 B # F 24 ; 5 F 6B; C

F F 1 2 ! M 3 B B ; $ B $ B ; 4 ! B M;C ; 5F C F C 6 BC

# $ # $

x

0

(OPBZ)

73+"$(-$"#2-%(1"$*%(8%$/(20+10(40.%#$8%(."#,".%'(4%*%(402%.(+%22% *-2"10.(+3+"$(-$"#2-%(402%.(+%22%((:4+);(G-'%(20+10(40.%#$8%(.-*%'(."#,".%' 4%*%( 402%.( +%22%:( 0$.0'( +"$5%#-( +3+"$( -$"#2-%$8%:( *%4%.( *-/0$%'%$ 4"#2%+%%$( 1"#-'0.( -$-( 8%$/( *-2"10.( 2"1%/%-( '%-*%&( 20+10( 2"=%=%#; :(=(:4+(+(0*C

–1L 2

x

0

Gambar 5.11

1L 2

Momen inersia untuk sumbu putar yang terletak pada pertengahan 1 batang adalah I = ML2. 12

9"."#%$/%$_ 0 =(+%22%(1"$*% * =(=%#%'(*%#-(402%.(+%22%('"(20+10(40.%# 73+"$( -$"#2-%( *%#-( 1"1"#%4%( 1"$.0'( 1"$*%( *"$/%$( 432-2-( 20+10 ."#."$.0( *%4%.( *-,-&%.( 4%*%( .%1",( 1"#-'0.( -$-;

Gerak Rotasi dan Kesetimbangan Benda Tegar

121

8a#"$'=
1a&#a+

A.+.s

1%.%$/( 2-,-$*"#

L.&"/'M/"+sia

+",%,0-( 402%.

C B :"=( BC M;

+",%,0-( 0=0$/

C B :"=( F M;

L

Ingatlah

1%.%$/( 2-,-$*"#

Momentum sudut merupakan besaran vektor. L

5-$5-$( .-4-2

!"#"$%&'()&*+#

2-,-$*"#( 4"=%,

+",%,0-( 20+10 2-,-$*"#

R

+",%,0-( 20+10 2-,-$*"#( 4"=%,

R

2"4"#.-( .%+4%' 4%*%( /%+1%#

R

:(=(M
C B :"=( C M<

C B C B := H M< BC M;

L

R 13,%( 4"=%,

+",%,0-( *-%+"."#

R 13,%( 1"#3$//%

13,%( 4"=%,

+",%,0-( *-%+"."#

R

+",%,0-( 2%,%& 2%.0( /%#-2 2-$//0$/$8%

C C :(=( O M<

C C ":(=( F M<

C X :(=( O M<

Sumber: Fundamental of Physics, 2001

122

Mudah dan Aktif Belajar Fisika untuk Kelas XI

3. Hubungan Momen Gaya dan Percepatan Sudut

y

!"#&%.-'%$( 1a&#a+' =;( D"10%&( 1"$*%( ."/%#( 1"#+%22%( 0( 1"#3.%24%*%(."#&%*%4(.-.-'(20+10"!;()$*%(.",%&(+"$/".%&0-(1%&A%( 4%*%( 1"$*% ."/%#(8%$/(1"#3.%2-(/%8%(8%$/(1"'"#=%(4%*%(1"$*%(+",-40.-(2",0#0&(1%/-%$ 1"$*%:(.".%4-(@3'02(4%*%(/%+1%#(."#2"10.(*-A%'-,-(3,"&(.-.-'(="8%$/(1"#=%#%' '" ."#&%*%4( 20+10( #3.%2-%" R%8%( .%$/"$2-%,( "" 1"'"#=%( *-( .-.-'( =( 2"&-$//% 1"$*%( 1"#/"#%'( #3.%2-( *"$/%$( 4"#5"4%.%$( .%$/"$2-%,( #.( '3$2.%$;( 7"$0#0. <0'0+( EE( N"A.3$:( 1"2%#( /%8%( .%$/"$2-%,( ."#2"10.( %*%,%& 5.(=(0"a.

(OPCU)

G-'%(#0%2('-#-(*%$(#0%2('%$%$(*%#-(A"+sa&aa/(B=C>KD(*-'%,-'%$(*"$/%$ =%#--=%#-( ':( %'%$( *-4"#3,"& 5.('(=(0(a. ' <010$/%$(%$.%#%(4"#5"4%.%$(.%$/"$2-%,((a.)(*%$(4"#5"4%.%$(20*0.(( ' ) %*%,%&(a.(=( ' (';(M,"&('%#"$%(-.0:(*-4"#3,"& 5.('(=(0 ' 'C(=(0"'C '

! r

(OPCC)

9"."#%$/%$_ / =(1"2%#(+3+"$(/%8%((N+) ' =( 1"2%#( 4"#5"4%.%$( 20*0.( (#%*S2) : =(+3+"$(-$"#2-%(('/+C)

P

/

x

O Garis kerja F

Lengan momen

Gambar 5.12 Gaya F bekerja pada sebuah partikel P pada benda tegar menghasilkan torsi / .

(OPCB)

L",%&( *-'".%&0-( 1%&A%( / =( 5.( '%" M,"&( '%#"$%( 5t" ."/%'( ,0#02( '( +%'% *-4"#3,"&( 4"#2%+%%$( +3+"$( /%8%( 2"1"2%# / =(0('C ' =(:( '

F

Kata Kunci • • • • • • •

benda diskrit benda tegar energi kinetik rotasi energi kinetik translasi momentum sudut sumbu putar torsi

Contoh 5.1 D"10%&(1%.%$/(&3+3/"$(+"+-,-'-(4%$=%$/(;(*%$(+%22%(0;"T%.%$/(."#2"10.(*-1"#"$/2",(2"&-$//%(*%4%.(1"#3.%2-(2"4"#.-(.%+4%'(4%*%(/%+1%#;(T%.%$/(*%,%+('"%*%%$ *-%+(4%*%(432-2-(&3#-c3$.%,;(L"$.0'%$,%&(1"2%#(4"#5"4%.%$(20*0.(( ' )(*%$(1"2%# 4"#5"4%.%$(.%$/"$2-%,(4%*%(0=0$/(1%.%$/((a.)('".-'%(1%.%$/(*-,"4%2'%$; 1 NaOa#P 2 R%8%(1"#%.(8%$/(1"'"#=%(4%*%(1%.%$/(%*%,%&(5(=(0"3> B *"$/%$(=%#%'(*(=( (d(*%#-(402%.(#3.%2-(("$/2",); C mg B 73+"$(E$"#2-%(1%.%$/(8%$/(*-4"#3,"&(*%#-(8a#"$'=
Tantangan untuk Anda Seorang pemain akrobat akan membutuhkan tongkat ketika melakukan aksi berjalan di atas tali. Jika ada dua buah tongkat yang sama panjang tetapi beratnya berbeda, tongkat manakah yang harus dipilih?

Gerak Rotasi dan Kesetimbangan Benda Tegar

123

4. Momentum Sudut dan Hukum Kekekalan Momentum Sudut

y

p sin !

! r L O

p d

D"4"#.-( &%,$8%( 4%*%( /"#%'( .#%$2,%2-:( 4%*%( /"#%'( #3.%2-( =0/%( ."#*%4%. '3$2"4( +3+"$.0+( 8%$/( *-2"10.( *"$/%$( +3+"$.0+( 20*0.;( !"$.-$/$8% '"1"#%*%%$(+3+"$.0+(20*0.(4%*%(/"#%'(#3.%2-(2%+%(*"$/%$(4"$.-$/$8% '"1"#%*%%$( +3+"$.0+( ,-$"%#( 4%*%( /"#%'( .#%$2,%2-; !%*%(1a&#a+'=
x

Q'='+(]((

Gambar 5.13 Diagram momen gaya atau torsi yang bekerja pada waktu membuka mur sebuah roda mobil.

(OPCF)

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sa&aa/' =<>@(*%4%. *-.0,-2'%$( 2"1%/%-( 1"#-'0.( (20*0.! ( =( ZU`); ;(=('?(=('07(=('"0 # '(=(0'C # M,"&( '%#"$%( 0'C( =( :>( A"+sa&aa/' B=C>@D( +"$=%*Q(=(:( $ #

(OPCO)

M,"&('%#"$%(1"2%#( / (=(: ' (*%$(1"2%#(;(=(: # (+%'%(*-4"#3,"& dL ! I d# ! I' dt dt

2"&-$//%

dL ! ' dt

(OPCW)

A"+sa&aa/' B=C>=D( +"$8%.%'%$( 1%&A%( =0+,%&( .3#2-( "'2."#$%,( 2%+% *"$/%$( ,%=0( 4"#01%&%$( +3+"$.0+( 20*0.;( A"+sa&aa/' B=C>ED( 2"1"$%#$8% *-*%4%.(*%#-(4"$0#0$%$(4"#2%+%%$(.3#2-(*%$(/%8%(*%,%+(1"$.0'(+3+"$.0+; >%4%.'%&( )$*%( +"$0#0$'%$( 4"#2%+%%$( ."#2"10.6( G-'%( / 18st1'2a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

Gambar 5.14 Momentum sudut ketika kedua tangan direntangkan adalah Ia # a.

124

(OPCX)

!%*%( 1a&#a+' =
Mudah dan Aktif Belajar Fisika untuk Kelas XI

9".-'%(40.%#%$(2"*%$/(1"#,%$/20$/(*%$('"*0%(.%$/%$(8%$/(+"+"/%$/ 1"1%$( *-#%4%.'%$( +"$*"'%.-( .010&:( 2"4"#.-( 4%*%( 1a&#a+' ="$/%$( *"+-'-%$:( 1"#,%'0( &010$/%$ : a#a ! : A#A [( : a % : A (*%$( #a & #A

(OPCY)

9"."#%$/%$_ : a =( +3+"$( -$"#2-%( '"%*%%$( a( ('/+C) # a =( 1"2%#( '"5"4%.%$( 20*0.( '"%*%%$" a( (#%*S2) : A =( 1"2%#( +3+"$( -$"#2-%( '"%*%%$( A( ('/+C) #b =( '"5"4%.%$( 20*0.( '"%*%%$( A( (#%*S2) )4,-'%2-(,%-$(*%#-(<0'0+(9"'"'%,%$(73+"$.0+(D0*0.(%*%,%&(/"#%' 4,%$".( *%,%+( +"$/",-,-$/-( 7%.%&%#-;( G3&%$$"2( 9"4,"#( +"$8%.%'%$( 1%&A% *%,%+(2",%$/(A%'.0("t (8%$/(2%+%:(2"10%&(4,%$".(%'%$(+"$8%40(,0%2(*%"#%& 8%$/( 2%+%;( !"#&%.-'%$( 1a&#a+( =
(OPCZ)

Gambar 5.15 Momentum sudut ketika kedua tangan dirapatkan (Ib # b).

Planet X

A Matahari A1

A2

B

Gambar 5.16 Lintasan sebuah planet mengelilingi Matahari berbentuk elips.

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

Contoh 5.2 D"3#%$/(4"#"$%$/(1"#+%22%(OU('/(+",3$5%.(+"$-$//%,'%$(4%4%$(.0+40(*%,%+ '3$@-/0#%2-(,0#02(*"$/%$('"5"4%.%$(20*0.(U:CO(40.%#%$(4"#(2"'3$(."#&%*%4(402%. +%22%$8%;(9"+0*-%$:(4"#"$%$/(+"$//0,0$/'%$(.010&$8%(*%$(/0,0$/%$(."#2"10. 1"#=%#--=%#-('-#%-'-#%(FU(5+;(>"$/%$(+"$/%$//%4(4"#"$%$/(2"1%/%-(2"10%&(1%.%$/ &3+3/"$(*"$/%$(4%$=%$/(B:W(+(2"2%%.(2".",%&(+",3$5%.:(*%$(+-#-4(2"10%&(13,% &3+3/"$(2%%.(1"#/0,0$/:(4"#'-#%'%$('"5"4%.%$(20*0.$8%(2%%.(1"#/0,0$/; NaOa#P >-'".%&0-_(M(=(OU('/[( #B (=(U:CO(40.%#%$S2[(<(=(FU(5+[(;(=(B:W(+; !%*%(2%%.(%A%,:(4"#"$%$/(1"#1"$.0'(1%.%$/(*"$/%$(43#32(*-(.-.-'(."$/%&(2"&-$//% +3+"$(-$"#2-%$8%(%*%,%& B B :B(=( M;C(=( (OU('/)(B:W(+)C(=(BU:WX('/+C BC BC !%*%(2%%.(+"$//0,0$/:(4"#"$%$/(1"#1"$.0'(13,%(*"$/%$(+3+"$(-$"#2-%$8%(%*%,%& C C :B(=( M
Ingatlah Hukum Kekekalan Momentum Sudut berlaku jika tidak ada momen gaya luar yang bekerja pada sistem.

Gerak Rotasi dan Kesetimbangan Benda Tegar

125

C D

9"5"4%.%$(20*0.(2%%.(+"$//0,0$/(*-&-.0$/(*"$/%$(4"#2%+%%$

:B #B(=(:C #C(%.%0( #C(=( #C(=(

:B # :(2"&-$//% :C B

BU: WX('/ + C (](U:CO(40.%#%$S2(=(B:HY(40.%#%$S2; B: Y('/ + C

5. Gerak Menggelinding

(%) R

F

v7 0

#=0

(1)

F

R

#70

(5)

N

# R O

F

fg mg

Gambar 5.17 (a) Benda bergerak translasi. (b) Benda bergerak rotasi. (c) Benda menggelinding pada bidang yang permukaannya kasar.

)$*%( 4%2.-( 2"#-$/( +"$=0+4%-( 1"$*%( 8%$/( 1"#/"#%'( +"$//",-$*-$/: +-2%,$8%( 2"10%&( 13,%( 8%$/( *-,"+4%#'%$( *-( %.%2( ,%$.%-( +"$*%.%#:( %.%0 #3*%-#3*%( 2"10%&( '"$*%#%%$( 8%$/( +",%=0( *-( =%,%$( #%8%;( 7"$//",-$*-$/ %*%,%&( 4"#-2.-A%( 1"#/"#%'$8%( 2"10%&( 1"$*%( 2"5%#%( .#%$2,%2-( *%$( #3.%2(1a&#a+' =%#-( 4"#2%+%%$( ."#2"10.( %'%$( *-4"#3,"& D3(=( :' < G-'%( /%8%( /"2"'( D3( 8%$/( 1"'"#=%( 4%*%( 2-,-$*"#( 1"#$-,%-( '3$2.%$( *%$ *-2012.-.02-'%$( '"( *%,%+( 4"#2%+%%$( /"#%'( .#%$2,%2-( (5" C" D3" =" 0a)( +%'% %'%$( *-4"#3,"& 5 a(= ( 0" B (OPFU)
C5 F0

9"."#%$/%$_ 5 =( 1"2%#( /%8%( 8%$/( 1"'"#=%( (N) a =( 1"2%#( 4"#5"4%.%$( .#%$2,%2-( (+S2C) 0 =( +%22%( 1"$*%( ('/)

126

Mudah dan Aktif Belajar Fisika untuk Kelas XI

(OPFB)

Contoh 5.3 D"10%&(2-,-$*"#(4"=%,(1"#+%22%(BO('/(+"+-,-'-(=%#--=%#-(CU(5+;(D-,-$*"#(."#2"10.(*-*3#3$/ 3,"&(/%8%(2"1"2%#(FU(N(2"4"#.-(4%*%(/%+1%#;(L"$.0'%$,%&(4"#5"4%.%$(8%$/(*-%,%+N 2-,-$*"#(."#2"10.:(=-'%_ %; .-*%'(%*%(/%8%(/"2"'(%$.%#%(2-,-$*"#(*%$ ,%$.%-((2-,-$*"#(+",0$50#S2",-4)[ F 1; ."#*%4%.(/"2"'%$(2"&-$//%(2-,-$*"#(+"$//",-$*-$/; NaOa#P >-'".%&0-_(0"=(BO('/[(5"=(FU(N[(<"=(CU(5+(=(U:C(+; fg 5 FU(N C mg ! C+S2 ; %; D-,-$*"#(+",0$50#((2",-4)[( a ! ! 0 BO('/ B C 1; D%%.(2-,-$*"#(+"$//",-$*-$/:(/0$%'%$(A"+sa&aa/'B=C>?D(*"$/%$(":(=( 0< : C C5 C # FU(N $ H +%'%( a ! ! ! +S2C ; F0 F #BO('/ $ F D"'%#%$/:(531%(."$.0'%$(4"#5"4%.%$(20*0.$8%(( ' );

b. Menggelinding pada Bidang Miring )$*%( .",%&( +"$/".%&0-( 1%&A%( 2-,-$*"#( %'%$( +"$//",-$*-$/( =-'% ."#*%4%.( /%8%( /"2"'( %$.%#%( 2-,-$*"#( *%$( 1-*%$/( 2"$.0&;( >"+-'-%$( &%,$8% 4%*%(1-*%$/(+-#-$/:(%/%#(2-,-$*"#(*%4%.(+"$/",-$*-$/(+%'%(&%#02(%*%(/%8% /"2"'( %$.%#%( 2-,-$*"#( *%$( 1-*%$/( +-#-$/; a$.0'(/"#%'(.#%$2,%2-:(1"#,%'0(4"#2%+%%$(03(2-$( ! (P(D/( =(0a"*%$ F" E" 03" 532" ! %( D-,-$*"#( %'%$( 1"#/"#%'( #3.%2-( =-'%( 2-,-$*"#( -$-( +"+-,-'4"#5"4%.%$( 2"1"2%#(a" E" at( 2"&-$//%( %'%$( *-4"#3,"&( 4"#5"4%.%$( 20*0. ' ; !"#5"4%.%$( 20*0.( *%#-( /"#%'( #3.%2-( 4%*%( 2"10%&( 2-,-$*"#( *-2"1%1'%$ %*%$8%(+3+"$(/%8%(*%#-(/%8%(/"2"';(!"#2%+%%$(/%8%(/"2"'(0$.0'(1"$*% 8%$/( +"$//",-$*-$/( 4%*%( 1-*%$/( +-#-$/( %*%,%&( D3( =( : aC ; < R%8%( ,%-$( 8%$/( 1"'"#=%( 4%*%( 2-,-$*"#:( .".%4-( .-*%'( +"$-+10,'%$ +3+"$(/%8%:(2"4"#.-(/%8%(1"#%.(.-*%'(*-4"#&-.0$/'%$;(<%,(-$-(*-'%#"$%'%$ /%8%(."#2"10.(1"'"#=%(*%#-(402%.(#3.%2-;(>"$/%$(+",%'0'%$(",-+-$%2-(*%#*0%( 4"#2%+%%$( *-( %.%2:( *-4"#3,"&( 4"#2%+%%$ 03 2-$ ! (OPFC) 03"2-$( ! "C": a (=(0a( 8 ( a ! C < 0 " :C < a$.0'(2-,-$*"#(4"=%,((:(=( B 0< C ):(4"#2%+%%$(4"#5"4%.%$$8%(%*%,%& C 03 2-$ ! 03 2-$ ! ! a! C B 0< F0 C 0" C C < a ! C 3 2-$ ! (OPFF) F

Ingatlah Gaya gesek akan menyebabkan silinder menggelinding. Gaya gesek ini berperan dalam menghasilkan momen gaya untuk silinder.

N fg mg sin ! mg cos ! mg

!

Gambar 5.18 Sebuah benda yang menggelinding pada bidang miring.

Contoh 5.4 D"10%&(2-,-$*"#(4"=%,(&3+3/"$(1"#+%22%(C('/(+"+-,-'-(=%#--=%#-(F(5+;(9"+0*-%$: 2-,-$*"#(."#2"10.(*-."+4%.'%$(4%*%(1-*%$/(+-#-$/(*"$/%$(20*0.('"+-#-$/%$(OF`; L"$.0'%$,%&(4"#5"4%.%$(8%$/(*-%,%+-(2-,-$*"#(=-'%_ %) .-*%'(%*%(/"2"'%$((,%$.%-(,-5-$)[ 1) 2-,-$*"#(+"$//",-$*-$/;

Gerak Rotasi dan Kesetimbangan Benda Tegar

127

NaOa#P >-'".%&0-_(0"=(C('/[(<"=(F(5+(=(F(]BUPC(+[( ! (=(OF` %; M,"&('%#"$%(1-*%$/(,-5-$:(2-,-$*"#(4"=%,(1"#/"#%'(2"4%$=%$/(1-*%$/(*"$/%$(5%#% +",0$50#((+"$//",-$5-#); 05 ! 0 a 8 03"2-$( ! (=(0"a a"=(3"2-$( ! =(BU(+S2C((2-$(OF`(=(BU(+S2C((U:Y)(=(Y(+S2C 1; D%%.(2-,-$*"#(4"=%,(+"$//",-$*-$/:(/0$%'%$(A"+sa&aa/'B=C>>D(*"$/%$ C C03 2-$ ! C5 B :(=( 0
c.

R M

T T

F

mg

Gambar 5.19 Beban dihubungkan dengan katrol.

(%)

T

a

mg

(1) R

#

R M

F

T

Gambar 5.20 (a) Gaya-gaya pada benda m. (b) Gaya-gaya pada katrol.

Beban Dihubungkan Melalui Katrol >-(9",%2(e:()$*%(.",%&(+"+4",%=%#-(."$.%$/(1"1%$(%.%0(1"$*%(8%$/ *--'%.( 3,"&( 2"0.%2( .%,-( *%$( *-&010$/'%$( *"$/%$( '%.#3,;( )'%$( .".%4-: +%22%( '%.#3,( *-%1%-'%$( '%#"$%( )$*%( 1",0+( +"+4",%=%#-( '3$2"4( +3+"$ -$"#2-%;( D"'%#%$/:( )$*%( .",%&( +"+4",%=%#-( +3+"$( -$"#2-%;( >"$/%$ *"+-'-%$:( )$*%( *%4%.( +"$//0$%'%$( '3$2"4( +3+"$( -$"#2-%( 2"&-$//% *%4%.( +"+4"#&-.0$/'%$( +%22%( '%.#3,( 4%*%( 2-2."+( '%.#3,( -$-; !"#&%.-'%$( 1a&#a+' =
(OPFO)

G-'%(."/%$/%$(.%,-(4%*%(A"+sa&aa/'B=C?@D(*-2012.-.02-'%$('"(A"+sa&aa/ B=C?=D( %'%$( *-4"#3,"&( 4"#2%+%%$ # 5 $ 03 $ 0a $ < C a! : 5 $ 03 a! : %.%0 (OPFW) "0
128

(OPFH)

Mudah dan Aktif Belajar Fisika untuk Kelas XI

C # 5 $ 03 $ M " C0

(OPFX)

9"."#%$/%$_ a =( 1"2%#( 4"#5"4%.%$( ,-$"%#( (+S2C) 5 =( 1"2%#( /%8%( .%#-'(N) 0 =( +%22%( 1"$*%( ('/) M =( +%22%( '%.#3,( ('/)

Tantangan untuk Anda

Contoh 5.5 !"#&%.-'%$( /%+1%#( *-( 2%+4-$/;( >0%( 10%&( 1"$*%( 8%$/ +%22%$8%((0B(=(C('/(*%$(0C(=(F('/(*-&010$/'%$(*"$/%$ 2"0.%2(.%,-(+",%,0-(2"10%&('%.#3,(*"$/%$(=%#--=%#-(BU(5+(*%$ +%22%('%.#3,(W('/;(L"$.0'%$,%&_ a T1 %; 4"#5"4%.%$(,-$"%#(2-2."+[ T2 1; ."/%$/%$(.%,-(GB(*%$(GC; m2 NaOa#P m1 %; D-2."+(+0,%-+0,%(*%,%+('"%*%%$(*-%+; 9".-'%(*-,"4%2:(2-2."+(+0,%-(1"#/"#%'('"(%#%&(0C(2"&-$//%(1"$*%(0B($%-'(*%$(0C(.0#0$ GB(P(0B(3(=(0B(a 0C(3"P(GC(=(0C(a GB(=(0B(3(+(0B(a """""""""""GC(=(0C((3"P(0C(a !"#,0(*-'".%&0-(1%&A%(.%,-(*-%$//%4(&3+3/"$; L-$=%0('%.#3,_ B 9 / (=(: ' [((:(=( 0'
Dengan kecepatan yang sama, mobil manakah di antara mobil yang bergerak di atas jalan kasar dan mobil yang bergerak di atas jalan licin, yang terlebih dahulu sampai? Mengapa demikian?

#

6. Energi dalam Gerak Rotasi

v

a. Energi Kinetik Rotasi D".-%4( 1"$*%( 8%$/( 1"#/"#%'( +"+-,-'-( "$"#/-( '-$".-';( D%+%( &%,$8% *"$/%$( 1"$*%( 8%$/( +",%'0'%$( /"#%'( #3.%2-:( 1"$*%( ."#2"10.( %'%$( +"+-,-'"$"#/-( '-$".-'( #3.%2-;( >-'".%&0-( "$"#/-( '-$".-'( .#%$2,%2-( %*%,%& B C B B 7"$/-$/%.(7(=(' # +%'%(98(=( 0((' # )C(=( 0'C # C; C C

98(=( 07C

(OPFY) Gambar 5.21 Benda bergerak translasi dengan kecepatan v sambil berotasi dengan kecepatan sudut # .

Gerak Rotasi dan Kesetimbangan Benda Tegar

129

>-'".%&0-(1%&A%(0'C(%*%,%&(+3+"$(-$"#2-%(+%'%(0$.0'(/"#%'(#3.%2-(+"$=%*B C

98"#3.%2-(=( : #

(OPFZ)

C

9"."#%$/%$_ =( "$"#/-( '-$".-'( .#%$2,%2-( (=30,") 98 98" #3.%2- =( "$"#/-( '-$".-'( #3.%2-( (=30,") ": =( +3+"$( -$"#2-%( 1"$*%( ('/+C) =( '",%=0%$( 20*0.( (#%*S2) # b. Energi Kinetik Translasi dan Rotasi L",%&()$*%('".%&0-(1%&A%(2"10%&(1"$*%(8%$/(1"#/"#%'(+"$//",-$*-$/ %'%$( +"+-,-'-( *0%( /"#%'%$:( 8%-.0( /"#%'( ,-$"%#( *%$( /"#%'( #3.%2-;( R%10$/%$ /"#%'(,-$"%#(*%$(=%#%'(#3.%2-(*-2"10.(/"#%'(.#%$2,%2-;(R"#%'(.#%$2,%2-(+"+-,-''"5"4%.%$(,-$"%#(7:(2"*%$/'%$(/"#%'(#3.%2-$8%(+"+-,-'-('"5"4%.%$(20*0.( # ; T"$*%( 8%$/( +"$//",-$*-$/( +"+-,-'-( "$"#/-( '-$".-'( .#%$2,%2-( *%$( "$"#/'-$".-'( #3.%2-;( D"5%#%( +%."+%.-2:( +"+"$0&-( 4"#2%+%%$ B C

B C

98(.3.%,(=( (07C(+( (: # 98(.3.%,(=(98(+(98"#3.%29"."#%$/%$_ 98".3.%, =( "$"#/-( '-$".-'( .3.%,

A v

C

h

B

Gambar 5.22 Silinder yang mula-mula diam bergerak menggelinding.

(OPHU)

c.

Hukum Kekekalan Energi Mekanik pada Gerak Rotasi !"#&%.-'%$( 1a&#a+( =<>>;( D"10%&( 2-,-$*"#( 8%$/( +0,%-+0,%( *-%+: +"$//",-$*-$/(*%#-()('"(T;(G-'%(*-%20+2-'%$(2",%+%(13,%(1"#3.%2-(.-*%'(%*% "$"#/-( 8%$/( &-,%$/( *%$( 1"#01%&( +"$=%*-( "$"#/-( '%,3#:( 1"#,%'0( <0'0+ 9"'"'%,%$( h$"#/-; 9?)(+(98) =(9?T(+(98T B C

B C

B C

03h(+(U =(U(+( 07C(+( : # C ((0$.0'(2-,-$*"#(4"=%,:(:(=( 0'C) B B 03h =( 07C(+( 0'C( 7 H C '

C

#$

F H

3h =( 7C >%#-( 4"#2%+%%$( ."#2"10.:( '"5"4%.%$( 2-,-$*"#( 4"=%,( '".-'%( 2%+4%-( **%2%#( 1-*%$/( +-#-$/( *%4%.( *-'".%&0-:( 8%-.0

F 3h H

7(=(

(OPHB)

A"+sa&aa/' B=C@ID( *%4%.( *-.0,-2'%$( *%,%+( 1"$.0'( 0+0+:( 8%-.0 C 3h B" 8

7(=(

(OPHC)

!%*%( 4"#2%+%%$( ."#2"10.:( 8( +"#04%'%$( '3$2.%$.%( /"3+".#-( 8%$/ *-+-,-'-(3,"&(1"$*%(*%$(*%,%+(1-*%$/(."'$-'(2"#-$/(*-2"10.(2"1%/%-(=%#-=%#-( /-#%2-;( N-,%-( 8( -$-( 1"#/%$.0$/( 4%*%( ="$-2( 1"$*%$8%;( a$.0'( 2-,-$*"# B C

C O

C F

4"=%,(8(=( :(0$.0'(13,%(4"=%,(8(=( :(*%$(0$.0'(13,%(1"#3$//%(8(=( ;

130

Mudah dan Aktif Belajar Fisika untuk Kelas XI

Contoh 5.6

Kata Kunci • lengan torsi • momen inersia

D"10%&(13,%(4"=%,(1"#+%22%(0"*%$(1"#=%#--=%#-(<"+"$//",-$*-$/(."#&%*%4(43#32$8% 4%*%(1-*%$/(+-#-$/(2"4"#.-(4%*%(/%+1%#;(L"$.0'%$,%&('",%=0%$(13,%('".-'%(2%+4%-(**%2%#(1-*%$/(=-'%(*-,"4%2(*%#-('".-$//-%$(h((*%#-('"%*%%$(*-%+); NaOa#P A T3,%(1"#/"#%'(+"$//",-$*-$/ 9?B")"98B E""9?I")"98I B B B B h 03hB")" :" # BC((+ 07BJ =("03hI")" ":" # IC+ "07IJ C C C C C C B B 03h(+(U(+(U =(U(+( C :#T " C 07 T

#

$

B

C 0< C *%$(7"E"<" # :(2"&-$//% O C B(C B C C )( 7 ) 03h E" * 0< +* + " 07 C, O -, < - C B C B C 3h E" 7 " 7 O C X C BU 3h 3h =( 7 8 7 ! BU X 9",%=0%$(13,%('".-'%(1"#/"#%'(+",0$50#(*"$/%$(1-*%$/(*-%$//%4(,-5-$_ 9?B(+(98B"E"9?I(+(98I B 03hB")"U"E"U")" 0"7C( 8 7 ! C 3 h ; C T%$*-$/'%$( 3,"&( )$*%;( 9",%=0%$( '".-'%( 13,%( 1"#/"#%'( +"$//",-$*-$/( %*%,%& BU 7! 3 h (*%$('",%=0%$('".-'%(13,%(1"#/"#%'(+",0$50#(%*%,%&( 7 ! C 3 h ;(>%4%. X *-2-+40,'%$(1%&A%(13,%(8%$/(1"#/"#%'(+"$//",-$*-$/(,"1-&(,%+1%.(*%#-4%*%(13,% 8%$/(1"#/"#%'(+",0$50#;(<%,(."#2"10.(*-2"1%1'%$(/"#%'(#3.%2-(4%*%(13,%(+"$=%*4"$/&%+1%.(."#&%*%4(,%=0(13,%;

a$.0'(13,%(4"=%,:( : !

Tes Kompetensi Subbab

B

5"+*aka/$a:'4a$a&'#%k%'$ati:a/< B;

!"#&%.-'%$(/%+1%#(1"#-'0.(-$-; 10 N a 30° O

F;

12 N b

C;

9N

L"$.0'%$,%&(+3+"$(/%8%(.3.%,(8%$/(1"'"#=%(4%*%(#3*% ."#&%*%4(43#32(!:(=-'%(a"=(BU(5+(*%$(A"=(CO(5+; D"10%&(2-,-$*"#(4"=%,(*"$/%$(=%#--=%#-(<"*%$(1"#+%22% M"*-/0$%'%$(2"1%/%-('%.#3,(0$.0'(+"$/%+1-,(%-#(20+0# *"$/%$(2"10%&("+1"#;(7%22%("+1"#(0(*%$(1%.%$/ 2-,-$*"#(*-%$//%4(,-5-$;(L"$.0'%$(4"#5"4%.%$("+1"# 2%%.(=%.0&('"(20+0#;

h+4%.(10%&(4%#.-'",(+%2-$/-+%2-$/(+%22%$8%(0% =(F('/:(01(=(C('/:(05"=(B('/:(*%$(0*(=(H('/(2"4"#..%+4%'(4%*%(/%+1%#;(L"$.0'%$(+3+"$(-$"#2-%(2-2."+ =-'%(20+10(40.%#$8%_ %; +",%,0-(20+10(BBK[ 1; +",%,0-(20+10(IIK; B

A

A 3 kg

B 2 kg

2m

2m A’

C 1 kg

D 4 kg

2m B’

Gerak Rotasi dan Kesetimbangan Benda Tegar

131

H;

D"10%&(2-,-$*"#(4"=%,(1"#+%22%(C('/(*-,".%''%$(4%*% 2"10%&(1-*%$/(+-#-$/(*"$/%$(20*0.('"+-#-$/%$(WU`; L"$.0'%$,%&(4"#5"4%.%$(8%$/(*-%,%+-$8%:(=-'%_ %; .-*%'(%*%(/"2"'[ 1; 2-,-$*"#(+"$//",-$*-$/; 7%22%(1"$*%(0B(=(B:Y('/(*%$(0C(=(C('/(*-&010$/'%$ *"$/%$('%.#3,(2"4"#.-(/%+1%#;(73+"$(-$"#2-%(2-2."+ '%.#3,(%*%,%&(:(=(B:X('/(0C:(*"$/%$('B(=(CU(5+(*%$('C =(OU(5+;

O;

' r1

r2 T2

T1 m1

m2

L"$.0'%$_ %; 4"#5"4%.%$(20*0.('%.#3,[ 1; ."/%$/%$(.%,-(GB(*%$(GC;

C. Kesetimbangan Benda Tegar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

9 5# ! U: NB

! NA

w fA

(OPHF)

9/ !U

(OPHH)

>"$/%$( *"+-'-%$:( 20%.0( 1"$*%( ."/%#( *-'%.%'%$( 2".-+1%$/( =-'%

! A

Gambar 5.23 Sebuah tangga bersandar pada dinding yang kasar dengan lantai yang kasar pula.

9 F ! U (*%$( 9 / ! U; D%,%&( 2%.0( 53$.3&( '"=%*-%$( '"2".-+1%$/%$( 1"$*%( ."/%#:( +-2%,$8% 2"10%&( .%$//%( 8%$/( 1"#2%$*%#( 4%*%( *-$*-$/;( !"#&%.-'%$( 1a&#a+' =<>?; D"10%&( 1%.%$/( )T( 1"#2%$*%#( 4%*%( *-$*-$/;( a=0$/( 1%A%&( )( 1"#%*%( 4%*% ,%$.%-(8%$/('%2%#(*%$(1%/-%$(%.%2(T(1"#2%$*%#(4%*%(*-$*-$/(\"#.-'%,(8%$/ =0/%( '%2%#;( G-'%( 4%$=%$/( 1%.%$/( ! :( 1"#%.( 1%.%$/( M:( ,%$.%-( *%$( *-$*-$/ 2%,-$/( ."/%'( ,0#02:( 2"#.%( 1%.%$/( +"+1"$.0'( 20*0.( ."#&%*%4( %,%2$8%( +%'% )$*%(*%4%.(+"$0#0$'%$(4"#2%+%%$(/%8%(*%$(+3+"$(/%8%(8%$/(+"+"$/%#0&-(1%.%$/(."#2"10.;(T%.%$/()T(*%,%+('"%*%%$(2".-+1%$/(2"&-$//%(28%#%. '"2".-+1%$/%$( %'%$( +"+"$0&-( 4"#2%+%%$( 1"#-'0.( -$-; 9 5# =(U FT( P(D) =(U F T =(D)

132

9 5L ! U

)*%40$( 28%#%.( '"*0%( 8%$/( &%#02( *-4"$0&-( %/%#( 1"$*%( 2".-+1%$/ %*%,%&( 1"$*%( .-*%'( +"+-,-'-( '"5"$*"#0$/%$( 0$.0'( 1"#3.%2-;( D8%#%. ."#2"10.( *-*%2%#-( 3,"&( *-$%+-'%( /"#%'( #3.%2-;( >"$/%$( *"+-'-%$:( 1"$*% ."/%#( 1"#%*%( *%,%+( '"2".-+1%$/%$;( G%*-( #"20,.%$( .3#2-( ,0%#( 8%$/( 1"'"#=% 4%*%( 1"$*%( &%#02( 2%+%( *"$/%$( $3,;( <%,( ."#2"10.( %*%,%&( 28%#%.( '"*0% 0$.0'( '"2".-+1%$/%$;

fB B

9 5$ ! U:

Mudah dan Aktif Belajar Fisika untuk Kelas XI

(OPHO)

9 Fy =(U DT( +(F)(P(M =(U

fB B

DT(+(F) =(M

(OPHW)

NB !

lengan torsi NB

+

G-'%(*-%20+2-'%$(.-.-'()(+"$=%*-(43#32:(4"#2%+%%$(+3+"$(/%8%$8% %*%,%&( 9/ (=(U; d"$/%$(.3#2-(FT( 8 ( ! (2-$( ! ;

W

1 2

d"$/%$(.3#2-(M( 8 ( ( ! (532( ! ;

!

d"$/%$(.3#2-(DT( 8 ( ! (532( ! ; G%*-:

A

1 FT( ! (2-$( ! (+"DT( ! (532( ! (=( M ! (532( ! 2

(OPHX)

>%#-('".-/%(4"#2%+%%$(."#2"10.:()$*%(*%4%.(+"$/".%&0-($-,%-(*%#-(/%8% /"2"'(%$.%#%(,%$.%-(*%$(1%.%$/()T:(/%8%($3#+%,(,%$.%-:(*%$(/%8%($3#+%,(*-$*-$/;

lengan torsi fB

lengan torsi w

Gambar 5.24 Lengan torsi dari setiap gaya yang bekerja pada tangga.

Contoh 5.7 D"10%&(1%.%$/()T(8%$/(4%$=%$/$8%(H(+"."#(1"#2%$*%#(4%*%(*-$*-$/(,-5-$(*-(.-.-'(T; D0*0.(8%$/(*-(1"$.0'(1%.%$/()T(*%#-(%,%2$8%(OF`:(2"*%$/'%$(1"#%.(1%.%$/(M;(G-'% 4%*%(2%%.(1%.%$/()T(."4%.(%'%$(."#/",-$5-#:(."$.0'%$,%&('3"@-2-"$(/"2"'(%$.%#%(1%.%$/ *%$(%,%2$8%; fB= 0 NaOa#P >-'".%&0-_(BI(=(@(=(H(+[( ! (=(OF`[((1"#%.(1"$*%(=(M i

95#=U(%"FT(P"D%(=(U(%(FT(=(D%

NB

B

FT(=(( s (F)(((."4%.(%'%$(."#/",-$5-#)(;;;;;;;;;;;;;;;;;;;;;;;;(B) i

95$=(U( 8 "F)(P(M(=(U(%(F)=(M(;;;;;;;;;;;;;;;;;;;;;;;;;;(C)

i

9 / =(U:(402%.(*-(B

Ingatlah

! =4m NA

w

!

B B FI"(532 ! P"M" ! 532 ! =(U 8 FI"(532 ! =( M"532(! C C B F FI""532(OFU( 8 U:W(FI(= (M(U:W) 8 FI= M(;;;;;;;;;(F) C W D012.-.02-'%$(!"#2%+%%$((C)(*%$((F)('"(4"#2%+%%$((B):(*-4"#3,"& B B B M= ( s"M 8 ( s"E ;(G%*-:('3"@-2-"$(/"2"'$8%(= ; C C C

fA

Keadaan setimbang berarti 9F = 0 dan 9/ = 0.

A

Contoh 5.8 D"10%&(1%.%$/(&3#-c3$.%,(*"$/%$(1"#%.(FUU(N(*%$(4%$=%$/(O(+ *-1"#-( "$/2",( 4%*%( 2"10%&( *-$*-$/;( a=0$/( 8%$/( 2%.0$8% *-.34%$/(*"$/%$(2"0.%2('%A%.(*%$(+"+1"$.0'(20*0.(OF` ."#&%*%4(&3#-c3$.%,((,-&%.(/%+1%#);()4%1-,%(2"2"3#%$/(8%$/ 1"#%.$8%(OUU(N(1"#*-#-(4%*%(=%#%'(C(+(*%#-(*-$*-$/:(."$.0'%$ ."/%$/%$('%A%.(*%$(/%8%(#"%'2-(4%*%(1%.%$/;

Kata Kunci

T

53° 0

• momen gaya • lengan torsi

5m

Gerak Rotasi dan Kesetimbangan Benda Tegar

133

NaOa#P R%8%-/%8%(.#%$2,%2-_

Ingatlah

T R

Batang homogen adalah batang yang letak titik beratnya tepat di tengah-tengah.

Ty

Ry

! Rx

9 5#(=(U 8 (<#(P(G#(=(U 8 (<(532(! (P(L(532(! (=(U 8 (<(532( ! (P(L(532(OF(=(U 8 (<(532(! (=(U:W(L 9 5$(=(U 8 (<$(+(G$(P(MB(P(MC(=(U

8 (<(2-$(! (+(G(2-$(OF(=(OUU(+(FUU 8 (<(2-$(! (+(U:Y(G(=(YUU ;;;(C)

Tx w2

;;;(B)

w1

R%8%-/%8%(#3.%2-_

+ 2m T

!

D/"2"'("$/2",(=(U 8 ,"$/%$(+3+"$(G([( ! (2-$( ! (8 (! (=(OF ,"$/%$(+3+"$(MB([( ! (2-$( ! (8 (! (=(ZU ,"$/%$(+3+"$(MC([( ! (2-$( ! (8 (! (=(ZU 9 / =(U ! (2-$((OF)(G(P( ! (2-$(! ((MB(P( ! (2-$( ! (MC(=(U 8 (O)((U:Y(G)(P((C:O)((B)((FUU)(P((C)((B)((OUU)(=(U 8 HL(=(B;XOU L(=(HFX:O(N(;;;(F)

w1

Pembahasan Soal

w2

Jarak sumbu roda depan dan sumbu roda belakang sebuah truk yang bermassa 1.500 kg adalah 2 m. Pusat massa truk 1,5 m di belakang roda depan. Jika g = 10 m/s2. Beban yang diterima roda depan adalah .... a. 1.250 N b. 2.500 N c. 3.750 N d. 5.000 N e. 6.250 N

! =5m

D012.-.02-'%$((F)('"((B)(*%$((C):(*-4"#3,"& <(532(! =(U:W((HFX:O) =(CWC:O(N <(2-$(! (+(U:Y((HFX:O)(=(YUU <(2-$(! (=(HOU(N < 2-$ ! .%$(! =( < 532! HOU(N (=(B:XB CWC: O(N ! =(OZ:XH G%*-:(/%8%(#"%'2-("$/2",(%*%,%&

Soal UMPTN Tahun 1995

=(

Pembahasan:

9/

=0

mg # AP $ – NB # AB $ = 0 NB

1! 2

mg # AP $ AB #1.500 $#10 $# 0,5$ = 2m = 3.750 N

< =(

=

HOU(N 2-$(OZ:XH

HOU(N U:YW =(OCF(N; =(

Jawaban: c

Tes Kompetensi Subbab

C

5"+*aka/$a:'4a$a&'#%k%'$ati:a/< B;

134

D"10%&( 1%.%$/( )T( 4%$=%$/$8%( C( +( *%$( 1"#%.$8% *-%1%-'%$;(a=0$/(T(*--'%.(*"$/%$('%A%.(8%$/(1%.%2 ."/%$/%$( +%'2-+0+$8%( HUU( N;( D"2"3#%$/( 8%$/ 1"#%.$8%(B;UUU(N(1"#*-#-(*-(%.%2(1%.%$/(2"=%0&(#:(2"4"#./%+1%#(*-(2%+4-$/;(T"#%4%'%&(=%#%'(+%'2-+0+(*%#.-.-'()(2"1",0+('%A%.(40.026

Mudah dan Aktif Belajar Fisika untuk Kelas XI

T A x tumpuan

B w 2m

C;

D"1%.%$/(1%,3'(8%$/(4%$=%$/$8%(Y(+(*%$(1"#%.$8% CUU(N(*-/%$.0$/'%$(2"4"#.-(4%*%(/%+1%#;(G-'%(=%#%' )T(=(B(+:(TK(=(H(+:(*%$(K>(=(F(+:(."$.0'%$,%& $-,%-((4"#1%$*-$/%$(."/%$/%$(.%,-(GB(*%$(GC;

T1

T2 1m A

F;

O;

<-.0$/,%&(/%8%(+-$-+0+(8%$/(&%#02(*-1"#-'%$(%/%# #3*%(*%4%.($%-':(=-'%(=%#--=%#-(#3*%(OU(5+(*%$(4"#5"4%.%$ /#%\-.%2-(BU(+S2C; D"10%&( 1%.%$/( )T( 4%$=%$/$8%( F( +( *%$( 1"#%.$8% 2"1"2%#(BCU(N;(a=0$/-0=0$/$8%(*--'%.(3,"&(.%,-(2"4"#.4%*%(/%+1%#;

4m

T1

3m C

B

'

D

T2 A

B

0,5 m

D"10%&(4%4%$(-',%$(1"#+%22%(FC('/(+"$"+4",(4%*% 2"1%.%$/(4-4%(8%$/(1"#%.$8%(*-%1%-'%$:(*%$(4%$=%$/$8%(B:O(+;(D%,%&(2%.0(0=0$/$8%(*--'%.(*"$/%$(.%,-: 2"*%$/'%$(0=0$/(8%$/(,%-$(+"$"+4",(4%*%(*-$*-$/ 2"4"#.-(.%+4%'(4%*%(/%+1%#;

w = 60 N

!%*%(=%#%'( BC (+"."#(*%#-()(*-/%$.0$/'%$(2"10%&(1"1%$ 8%$/(1"#%.$8%(WU(N;(L"$.0'%$(+%2-$/-+%2-$/(/%8% ."/%$/(.%,-(*%$(1"2%#(20*0.( ' ; W;

T

1 L 4

C 30°

0,5 m

B

3 L 4

Sumber Ilmu 1m

53°

2.000 N

A

L"$.0'%$,%&(."/%$/%$(8%$/(*-+-,-'-(.%,-; D"10%&(#3*%(1"#+%22%(CU('/(&"$*%'(*-$%-''%$('" 2"10%&(0$*%'%$(2".-$//-(CU(5+;

H;

30°

2,5m

D"10%&(1%.%$/()T(1"#%.$8%(HUU(N;(D"10%&("$/2", *-."+4%.'%$( *-( .-.-'( ):( *%$( *-( .-.-'( K( *--'%.( 4%*% ."+13'(*"$/%$(2"0.%2(.%,-(.%'(1"#+%22%;(G-'%(2-2."+ 2"-+1%$/:(&-.0$/,%&_ %; ."/%$/%$(.%,-[ 1; 1"2%#(/%8%("$/2",((2-$(OF`(=(U:YU);

F

R h

40 cm

Rangkuman B;

!32-2-( 20*0.( 1"$*%( ."/%#( 8%$/( 1"#/"#%'( #3.%2*-$8%.%'%$(*"$/%$(4"#2%+%%$

! ! C;

F;

s '

"t % U

*# * C! ! *t *t C 73+"$(/%8%(%.%0(.3#2-(+"#04%'%$(1"2%#%$(8%$/ +"$8"1%1'%$(2"10%&(1"$*%(."/%#(5"$*"#0$/(0$.0' 1"#3.%2-(."#&%*%4(43#32$8%; / (=(+(](J(=('5(2-$(! (=(5* *"$/%$(*(=('(2-$(! (=(+3+"$(,"$/%$;

'!

9"5"4%.%$(20*0.(#%.%-#%.%(1"$*%(."/%#(8%$/(1"#/"#%' #3.%2-(*-$8%.%'%$(*"$/%$(4"#2%+%%$ "! #! "t )*%40$('"5"4%.%$(20*0.(2"2%%.$8%_

# ! ,-+

!"#5"4%.%$(20*0.(2"2%%.(1"$*%(."/%#(8%$/(1"#3.%2*-$8%.%'%$(*"$/%$(4"#2%+%%$_

"! *! ! "t *t

H;

Gerak Rotasi dan Kesetimbangan Benda Tegar

135

O;

W;

X;

!%2%$/%$(*0%(10%&(/%8%(8%$/(2"=%=%#:(2%+%(1"2%#: *%$(1"#,%A%$%$(%#%&(*-2"10.('34",;(T"2%#$8%(2"10%& '34",(*-$8%.%'%$(*"$/%$(+3+"$('34",:(8%-.0 M"=(5 *:(*"$/%$(*(=(=%#%'(%$.%#%(*0%(/%8%; M#"20,.%$(=( 9M 73+"$(-$"#2-%(%*%,%&(0'0#%$('"5"$*"#0$/%$(20%.0 1"$*%(0$.0'(+",%'0'%$(/"#%'(#3.%2-;(73+"$(-$"#2-% *-."$.0'%$( 3,"&( +%22%( *%$( 43,%( *-2.#-102-( +%22% ."#&%*%4(20+10(40.%#; :(=( 90"'C a$.0'(2"10%&(1"$*%(8%$/(+"+-,-'-(*-2.#-102-(+%22% 8%$/('3$.-$0:(1"#,%'0(4"#2%+%%$ C :(=( . ' * 0

73+"$( -$"#2-%( 1"1"#%4%( 1"$.0'( 1"$*%( *"$/%$ 20+10(40.%#(1"#%*%(4%*%(402%.(+%22%$8%(%*%,%& 2"1%/%-(1"#-'0.; B T%.%$/_(:(=( M;C:(;(=(4%$=%$/(1%.%$/; BC D-,-$*"#(.-4-2(1"#3$//%_(:(=(M
Y; !"#5"4%.%$(.%$/"$2-%,(8%$/(*-%,%+-(1"$*%(1"#+%22% '%#"$%(4"$/%#0&(/%8%(+"$0#0.(<0'0+(EE(N"A.3$ %*%,%& 5.(=(0"a. !"#2%+%%$(+3+"$(/%8%(2"1"2%# / =(:( ' Z; T"2%#(+3+"$.0+(20*0.(."#&%*%4(402%.(,-$/'%#%$(*%#2"10%&(1"$*%(1"#.-.-'(+%22%((0(8%$/(1"#/"#%'(+",-$/'%#(+"+"$0&-(4"#2%+%%$ ;='(](?(((%.%0("";(=(:(% # BU; 7"$//",-$*-$/(%*%,%&(4"#-2.-A%(1"#/"2"'$8%(2"10%& 1"$*%(2"5%#%(.#%$2,%2-(*%$(#3.%2-;()4%1-,%(.-*%'(."#=%*2",-4:('"*0%(/"#%'(1"$*%(1"#,%$/20$/(2"5%#%(1"#2%+%%$(*%$(=%#%'(8%$/(*-."+40&(*%,%+(2%.0(40.%#%$(2%+% *"$/%$('",-,-$/(1"$*%;(h$"#/-('-$".-'(/"#%'(+"$//",-$*-$/(%*%,%& B B 98(=(98".#%$2,%2-(+(98"#3.%2-((=( 07C(+( : # C C C BB; D0%.0(1"$*%(."/%#(1"#%*%(*%,%+('"%*%%$(2".-+1%$/ =-'%(#"20,.%$(/%8%(8%$/(1"'"#=%(4%*%(1"$*%(2%+% *"$/%$($3,; 95(=(U( 8 95#(=(U(*%$( 95$(=(U 9 / =(U

Peta Konsep 1"+ak'2.tasi +"+1%&%2

9"2".-+1%$/%$ T"$*%(L"/%#

+"$/&%2-,'%$

73+"$ R%8%

73+"$ E$"#2-%

73+"$.0+ D0*0.

%$%,3/-

%$%,3/-

%$%,3/-

R%8% (J)

7%22% (0)

73+"$.0+(d-$"%# (()

=-'%( .-*%'( %*% /%8%( ,0%#:( 1"#,%'0

28%#%.$8%

<0'0+(9"'"'%,%$ 73+"$.0+(D0*0.

Refleksi Setelah mempelajari bab ini, tentu Anda dapat mengetahui konsep momen gaya dan momen inersia serta pengaruhnya terhadap gerak rotasi. Selain itu, Anda juga dapat mengetahui konsep momentum sudut, gerak rotasi, dan gerak translasi. Dari keseluruhan materi, bagian manakah yang sulit dipahami? Coba diskusikan dengan teman atau guru Fisika Anda.

136

Mudah dan Aktif Belajar Fisika untuk Kelas XI

Membuka mur dengan kunci bertangan panjang lebih mudah dibanding dengan kunci bertangan pendek. Pengetahuan ini diperoleh dengan mempelajari bab ini. Nah, coba Anda sebutkan manfaat lain mempelajari bab ini.

Tes Kompetensi Bab 5 S< Ai$i:$a:'sa$a:'sat%'*aOa#a/'Ta/6'(a$i/6't"(at'4a/'k"+*aka/$a:'(a4a'#%k%'$ati:a/< B;

C;

D"10%&(1"$*%(8%$/(1"#1"$.0'(2-,-$*"#(4"=%,(1"#=%#-=%#-( <( *%$( 1"#+%22%( 0;( 9"+0*-%$:( 1"$*%( ."#2"10. *-40.%#(4%*%(20+10$8%(*"$/%$(4"#-3*"(G;(T"2%#("$"#/'-$".-'(#3.%2-$8%(%*%,%&(;;;; : C M< C *; %; : C M
F;

H;

O;

O F(+S2

";

C:O(+S2

5; O( C (+S2 D"10%&( 13,%( 4"=%,( 1"#.#%$2,%2-( *%$( 1"#3.%2-( *"$/%$ '"5"4%.%$(,-$"%#(*%$('"5"4%.%$(20*0.(+%2-$/-+%2-$/(7 *%$(# ;(h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c3$.%,;(G-'%(4"#5"4%.%$(/#%\-.%210+-(%*%,%&(3:(2-,-$*"#(."#2"10.(%'%$(;;;; %; +",0$50#(*"$/%$(4"#5"4%.%$(3(2-$(! 1; +",0$50#(*"$/%$(4"#5"4%.%$( F "3(2-$(! C 5; +"$//",-$*-$/(*"$/%$(4"#5"4%.%$(3(2-$(! B *; +"$//",-$*-$/(*"$/%$(4"#5"4%.%$( (3(2-$(! C "; +"$//",-$*-$/(*"$/%$(4"#5"4%.%$( C (3(2-$(! F

W; >0%(1"$*%()(*%$(T(+%2-$/-+%2-$/(+%22%$8%(O('/: *-&010$/'%$(3,"&(1%.%$/(8%$/(4%$=%$/$8%(B(+((+%22% 1%.%$/( *-%1%-'%$);( G-'%( 402%.( 1%.%$/( *-/0$%'%$ 2"1%/%-(20+10(40.%#:(+3+"$(-$"#2-%(4%*%(402%.(1%.%$/ ."#2"10.(%*%,%&(;;;; %; C:O('/+C *; H:U('/+C C 1; F:U('/+ "; O:U('/+C C 5; F:O('/+ ' X; D"10%&(#3*%(*%4%.(+"$//",-$*-$/(.%$4%(2",-4(4%*% 2"10%&(1-*%$/(*%.%#(8%$/ F=2N '%2%#;(7%22%(#3*%(U:O('/(*%$ =%#--=%#-$8%( CU( 5+;( j3*% *-.%#-'(*"$/%$(/%8%(5"=(C(N(2"&-$//%(1"#/"#%'(*"$/%$ 4"#5"4%.%$(20*0.('3$2.%$(2"4"#.-(.%+4%'(4%*%(/%+1%#; T"2%#(+3+"$(/%8%(8%$/(1"'"#=%(4%*%(#3*%(%*%,%&(;;;; %; $3, *; U:O(N+ 1; U:C(N+ "; U:Y(N+ 5; U:H(N+ Y; D"10%&(#3*%(1"#1"$.0'(2-,-$*"#(1"#3$//%(+"+-,-'-(=%#-=%#-(CU(5+(*%$(+%22%(O('/;(!%*%(#3*%(1"'"#=%(+3+"$ /%8%( 2"1"2%#( BW( N+;( T"2%#( 4"#5"4%.%$( 20*0.( #3*% ."#2"10.(%*%,%&(;;;; %; U:W(#%*S2C *; CH(#%*S2C 1; W(#%*S2C "; YU(#%*S2C 5; BC(#%*S2C Z; !"#&%.-'%$(/%+1%#(1"#-'0.; y 2m a 3m

a

O

2a

m x

L-/%(10%&(4%#.-'",(*"$/%$(+%22%(0:(C0:(*%$(F0(*-4%2%$/(4%*%(0=0$/('"#%$/'%(8%$/(+%22%$8%(*-%1%-'%$; D-2."+(."#,".%'(4%*%(1-*%$/(#$;(G-'%(2-2."+(*-40.%# ."#&%*%4(20+10-$>(+3+"$(-$"#2-%(2-2."+(*-(.-.-'(! %*%,%&(;;;; %; X(0a *; W(0aC 1; O(0a "; X(0aC 5; O(0aC BU; !"#&%.-'%$(/%+1%#(1"#-'0.;

m1

m2

Gerak Rotasi dan Kesetimbangan Benda Tegar

137

>0%(10%&(1"$*%(8%$/(+%2-$/-+%2-$/(+"+-,-'-(+%22% 0B(=(H('/(*%$(0C(=(C('/(*-&010$/'%$(*"$/%$('%.#3, 4"=%,(1"#+%22%(H('/;(G-'%(4"#5"4%.%$(/#%\-.%2-(3(=(BU(+S2C: 4"#5"4%.%$(8%$/(*-%,%+-(0B(*%$(0C(%*%,%&(;;;; %; BU(+S2C *; C:O(+S2C 1; O(+S2C "; C(+S2C 5; F:FF(+S2C BB; >0%( 1"$*%:( +%2-$/B +%2-$/(1"#+%22%(0B=(H('/ *%$(0C(=(H('/(*-&010$/m1 '%$( *"$/%$( '%.#3,( 4"=%, A m2 30° 8%$/(+%22%$8%(H('/(2"4"#..%+4%'(4%*%(/%+1%#;(G-'%(4"#+0'%%$(1-*%$/(+-#-$/ )T(,-5-$(*%$('%.#3,(.-*%'(2",-4:(1"2%#(4"#5"4%.%$(1"$*% 0B:(*%$(0C(%*%,%&(;;;;((3(=(BU(+S2C) %; B:U(+S2C *; C:C(+S2C C 1; B:O(+S2 "; C:O(+S2C C 5; C:U(+S2 BC; G-'%(*0%(#3*%(+%2-$/-+%2-$/(1"#=%#--=%#-(
C; F; H;

O;

NaOa#$a:'("+ta/Taa/'#"+ik%t'i/i'4"/6a/'t"(at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t( #%*S2C;( G-'%( =%#--=%#-( ,-$/'%#%$$8%(H(5+:(&-.0$/,%&_ %; 4"#5"4%.%$(.%$/"$2-%,(4%*%(2%%.(t(=(C2[ 1; '"5"4%.%$(,-$"%#(4%*%(2%%.(t(=(C2[ 5; 4%$=%$/(,-$.%2%$(8%$/(*-."+40&(4%*%(2%%.(t(=(C2; D"10%&('%.#3,(8%$/(1"#04%(#3*%(4"=%, &3+3/"$:(*-/%$.0$/(4%*%(20+10$8%; !%*%(."4-(#3*%(*-,-,-.'%$(.%,-:('"+0*-%$ 0=0$/(.%,-(-.0(*-.%#-'(*"$/%$(1"2%#(/%8% 5(=(W(N(\"#.-'%,('"(1%A%&:(2"4"#.-(4%*% /%+1%#; F

138

Mudah dan Aktif Belajar Fisika untuk Kelas XI

T1 BF; !%*%( /%+1%#( *-( 2%+4-$/: C +%22%(1%,3'():(+%22%(1"1%$ A licin T:(*%$(+%22%(#3*%('%.#3, T2 1"#3$//%(K(+%2-$/-+%2-$/ %*%,%&(C('/:(X('/:(*%$(B('/; G-'%((3(=BU(+S2C:(."/%$/%$ B .%,-"GB(%*%,%&(;;;; %; FU(N *; Y(N 1; CU(N "; X(N 5; BH(N BH; D"10%&(5%'#%+(*"$/%$(=%#--=%#-(<(1"#40.%#(1"#%.0#%$ +",%,0-(20+10(&3#-c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

W;

X;

Y; Z;

BU;

G-'%(+%22%('%.#3,(O('/(*%$(=%#--=%#-$8%(BC(5+:(&-.0$/,%&_ %; 4"#5"4%.%$(.%,-[ 1; +3+"$.0+(20*0.$8%(4%*%(2%%.(t(=(U:O(2"'3$[ 5; 4%$=%$/(.%,-(8%$/(."#.%#-'(2",%+%(C(2; D"10%&( 2-,-$*"#( 1"#,01%$/( 1"#+%22%( W( '/( *%$( =%#-=%#-$8%(HO(5+(1"#40.%#(*"$/%$('"5"4%.%$(CUU(#4+ ('/tat6/2"?1'"062Nt1);(L"$.0'%$,%&(+3+"$(-$"#2-%(*%$ "$"#/-('-$".-'(#3.%2-(#3*%(."#2"10.6 D"10%&(#3*%(/-,%(*"$/%$(+3+"$(-$"#2-%(F:Y('/+C(3,"& 20%.0(.3#2-(*-4"#5"4%.(&-$//%(*%,%+(W(40.%#%$(2%=%; 9"5"4%.%$(20*0.$8%(1"#01%&(*%#-(C(40.%#%$S2(+"$=%*O(40.%#%$S2;(T"#%4%'%&(1"2%#(.3#2-(#3*%(."#2"10.6 L"$.0'%$,%&(.3#2-(8%$/(&%#02(*-1"#-'%$(%/%#(*%,%+(A%'.0 BU(*".-'(*%4%.(+"+1"#-('"5"4%.%$(20*0.(2"1"2%#(FUU(#4+ 4%*%(#3*%(/-,%(OU('/(*"$/%$(=%#--=%#-(HU(5+;((:(=(M
Bab

6 Sumber: www.chez.com

Pesawat dapat terbang karena mengalami gaya angkat yang bebas pada sayapnya.

Fluida Hasil yang harus Anda capai: menerapkan konsep dan prinsip mekanika klasik sistem kontinu dalam menyelesaikan masalah. Setelah mempelajari bab ini, Anda harus mampu: menganalisis hukum-hukum yang berhubungan dengan fluida statis dan dinamis serta penerapannya dalam kehidupan sehari-hari.

!"#na&'a&()nda(b"#tan-a.(/"n0a1a(1"2a3at(da1at(t"#ban04(!"2a3at da1at( t"#ban0( 'a#"na( /"n0ala/i( 0a-a( an0'at( -an0( b"2a#7( 8a-a( an0'at 1ada(1"2a3at(di2"bab'an(ol"&('on2t#u'2i(2a-a1(1"2a3at(-an0(/"n-"bab'an adan-a( 1"#b"daan( '"c"1atan( ali#( da#i(
A. Fluida Statis B. Viskositas Fluida C. Fluida Dinamis

139

Tes Kompetensi Awal 2,$,34# #,#5,3"6"%7 89.-,5 :347;"< 8,%6"8".3"= -9"3>-9"3 $,%784? ;"3"# $484 3"?7=".( 17 !"#na&'a&( )nda( datan0( '"( t"/1at( cuci( /obil4 lo0a/(/ulia("/a2(&an-a(d"n0an(/"nc"lu1'ann-a('" Uu'u/( a1a'a&( -an0( dit"#a1'an( dala/( alat( 1"n0A dala/(ai#4 an0'at(/obil(di(2ana4(=a0ai/ana(ca#a('"#?a(alat(1"n0A 37 E"n0a1a(n-a/u'(da1at(b"#?alan(di(ata2(1"#/u'aan an0'at(/obil(t"#2"but4 ai#4 27 !"#ca-a'a&( )nda( ?i'a( ada( t"/an( )nda( -an0 47 H"la2'an(d"n0an(ba&a2a/()nda(2"ndi#i(ca#a('"#?a(da#i /"n-ata'an( ba&3a( dia( bi2a( /"n"ntu'an( '"a2lian W"ntu#i/"t"#(dan(1i1a(1itot7

A. Fluida Statis Fluida(/"#u1a'an(Cat(-an0(da1at(/"n0ali#7(Donto&(
1. Tekanan

Gambar 6.1 Tekanan yang dilakukan seorang anak terhadap meja.

Doba()nda(t"'an(2"bua&(1ul1"n('"(dala/(tana&.('"/udian(bandin0A 'an( tin0'at( '"2u'a#ann-a( d"n0an( ?a#u/( -an0( dit"'an( '"( dala/( tana&7 !ul1"n( a'an( l"bi&( 2u'a#( /a2u'( '"( dala/( tana&( da#i1ada( ?a#u/( -an0 di/a2u''an( '"( dala/( tana&7( E"n0a1a( d"/i'ian4 Fin0'at('"2ulitan(2"2"o#an0(dala/(/"n"'an(2uatu(b"nda.(b"#&ubun0an d"n0an( lua2( da"#a&( -an0( dit"'an7( S"/a'in( lua2( da"#a&( -an0( dit"'an. 2"/a'in( '"cil( t"'anan( -an0( di&a2il'an7( -&!.+.+/ #&%0$.!.+/ )&'.%/ 1.2. 2.+1/ )&!&%3./ $.4./ '0.50/ $&%#0!..+/ 4().1(/ 4&+1.+/ *0.'/ $&%#0!..+/ 5&%'&)057 Hi'a(0a-a(6(b"'"#?a(t"0a'(lu#u2(1ada(1"#/u'aan(b"nda(2"lua2(7.(b"2a#n-a t"'anan( 2"ca#a( /at"/ati2( dituli2'an( 2"ba0ai( b"#i'ut7

@"t"#an0an: $ O(t"'anan(IPQ/2( O(1a2calM 6 O(0a-a(IPM 7 O( lua2( bidan0( t"'an( I/2M

$! 6 7

IJK1M

2. Tekanan Hidrostatik A

h

!"#&ati'an( !"#$"% '()7( !ada( 0a/ba#( t"#2"but( t"#li&at( 2"bua&( tabun0 b"#i2i( Cat( cai#( b"#/a22a( ?"ni2( ! .( '"dala/an( 8.( dan( lua2( 1"na/1an0( 77( Sat cai#(-an0(b"#ada(di(dala/(b"?ana(/"/ili'i(0a-a(b"#at(*(-an0(/"n"'an(da2a# tabun07( S"/a'in( tin00i( 1"#/u'aan( Cat( cai#.( 2"/a'in( b"2a#( t"'anan( -an0 di&a2il'an( 1ada( da2a#( tabun07( S"ca#a( /at"/ati2.( &ubun0an( anta#a( b"2a# t"'anan( -an0( di&a2il'an( dan( '"tin00ian( Cat( cai#( dituli2'an( 2"ba0ai( b"#i'ut7

! 187 #1 " ! 9 # (1 ! (O( ! 18 ! $! : ! 7 7 7 7

w

Gambar 6.2 Tekanan hidrostatik pada dasar tabung.

="#da2a#'an(+,%-"#"". /'0)1.(da1at(di2i/1ul'an(ba&3a(1"#2a/aan t"'anan( &id#o2tati'( adala& $ ! ! 18

@"t"#an0an: $ O( t"'anan( &id#o2tati'( IPQ/2M( atau( !a ! O(/a22a(?"ni2(Cat(cai#(I'0Q/3M

140

IJK2M

Mudah dan Aktif Belajar Fisika untuk Kelas XI

IJK3M

8 O( '"dala/an( Cat( cai#( I/M 1 O( 1"#c"1atan( 0#aWita2i( I/Q22M >a#i(1"#2a/aan(t"#2"but.(da1at(di1"la?a#i(ba&3a(t"'anan(&id#o2tati' 2an0at( di1"n0a#u&i( ol"&( 0a-a( 0#aWita2i( dan( '"dala/an( Cat( cai#7 !"#&ati'an(!"#$"% '(@7( !ada( 'a2u2( 2"1"#ti( ini( Iuntu'( Cat( cai#( -an0 2"?"ni2M.( t"'anan( Cat( cai#( tida'( b"#0antun0( 1ada( lua2( 1"na/1an0( dan b"ntu'(b"?ana.(t"ta1i(b"#0antun0(1ada('"dala/an(Cat(cai#7(Hadi.(t"'anan &id#o2tati'( 1ada( titi'( ).( =.( dan( D( adala&( 2a/a( b"2a#7( Xl"&( 'a#"na( itu. b"#da2a#'an( +,%-"#"". /'0)1( a'an( dida1at $)(O($=(O($D(O( ! 18

A

B

C

Gambar 6.3 Tekanan hidrostatik pada titik A, B, dan C adalah sama.

IJK4M

!"#&ati'an( !"#$"% '(A7( EulaA/ula( b"?ana( 1ada( 0a/ba#( t"#2"but dii2i(Cat(cai#(1"#ta/a(-an0(b"#/a22a(?"ni2( !1 7(@"/udian.('"(dala/(/ulut b"?ana(2"b"la&('anan(di/a2u''an(Cat(cai#('"dua(-an0(b"#/a22a(?"ni2( !27 Fiti'(=(b"#ada(1ada(1"#bata2an('"dua(Cat(cai#(t"#2"but(dan(dit"'an(ol"& Cat(cai#('"dua(2"tin00i(827Fiti'()(b"#ada(1ada(Cat(cai#(1"#ta/a(dan(dit"'an ol"&( Cat( cai#( 1"#ta/a( 2"tin00i( 817( Fiti'( )( dan( =( b"#ada( 1ada( 2atu( 0a#i27 S"2uai( d"n0an( Uu'u/( Uid#o2tati'a.( '"dua( titi'( t"#2"but( /"/ili'i t"'anan(-an0(2a/a7()'an(t"ta1i.(t"'anan(1ada(titi'(D(dan(>(tida'(2a/a 'a#"na( ?"ni2( Cat( cai#( di( '"dua( titi'( t"#2"but( b"#b"da7 $)(O($=

!1 81B(O( ! 2 82B

h

IJK5M

Zntu'( l"bi&( /"/a&a/i( t"ntan0( t"'anan( &id#o2tati'a.( la'u'anla& )'tiWita2( Fi2i'a( b"#i'ut( ini7

h1

C

D

A

B

h2

air

Gambar 6.4 Pipa U diisi dua zat cair berbeda, tekanan di A sama dengan tekanan di B.

Aktivitas Fisika 6.1 Tekanan Hidrostatik Tujuan Percobaan Memahami tekanan hidrostatika Alat-Alat Percobaan 1. Sebuah ember 2. dua buah gelas plastik bening Langkah-Langkah Percobaan 1. Isilah ember dengan air. 2. Jawablah pertanyaan berikut sebelum melakukan percobaan. a. Apa yang akan terjadi jika sebuah gelas plastik dicelupkan perlahan ke dalam air dalam keadaan terbalik? Jelaskan apa yang akan terjadi, berikut alasannya. b. Lakukan hal yang sama, namun dengan gelas yang diberi lubang pada dasar gelasnya. Jelaskan apa yang akan terjadi, berikut alasannya. 3. Buktikanlah jawaban Anda dengan melakukan percobaan. 4. Buatlah hukum tentang tekanan menurut versi Anda, berdasarkan jawaban dan hasil percobaan yang Anda peroleh. 5. Bandingkanlah dengan hukum hidrostatika yang telah Anda pelajari. 6. Buatlah kesimpulan dari percobaan tersebut.

Contoh 6.1 S"bua&(t"/1at(ai#(b"#b"ntu'('ubu2(/"/ili'i(1an?an0(#u2u'(J[(c/(dii2i(1\[(lit"#(ai# I/a22a(?"ni2(ai#(O(1[3('0Q/3M7(Hi'a(1(O(1[(/Q22.(t"ntu'anla&: a7 t"'anan(&id#o2tati'(1ada(da2a#('ubu2] b7 0a-a(&id#o2tati'(1ada(da2a#('ubu2](dan c7 0a-a(&id#o2tati'(1ada(titi'(=(-an0(b"#?a#a'([.25((/(da#i(1"#/u'aan(ai#7

Fluida

141

C"*"$D >i'"ta&ui: 9 O(1\[(lit"#(O([.1\(/3] 1 O(1[(/Q22] ' O(J[(c/(O([.J(/7

! O(1[3('0Q/3]

7 O([.3J(/2]

9 [.1\(/ 3 8)(O( (O( ((O([.5(/ 7 [. 3J(/2

hA hB s = 60 cm

a7

$) O ! 1(8) O(17[[[('0Q/3(`(1[(/Q22(`([.5((/(O(57[[[(!a b7 6) O($)(7 O(57[[[(!a(`([.3J(/2(O(17\[[(P c7 $ = O ! 1((8= O(17[[[('0Q/3(`1[(/Q22(`([.25((/(O(275[[(!a 6= O($=((7//O(275[[(!a(`([.25(/(O(b[[(P Hadi.(b"2a#(t"'anan(&id#o2tati'(1ada(da2a#('ubu2(adala&($)O(57[[[(!a.(0a-a(&id#o2tati'(1ada da2a#('ubu2(adala&(6)(O(17\[[(P.(dan(0a-a(&id#o2tati2(1ada(titi'(=(adala&(6=O(b[[(P7

Contoh 6.2

P piston

zat cair

Gambar 6.5 Tabung Pascal

F1 p1

A2

A1 F2

p2

Gambar 6.6 Prinsip kerja dongkrak hidrolik.

142

!ada(0a/ba#(b"#i'ut.(2"bua&(1i1a(b"#b"ntu'(&u#u<(Z(dii2i(d"n0an(ai#.( !ai# (O(1(0Qc/37 @a'i(1i1a(2"b"la&('i#i(dii2i(b"n2in(d"n0an( !b"n2in (O([.^(0Qc/3(2"tin00i(4(c/7(S"b"la& 'anan( dii2i( /in-a'( tana&( d"n0an( !/in-a' O( [.\( 0Qc/3( 2"tin00i( \( c/7( Uitun0la& 1"#b"daan(tin00i(ai#(anta#a(1i1a('anan(dan(1i1a('i#i7 C"*"$D minyak tanah >i'"ta&ui: bensin !ai# O(1(0Qc/3 !b"n2in O([.^(0Qc/3 h2 h3 !/in-a' O([.\(0Qc/3 h1{ ////////82 O(4(c/ A B ////////83 O(\(c/ F"'anan(&id#o2tati'(di()(O(t"'anan(&id#o2tati'(di(= I !ai# (81M(_(I !b"n2in (82M(O( !/in-a' (83 air I1(`(81M(_(I[.^(`(4M(O(([.\(`(\ J. 4 " 2.\ 81(O( (O(1.J(c/ 1 Hadi.(1"#b"daan(tin00i(ai#(1ada('"dua(1i1a(adala&(1.J(c/7

3. Hukum Pascal !"#an0'at( '"#?a( Uu'u/( !a2cal( di1"#li&at'an( 1ada !"#$"% '(E7 !"#an0'at( t"#2"but( t"#di#i( ata2( tabun0( -an0( dib"#i( luban0( d"n0an( dia/"t"# -an0( 2a/a7( !i2ton( b"'"#?a( 2"ba0ai( 1"n0i2a1( dan( tan0'ai( 1i2ton( b"#.'<.*7 !ada( !"#$"% '('.( di1"#li&at'an( 1#o2"2( '"#?a( don0'#a'( &id#oli'( -an0 b"'"#?a( b"#da2a#'an( Uu'u/( !a2cal7( >on0'#a'( &id#oli'( t"#di#i( ata2( b"?ana d"n0an( dua( 'a'i( -an0( /a2in0A/a2in0( dib"#i( 1"n0i2a17( @"dua( 1"n0i2a1( ini /"/ili'i(dua(1"na/1an0(b"#b"da.(-aitu(71(dan(72.(di(/ana(71(a(727

Mudah dan Aktif Belajar Fisika untuk Kelas XI

Hi'a( 1"n0i2a1( 1( dit"'an( d"n0an( 0a-a( 61.( Cat( cai#( a'an( /"n"#u2'an t"'anan( t"#2"but( '"( 2"0ala( a#a&7( ="2a#n-a( t"'anan( 1ada( 1"n0i2a1( 1 din-ata'an( d"n0an( 1"#2a/aan 6 $1(O( 1 IJKJM 71 Hi'a( di( ata2( 1"n0i2a1( 2( dil"ta''an( b"ban.( 0a-a( an0'at( '"( ata2( 1ada 1"n0i2a1( 2( adala&( 62.( -an0( din-ata'an( d"n0an( 1"#2a/aan 6 $2(O( 2 IJK^M 72 E"nu#ut( Uu'u/( !a2cal.( t"'anan( -an0( dit"#u2'an( '"( 2"0ala( a#a& adala&( 2a/a( b"2a#( 2"&in00a $1(O($2

61 62 (O( 71 72

IJK\M

Hi'a( b"ntu'( 1"na/1an0( tabun0( b"#u1a( lin0'a#an( d"n0an( ?a#iA?a#i( %1 dan( %2.( a'an( di1"#ol"&( 1"#2a/aan

6 61 6 6 (O( @2 (atau( 12 (O( 22 2 %@ %1 41 42

F2

Gambar 6.7 Pengangkat hidrolik menerapkan Konsep Hukum Pascal.

Tokoh Douglas Dean Osheroff (1945 – sekarang)

IJKbM

>ia/"t"#(1"na/1an0(1ada(+,%-"#"". /'0F1(adala&(4A(dan(4@7(Hadi. d"n0an(0a-a(-an0('"cil.()nda(da1at(/"n0an0'at(b"ban(-an0(b"2a#7(!#in2i1 !a2cal( t"#2"but( 2"#in0( di?u/1ai( dala/( '"&idu1an( 2"&a#iA&a#i.( 2"1"#ti don0'#a'( /obil( dan( 1o/1a( &id#oli'7

Contoh 6.3 S"bua&(1o/1a(&id#oli'(/"/ili'i(1i1a('"cil(b"#?a#iA?a#i(2(c/.(2"dan0'an(1i1a(b"2a# b"#?a#iA?a#i(2[(c/7()0a#(b"ban(-an0(b"#atn-a(47[[[(P(nai'(2"tin00i(5(c/.(t"ntu'anla&: a7 0a-a(-an0(di'"#?a'an(1ada(1i1a('"cil] b7 ?a#a'(-an0(dit"/1u&(1"n0i2a1(1i1a('"cil7 C"*"$D >i'"ta&ui: %1 O(2(c/] %2(O(2[(c/] 62((O(47[[[(P] 82((O(5(c/7

61 6 6 (O( 22 ( # 1 2 O 47[[[ %12 I4M I2[M2 %2 4[[(61 O(J47[[[ 61 O((1J[(P b7 ?1(O(?2( # 61(`(81(O(62(`(82 1J[(`(81(O(47[[[(`(4 81(O(1[[(c/ Hadi.(dibutu&'an(0a-a(2"b"2a#(4[[(P(dan(?a#a'(1"n0i2a1(1[[(c/(1ada(1i1a('"cil7

a7

F1

Sumber: Republika, 19 November 2005

Douglas Dean Osheroff dilahirkan pada tahun 1945. Setelah menyelesaikan pendidikan sarjananya di California Institute Of Technology, ia pindah ke Cornell University untuk mengambil gelar doktor. Di sana, ia bertemu dengan David M. Lee dan Robert C. Richardson. Bersama dua koleganya tersebut, ia melakukan penelitian selama bertahun-tahun sampai menemukan satu fenomena yang menghebohkan dunia ilmiah, yaitu superfluiditas. Superfluiditas tersebut terjadi ketika helium-3 didinginkan mendekati suhu nol mutlak (–273,15°C). Pada suhu tersebut, helium-3 tidak lagi memiliki viskositas dan friksi sehingga dapat meluap dari sebuah cangkir datar melalui pori-pori yang teramat kecil. Fenomena lainnya adalah helium-3 ini dapat melawan gaya gravitasi Bumi. Atas penemuannya ini, Osherhof bersama kedua rekannya mendapat hadiah Nobel pada tahun 1996.

Fluida

143

4. Hukum Archimedes IaM

IbM

35 N 50 N

w

air

Gambar 6.8 Berkurangnya berat benda di dalam zat cair disebabkan oleh gaya ke atas yang dikerjakan oleh zat cair.

S"bua&(balo'(diti/ban0(d"n0an(n"#aca(1"0a2(2"1"#ti(1ada(!"#$"% '(G"7 Ei2al'an( balo'( t"#2"but( /"/ili'i( b"#at( 5[( P.( '"/udian( balo'( di/a2u''an '"(dala/(b"?ana(-an0(b"#i2i(ai#(/!"#$"% '(G$17(="#at(balo'(a'an(b"#'u#an0. /i2aln-a( /"n?adi( 35( P7( E"nu#ut( )nda.( a1a'a&( -an0( /"n-"bab'an b"#'u#an0n-a( b"#at( balo'( t"#2"but4( ="#'u#an0n-a( b"#at( balo'( '"ti'a di/a2u''an( '"( dala/( ai#( di2"bab'an( ol"&( adan-a( 0a-a( t"'an( '"( ata2( da#i ai#7(8a-a('"(ata2(da#i(ai#('ali(1"#ta/a(di'"ta&ui(ol"&(H%I=7#,;,-! 2"&in00a 0a-a( t"#2"but( dina/a'an( 0a-a( )#c&i/"d"27 J484# H%I=7#,;,-( b"#bun-i.( )&+4./ 2.+1/ 5&%<&*0$/ !&/ 4.*.#/ B*0(4.C ).(!/'&).1(.+/.5.0$0+/'&*0%08+2.C/.!.+/#&+1.*.#(/1.2./!&/.5.'/'&)&'.%/)&%.5 ;.5/ <.(%/ 2.+1/ 4($(+4.8!.+/ "*&8/ )&+4./ 5&%'&)05,( ="2a#n-a( 0a-a( )#c&i/"d"2 t"#2"but( din-ata'an( d"n0an( 1"#2a/aan :)(O(#D( B(O( !C9D( B

IJK1[M

@"t"#an0an: 67 O( 0a-a( )#c&i/"d"2( IPM !C O( /a22a( ?"ni2(
Contoh 6.4 S"bua&(batu(-an0(Wolu/"n-a(27[[[(c/3(b"#ada(di(dala/(ai#7(Hi'a(/a22a(?"ni2(ai# 1(0Qc/ 3.(t"ntu'an(0a-a(t"'an('"(ata2(1ada(batu7 C"*"$D >i'"ta&ui: !ai# O(1(0Qc/3(O(17[[[('0Q/3 colu/"(batu(O(Wolu/"(Cat(cai#(-an0(di1inda&'an 9=(O(27[[[(c/3(O(2(`(1[K3(/3 1(((O((1[(/Q22 8a-a('"(ata2(O(0a-a()#c&i/"d"2 6) O( !ai# 19= O(I17[[[('0Q/3M(I1[(/Q22M(I2(`(1[K3(/3M(O(2[(P7

)dan-a( 0a-a( '"( ata2( I0a-a( )#c&i/"d"2M( 1ada( 2"bua&( b"nda( -an0 /a2u'('"(dala/(Cat(cai#.(/"n-"bab'an(b"nda(da1at(/"n0a1un0.(/"la-an0. atau( t"n00"la/7 a. Benda Mengapung Hi'a( &an-a( 2"ba0ian( b"nda( -an0( t"#c"lu1( '"( dala/( Cat( cai#.( b"nda di2"but(/"n0a1un07(>ala/('"adaan(ini.(b"#at(b"nda(a(0a-a('"(ata2(da#i Cat( cai#7( S"ca#a( /at"/ati2( dituli2'an( 2"ba0ai( b"#i'ut7 * a(:) # =" a( !D B9D ! = 9=( Ba/ !D 9DB

! = 9= a( !D 9D

Gambar 6.9 Perahu dapat terapung di atas air karena massa jenisnya lebih kecil dari massa jenis air.

144

IJK11M

@"t"#an0an: 9D(O(Wolu/"(b"nda(-an0(t"#c"lu1(I/3M 9E(O(Wolu/"(b"nda(2"lu#u&n-a(I/3M +,%-"#"". /'0KK1( /"nun?u''an( ba&3a( 2u1a-a( b"nda( /"n0a1un0. /a22a(?"ni2(b"nda(&a#u2(l"bi&('"cil(da#i1ada(/a22a(?"ni2(Cat(cai#(I ! = a ! CM7

Mudah dan Aktif Belajar Fisika untuk Kelas XI

b. Benda Melayang Hi'a( 2"lu#u&( ba0ian( b"nda( b"#ada( di( dala/( Cat( cai#.( na/un( b"nda t"#2"but( tida'( 2a/1ai( /"n-"ntu&( da2a#( tabun0( /a'a( b"nda( di'ata'an /"la-an07(>ala/('"adaan(2"i/ban0.(b"#at(b"nda(2a/a(d"n0an(0a-a(t"'an '"( ata2( ol"&( Cat( cai#7( S"ca#a( /at"/ati2( da1at( dituli2'an( 2"ba0ai( b"#i'ut7 * O((:) # =B O( !D B9D ! = 9=B O( !D 9DB

!D 9 D O( ! = 9=

IJK12M

S"1"#ti( 1ada( !"#$"% '(KL.( 2"lu#u&( b"nda( /a2u'( '"( dala/( Cat( cai# 2"&in00a( Wolu/"(b"nda(2a/a(d"n0an(Wolu/"(Cat( cai#(-an0( di1inda&'an7 Xl"&( 'a#"na( itu.( untu'( 'a2u2( /"la-an0.( /a22a( ?"ni2( b"nda( dan( /a22a ?"ni2( Cat( cai#( adala&( 2a/a7 c.

Benda Tenggelam ="nda( t"n00"la/( t"#?adi( 'a#"na( 0a-a( b"#at( b"nda( -an0( l"bi&( b"2a# da#i1ada( 0a-a( t"'an( '"( ata27( ="nda( -an0( t"n00"la/( a'an( /"n-"ntu& da2a#(tabun0.(2"1"#ti(-an0(t"#li&at(1ada(!"#$"% '(KK7(S"ca#a(/at"/ati2 da1at( dituli2'an( 2"ba0ai( b"#i'ut7 * d(:) # =B d/:) ! = B9= F !D B9D Xl"&('a#"na(Wolu/"(b"nda(-an0(t"n00"la/(2a/a(d"n0an(Wolu/"(Cat cai#( -an0( di1inda&'an.( -aitu( 9=( O( 9D.( da1at( dituli2'an( ba&3a

! = d !D

IJK13M

Gambar 6.10 Penyelam dan ikan-ikan dapat melayang di air. Tahukah Anda, mengapa ikan dan penyelam dapat melayang dalam air?

Gambar 6.11 Batu tenggelam dalam air karena massa jenis batu lebih besar daripada massa jenis air.

Hadi.(?i'a(/a22a(?"ni2(b"nda(l"bi&(b"2a#(da#i1ada(/a22a(?"ni2(Cat(cai#. b"nda( a'an( t"n00"la/7

Contoh 6.5 S"bua&(b"nda(?i'a(b"#ada(di(uda#a(b"#atn-a(J[(P7(Hi'a(diti/ban0(di(dala/(ai#.(b"#at b"nda(t"#2"but(2"ola&Aola&(/"n?adi(3J(P7(Hi'a(/a22a(?"ni2(ai#(O(1(0Qc/3.(t"ntu'anla& /a22a(?"ni2(b"nda(t"#2"but(I1/O(1[(/Q22M7 C"*"$D ="#at(b"nda(di(uda#a(O(:uda#a(O(J[(P](="#at(b"nda(di(ai#(O(:ai#(O(3J(P7 !ai# (O(1[3(('0Q/3 8a-a(t"'an('"(ata2(-an0(b"'"#?a(1ada(b"nda(adala& 6) O(:uda#a(K(:(ai#(O(J[(P(K(3J(P(O(24(P 8a-a()#c&i/"d"2: 67 24(P 6) O( !D 9D(1/ # /9D(O( ! 1 (O( 3 (O(24(`(1[K4(/3(O(274[[(c/3 3 1[ ('0Q/ $ 1[(/Q22 D Ea22a(b"nda: : #= O( uda#a (O( J[(P 2 (O(J('0(O(J7[[[(0 1 1[(/Q2 2"&in00a(/a22a(?"ni2(b"nda(adala& # J7[[[(0 (O((2.5(0Qc/3 != O( = (O( 9= 274[[(c/ 3 Hadi.(/a22a(?"ni2(b"nda(t"#2"but(adala&(2.5(0Qc/37

Ingatlah !benda % ! fluida $ mengapung !benda ! ! fluida $ melayang !benda & ! fluida $ tenggelam

Fluida

145

5. Penerapan Hukum Archimedes

Gambar 6.12 Balon udara merupakan salah satu penerapan Hukum Archimedes. IaM

IbM

Gambar 6.13 (a) Hidrometer di dalam raksa. (b) Hidrometer di dalam air.

!"n"#a1an( Uu'u/( )#c&i/"d"2( da1at( )nda( ?u/1ai( dala/( '"&idu1an 2"&a#iA&a#i7(Donto&n-a(#a'it.(1"#a&u.('a1al(laut.(dan(balon(uda#a7(!ada(da2a#A n-a.(2"/ua(?"ni2('"nda#aan(laut(/"n00una'an(1#in2i1(&u'u/()#c&i/"d"27 =adan('a1al(dibuat(b"#on00a(a0a#(da1at(/"/inda&'an(Wolu/"(ai#(laut(l"bi& b"2a#( 2"&in00a( /a22a( ?"ni2( 'a1al( /"n?adi( l"bi&( '"cil( dan( 0a-a( an0'at( ol"& ai#(laut(2"/a'in(b"2a#7(>a#i('"t"#an0an(ini.(da1at(di'"ta&ui(1"n-"bab('a1al laut(-an0(/"/ili'i(/a22a(2an0at(b"2a#(da1at(t"#a1un0(1ada(1"#/u'aan(ai#7 !#in2i1( Uu'u/( )#c&i/"d"2( ?u0a( di0una'an( 1ada( 1"n"#ban0an( balon uda#a7(=alon(uda#a(da1at(t"#an0'at(?i'a(/a22a(?"ni2(da#i('"2"lu#u&an(balon uda#a( t"#2"but( l"bi&( '"cil( da#i1ada( /a22a( ?"ni2( uda#a7( colu/"( 0a2( dala/ balon( uda#a( &a#u2( di1"#b"2a#( atau( /"n00una'an( 0a2( -an0( /a22a( ?"ni2n-a l"bi&('"cil(da#i1ada(/a22a(?"ni2(uda#a(lua#(a0a#(balon(t"#2"but(da1at(t"#an0'at7 @"tin00ian(balon('"ti'a(t"#ban0(da1at(diatu#(d"n0an(/"na/ba&'an 0a2( '"( dala/( balon( uda#a7( Ea22a( b"ban( -an0( da1at( dian0'at( ol"&( balon uda#a( adala& # ! 9EI !u " ! 0 M IJK14M @"t"#an0an: # O( /a22a( b"nda( I'0M 9E O(Wolu/"(b"nda(I/3M ! u O( /a22a( ?"ni2( uda#a( I'0Q/3M ! 0 O(/a22a(?"ni2(0a2(I'0Q/3M Uu'u/( )#c&i/"d"2( ?u0a( di/an
6. Tegangan Permukaan

Gambar 6.14 Serangga dapat berjalan di atas air karena adanya tegangan permukaan.

B

A

Gambar 6.15 Dua molekul zat cair yang berbeda posisi memiliki gaya kohesi yang berbeda.

146

Fa&u'a&()nda(-an0(di/a'2ud(d"n0an(t"0an0an(1"#/u'aan(Cat(cai#4 !"#na&'a&( )nda( /"li&at( 2"#an00a( -an0( da1at( b"#?alan( di( ata2( ai#4 E"n0a1a( 2"#an00a( t"#2"but( da1at( /"la'u'ann-a4( F"0an0an( 1"#/u'aan Cat(cai#(t"#?adi('a#"na(adan-a('o&"2i.(-aitu(0a-a(ta#i'A/"na#i'(anta#1a#ti'"l 2"?"ni27(Donto&(-an0(/"n00a/ba#'an(adan-a(t"0an0an(1"#/u'aan(adala& balon( -an0( t"#buat( da#i( ai#( 2abun7( )nda( bi2a( /"/bu'ti'ann-a( d"n0an ca#a(/"nc"lu1'an(tan0an()nda('"(dala/(ai#(2abun(t"#2"but.(lalu(buatla& lin0'a#an( d"n0an( ?a#i( ?"/1ol( dan( t"lun?u'( )nda.( /a'a( a'an( t"#li&at( ai# 2abun( -an0( /"/b"ntu'( bidan0( data#7 !"#&ati'an(!"#$"% '(KE7(8a/ba#(t"#2"but(/"nun?u''an(0a-a('o&"2i -an0(b"'"#?a(1ada(/ol"'ul()(dan(/ol"'ul(=7(Eol"'ul()(/"n0ala/i(0a-a 'o&"2i(da#i(2"0ala(a#a&(-an0(2a/a(b"2a#(2"&in00a(da1at(din-ata'an(ba&3a /ol"'ul( t"#2"but( b"#ada( dala/( '"2"i/ban0an7( ="#b"da( d"n0an( /ol"'ul =( -an0( t"#l"ta'( 1ada( 1"#/u'aan( Cat( cai#7( Eol"'ul( ini( &an-a( /"n0ala/i 0a-a('o&"2i(ol"&(1a#ti'"lA1a#ti'"l(-an0(b"#ada(di(ba3a&(dan(di(2a/1in0n-a 2a?a7( )'ibatn-a.( 1ada( 1"#/u'aan( ai#( t"#?adi( ta#i'an( '"( ba3a&( 2"&in00a 1"#/u'aan( Cat( cai#( 2"1"#ti( 2"la1ut( ti1i27( )/atila&( ?i'a( 1i2au( 2il"t dit"/1at'an( 2"ca#a( /"lintan0( 1ada( 1"#/u'aan( ai#7( ealau1un( /a22a ?"ni2n-a( l"bi&( b"2a#( dibandin0'an( /a22a( ?"ni2( ai#.( 2il"t( t"#2"but( da1at t"#a1un0( 'a#"na( adan-a( t"0an0an( 1ada( 1"#/u'aan( ai#7

Mudah dan Aktif Belajar Fisika untuk Kelas XI

!"#&ati'an( 2"?u/la&( t"t"2an( "/bun( 1a0i( -an0( ?atu&( di( ata2( #u/1ut7 F"t"2an(t"#2"but(a'an(b"#b"ntu'(2"1"#ti(bolaAbola('"cil7(8a-a('o&"2i(/ol"'ulA /ol"'ul( -an0( t"#l"ta'( 1ada( 1"#/u'aan( ai#( '"( a#a&( dala/( a'an( 2a/a( b"2a# 2"&in00a( t"t"2an( ai#( t"#2"but( a'an( b"#b"ntu'( bola7( F"la&( di'"ta&ui( ba&3a bola( /"#u1a'an( ban0un( #uan0( -an0( /"/ili'i( lua2( 1"#/u'aan( t"#'"cil7( !"#A /u'aan( ai#( ini( /"n-"#u1ai( 2"la1ut( t"0an0( -an0( "la2ti27 Zntu'( /"n0"ta&ui( b"2a#( t"0an0an( 1"#/u'aan( t"#2"but.( 1"#&ati'anla& conto&(b"#i'ut7()/billa&(2"1oton0('a3at.('"/udian(b"ntu'la&(/"n-"#u1ai b"ntu'( Z( 2"1"#ti( 1ada( !"#$"% '(KM7( @"dua( 'a'i( 'a3at( Z( di&ubun0'an d"n0an('a3at()=(d"n0an(1an?an0( ! (dan(b"#at(*17(Hi'a('a3at(Z(dic"lu1'an '"( dala/( b"?ana( -an0( b"#i2i( ai#( 2abun.( '"/udian( 1ada( batan0( 7E( dib"#i 2"bua&(b"ban(2"b"#at(:@( .(a'an(di1"#ol"&(0a-a(t"0an0an(1"#/u'aan(6./-aitu 6/G/:A/H/:@ IJK15M Xl"&( 'a#"na( 2i2i( 'a3at( -an0( 'onta'( d"n0an( 1"#/u'aan( ai#( ada( dua 2i2i.( 2i2i( lua#( ! 1 ( dan( 2i2i( dala/( ! 2 ( d"n0an( 1an?an0( dian00a1( 2a/a7/ Hadi. 1an?an0( 2i2i( 'a3at( total( -an0( 'onta'( d"n0an( ai#( 2"1an?an0( 2! ( 2"&in00a t"0an0an( 1"#/u'aan( 1ada( la#utan( 2abun( adala&

%! 6 2!

IJK1JM

@"t"#an0an: % O t"0an0an( 1"#/u'aan( IPQ/M.( da1at( dian00a1( 2"ba0ai( 0a-a( 2"tia1 2atuan( 1an?an0 ! G 1an?an0( 'a3at( I/M Hi'a( '( adala&( 1"#1inda&an( 'a3at.( +,%-"#"". /'0K'1( da1at( dituli2 2"ba0ai( b"#i'ut7 6' u2a&a %! ! IJK1^M 2!' lua2 Hadi.( t"0an0an( 1"#/u'aan( da1at( 1ula( dia#ti'an( 2"ba0ai( u2a&a( 2"tia1 2atuan(lua2.(dan(2atuann-a(adala&(?oul"Q/"t"#2(IHQ/2M7(Zntu'(l"bi&(/"/aA &a/i(<"no/"na(t"ntan0(t"0an0an(1"#/u'aan.(la'u'anla&()'tiWita2(Fi2i'a b"#i'ut( ini7

Aktivitas Fisika 6.2

Gambar 6.16 Tetesan air yang jatuh ke atas rumput.

B

A

Langkah-Langkah Percobaan 1. Ambil jarum yang sudah diolesi minyak pelumas, kemudian simpan jarum tersebut di atas kertas tisu. 2. Letakkan jarum dan kertas tisu secara perlahan-lahan di atas permukaan air. 3. Amati yang terjadi pada jarum dan kertas tisu tersebut. 4. Taburkan detergen secara perlahan-lahan di sekitar jarum yang terapung, kemudian amati yang terjadi pada jarum tersebut. 5. Dari hasil Aktivitas Fisika 6.2, lakukanlah diskusi tentang hasil kegiatan tersebut bersama teman dan guru Fisika Anda. Kemudian, presentasikan hasil diskusi tersebut.

B w1

!2

!1

s

w2

Gambar 6.17 Tegangan permukaan air sabun pada kawat.

Pembahasan Soal Sebuah benda terapung di atas permukaan air yang berlapiskan minyak. Sebanyak 50 % volume benda berada di dalam air dan 30 % di dalam minyak. Jika massa jenis minyak = 0,8 g/cm3 maka massa jenis benda tersebut adalah .... a. 0,62 g/cm 3 b. 0,68 g/cm 3 c. 0,74 g/cm 3 d. 0,78 g/cm 3 e. 0,82 g/cm 3 Soal UMPTN Tahun 1993 Pembahasan:

Tegangan Permukaan Tujuan Percobaan Memahami fenomena tegangan permukaan Alat-Alat Percobaan 1. Panci berisi air 2. Jarum 3. Kertas tisu 4. Minyak pelumas 5. Detergen

F A

30 %

minyak

50 %

air

Benda dalam keadaan setimbang, maka gaya berat benda sama dengan gaya angkat Archimedes oleh air dan minyak. mbg = FA (air) + FA (minyak) ! bVb g = ! aVa g + ! mVm g !b

= !a

Va V + !m m Vb Vb

= (1 g/cm3)(50 %) + (0,8 g/cm3)(30 %) = 0,74 g/cm 3 Jawaban: c

Fluida

147

Tugas Anda 6.1 Tegangan permukaan dapat dikatakan sebagai kecenderungan permukaan zat cair untuk berkontraksi (mengerut). Menurut Anda, bagaimanakah sifat tegangan permukaan zat cair ketika zat cair tersebut dipanaskan?

@"ti'a( ?a#u/( -an0( b"#ada( di( ata2( '"#ta2( ti2u( di( l"ta''an( 2"ca#a 1"#la&anAla&an( di( ata2( 1"#/u'aan( ai#.( ?a#u/( dan( ti2u( a3aln-a( a'an t"#a1un0( di( ata2( 1"#/u'aan( ai#7( S"2aat( '"/udian.( '"#ta2( ti2u( a'an /"n-"#a1( ai#( 2"&in00a( /"n?adi( ba2a&( dan( t"n00"la/.( 2"dan0'an( ?a#u/ t"ta1( t"#a1un0( a'ibat( adan-a( t"0an0an( 1"#/u'aan7 Ha#u/( a'an( t"n00"la/( '"ti'a( bubu'( d"t"#0"n( ditabu#'an( di( 2"'ita# ?a#u/( -an0( t"#a1un07( Ual( t"#2"but( di2"bab'an( /"n0"ciln-a( t"0an0an 1"#/u'aan( ai#( 'a#"na( d"t"#0"n( b"#"a'2i( d"n0an( /in-a'( 1"lu/a2( 1ada ?a#u/7( )'ibatn-a.( ?a#u/( /"n?adi( ba2a&( dan( t"n00"la/7

Contoh 6.6 S"batan0('a3at(dib"n0'o''an(2"1"#ti(&u#u<(Z7(@"/udian. 'a3at('"cil(!f(-an0(b"#/a22a([.3(0(di1a2an0(1ada('a3at t"#2"but(2"1"#ti(1ada(0a/ba#7(S"lan?utn-a.('a3atA'a3at ini(dic"lu1'an(dala/(la1i2an(2abun(dan(dian0'at(W"#ti'al 2"&in00a(t"#b"ntan0(2atu(la1i2an(2abun7(Fa/1a'('a3at '"cil( !f( /"n0ala/i( 0a-a( ta#i'( '"( ata27( )0a#( t"#?adi Q '"2"ti/ban0an(/a'a(1ada('a3at('"cil(!f(di0antun0'an P /a22a(2"b"#at([.2(0#a/7 0,2 gram Hi'a(1an?an0('a3at(!f(O(1[(c/.(&itun0la&(t"0an0an(1"#/u'aan(la1i2an(2abun(t"#2"but7 Ign0at.(la1i2an(2abun(/"/ili'i(2(1"#/u'aan(-aitu(d"1an(dan(b"la'an0M C"*"$D !ada('"adaan(2"ti/ban0.(0a-aA0a-a(-an0(b"'"#?a(2a/a(b"2a#7(8a-a('"(ba3a&(adala& b"#at('a3at(dan(b"#at(b"ban7()da1un(0a-a('"(ata2(adala&(0a-a(t"0an0(1"#/u'aan7 6(O(:'(_(:[ # ' #b 1 2 % !(O(I#'(_(#bM(1( $( % (O( ' 2! >i'"ta&ui: #'(O([.3(0(O([.3(`(1[K3('0](#=(O([.2(0(O([.2(`(1[K3('0] 1 O(b.\(/Q22]( ! (O(1[(c/(O([.1(/7 Ea'a(di1"#ol"&.

Kata Kunci • • • • • • • • •

gaya Archimedes kapilaritas melayang mengapung meniskus cekung meniskus cembung tegangan permukaan tekanan hidrostatik tenggelam

% O( #' ' # b 1 2!

O(

air

FA

&

F

Fk

IaM raksa

FA

& Fk

F

IbM Gambar 6.18 (a) Meniskus cekung (b) Meniskus cembung

148

"[. 3$1[

"3

('0 ' [.2( $1[ "3 ('0 # b.\(/Q22 2$ [.1(/

O([.[245(PQ/7

a. Meniskus Cembung dan Meniskus Cekung 8a-a(ta#i'(/"na#i'(anta#a(1a#ti'"lA1a#ti'"l(-an0(2"?"ni2(dala/(2uatu Cat(di2"but(0a-a(!"8&'(.(2"dan0'an(0a-a(.48&'((adala&(0a-a(ta#i'(/"na#i' anta#a( 1a#ti'"lA1a#ti'"l( -an0( tida'( 2"?"ni27( Donto&( 0a-a( .48&'(( adala& t"t"2an( ai#( 1ada( 1"#/u'aan( 'aca( -an0( la/aAla/a( a'an( /"lua27( Ual t"#2"but( t"#?adi( 'a#"na( 0a-a( ad&"2i( 1a#ti'"l( 'aca( dan( ai#( l"bi&( b"2a# da#i1ada( 0a-a( 'o&"2i7( ="#b"da( d"n0an( ai#.( ?i'a( #a'2a( dit"t"2'an( 1ada 1"#/u'aan( 'aca( /a'a( #a'2a( t"#2"but( a'an( /"n00u/1al7( !"n00u/1alan #a'2a( t"#?adi( 'a#"na( 0a-a( 'o&"2i( l"bi&( b"2a#( da#i1ada( 0a-a( ad&"2in-a7 )'ibat( <"no/"na( t"#2"but.( ?i'a( '"dua( cai#an( t"#2"but( di/a2u''an '"(dala/(tabun0('aca.(a'an(t"#li&at(2"1"#ti(1ada(!"#$"% '(KG7(>i'"ta&ui 6!( adala&( 0a-a( 'o&"2i( dan( 67( adala&( 0a-a( ad&"2i7( !"#$"% '(KG/"1 /"nun?u''an(#&+('!0'/<&!0+1(-an0(t"#?adi('a#"na(0a-a(ad&"2i(l"bi&(b"2a# da#i1ada( 0a-a( 'o&"2i7( )da1un( !"#$"% '(KG/$1( /"#u1a'an( #&+('!0'

Mudah dan Aktif Belajar Fisika untuk Kelas XI

<&#)0+1( -an0( t"#?adi( 'a#"na( 0a-a( 'o&"2i( -an0( l"bi&( b"2a#( da#i1ada( 0a-a ad&"2i7( Sudut( 'onta'( & ( 1ada( /"ni2'u2( c"'un0( adala&( 2udut( lanci1 Iab[hM7(S"bali'n-a.( 2udut('onta'(1ada(/"ni2'u2(c"/bun0(adala&(2udut tu/1ul( Idb[hM7 b. Kapilaritas I&3.*./ !.$(*.%(5.'( adala&( 1"#i2ti3a( nai'( atau( tu#unn-a( 1"#/u'aan( Cat cai#( /"lalui( luban0Aluban0( '"cil( atau( 'a1il"#7( )lat( -an0( da1at( di0una'an untu'( /"n0a/ati( 0"?ala( 'a1ila#ita2( adala&( 1i1a( 'a1il"#7( Hi'a( 1i1a( 'a1il"# di/a2u''an('"(dala/(tabun0(-an0(b"#i2i(ai#.(1"#/u'aan(ai#(di(dala/(1i1a 'a1il"#( a'an( nai'.( 2"1"#ti( t"#li&at( 1ada( !"#$"% '(KF7( )'an( t"ta1i.( ?i'a 1i1a('a1il"#(di/a2u''an('"(dala/(tabun0(#a'2a.(1"#/u'aan(#a'2a(di(dala/ tabun0(t"#2"but(a'an(tu#un7(Fa&u'a&()nda.(/"n0a1a(&al(t"#2"but(t"#?adi4 !"#&ati'an( !"#$"% '()L7( ="ntu'( 1i1a( 'a1il"#( -an0( /"n-"#u1ai tabun0( a'an( /"n-"bab'an( Cat( cai#( /"n-"ntu&( dindin0( 2"b"la&( dala/ 2"&in00a( 1"#/u'aan( Cat( cai#( /"na#i'( 1i1a( d"n0an( 0a-a( 2"b"2a# 6- O(2 ' % % )da1un( '"lilin0( dindin0( 1i1a( 'a1il"#( O( 2 ' % >indin0( 1i1a( 'a1il"#( /"/b"#i'an( 0a-a( #"a'2i( t"#&ada1( Cat( cai#( 2"b"2a# 6-(O(2 ' % % co2& 8a-a(ini(dii/ban0i(ol"&(b"#at(Cat(cai#(2"tin00i(2(dala/(1i1a.(-aitu(2"b"2a# * G/#B G/ ! 9B 2 ' % % co2& O( ! ' %22B 2"&in00a( di1"#ol"&( tin00i( Cat( cai#( di( dala/( 1i1a( 'a1il"#.( -aitu 2% co2& 2(O( IJK1\M ! B% @"t"#an0an: 2 G/tin00i( Cat( cai#( I/M % O( t"0an0an( 1"#/u'aan( dala/( 1i1a( 'a1il"#( IPQ/M & O( 2udut( 'onta' ! O(/a22a(?"ni2(Cat(cai#(I'0Q/3M 1 G/ 1"#c"1atan( 0#aWita2i( I/Q22M % O( ?a#iA?a#i( 1i1a( 'a1il"#( I/M

Tes Kompetensi Subbab

pipa kapiler

air

raksa

Gambar 6.19 Gejala kapilaritas pada pipa kapiler.

% cos &

% & A

B y

Gambar 6.20 Pada keadaan setimbang, gaya tegangan permukaan di titik A sama dengan di titik B.

A

N,%6"8".3"= ;"3"# $484 3"?7=".( 17

27

37

S"bua&(d#u/(b"#i2i(/in-a'(-an0(/"/ili'i(/a22a(?"ni2 \[[('0Q/3(dan(tin00in-a(152(c/7(="#a1a'a&: a7 t"'anan(&id#o2tati'(1ada(da2a#(d#u/] b7 t"'anan(&id#o2tati'(di(titi'(-an0(b"#ada(1[[(c/ di(ata2(da2a#(d#u/7 S"bua&( 1i1a( b"#b"ntu'( &u#u<( Z( dii2i( d"n0an( ai#7 @"/udian.('a'i(2"b"la&('i#i(dii2i(/in-a'(&in00a(ai# t"#d"2a'(2"?au&(3(c/(da#i('"dudu'an(2"ti/ban0n-a7 Hi'a( !ai# (O(1(0Qc/3.( !/in-a' (O([.\(0Qc/3.(dan(lua2 1"na/1an0(1i1a(O(2(c/2.(&itun0la&(ban-a'(/in-a' -an0(di/a2u''an('"(dala/(1i1a7 >ua(b"?ana(-an0(b"#&ubun0an.(b"#i2i(ai#(dan(#a'2a I ! (O(13.J(0Qc/3M7

air b

2,5 cm B

A air raksa

a7

b7

="#a1a'a&(1an?an0(la?u#(ai#(2u1a-a(?a#a'(anta#a '"dua(1"#/u'aan(#a'2a(dala/(b"?ana(t"#2"but 2.5(c/4 ="#a1a( c/3( al'o&ol( I ! ( O( [.\( 0Qc/ 3M( &a#u2 dituan0'an(di(ata2(#a'2a(a0a#(1"#/u'aan(ai#(nai' 1(c/4(Ilua2(1"na/1an0(b"?ana(O(5(c/2M

Fluida

149

47

8a/ba#(b"#i'ut(/"lu'i2'an(2"bua&(1o/1a(&id#oli'7 F

!"na/1an0('"cil(lua2n-a(O(2[(c/2(dan(lua2(1"na/1an0 b"2a#(O(5[[(c/27(Hi'a(1ada(1"na/1an0(-an0('"cil(dib"#i 0a-a( 1[[( P.( b"#a1a'a&( 0a-a( -an0( b"'"#?a( 1ada 1"na/1an0(b"2a#4

57

S"bua&(balo'(-an0(Wolu/"n-a(4(/3(dan(/a22a(?"ni2n-a O( J[[( '0Q/3.( di/a2u''an( '"( dala/( /in-a'( -an0 /a22a(?"ni2n-a(O(\[[('0Q/37 a7 =a0ai/ana'a&(1o2i2i(b"nda4 b7 Uitun0(Wolu/"(b"nda(1ada(1"#/u'aan(/in-a'7 c7 Uitun0( 0a-a( )#c&i/"d"2( -an0( b"'"#?a( 1ada b"nda(t"#2"but7

B. Viskositas Fluida O"$,3 '(K @o"a#a& !la2/a(da#a& jt&il(al'o&ol Xli(IS)j(1[M 8li2"#in Zda#a Uid#o0"n Za1(ai#

O,#5,%"?4% /PQ1 [ 2[ 1[[ 3^ 3^ 2[ 3[ 2[ 2[ [ 1[[

/+" -1 1.\(`(1[K3 1.[(`(1[K3 [.3(`(1[K3 ) (4(`(1[K3 K3 )(1.5(`(1[ 1.2(`(1[K3 2[[(`(1[K3 175[[(`(1[K3 [.[1\(`(1[K3 [.[[b(`(1[K3 [.[[13(`(1[K3 Sumber: Physics, 1993

9('!"'(5.'(atau('"'"ntalan(/"#u1a'an(0"2"'an(-an0(di/ili'i(ol"&(
1. Hukum Stokes Fluida(id"al(adala&(
IaM

IbM Gambar 6.21

(a) Sebuah kelereng dijatuhkan ke dalam fluida ideal. (b) Sebuah kelereng dijatuhkan ke dalam fluida tak ideal.

150

IJK1bM

@"t"#an0an: 6J O(0a-a(Sto'"2(IPM ( O( 'o"
Mudah dan Aktif Belajar Fisika untuk Kelas XI

!ada( !"#$"% '()K/$1.( 0a-aA0a-a( -an0( b"'"#?a( 1ada( '"l"#"n0( adala& 0a-a(b"#at('"l"#"n0(-an0(dii/ban0i(ol"&(0a-a(Sto'"2(dan(0a-a()#c&i/"d"27 !"n0i/ban0an(0a-a(t"#2"but(t"#u2(b"#lan?ut(2"i#in0(d"n0an(0"#a'('"l"#"n07 !ada(2aat(t"#t"ntu.(0a-a(-an0(b"'"#?a(2"i/ban0(2"&in00a(#"2ultan(2"lu#u&(0a-a t"#2"but( a'an( 2a/a( d"n0an( nol7( Hi'a( b"nda( b"#0"#a'( d"n0an( '"c"1atan /a'2i/u/( -an0( t"ta1.( '"c"1atann-a( ini( di2"but( !&<&$.5.+/ 5&%#(+.*7( S"ca#a /at"/ati2.('"c"1atan(t"#/inal(da1at(ditu#un'an(da#i(#u/u2A#u/u2(b"#i'ut7 * : O([ #B(K(:)(K(:2 O([ :2 O(#B/(K(:)

IJK2[M

FA Fs

w = mg

Gambar 6.22 Gaya-gaya yang bekerja pada kelereng di dalam fluida.

Zntu'( 0a-a( '"( ata2( I)#c&i/"d"2M: :7(O(9) ! f B Zntu'( 0a-a( Sto'"2: :2(O(J ' ( %Kt ="#at(b"nda.(*(O(#B(O( ! ) 9)( B )da1un('"c"1atan(t"#/inal(b"nda(2"t"la&(0a-aA0a-a(-an0(b"'"#?a(2"i/ban0 adala&

K5 !

1K) " !) " ! B # J'( %

IJK21M

Zntu'( b"nda( b"#b"ntu'( bola( d"n0an( ?a#iA?a#i( %( /a'a( Wolu/"( b"nda 4 9b(O( ' % 3 3 Hadi. 1% 2 " ! ) " ! B # 2 K5 ! b (

IJK22M

2"dan0'an( Wi2'o2ita2n-a( adala& %2 1 (!2 " !) " ! B # b K5

IJK23M

@"t"#an0an: ! b O( /a22a( ?"ni2( b"ndaQbola( I'0Q/3M ! f O( /a22a( ?"ni2(
Contoh 6.7 S"bua&('"l"#"n0(-an0(b"#?a#iA?a#i([.5(c/(di?atu&'an('"(dala/(/in-a'(1"lu/a2(-an0 b"#ada(dala/(tabun07(F"ntu'anla&('"c"1atan(t"#/inal(-an0(dica1ai('"l"#"n0.(?i'a /a22a(?"ni2(/in-a'(\[[('0Q/3.('o"
Kata Kunci • gaya stokes • kecepatan terminal • viskositas

Fluida

151

2

"

#

1% 2 " !) " ! B # 2 5 $ 1[ "3 (/ K t O( 2 (O( (`(1[(/Q22(`(I27J[[('0Q/3(K(\[[('0Q/3M b 3.[ $ 1[ "2 (!a 2 b ( O(3.33(/Q2 Hadi.('"c"1atan(t"#/inal('"l"#"n0(adala&(3.33(/Q27

"

Tes Kompetensi Subbab

#

B

N,%6"8".3"= ;"3"# $484 3"?7=".( 17

@"c"1atan(t"#/inal(-an0(dica1ai(ol"&(2"t"t"2(/in-a' I ! # (O(\21.3('0Q/3M(-an0(?atu&(di(uda#a(I !uda#a (O 1.3( '0Q/3M( adala&( [.15( //Q27( Uitun0la&( ?a#iA?a#i t"t"2an(/in-a'(t"#2"but(?i'a(( (O(1.\(`(1[K5('0Q/27

27

Uitun0la&('"c"1atan(/a'2i/u/(I'"c"1atan(t"#/inalM da#i( 2"bua&( bola( ba?a( b"#dia/"t"#( 2( //( -an0 di?atu&'an(dala/(2"?"ni2(/in-a'(I ! (O(bJ5('0Q/3M -an0(/"/ili'i(('o"
C. Fluida Dinamis turbulen laminer

Sumber: Dokumentasi Penerbit

Gambar 6.23 Aliran laminer dan aliran turbulen pada asap rokok.

A

B

D

E

P

Q

X

Y

C F R Z

Gambar 6.24 Garis aliran A–B–C, D–E–F, P–Q–R, dan X–Y–Z merupakan garis aliran laminer.

>ala/( ala/(ala/( "n0an d"/i'ian.( B*0(4./ (4&.*( adala&(
1. Persamaan Kontinuitas

v1 A1 + s1

v2 + s2

A2

Gambar 6.25 Fluida mengalir pada penampang yang berbeda.

152

!"#&ati'an(!"#$"% '()E7(!ada(0a/ba#(t"#2"but.(Cat(cai#(/"lalui(2"bua& 1i1a(1ada(1"na/1an0(71(d"n0an('"c"1atan(ali#an(K1(/"nu?u('"(1"na/1an0 -an0( l"bi&( 2"/1it( 72/ d"n0an( '"c"1atan( ali#an( K27( >"n0an( a2u/2i( ba&3a
Mudah dan Aktif Belajar Fisika untuk Kelas XI

91 O 9 2 71 + ' 1 O 7 2 + ' 2 71IK1 + 5M O 72IK2 + 5M Zntu'( 2"lan0( 3a'tu( -an0( 2a/a.( a'an( di1"#ol"& 71K1(O(72K2

Ingatlah IJK24M

atau L1(O(L2 IJK25M @"t"#an0an: 71 O(lua2(1"na/1an0(1(I/2M 72(O(lua2(1"na/1an0(2(I/2M K1 O('"c"1atan(Cat(cai#(1ada(1"na/1an0(1(I/Q22M K2 O('"c"1atan(Cat(cai#(1ada(1"na/1an0(2(I/Q22M L1 O(71(K1(O(d"bit(Cat(cai#(di(1"na/1an0(1(I/3Q2M L2 O(72(K2(O(d"bit(Cat(cai#(di(1"na/1an0(2(I/3Q2M +,%-"#"". /'0)A1( dan( +,%-"#"". /'0)E1( dina/a'an( $&%'.#..+ !"+5(+0(5.'7

Contoh 6.8 S"bua&(1i1a(-an0(lua2(1"na/1an0n-a(12(c/ (dan(1\(c/ (diali#i(ai#7(!ada(1"na/1an0(-an0 b"2a#.(la?u(ali#an(ai#n-a(adala&(4(/Q27(="#a1a'a&(la?u(ali#an(ai#(1ada(1"na/1an0(-an0('"cil4 C"*"$D >i'"ta&ui: 71(O(1\(c/2(O(1\(`(1[K4(/2 72(O(12(c/2(O(12(`(1[K4(/2 K1(O(4(/Q2 >"n0an(/"n00una'an(1"#2a/aan(d"bit(ai#.(di1"#ol"& 7 1\ $ 1[ "4 K2 O( 1 /K1(O( (`(4(/Q2(O(J(/Q2 72 12 $ 1[ "4 2

2

Aktivitas Fisika 6.3 Persamaan Kontinuitas Tujuan Percobaan Mengamati dan memahami persamaan kontinuitas Alat-Alat Percobaan 1. Dua buah selang yang berdiameter 1 cm atau lebih dengan panjang masingmasing 2 meter 2. Dua buah ember 3. Plastik tebal. Langkah-Langkah Percobaan 1. Tutuplah salah satu ujung selang dengan plastik tebal yang telah dilubangi. Diameter lubang plastik ±0,5 cm. 2. Sambungkan kedua selang pada kran yang aliran airnya sama besar. 3. Jawablah pertanyaan berikut. a. Untuk posisi kedua selang sama, semburan air pada selang manakah yang paling jauh? b. Apa yang akan terjadi jika dalam selang waktu yang sama, setiap air selang dialirkan pada ember yang berukuran sama? 4. Tulislah kesimpulan dari percobaan tersebut. 5. Buatlah Hukum Kontinuitas menurut versi Anda berdasarkan percobaan yang telah Anda lakukan. 6. Bandingkan dengan Hukum Kontinuitas yang sudah Anda pelajari.

Prinsip utama dari persamaan kontinuitas adalah pada selang waktu yang sama, debit fluida akan sama.

Informasi untuk Anda Seorang penyelam pemula sedang menarik napas pada kedalaman L untuk berenang ke atas. Dia mengabaikan instruksi untuk mengeluarkan napas secara perlahanlahan selama menuju ke permukaan. Selama perjalanan ke atas, tekanan udara luar pada tubuhnya berkurang hingga mencapai tekanan atmosfer. Tekanan darahnya juga berkurang sampai normal kembali. Oleh karena ia tidak membuang napas, ketika sampai ke permukaan terdapat perbedaan antara tekanan udara di dadanya dengan di dalam paru-parunya. Perbedaan tekanan ini dapat mengakibatkan paru-parunya pecah. Selain itu, tekanan darahnya turun drastis sehingga udara pun masuk ke dalam jantungnya. Hal ini dapat mengakibatkan kematian bagi penyelam tersebut.

Information for You A novice scuba diver takes enough air from his tank to fully expand his lung at depth L and swimming to the surface. He ignores instructions and fails to exhale during his ascent. As he ascends, the external pressure on him decreases, until it reaches the atmosphere pressure at the surface. His blood pressure also decreases, until it become normal again. However, because he does not exhale the air pressure in his lungs remain at the value it had at depth L. This pressure difference can explode his lungs. Besides that, his blood pressure decrease drastically which then carries the air to the heart. This two things can kill that novice diver. Sumber: Fundamentals of Physics, 2001

Fluida

153

A

2. Hukum Bernoulli B

C

v

Gambar 6.26 Fluida mengalir.

v1 + t p1 A1 v2 + t

h1

!ada( b"?ana( b"#&ubun0an.( 1"#/u'aan( Cat( cai#( 1ada( 2"tia1( t"/1at a'an( 2a/a( tin00i7( Ual( t"#2"but( b"#la'u( 1ada( Cat( cai#( -an0( dia/7( Hadi. ?i'a( Cat( cai#( t"#2"but( b"#0"#a'.( '"adaan( t"#2"but( tida'( a'an( t"#?adi7 !"#&ati'an(!"#$"% '()'7( Hi'a( Cat( cai#( dala/( tabun0( tida'( b"#0"#a' /a'a( tin00i( 1"#/u'aan( Cat( cai#( 1ada( 1i1a( ).( 1i1a( =.( dan( 1i1a( D( a'an 2a/a7( Pa/un.( tin00i( 1"#/u'aan( Cat( cai#( 1ada( 2"tia1( 1i1a( a'an( b"#b"da ?i'a( Cat( cai#( t"#2"but( /"n0ali#( '"( 'anan7 )nda( t"la&( /"n0"ta&ui( ba&3a( '"la?uan( Cat( cai#( 1alin0( b"2a#( t"#da1at 1ada(1i1a(-an0(2"/1it.(na/un(a1a'a&(&al(t"#2"but(b"#la'u(1ula(1ada(t"'ananA n-a4( Zntu'( /"n0"ta&ui( ?a3aban( t"#2"but.( 1"#&ati'an( !"#$"% '()M7 S"ca#a(/at"/ati2.(1"#2a/aan(-an0(/"n00a/ba#'an(ali#an(
p2

0'.8. O(1.2./M(3.%.! ? O(6' G/$7K5

h2

Gambar 6.27 Perbedaan ketinggian fluida mengalir.

Tokoh Daniel Bernoulli (1700–1782)

IJK2JM

Z2a&a( total( -an0( di0una'an( untu'( /"n0ali#'an(
,1 2 1 2$1K1715(K($2K2725O( . 2 #K2 " 2 #K1 / (_(I#182(K(#181M 0 1 1 2 1 $1K1715(_( #K12 (_(#181(O($2K2725(_( #K2 (_(#182 777IllM 2 2 !"#&ati'an(+,%-"#"". /R17(?2(b"#tanda(n"0ati<('a#"na(a#a&(0a-a(62 b"#la3anan( a#a&( d"n0an( a#a&( 0"#a'( "n0an(/"n2ub2titu2i'an(+,%-"#"". /RRR1('"(+,%-"#"". /RR1(a'an di&a2il'an( 1"#2a/aan

Sumber: World Book Encyclopedia

Daniel Bernoulli adalah putra dari Johan Bernoulli, lahir di kota Basel dan bekerja sebagai dosen Matematika di Universitas Basel. Pamannya seorang matematikawan di Universitas tersebut yang pernah menciptakan materi baru dalam teori probabilitas, analisis geometri, dan kalkulus variasi. Bernoulli berhasil menciptakan prinsip hidrodinamika dan perhitungan aliran fluida. Selain itu, Bernoulli sangat berperan dalam mengembangkan teori probabilitas, kalkulus, dan persamaan diferensial.

154

$19/H/ 1 #K12 _(#181(G/$29_ 1 #K22 _(#182 IJK2^M 2 2 Hi'a()nda( /"n2ub2titu2i'an( 9 ! # ('"(+,%-"#"". /'0)M1.( a'an( di1"#ol"& ! $1 # _ 1 #K12 _(#181(O($2 # _ 1 #K22 _(#182 ! 2 ! 2

IJK2\M

@"/udian.( ?i'a( )nda( /"n0ali'an( +,%-"#"". /'0)G1( d"n0an( ! .( a'an di1"#ol"& $1(_( 1 ! K12 _( ! gh 1(O($2(_( 1 ! K22 _( ! 18 2 2 2

IJK2bM

+,%-"#"". /'0)F1( di2"but( ?u0a( >&%'.#..+/ E&%+"0**(.( -an0( 2"ca#a( u/u/ da1at( din-ata'an( d"n0an( 1"#2a/aan( b"#i'ut( ini7

Mudah dan Aktif Belajar Fisika untuk Kelas XI

1 $(_( 2 ! K2 _( ! 18 (O('on2tan

IJK3[M

="#da2a#'an(1"#2a/aan(="#noulli.(di'"ta&ui(ba&3a(t"'anan(di(dala/
3. Penerapan Hukum Bernoulli a. Alat Penyemprot Nyamuk !"#&ati'anla&( !"#$"% '()G( -an0( /"/1"#li&at'an( 2"bua&( alat 1"n-"/1#ot( n-a/u'7( )lat( t"#2"but( /"n00una'an( 1#in2i1( Uu'u/ ="#noulli7( Hi'a( 1"n0i2a1( 1o/1a( dit"'an.( uda#a( a'an( /"n0ali#( d"n0an '"c"1atan( tin00i( dan( '"lua#( /"lalui( luban0( 2"/1it( 1ada( tabun0( uda#a7 @"c"1atan(uda#a(-an0(tin00i(/"n-"bab'an(t"'anan(1ada(1"#/u'aan(1i1a W"ntu#i(/"n?adi(#"nda&7(Ual(t"#2"but(/"n-"bab'an(cai#an(obat(n-a/u'(da1at nai'('"(ata2(/"lalui(1i1a(W"ntu#i(dan(/"n-"/bu#('"lua#(b"#ca/1u#(uda#a7 b. Daya Angkat pada Sayap Pesawat Terbang Fa&u'a&( )nda( -an0( /"n-"bab'an( 1"2a3at( da1at( t"#ban04( !"2a3at da1at( t"#ban0( 'a#"na( adan-a( da-a( an0'at( 1ada( 2a-a17( >a-a(an0'at(1ada 1"2a3at(t"#ban0.(?u0a(/"n00una'an(1#in2i1(Uu'u/(="#noulli7(="ntu'(ba0ian ata2(2a-a1(1"2a3at(-an0(c"/bun0(/"n-"bab'an(adan-a(1"#b"daan(la?u(uda#a 1ada( ba0ian( ata2( dan( ba0ian( ba3a&n-a.( 2"1"#ti( di0a/ba#'an( ol"&( 0a#i2A0a#i2 0a-a(1ada(!"#$"% '()F7()li#an(uda#a(1ada(ba0ian(ata2(2a-a1(b"#0"#a'(l"bi& c"1at( da#i1ada( ba0ian( ba3a&n-a7( E"nu#ut( Uu'u/( ="#noulli.( t"'anan( 1ada ba0ian(ata2(1"2a3at(/"n?adi(l"bi&('"cil(da#i1ada(t"'anan(1ada(ba0ian(ba3a& 2a-a17(!"#b"daan(t"'anan(inila&(-an0(/"/buat(adan-a(0a-a(an0'at('"(ata2. -an0(b"2a#n-a(da1at(dituli2'an(2"ba0ai(b"#i'ut7 61(K(62 O I$1(K($2M(7 1 61(K(62 O I ! K12(K( ! K22M(7 2 1 IJK31M 61(K(62 O 2 ! 7IK22(K(K12M

F

pipa venturi

Gambar 6.28 Alat penyemprot nyamuk.

gaya angkat (F1)

gaya berat (F2)

Gambar 6.29 Garis arus fluida ideal pada sayap pesawat terbang.

="#da2a#'an(+,%-"#"". /'0@K1. da1at(dianali2i2(ba&3a(?i'a(1"2a3at b"#0"#a'( l"bi&( c"1at( /a'a( a'an( /"n0&a2il'an( 0a-a( an0'at( -an0( l"bi& b"2a#( 1ula7( >"n0an( d"/i'ian.( 2"/a'in( lua2( 1"na/1an0( 2a-a1.( 2"/a'in b"2a#( 1ula( 0a-a( an0'atn-a7

Contoh 6.9 S"bua&(1"2a3at(t"#ban0(d"n0an(lua2(1"na/1an0(2a-a1(4[(/2(b"#0"#a'(2"&in00a /"n0&a2il'an(1"#b"daan('"c"1atan(ali#an(uda#a(1ada(ba0ian(ata2(2a-a1(1"2a3at(dan ba0ian(ba3a&n-a.(-an0(/a2in0A/a2in0(b"2a#n-a(24[(/Q2(dan(2[[(/Q27(="#a1a'a& b"2a#(0a-a(an0'at(1ada(2a-a1.(?i'a(/a22a(?"ni2(uda#a(1.3('0Q/34 C"*"$D >i'"ta&ui: 7/O(1[(/2](K2(O(24[(/Q2 K1(O(2[[(/Q2]( ! (O(1.3('0Q/3 1 2 2 61(K(62 O( ! 7 " K2 " K1 # 2 1 O( (`(1.3('0Q/3(`(4[(/2(`(mI24[/Q2M2(K(I2[[/Q2M2n(O(45^7J[[(P 2 Hadi.(0a-a(an0'at(1ada(2a-a1(1"2a3at(t"#2"but(adala&(45^7J[[(P7

Fluida

155

c.

karburator

Sumber: www.firetrucks.uw.hu

Gambar 6.30 Karburator pada motor.

h p1

v1

h1

p2

v2 h2

Karburator @a#bu#ato#( /"#u1a'an( alat( 1"nca/1u#( ba&an( ba'a#( dan( uda#a7 !"nca/1u#an( t"#2"but( b"#tu?uan( untu'( /"/1"#/uda&( 1"/ba'a#an7 @a#bu#ato#( t"#di#i( ata2( tan0'i( 'a#bu#ato#.( 1"la/1un0.( 1i1a( W"ntu#i.( dan 1"n-"/1#ot( uda#a( I+";*&M7( Zda#a( -an0( /a2u'( '"( dala/( 'a#bu#ato# /"/ili'i( '"c"1atan( -an0( tin00i( 2"&in00a( /"n-"bab'an( t"'anan( 1ada u?un0( 1i1a( W"ntu#i( /"n?adi( #"nda&7( F"'anan( -an0( #"nda&( 1ada( u?un0 1i1a( W"ntu#i( /"n-"bab'an( ba&an( ba'a#( cai#( '"lua#( da#i( tabun0( ba&an ba'a#( /"lalui( 1i1a( W"ntu#i( /"nu?u( +";*&7( S"/bu#an( ba&an( ba'a#( cai# -an0(b"#ca/1u#(d"n0an(uda#a(da1at(/"n0&a2il'an(0a2(-an0(di2"but(#.+;&* -an0( b"#2i"/i'ian( 2"t"#u2n-a 2"&in00a( #oda( a'an( b"#0"#a'( 2"i#in0( d"n0an( 0"#a'an( nai'( tu#un( 1i2ton t"#2"but7 d. Pipa Venturi S"lain( di/an"n0an( /"n00una'an &u'u/( ="#noulli.( di1"#ol"& $2 " $1 ! 1 ! " K22 " K12 # 2

Gambar 6.31 Pipa venturi.

IJK32M

>a#i( 1"#2a/aan( 'ontinuita2( di1"#ol"&

71 K1 K2(O( 7 2

IJK33M

Hi'a( +,%-"#"". /'0@@1( di2ub2titu2i'an( '"( +,%-"#"". /'0@)1.( di1"#ol"& ,, 7 - $2 " $1 ! 1 ! K12 . . 1 / " 1 / 2 0 0 72 1 1

IJK34M

Fa/1a'( da#i( !"#$"% '(@L.( 2"li2i&( '"tin00ian( Cat( cai#( 1ada( 1i1a W"ntu#i( adala&( 87( Ual( t"#2"but( di2"bab'an( adan-a( 1"#b"daan( t"'anan +$ 7( E"nu#ut( &u'u/( &id#o2tati'.( 1"#b"daan( t"'anan( t"#2"but( adala& +$ ! ! 18 7( >"n0an( /"/a2u''an( 1"#b"daan( t"'anan( ini( '"( dala/ +,%-"#"". /'0@A1.( di1"#ol"&

218 2

K1(O( , 71 - " 1 .7 / 0 21 @"t"#an0an: K1 O! '"c"1atan( Cat( cai#( -an0( diu'u#( I/Q2M ! O( /a22a( ?"ni2( Cat( cai#( -an0( diu'u#( I'0Q/3M 71 O(lua2(1"na/1an0(1i1a(b"2a#(I/2M 72 O(lua2(1"na/1an0(1i1a('"cil(I/2M 8 O( 1"#b"daan( tin00i( #a'2a( I/M 1 O( 1"#c"1atan( 0#aWita2i( I/Q22M

156

Mudah dan Aktif Belajar Fisika untuk Kelas XI

IJK35M

e. Venturimeter dengan Manometer !"#$"% '(@)(/"nun?u''an(W"ntu#i/"t"#(-an0(dil"n0'a1i(/ano/"t"# dan(dii2i(d"n0an(Cat(cai#(-an0(/"/ili'i(/a22a(?"ni2( ! o7(>"n0an(/"n00una'an 1"#2a/aan(="#noulli.('"c"1atan(
tekanan tinggi tekanan rendah v1 .1

.2

v2

h A

B

Gambar 6.32

IJK3JM

Venturimeter yang dilengkapi manometer.

F"'anan( &id#o2tati'( di( )( O( t"'anan( &id#o2tati'( di( =( 2"&in00a

! 181 ' $1 ! ! o 182 ' $2 $1(K($2(O( ! o 182(K ! 181

IJK3^M

71K1(O(72K2

IJK3\M

!"#2a/aan( 'ontinuita2: >"n0an( /"la'u'an( 2ub2titu2i'an( da#i( +,%-"#"". /'0@M1( dan +,%-"#"". /'0@G1 '"( dala/( +,%-"#"". /'0@'1.( dida1at'an( 1"#2a/aan 218 " ! 2 " ! # K1(O(72( ! 7 " 7 " 1 2#

IJK3bM

@"t"#an0an: K1 O( '"c"1atan( Cat( cai#( -an0( diu'u#( I/Q2M ! o O( /a22a( ?"ni2( #a'2a( I'0Q/3M ! O( /a22a( ?"ni2( Cat( cai#( -an0( diu'u#( I'0Q/3M 71 O(lua2(1"na/1an0(1i1a(b"2a#(I/2M 72 O(lua2(1"na/1an0(1i1a('"cil(I/2M 8 O( 1"#b"daan( tin00i( #a'2a( I/M 1 O( 1"#c"1atan( 0#aWita2i( I/Q22M f.

Pipa Pitot !i1a( 1itot( adala&( alat( untu'( /"n0u'u#( '"la?uan( 0a2( atau( uda#a7 !"#&ati'an(!"#$"% '(@@7(!i1a(1itot(t"#di#i(ata2(1i1a(W"ntu#i(-an0(b"#i2i'an #a'2a7(Z?un0()(t"#bu'a('"(ata2.(2"dan0'an(u?un0(=(t"#bu'a(/"/an?an0 2"a#a&( d"n0an( datan0n-a( uda#a7( !"#b"daan( tin00i( #a'2a( dala/( 1i1a di2"bab'an( ol"&( 1"#b"daan( t"'anan( di( )( dan( =7 )li#an(uda#a(-an0(/a2u'('"(dala/(tabun0(dit"#u2'an('"(dala/(1i1a /"lalui(u?un0(=.(d"n0an('"c"1atan(b"#'u#an0(&in00a(/"nca1ai(nol7(!ada '"adaan(t"#2"but.(t"'anan(di(=(2a/a(d"n0an(t"'anan(di(titi'(>(dan(0a2 dala/( '"adaan( dia/7 >"n0an( /"n00una'an( 1"#2a/aan( ="#noulli.( ( d"n0an( 87( O( 8E( dan '"c"1atan( 0a2( di( =( 2a/a( d"n0an( nol.( a'an( dida1at

aliran gas A

v1

v2

B 2

1

p1 h D

C

Gambar 6.33 Pipa pitot

Fluida

157

$1 ' 1 ! K12 ! $2 2 $2 " $1 ! 1 ! K12 2

IJK4[M

="da(t"'anan(anta#a(titi'(1(dan(titi'(2(I$2(K($1M(2a/a(d"n0an(t"'anan &id#o2tati'( Cat( cai#( di( dala/( /ano/"t"#.( -aitu $2 " $1 ! ! o 18

>"n0an(/"la'u'an(2ub2titu2i(+,%-"#"". /'0AL1('"(+,%-"#"". /'0AK1. di1"#ol"& 1 ! K 2 ! ! o 18 2 1 2! o 18 2 ((((((( K1 ! !

Kata Kunci • • • • • •

K1 !

aliran turbulen aliran laminer hukum Bernoulli manometer persamaan kontinuitas venturimeter

Tes Kompetensi Subbab

IJK41M

2! o 18 2! o 18 K! ! ((atau((( !

IJK42M

@"t"#an0an: K O( '"c"1atan( ali#( 0a2Quda#a( I/Q2M ! o O( /a22a( ?"ni2( ai#( #a'2a( I'0Q/3M ! O( /a22a( ?"ni2( 0a2Quda#a( I'0Q/3M 8 O( 1"#b"daan( tin00i( ai#( #a'2a( I/M

C

N,%6"8".3"= ;"3"# $484 3"?7=".( 17

27

37

158

="#at(2"bua&(1"2a3at(-an0(/"/ili'i(lua2(total(2a-a1 2[(/2(adala&(157[[[(P7(@"c"1atan(ali#an(uda#a(1ada ba0ian( ba3a&( 2a-a1( \[( /Q27( ="#a1a'a&( '"c"1atan ali#an(uda#a(1ada(ba0ian(ata2(2a-a1(?i'a(0a-a(an0'at dina/i'n-a( 2a/a( d"n0an( b"#at( 1"2a3at( t"#2"but4 I1"2a3at(dala/('"adaan(2"i/ban0M7(Ea22a(?"ni2(uda#a 2aat(itu(1.2('0Q/37 S"bua&(ba'(t"#bu'a(b"#i2i(ai#(2"tin00i(5(/7(="#a1a'a& '"c"1atan( '"lua#n-a( ai#( 1ada( 2"bua&( luban0( -an0 t"#l"ta'( di( da2a#( ba'.( ?i'a( lua2( 1"#/u'aan( luban0 t"#2"but([.5(c/24(Uitun0(ban-a'n-a(ai#(-an0(da1at dita/1un0(dala/(3a'tu(1(?a/7 ="#a1a'a&(0a-a('"(ata2(-an0(diala/i(ol"&(2"bua& 1"2a3at(-an0(/"/ili'i(l"ba#(2a-a1(total(15(/2.(?i'a '"c"1atan(ali#an(uda#a(di(ata2(dan(di(ba3a&(2a-a1 J[(/Q2(dan(5[(/Q24(Ea22a(?"ni2(uda#a(1ada('"tin00ian itu(1.1('0Q/37

Mudah dan Aktif Belajar Fisika untuk Kelas XI

47

57

J7

S"bua&(1"2a3at(/"nda1at(t"'anan('"(ata2(2"b"2a# b3.J(PQ/27(Hi'a('"c"1atan(ali#an(uda#a(1ada(ba0ian ata2(2a-a1(1"2a3at(4[(/Q2.(b"#a1a'a&('"c"1atan(ali#an uda#a(1ada(ba0ian(ba3a&(2a-a1(1"2a3at(t"#2"but(?i'a /a22a(?"ni2(uda#a(1.2('0Q/34 !"#b"daan(tin00i(#a'2a(dala/(2"bua&(/ano/"t"#(2uatu W"ntu#i/"t"#(iala&(4(c/7(="#a1a'a&('"c"1atan(ai#(1ada 1"na/1an0(-an0(l"bi&(b"2a#.(?i'a(lua2(1"na/1an0(-an0 b"2a#( dan( '"cil( /a2in0A/a2in0( 5[( c/2( dan( 3[( c/24 >i'"ta&ui(/a22a(?"ni2(#a'2a(13.J(0#Qc/37 @"c"1atan(ali#an(1ada(ba0ian(1i1a(-an0(b"2a#(da#i 2uatu(W"ntu#i/"t"#(2[(c/Q27(="#a1a'a&(1"#b"daan tin00i(#a'2a(I/a22a(?"ni2(13.J(0Qc/3M(1ada(/ano/"t"# ?i'a(1"#bandin0an(anta#a(lua2(1"na/1an0(b"2a#(dan '"cil(adala&(3(:(14

Rangkuman 17

27

F"'anan(/"#u1a'an(b"2a#(0a-a(-an0(b"'"#?a(1ada 2uatu(1"#/u'aan(diba0i(d"n0an(lua2(0a-a7

5! : 7 F"'anan( &id#o2tati'a( /"#u1a'an( t"'anan( -an0 diala/i(Cat(cai#(1ada('"dala/an(t"#t"ntu7(F"'anan &id#o2tati'a(2an0at(di1"n0a#u&i(ol"&(0a-a(0#aWita2i dan('"dala/an(ai#7 5(O ! B8 Uu'u/(!a2cal(/"n-ata'an(ba&3a(t"'anan(-an0 dib"#i'an(1ada(2uatu(Cat(cai#(dala/(#uan0(t"#tutu1 dit"#u2'an(2a/a(b"2a#('"(2"0ala(a#a&7(!#in2i1('"#?a don0'#a'(&id#oli'(dan(1"n0an0'at(&id#oli'(b"'"#?a b"#da2a#'an(Uu'u/(!a2cal7

% ! 6 2! 8"?ala('a1ila#ita2(adala&(1"#i2ti3a(nai'(atau(tu#unn-a 1"#/u'aan(Cat(cai#(/"lalui(luban0Aluban0('"cil(atau 'a1il"#7(Fin00i(Cat(cai#(di(dala/(1i1a('a1il"#(adala& 2(O( J7

61 62 71 O( 7 2 37

47 57

Uu'u/()#c&i/"d"2(b"#bun-i.(b"nda(-an0(t"#c"lu1 '"( dala/(
^7

2% co2 & ! 1%

ci2'o2ita2( atau( '"'"ntalan( adala&( 0"2"'an( -an0 di/ili'i(ol"&(
\7

Fluida

159

Peta Konsep :347;" /"/ba&a2

Fluida(Stati2

Fluida(>ina/i2

/"/ba&a2

dian00a1

F"'anan(Uid#o2tati2

Fluida(gd"al

Uu'u/()#c&i/"d"2 F"0an0an(!"#/u'aan Uu'u/(!a2cal

/"n0&a2il'an

!"#2a/aan(@ontinuita2 !"#2a/aan(="#noulli dia1li'a2i'an( 1ada

@a1ila#ita2

p 8a-a()n0'at(!"2a3at p Fabun0(c"ntu#i p !i1a(!itot

!"#2a/aan(ci2'o2ita2

Refleksi Setelah mempelajari bab ini, Anda tentu dapat mengetahui konsep tekanan pada zat cair,hukum-hukum yang berlaku baik pada zat cair yang diam maupun pada zat cair yang bergerak. Dari materi-materi yang ada pada bab ini, bagian manakah yang menurut Anda paling sulit

160

Mudah dan Aktif Belajar Fisika untuk Kelas XI

dipahami? Coba Anda diskusikan dengan teman atau guru Fisika Anda. Dalam bab ini, dijelaskan pula beberapa manfaat dari konsep yang dibahas. Coba sebutkan manfaat yang Anda peroleh setelah mempelajari materi pada bab ini.

Tes Kompetensi Bab 6 H( +737=3"= -"3"= -"?4 6"*"$". S".B 5"37.B ?,5"? ;". 8,%6"8".3"= 5";" $484 3"?7=".( 17

27

37

47

57

J7

^7

S"'"1in0( /ata( uan0( lo0a/( ?i'a( dic"lu1'an( dala/ (/"/ili'i(lua2 1"na/1an0(^.5(/2(-an0 b"#0"#a'( b"ba2( tan1a 0"2"'an( 2"&in00a( da1at 1 m x /"n"'an(1"0a2(2"?au&(O7 Hi'a(nilai('on2tanta(1"0a2 P O(^75[[(PQ/(dan(/a22a ?"ni2(Cat(cai#(5[[('0Q/3.(1an?an0(O(O(7777 a7 [.4(/ d7 [.^(/ b7 [.5(/ "7 1(/ c7 [.J(/ S"bua&(a'ua#iu/(dii2i(ai#(/"lalui(2"bua&('"#an(-an0 d"bitn-a([.5(lit"#(1"#(2"'on7(F"#n-ata.(ada(luban0(-an0 lua2n-a(1.25(c/2(t"1at(di(da2a#('aca(a'ua#iu/7(Fin00i ai#(/a'2i/u/(dala/(a'ua#iu/(t"#2"but(adala&(7777

a7 2[(c/ d7 \[(c/ b7 4[(c/ "7 1[[(c/ c7 J[(c/ \7 S"bua&(b"nda(t"#a1un0(di(ata2(1"#/u'aan(ai#(-an0 dila1i2i(/in-a'7(S"ban-a'(5[(q(Wolu/"(b"nda(b"#ada di(dala/(ai#.(3[q(di(dala/(/in-a'.(dan(2i2an-a(b"#ada di(ata2(1"#/u'aan(/in-a'7(Hi'a(/a22a(?"ni2(/in-a'(O [.\(0Qc/3.(/a22a(?"ni2(b"nda(t"#2"but(adala&(7777 a7 [.J2(0Qc/3 d7 [.^\(0Qc/3 b7 [.J\(0Qc/3 "7 [.\2(0Qc/3 c7 [.^4(0Qc/3 b7 )i#(/"n0ali#(/"l"3ati(1i1a(W"ntu#i/"t"#(2"1"#ti(1ada 0a/ba#(b"#i'ut(ini7 45 cm

v A1

A2

Hi'a(lua2(1"na/1an0(71(dan(72(/a2in0A/a2in0(5(c/2 dan(4(c/2.(dan(1(O(1[(/Q22.('"c"1atan(ai#(IKM(-an0 /"/a2u'i(1i1a(W"ntu#i/"t"#(adala&(7777 a7 3(/Q2 d7 b(/Q2 b7 4(/Q2 "7 25(/Q2 c7 5(/Q2 1[7 !"#&ati'an(0a/ba#(b"#i'ut(ini7 F"'anan(di(1i1a(1(dan(1i1a 2(b"#tu#utAtu#ut($1(dan($27 h )da1un(K1(dan(K2((/"#u1aA 'an( '"c"1atan( ali#an( ai# 1ada( 1i1a( 1( dan( 27( Hi'a v1 2"li2i&(tin00i(1"#/u'aan(ai# v P2 2 P1 1ada(1i1a(1(dan(2(2"b"2a#(8 dan(/a22a(?"ni2(ai#(2"b"2a#( ! .(di1"#ol"&(&ubun0an(7777 a7 K1(K(K2(O( ! 18 d, $1(_($2((O( ! 18 b7 $1(K($2(O( ! 18 "7 K2(K(K1(O( ! 18 c7 $2(K($1(O( ! 18 117 S"bua&( 1i1a( 'a1il"#( -an0( b"#dia/"t"#( [7JJ( // di/a2u''an(t"0a'(lu#u2('"(dala/(b"?ana(-an0(b"#i2i #a'2a(I/a22a(?"ni2( ! (O13.J2(0Qc/3M7(Sudut('onta' anta#a(#a'2a(d"n0an(1i1a(adala&(143h(I2in(3^h(O([.JM7 Hi'a(t"0an0an(1"#/u'aan(Cat(cai#(adala&([.4\(PQ/. 1"nu#unan( '"tin00ian( #a'2a( dala/( 1i1a( 'a1il"# di&itun0(da#i(1"#/u'aan(Cat(cai#(dala/(b"?ana(I1(O 1[(/Q22M(adala&(7777 a7 12[(c/ d7 2.2^(c/ b7 1.JJ(c/ "7 3.[[(c/ c7 2.[[(c/

Fluida

161

127 S"bua&( lo0a/( b"#b"ntu'( bola( b"#?a#iA?a#i( [.\( c/ b"#0"#a'(W"#ti'al('"(ba3a&(d"n0an('"la?uan(t"ta1 2"b"2a#([.5(c/Q27(Hi'a(/a22a(?"ni2(i'"ta&ui(0a#i2(t"n0a&(t"t"2(ai#(&u?an([.5(//.(/a22a ?"ni2(uda#a(1.3[('0Q/3.(dan('o"i(uda#a.(n"#aca((/"nun?u''an(2'ala(12(P7(S"t"la& b"nda( di/a2u''an( '"( dala/( ai#( I ! ( O( 1( 0Qc/3M. n"#aca( /"nun?u''an( an0'a( \( P7( colu/"( b"nda t"#2"but(adala&(7777 a7 4(`(1[K4(/3 d7 ^(`(1[K4(/3 K4 3 b7 5(`(1[ (/ "7 \(`(1[K4(/3 K4 3 c7 J(`(1[ (/ 157 S"#an00a(da1at(b"#di#i(di(ata2(1"#/u'aan(ai#(a'ibat adan-a(7777 a7 0a-a()#c&i/"d"2 d7 0a-a(#"0an0an b7 0a-a(!a2cal "7 2i
C"*"$3"= 5,%?".S"". $,%784? 7.7 ;,.B". ?,5"?(

17

Suatu(2i2t"/(1"n-"diaan(ai#(&a#u2(/a/1u(/"n-u1lai ai#(2a/1ai(1ada('"tin00ian(5[(/(2"ca#a(t"0a'(lu#u27 ="#a1a'a&(t"'anan(-an0(di1"#lu'an(untu'(/"nca1ai '"tin00ian(t"#2"but4 ="#at(2"bua&(b"nda(di(uda#a(37[[[(P7(Hi'a(diti/ban0 di(dala/(ai#.(b"#atn-a(2[[(P7(@"/udian.(b"nda(t"#2"but diti/ban0(di(dala/(/in-a'(I ! (O([.^(0Qc/3M7 a7 ="#a1a'a&(Wolu/"(b"nda(t"#2"but4 b7 ="#a1a'a&(b"#at(b"nda(di(dala/(/in-a'4 !ada(2"bua&('ola/(-an0(ba0ian(da2a#n-a(b"#u'u#an [.5(`(1(/(dituan0'an(2(/3(ai#(I ! (O(1(0Qc/3M7 a7 ="#a1a'a&(tin00i(ai#(di(dala/('ola/(itu4 b7 ="#a1a'a&(0a-a(-an0(b"'"#?a(1ada(da2a#('ola/4 c7 ="#a1a'a&(0a-a(-an0(b"'"#?a(1ada(2"tia1(dindin0 'ola/4

27

37

162

Mudah dan Aktif Belajar Fisika untuk Kelas XI

1^7 S"bua&(1"2a3at(t"#ban0(d"n0an(lua2(1"na/1an0(2a-a1 2[( /2( b"#0"#a'( 2"&in00a( /"n0&a2il'an( 1"#b"daan '"c"1atan(ali#an(uda#a(1ada(ba0ian(ata2(2a-a1(1"2a3at dan(ba0ian(ba3a&n-a.(/a2in0A/a2in0(b"2a#n-a(25[(/Q2 dan(2[[(/Q27(="2a#n-a(0a-a(an0'at(1"2a3at(?i'a(/a22a ?"ni2(uda#a(1.3('0Q/3(adala&(7777 a7 2b2.5(P d7 2b275[[(P b7 27b25(P "7 27b257[[[(P c7 2b725[(P 1\7 rua2(1"na/1an0('"#an(1ada(2"bua&(ba'(adala&(4(c/27 >ala/(1[(d"ti'.(ai#(-an0(t"#ta/1un0(di(ba'(t"#2"but adala&(1[[(lit"#7(@"c"1atan(#ataA#ata(ai#(-an0('"lua#(da#i '"#an(t"#2"but(adala&(7777 a7 5(/Q2 d7 2[(/Q2 b7 1[(/Q2 "7 25(/Q2 c7 15(/Q2 1b7 !"#&ati'an(0a/ba#(b"#i'ut7

h1 h2

A

C

Hi'a(81(O(1.J(/./82(O([.\(/.(dan(ai#(?atu&(di(D.(?a#a' anta#a(titi'()(dan(D(O(777(/ a7 1.J d7 2.2 b7 1.\ "7 2.4 c7 2.[ 2[7 S"bua&(1i1a(-an0(lua2(1"na/1an0n-a(/a2in0A/a2in0 1[(c/2( dan( 1J( c/2( diali#i( ai#7( ra?u( ali#an( ai#( 1ada 1"na/1an0(-an0(b"2a#(adala&(5(/Q2.(la?u(ali#an(1ada 1"na/1an0(-an0('"cil(adala&(7777 a7 [.3125(/Q2 d7 312.5(/Q2 b7 3.125(/Q2 "7 3125(/Q2 c7 31.25(/Q2 47

57

!"#b"daan(tin00i(ai#(#a'2a(dala/(/ano/"t"#(2"bua& W"ntu#i/"t"#(adala&(5(c/7(Hi'a(lua2(1"na/1an0(1i1a b"2a#(1[[(c/2(dan(1i1a('"cil(1(c/2..( ! ai#(O(1[3('0Q/3. dan(/a22a(?"ni2(ai#(#a'2a(13.J(`(1[3('0Q/3(.(1(O(1[(/(Q22. &itun0la&('"c"1atan(ali#an(ai#(2aat(itu7 S"bua&('ola/(d"n0an(Wolu/"(5(/3(dala/('"adaan 'o2on0(diali#i(ai#(l"3at(2"lan0(1la2ti'(-an0(b"#1"na/1an0 4(c/27(Hi'a(ai#(/"n0ali#(d"n0an('"c"1atan(1[(/Q2.(2"t"la& b"#a1a(d"ti''a&('ola/(t"#2"but(1"nu&4

Bab

7 Sumber: www.dailytimes.com.pk

Balon udara dapat terbang karena di dalamnya berisi udara panas yang lebih ringan daripada udara di sekitarnya.

Teori Kinetik Gas Hasil yang harus Anda capai: menerapkan konsep termodinamika dalam mesin kalor. Setelah mempelajari bab ini, Anda harus mampu: mendeskripsikan sifat-sifat gas ideal monoatomik.

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

A. Gas Ideal B. Prinsip Ekuipartisi Energi C. Kecepatan Efektif Partikel Gas

163

Tes Kompetensi Awal Sebelum mempelajari konsep Teori Kinetik Gas, kerjakanlah soal-soal berikut dalam buku latihan. I4 ?"#/26(,&>1,21%&-(*&+(,-&2")'(3(2&'$&(281*<")?&73(= V4 Q",-(3(&#(.1,&/'()(&'(3(2&2")#(,-?&@(-($8(,(&>()( 6(%&-(*&2")*"#/2&2")8(*/6&-(*&$'"(.? 8",-",'(.$6(,&#(.1,&/'()(&(-()&'(3(2&#")-")(6&,($60 K4 73(6(%&+(,-&'$8(6*/'&'",-(,&81.()$2(*&-(*? 2/)/,0&'(,&#")#".16? W4 73(&3",-")2$(,&'()$&",")-$&'(.(8&-(*?

A. Gas Ideal 5(%/6(%& 7,'(& +(,-& '$8(6*/'& '",-(,& -(*& $'"(.?& @(-($8(,(6(% #",2/6&'()$&3")*(8((,&-(*&$'"(.?&A,2/6&8",-"2(%/$,+(0&3".(9()$.(%&/)($(, #")$6/2& *">()(& *(6*(8(4

1. Pengertian Gas Ideal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

y l A x

z

Gambar 7.1 Gerak arah partikel-partikel gas dalam ruang tertutup.

tekanan (p)

2. Persamaan Gas Ideal Robert Boyle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

p2

100 K isotermal

p1 V1

V2

volume (V)

Gambar 7.2 Grafik hubungan tekanan (p) terhadap volume (V) pada suhu konstan.

164

HLMIO

S"2")(,-(,T ! R&2"6(,(,&HFU8K&(2(/&;(O " R&P1./8"&H8VO Persamaan (7–1)& '$6",(.& *"#(-($& E/6/8& @1+."& '(,& #").(6/& /,2/6 %(83$)&*"8/(&-(*&'",-(,&6")(3(2(,&)",'(%4&C)(<$6&%/#/,-(,&(,2()(&2"6(,(, '(,& P1./8"& -(*& 2(83(6& 3('(& Gambar 7.24& D$6(& 2"6(,(,& '$2/)/,6(,0 P1./8"& -(*& (6(,& ,($64& ?"#(.$6,+(0& 9$6(& 2"6(,(,& -(*& '$,($66(,0& P1./8" -(*& (6(,& 8",-">$.0& '",-(,& *+()(2& */%/& -(*& 2"2(34

Mudah dan Aktif Belajar Fisika untuk Kelas XI

Charles&HILWJMIXKVO&'(,&Joseph Gay Lussac&HILLXMIXYZO&8".(6/6(, 3",-(8(2(,&'",-(,&3")>1#((,&2",2(,-&%/#/,-(,&(,2()(&*/%/&'(,&P1./8" 3('(& 2"6(,(,& 2"2(34& Q")"6(& 8",-(2(6(,0& 9$6(& 2"6(,(,& -(*& '(.(8& )/(,2")2/2/3& '$9(-(& 61,*2(,0& P1./8"& -(*& *"#(,'$,-& '",-(,& */%/& 8/2.(6,+(4 ?">()(& 8(2"8(2$*0& '$,+(2(6(,& '",-(,& 3")*(8((, " " " &R&61,*2(,&&&&&(2(/&&&&& I &R& K $ $I $K

HLMKO

S"2")(,-(,T "&R&P1./8"&H8VO $&R&*/%/&8/2.(6&H%O

Tokoh Joseph Louis Gay Lussac (1778–1850)

D$6(&*/%/&-(*&#$(*(,+(&'$,+(2(6(,&'(.(8& t[\0&*/%/&8/2.(6&$&8",-= -/,(6(,& *(2/(,& S".P$,& HSO& '$,+(2(6(,& '",-(,& 3")*(8((, $&R&t&]&KLV

HLMVO

\%()."*& '(,& C(+& !/**(>& 9/-(& #")%(*$.& 8",+".$'$6$& %/#/,-(,& (,2()( */%/&'(,&2"6(,(,&3('(&P1./8"&2"2(34&S"'/(,+(&8",-(2(6(,0&9$6(&P1./8" -(*& +(,-& #")('(& '(.(8& )/(,-& 2")2/2/3& '$9(-(& 61,*2(,0& 2"6(,(,& -(* *"#(,'$,-& '",-(,& */%/& 8/2.(6,+(4& ?">()(& 8(2"8(2$*0& '(3(2& '$,+(2(6(, '",-(,& 3")*(8((, !I !K ! R&61,*2(,&&&&&(2(/&&&& $ &R& $ HLMWO $ I K @")'(*()6(,& Persamaan& (7–2O& '(,& (7–4)0& 3('(& 6")(3(2(,& )",'(%0 %(*$.& 6(.$& !"& *"#(,'$,-& '",-(,& 2"83")(2/)& $0& *"*/($& '",-(,& 3")*(8((, !" !' &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&!"&R&'$&&&&(2(/&&& HLMYO $ '",-(,& '& ('(.(%& 61,*2(,2(& 6"*"#(,'$,-(,& +(,-& *"*/($& '",-(,& *(2/ 8(>(8& -(*& 2")2",2/4 D$6(& $,'"6*& I& '$-/,(6(,& /,2/6& ,$.($& !0& "0& '(,& $& (G(.0& *"'(,-6(, $,'"6*& K& '$-/,(6(,& /,2/6& ,$.($ !0& "0& '(,& $& (6%$)0& '$3")1."%& 3")*(8((, #")$6/24 !I "I !K "K ! HLMJO $I $K Persamaan&(7–5)&'(,&(7–6)&'$*"#/2&3")*(8((,&Hukum Boyle-Gay Lussac4 E/6/8& @1+."=C(+& !/**(>& #").(6/& /,2/6& -(*& $'"(.& +(,-& 8(**(& '(, 9/8.(%&81.&-(*,+(&2"2(34&D$6(&8(**(&'(,&9/8.(%&81.&-(*,+(&2$'(6&2"2(30 3")*(8((,& 6"('((,& -(*& $'"(.& #")/#(%& 8",9('$

!" &R&'&'",-(,&'&R&() $ !" ! () &(2(/&!"&R&(#)#$ $

HLMLO

Sumber: Jendela Iptek 3, 1997

Ia dilahirkan di Prancis tahun 1778. Setahun setelah lulus dari politeknik Paris, ia ditawari pekerjaan oleh Claude-Louis Berthollet, kimiawan Prancis yang terkemuka. Berthollet memiliki laboratorium sendiri dan memimpin sekelompok ilmuwan muda di daerahnya. Gay Lussac mengadakan banyak riset bersama Berthollet dan Pierre Simon Laplace, dua ilmuwan yang dibiayai dan dilindungi oleh Napoleon Bonaparte. Gay-Lussac selamat dari arus revolusi Prancis, tetapi ayahnya tertangkap dan dipenjarakan. Pada 1802, ia mengulangi percobaan Alexander Cesar Charles. Ia menemukan fakta bahwa jika gas dipanaskan pada suhu tetap, volumenya akan bertambah sebanding dengan suhu mutlak. Jika suhunya dinaikkan dua kali lipat, volumenya akan meningkat dua kali. Hukum ini kali pertama ditemukan oleh Charles. Akan tetapi, karena Charles tidak mempublikasikannya, hukum tersebut kadang-kadang disebut hukum Charles, kadangkadang disebut Hukum Gay-Lussac.

S"2")(,-(,T (&R&9/8.(%&81.&-(* )&R&X0VIW&DU81.S&H2"2(3(,&/8/8&-(*O D/8.(%&81.&-(*&H(O&8")/3(6(,&3")#(,'$,-(,&(,2()(&8(**(&-(*&'",-(, 8(**(&81."6/.&)".(2$<,+(&H*O4&?">()(&8(2"8(2$*0&9/8.(%&81.&-(*&H(O&'(3(2 '$,+(2(6(,& '",-(,& 3")*(8((, (&R& + &&&&&(2(/&&&&&+&R&(* *

HLMXO

Teori Kinetik Gas

165

D$6(& Persamaan (7–8)& '$*/#*2$2/*$6(,& 6"& '(.(8& Persamaan (7–7)0 (6(,& '$3")1."%& 3")*(8((,& #")$6/24 !"&R&

V (m3)

HLMNO

B()$&Persamaan (7–9)0&'(3(2&'$2",2/6(,&8(**(&9",$*&H " O&*/(2/&-(*0 +($2/ + ,* " R& &R& HLMIZO " )$

p1 p2

p3

T (K)

?".($,& '(3(2& '$,+(2(6(,& '(.(8& 9/8.(%& 81.0& 3")*(8((,& /8/8& -(* $'"(.& 9/-(& '(3(2& '$,+(2(6(,& '(.(8& 9/8.(%& 3()2$6".& -(*& 2")*"#/2& HNO4 D/8.(%&3()2$6".&-(*&8")/3(6(,&%(*$.&6(.$&9/8.(%&81.&-(*&2")*"#/2&'",-(, #$.(,-(,& 7P1-)('14 N&R&(N7

Gambar 7.3 Grafik hubungan volume (V) terhadap suhu mutlak (T) secara isobarik dengan p1 > p2 > p3. p (Pa)

+ #)$ *

V1 V2

V3

T (K)

Gambar 7.4 Grafik hubungan tekanan (p) terhadap suhu mutlak secara isokhorik dengan V 1 > V2 > V 3.

Ingatlah Pada suhu kamar dan tekanan tertentu, gas dapat memiliki sifat yang mendekati gas ideal.

N (&R& N

.

HLMIIO

D$6(&Persamaan& (7–11)& '$*/#*2$2/*$6(,& 6"& '(.(8& Persamaan& (7–7)0 (6(,& '$3")1."%& 3")*(8((,& #")$6/24 N !"&R& N &)$ . D$6(& /& R& ) 0& 3")*(8((,& 2")*"#/2& 8",9('$ N. !"&R& N/$ HLMIKO S"2")(,-(,T N R& 9/8.(%& 3()2$6".& -(* N 7 R&#$.(,-(,&7P1-(')1&R&J0ZKV&^&IZKV&81."6/.U81. / R&2"2(3(,[email protected]`8(,&R&I0VX&^&IZMKV&DUS

Contoh 7.1 ?(2/&81.&-(*&8","83(2$&P1./8"&I&8V&'(,&*/%/&-(*&3('(&*((2&2")*"#/2&('(.(%&IKL[\4 5",2/6(,.(%&2"6(,(,&-(*&2")*"#/24 Jawab: B$6"2(%/$T (&R&I&81. )&R&X0VIW&DU81.S "&R&I&8V $#R&IKL&[\&R&HIKL&]&KLVO&R&WZZ&S B",-(,&8",--/,(6(,&3")*(8((,& !#"&R&(##)#$0&'$3")1."% !HI&8VO&R&HI&81.OHX0VIW&DU681.SOHWZZ&SO& !#!&R&V0VKJ&^&IZV&FU8K D('$0&2"6(,(,&-(*&2")*"#/2&('(.(%& !&R&V0VKW&^&IZV&FU8K4

Contoh 7.2 ?(2/&.$2")&-(*&8"8$.$6$&2"6(,(,&I&(28&3('(&2"83")(2/)&MKV[\4&@")(3(6(%&2"6(,(, -(*&2")*"#/2&9$6(&P1./8",+(&8",9('$&Z0Y&.$2")&'(,&2"83")(2/),+(&8",9('$&LL[\? Jawab: B$6"2(%/$T $I&R&HMKV&]&KLVO&R&KYZ&S_&"K&R&Z0Y&.$2") $K&R&HLL&]&KLVO&R&VYZ&S_&!I&R&I&(28 "I&R&I&.$2")

166

Mudah dan Aktif Belajar Fisika untuk Kelas XI

B",-(,&8",--/,(6(,&Persamaan (7–6)0&'$3")1."% !K #Z0 Y&! $ #I&(28 $#I&! $ !I"I !K "K !& &R& ! VYZ&S KYZ&S $I $K !K&R&K0X&(28 D('$0&2"6(,(,&-(*&2")*"#/2&('(.(%&K0X&(284

Contoh 7.3 ?"#/(%&2(#/,-&+(,-&P1./8",+(&I&.$2")&8"8$.$6$&./#(,-&+(,-&8"8/,-6$,6(,&/'()( 6"./()& '()$& 2(#/,-4& Q/.(=8/.(& */%/& /'()(& '(.(8& 2(#/,-& ('(.(%& KL[\4& 5(#/,'$3(,(*6(,&%$,--(&*/%/,+(&8",9('$&IKL[\4&5",2/6(,&3")#(,'$,-(,&(,2()(&8(**( -(*&+(,-&6"./()&'()$&2(#/,-&'(,&8(**(&(G(.,+(4 Jawab: 5(#/,-
>1)&*"%$,--(&2"6(,(,&2$'(6&#")/#(%&H!&61,*2(,O&8"*6$3/,&'$3(,(*6(,4 $I&R&KL&]&KLV&R&VZZ&S0&$K&R&IKL&]&KLV&R&WZZ&S !" * I + " '",-(,&8",--/,(6(,&3")*(8((,&!#"&R &)#$&(2(/&+&R& * ) $ !" * I B(.(8&%(.&$,$0&& &61,*2(,&*"%$,--(&&+& # ) $ D$6(&'$8$*(.6(,&8(**(&(G(.&-(*&R&+I&'(,&8(**(&(6%$)&-(*&'(.(8&2(#/,-&('(.(%&+K0 '(3(2&'$2/.$* +K $ &R& I R& VZZ&S &&&(2(/#+K&R& V +I4 +I $K WZZ&S W a."%&6()",(&8(**(&-(*&+(,-&2")*$*(&+K&R& V +I0&#")()2$&2".(%&6"./()&-(*&*"#(,+(6& $ +0 W I +($2/& $ +&R#+K&M&+I&R& +I4 W B",-(,&'"8$6$(,0&3")#(,'$,-(,&(,2()(&8(**(&-(*&+(,-&6"./()&'(,&8(**(&-(*&&(G(.,+( ('(.(%&&

Kata Kunci • gas ideal • jumlah mol

$+ &R& I 4 +I W

Tes Kompetensi Subbab

A

Kerjakanlah dalam buku latihan. I4 ?(2/&81.&-(*&8","83(2$&P1./8"&KZZ&'8V4&?/%/&-(* 3('(&*((2&$2/&IKL[\4&5",2/6(,.(%&2"6(,(,&-(*&2")*"#/24 K4 ?(2/& .$2")& -(*& 3('(& 2"6(,(,& I& (281*<")& 8"8$.$6$ 2"83")(2/)&KL[\4&@")(3(6(%&2"6(,(,&-(*&2")*"#/2&9$6( P1./8",+(&'$/#(%&8",9('$&Z0Y&.$2")&'(,&2"83")(2/)= ,+(&8",9('$&LL[\? V4 @")(3(6(%&P1./8"&X&-)(8&-(*&%".$/8&3('(&*/%/&IY[\ '(,&2"6(,(,&&WXZ&88E-?&H*)&R&W&6-U681.O

W4

?"#/(%&2(,-6$&/'()(&+(,-&#")$*$&KZ&6-&/'()(&3('(&2"6(,(, N&(28&'$*$83(,&'$&2"83(2&+(,-&#")*/%/&J[\4&;('(&*((2 '$3$,'(%6(,& 6"& #",-6".& +(,-& #")*/%/& VL[\0& 6(2/3 3",-(8(,&3('(&2(,-6$&8"8#"#(*6(,&*"9/8.(%&/'()(4 D$6(&6(2/3&#"6")9(&6"2$6(&/'()(&'(.(8&2(#/,-&8"."#$%$ N0Y&(280&2",2/6(,&8(**(&/'()(&+(,-&'$#"#(*6(,?

B. Prinsip Ekuipartisi Energi ;('(&#(%(*(,&*"#"./8,+(0&2".(%&'$9".(*6(,&#(%G(&*"2$(3&3()2$6".&-(* $'"(.&*".(./&#")-")(6& *"%$,--(& 8",-%(*$.6(,& ",")-$& 6$,"2$64& a."%&6()",( *$<(2& -(*& $'"(.& '$2$,9(/& *">()(& 6"*"./)/%(,0& ",")-$& 6$,"2$6& *"2$(3& 3()2$6".= ,+(& 8")/3(6(,& ",")-$& 6$,"2$6& )(2(=)(2(4& E(.& 2")*"#/2& 8",+"#(#6(, 2$8#/.,+(& 3)$,*$3& "6/$3()2$*$& ",")-$4

Teori Kinetik Gas

167

1. Tekanan Gas dalam Ruang Tertutup

y !

dinding A

z

m0

vx

! dinding B

x

Gambar 7.5 Tanda panah menyatakan momentum sebuah molekul setelah menumbuk dinding.

;")%(2$6(,& Gambar 7.54& ?/(2/& -(*& $'"(.& 2")6/)/,-& '(.(8& *"#/(% 6/#/*& +(,-& 8"8$.$6$& 3(,9(,-& )/*/6& ! 4& ?"#/(%& 3()2$6".& '()$& -(*& $'"(. 2")*"#/2& #")-")(6& '(.(8& ()(%& */8#/-0& '",-(,& 6">"3(2(,& 1 0 & '(, 8".(6/6(,& -")(6& #1.(6=#(.$6& '()$& '$,'$,-& 7& 6"& '$,'$,-& @0& 6"8/'$(, 6"8#(.$&.(-$&6"&'$,'$,-&74&D()(6&+(,-&'$2"83/%&3()2$6".&2")*"#/2&('(.(% K ! 4&S">"3(2(,&*".(8(&#")-")(6&*".(./&*(8(&6()",(&2/8#/6(,&+(,-&2")9('$ (,2()3()2$6".& '(,& '$,'$,-& '$(*/8*$6(,& *"#(-($& 2/8#/6(,& .",2$,-& *"8= K!

3/),(4& b(62/& 2"83/%& 3('(& -")(6& #1.(6=#(.$6& 2")*"#/2& ('(.(%& t& R& 1 0 0 *"'(,-6(,& #(,+(6,+(& 2/8#/6(,& 3")& *(2/(,& G(62/& +(,-& '$#/(2& 1."% 1 3()2$6".& '(,& '$,'$,-& @& ('(.(%& 0 4& 7'(3/,& 3")/#(%(,& 818",2/8& +(,K! '$(.(8$& 81."6/.& '(3(2& '$2/.$*6(,& *"#(-($& #")$6/24 &&&&&&&&&&&&&&3")/#(%(,&818",2/8&R&818",2/8&(6%$)&M&818",2/8&(G(. $p &R&M+3v0&M&+3v0 $p R&MK&+3v0

Tantangan untuk Anda

HLMIVO

5(,'(& ,"-(2$<& 3('(& 818",2/8& (6%$)& 3()2$6".& 8",/,9/66(,& ()(% -")(6&3()2$6".&*"2".(%&2/8#/6(,0&+(,-&#").(G(,(,&()(%&'",-(,&()(%&-")(6 (G(.,+(4& B()$& 3")*(8((,& 3")/#(%(,& 818",2/8& 2")*"#/20& '(3(2& '$>()$ -(+(& +(,-& #"6")9(& 3('(& 3()2$6".0& +($2/& 3")/#(%(,& 818",2/8& +(,'$3$,'(%6(,& 1."%& 3()2$6".& 6"& '$,'$,-& 3")& *(2/(,& G(62/4 $p F R& $t %K+ 3 v 0 F R& K! 10 %+3 v 0K F R& HLMIWO ! ;('(& 6",+(2((,,+(0& 3()2$6".& +(,-& 8",/8#/6& '$,'$,-& 2$'(6& %(,+( *(2/& 3()2$6".0& 2"2(3$& *"9/8.(%& N& 3()2$6".4& a."%& 6()",(& $2/0& -(+(& +(,'$2")$8(& '$,'$,-& (6$#(2& 2/8#/6(,& N& 3()2$6".& ('(.(%

% N +3 v 0K F0&R& !

Sumber: Fundamentals of Physics, 2001

Pernahkah Anda minum minuman bersoda? Ketika Anda membuka tutup botolnya, akan terbentuk kabut tipis di sekitar tutup botol tersebut. Mengapa hal ini terjadi?

HLMIYO

5(,'(&,"-(2$<&3('(&Persamaan (7–15)&%(,+(&8",/,9/66(,&()(%&-(+(,+( *(9(4&D$6(&7,'(&%(,+(&$,-$,&8",-"2(%/$&#"*(),+(0&2(,'(&,"-(2$<&2")*"#/2&'(3(2 '$%$.(,-6(,4& A,2/6& 8",-"2(%/$& 2"6(,(,& +(,-& '$(.(8$& '$,'$,-& 2(#/,-0 3")*(8((,& 2")*"#/2& '$#(-$& '",-(,& ./(*& 3")8/6((,& 6/#/*& H7O4& E(.& 2")*"#/2 '$6()",(6(,& 2"6(,(,& 8")/3(6(,& 3")/#(%(,& 818",2/8& +(,-& '$3$,'(%6(, 1."%&*"9/8.(%&3()2$6".&6"&'$,'$,-&3")&*(2/(,&G(62/&/,2/6&*"2$(3&*(2/(,&./(*4 N +3 v 0 K F p0&R& 0 &R& . !. a."%& 6()",(& !. R& P1./8"& H"O0& (6(,& '$'(3(26(,& 3")*(8((, N +3 v 0K HLMIJO " p0& ('(.(%& 2"6(,(,& 3('(& '$,'$,-& /,2/6& */8#/-04& B",-(,& >()(& +(,*(8(0& 2"6(,(,& -(*& 3('(& '$,'$,-& 2"-(6& +(,-& *"()(%& */8#/-2& '(,& */8#/-3 '$)/8/*6(,& *"#(-($& #")$6/24

p0&R&

168

Mudah dan Aktif Belajar Fisika untuk Kelas XI

N+3 v 2K N+3 v 3 K &&'(,&&p`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p2&R&

'(.(8& #",2/6& ",")-$& 6$,"2$6& )(2(=)(2(& # 6/ $ & '()$& 3()2$6".& -(*0& +($2/ E /&R& I #+3 v K K +3 v K&R&K&6/ D('$0

! R& K N 6/ V "

HLMIXO

S"2")(,-(,T& 6/ R& ",")-$& 6$,"2$6& )(2(=)(2(& *(2/& 3()2$6".& -(*& H91/."O4

Contoh 7.4 D$6(&6">"3(2(,&3()2$6".&-(*&8",9('$&'/(&6(.$&6">"3(2(,&*"8/.(0&2",2/6(,.(%&#"*(),+( 2"6(,(,&+(,-&'$%(*$.6(,4 Jawab: K I N+ ! 1 E/#/,-(,&2"6(,(, H!O&2")%('(3&6".(9/(,&H1O&('(.(%&!&R& V " K a."%&6()",(&,$.($&I N+ &61,*2(,0&,$.($&!&*"#(,'$,-&'",-(,& 1 &&*"%$,--( V " K !K 1KK #K1I $ ! ! !W !I 1IK 1I D('$0&2"6(,(,&-(*&8",9('$&"83(2&6(.$&2"6(,(,&*"8/.(4

Contoh 7.5 ?"#/(%&2(#/,-&'",-(,&P1./8"&Z0V&8V&8",-(,'/,-&K&81.&E".$/8&3('(&*/%/&KL[\4 B",-(,&8",-(,--(3&E".$/8&*"#(-($&-(*&$'"(.0&2",2/6(,T (4 ",")-$&6$,"2$6&-(*&E".$/8_ #4 ",")-$&6$,"2$6&)(2(=)(2(&*"2$(3&81.&-(*&E".$/8&2")*"#/24 Jawab: (4 B$6"2(%/$T P1./8"&2(#/,-&"&R&Z0V&8V_&&&&&(&R&K&81. $#R&HKL&]&KLVO&S

Teori Kinetik Gas

169

Pembahasan Soal Sebuah ban sepeda memiliki volume 100 cm3. Tekanan awal dalam ban sepeda adalah 0,5 atm. Ban tersebut dipompa dengan suatu pompa yang volumenya 50 cm3. Jika diasumsikan temperatur tidak berubah, tekanan dalam ban sepeda setelah dipompa 4 kali adalah .... a. 0,1 atm d. 4,5 atm b. 2,5 atm e. 5,0 atm c. 4,0 atm Soal Tes ITB Tahun 1975 Pembahasan: Volume ban = V1 = 100 cm2 p1 = 0,5 atm V2 = 4 × 50 cm3 = 200 cm3 p2 = 76 cmHg = 1 atm Setelah pemompaan ban selesai maka akan berlaku: pban Vban = p1V1 + p2V2 pban

= =

p1V1 + p2V2 Vban #0,5 atm$#100 cm3 $ + #1atm$#200 cm3 $ 100 cm3

= 2,5 atm. Jadi, tekanan ban setelah dipompa sebesar 2,5 atm. Jawaban: b

#4

B",-(,&8",--/,(6(,&Persamaan (7–18)0&'$3")1."% KN V V 6 &(2(/&N 6/ R& &!"& ! N 6/ R& (#)$ !&R& V" / K K V N 6/ R& HK&81.O&HX0VIW&DU81.SO&HVZZ&SO&R&L4WXK0J&D K D('$0&",")-$&6$,"2$6&212(.&-(*&('(.(%&L4WXK0J&91/."4 D/8.(%&81."6/.&-(*&('(.(%&N&R&(&N7 N&R&HK&81.O&HJ0ZKV&^&IZKV&81."6/.U81.O&R&IK0ZWW&^&IZKV c,")-$&6$,"2$6&)(2(=)(2(&*"2$(3&81."6/.&('(.(% L4WXK0J&D ! J0KV " IZ %KI &91/."4 6/ ! N6 / ! N IK0ZWW " IZKV A,2/6&6(*/*&P1./8"&-(*&2$'(6&'$3")%$2/,-6(,4

2. Energi Kinetik dan Energi Dalam Gas B(.(8&2$,9(/(,&8$6)1*613$*0&3()2$6".=3()2$6".&'(.(8&-(*&*".(./&#")-")(6 *"%$,--(&3()2$6".=3()2$6".&2")*"#/2&8"8$.$6$&",")-$&6$,"2$64&;")*(8((,&",")-$ 6$,"2$6& 3('(& 3()2$6".& -(*& $'"(.& '(3(2& '$2/)/,6(,& *"#(-($& #")$6/24 !" R& N/$ I ! R& &+1K& N V " ?/#*2$2/*$& '()$& 6"'/(& 3")*(8((,& 2")*"#/2& (6(,& 8",-%(*$.6(,& 3")= *(8((,& #")$6/24 I N/$ R& +1K& N " V " I K +1 R#/$ V K I K # +1 R&/$ V K I #+1K R& K &/$ V K

# $

# $

#

$

V &/$ HLMINO K Q/,>/.,+(& <(621)& 3",-(.$& V& 3('(& Persamaan (7–19)& '$*"#(#6(,& 1."% 3")*(8((,& )(2(=)(2(& 61831,",& P"621)& 6">"3(2(,4 '",-(,&&&&&&&&10&R&12&R&13 1K&R&10K&]&12K&]&13K 1K&R&V10K4

6/ R&

a."%&6()",(&$2/0&<(621)&3",-(.$&V&#")6($2(,&'",-(,&'")(9(2&6"#"#(*(, -")(6& 3()2$6".& +(,-& #")2)(,*.(*$& 6"& ()(%& */8#/-00& 20& '(,& 34& Persamaan (7–19)&#").(6/&/,2/6&-(*&81,1(218$6&+(,-&#")2"6(,(,&)",'(%4&\1,21% -(*& 81,1(218$6& ('(.(%& %".$/8& HE"O0& ,"1,& HF"O0& '(,& ()-1,& H7)O4 A,2/6&-(*&'$(218$60&*"3")2$&EK0&aK0&'(,&FK0&3('(&*/%/&'(,&2"6(,(, V )",'(%& ",")-$& 6$,"2$6,+(& & /$4& 76(,& 2"2(3$0& #")'(*()6(,& "6*3")$8",0 K Y '$'(3(26(,& #(%G(& 3('(& */%/& *"'(,-& ",")-$& 6$,"2$6,+(& *"#"*()& & /$4 K L ;('(& */%/& '(,& 2"6(,(,& 2$,--$0& ",")-$& 6$,"2$6,+(& *"#"*()& /$4& 5(%/6(% K 7,'(0& 8",-(3(& '"8$6$(,? ;")%(2$6(,& Gambar 7.64& ;('(& -(*& '$(218$60& '/(& (218,+(& '$(,--(3 *"#(-($& #1.(& 6">$.& +(,-& '$%/#/,-6(,& 1."%& *"#/(%& 3"-(*4& ;/*(2& 8(**( 3()2$6".& 8".(6/6(,& -")(6& 2)(,*.(*$& '",-(,& 61831,",& 6">"3(2(,& 3('( */8#/-00& */8#/-20& '(,& */8#/-3# *"%$,--(& 8"8$.$6$& V& '")(9(2& 6"#"#(*(, /,2/6& -")(6& 2)(,*.(*$& HGambar 7.6 (a)O4

170

Mudah dan Aktif Belajar Fisika untuk Kelas XI

;('(& */%/& *"'(,-0& 3()2$6".& -(*& '$(218$60& *".($,& 8".(6/6(,& -")(6 2)(,*.(*$0& '(3(2& 9/-(& #")12(*$& 2")%('(3& */8#/-00& */8#/-20& '(,& */8#/-30 *"3")2$&2").$%(2&3('(&Gambar 7.6 (b)&'",-(,&",")-$&6$,"2$6&600&620&'(,&634 d12(*$&3('(&*/8#/-0&8",-%(*$.6(,&,$.($&+(,-&*(,-(2&6">$.&6()",(&*/8#/ )12(*$& 8".(./$& */8#/& 6"'/(& 3()2$6".4& 7'(3/,& )12(*$& 2")%('(3& */8#/-2& '(,

I */8#/-3# 8",-%(*$.6(,& ",")-$& 6$,"2$6& )(2(=)(2(0& +($2/& K^ /$ R /$4 & a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

y

x z

H#O

x

y

H>O

z

HLMKIO

B",-(,& '"8$6$(,0& #"*(),+(& ",")-$& 6$,"2$6& 3()2$6".& #")-(,2/,-& 3('( */%/&'(,&2"6(,(,&+(,-&(6(,&8"8",-()/%$&-")(6(,&'()$&3()2$6".&2")*"#/24 ;('(&*"2$(3&-")(6(,&H2)(,*.(*$0&)12(*$0&'(,&P$#)(*$O0&*"2$(3&3()2$6".&8"8$.$6$ >()(& /,2/6& 8",+$83(,& ",")-$,+(4 ;",$,9(/(,& ",")-$& 6$,"2$6& *"3")2$& $,$& '$,(8(6(,& !78(s8!# e/;8!<7t8s8 e(e7=84&;)$,*$3&$,$&8",+(2(6(,&#(%G(&/,2/6&*/(2/&*$*2"8&3()2$6".&-(*&3('( */%/& 8/2.(6& $& '",-(,& *"2$(3& 3()2$6".,+(& 8"8$.$6$& >& '")(9(2& 6"#"#(*(, H?e=7ee# o># >7ee?o+O0& ",")-$& 6$,"2$6& )(2(=)(2(& *"2$(3& 3()2$6".& 66& ('(.(%

&I ' 66 R > ( /$ ) *K +

z

H(O

HLMKKO

x y

Gambar 7.6 Gerak molekul diatomik: (a) gerak translasi dari pusat massa; (b) gerak rotasi terhadap sumbu kartesius; dan (c) gerak vibrasi sepanjang sumbu molekul.

a."%&6()",(&-(*&2")'$)$&(2(*&N&3()2$6".0&9/8.(%&*"./)/%&",")-$&6$,"2$6 3()2$6".& -(*& '(.(8& */(2/& )/(,-& 2")2/2/3& H'$*"#/2& 9/-(& ",")-$& '(.(8& -(*O '$,+(2(6(,& '",-(,& 3")*(8((, A&R&N6/

&I ' A R N> ( /$ ) *K +

HLMKVO

A,2/6&-(*&'$(218$60&*"3")2$&-(*&EK0&aK0&'(,&FK&8"8$.$6$&",")-$&'(.(8 HAO& *"#(-($& #")$6/24 I4 ;('(&*/%/&)",'(%&HeKYZ&SO_&>&R&V&H2$-(&'")(9(2&6"#"#(*(,O V A&R&N66&R& N#/#$ K

K4

HLMKWO

;('(&*/%/&*"'(,-&HeYZZ&SO_&>&R&Y&H.$8(&'")(9(2&6"#"#(*(,O Y K

A&R&N66&R& N#/#$

HLMKYO

Ingatlah • Untuk gas monoatomik, f = 3. • Untuk gas diatomik suhu sedang, f = 5. • Untuk gas diatomik suhu tinggi, f = 7.

Teori Kinetik Gas

171

Kata Kunci • • • •

ekuipartisi energi energi dalam gas energi kinetik gas tekanan gas

V4

;('(&*/%/& 2$,--$& HeI4ZZZ& SO_& >&R&L&H2/9/%& '")(9(2& 6"#"#(*(,O L K

A&R&N66&R& N#/#$

HLMKJO

D$6(&*/(2/&-(*&'(.(8&*"#/(%&2(#/,-&8",-(.(8$&3")/#(%(,&*/%/&'()$ $I&8",9('$&$K0&",")-$&'(.(8&-(*&9/-(&(6(,&8",-(.(8$&3")/#(%(,4&A,2/6 -(*& 81,1(218$60& #").(6/ V K

V K

$ A#R& (#)&H $ $O&R& (#)&H$K&M&$IO

?">()(& /8/8& '$2/.$*

V K

$ A&R& (#)& $ $

HLMKLO

HLMKXO

Contoh 7.6 ?"#/(%&2(,-6$&#")$*$&K&81.&-(*&%".$/8&#")*/%/&KZ[\4&D$6(&%".$/8&'$(,--(3&*"#(-($&-(* $'"(.0&%$2/,-.(%&",")-$&212(.&*$*2"8&'(,&9/-(&",")-$&6$,"2$6&)(2(=)(2(&*"2$(3&81."6/.4 Jawab: V c,")-$&212(.&81."6/.0&60#'(3(2&'$%$2/,-&'",-(,&)/8/*& ()$#H6()",(&%".$/8&('(.(% K -(*&81,1(218$6O4&7'(3/,&",")-$&)(2(=)(2(&3")&81."6/.0&6/0#'(3(2&'$%$2/,-&'",-(, V )/8/*& /$4 K B$6"2(%/$T (#R&K&81._ )#R&X0VI&DU81.S $#R&KLV&]&KZ&R&KNV&S V 6 5# ()$ K V R& HK&81.OHX0VIW#DU81.SOHKNV&SO#R&L4VZX&D K V 6 / R& #/$ K V 5& HI0VX&^&IZMKV#DUS&OHKNV&SO&R&J0ZL&^&IZMKI&D4 K

Contoh 7.7 5",2/6(,&",")-$&'(.(8&'()$&*(2/&81.&-(*&81,1(218$6&3('(&*/%/&IKL[\4 Jawab: B$6"2(%/$T ( R&I&81. 5 R&HIKL&]&KLVO&R&WZZ&S N7 R&J0ZKV&^&IZKVU81. ) R&X0VIW&DU81.S N R&(#N7B a."%&6()",(&-(*&81,1(218$6&8(6( V V A&R& (#)$&R& HI&81.O&HX0VIW&DU81.&SO&HWZZ&SO K K A&R&W4NXX0W&D4

172

Mudah dan Aktif Belajar Fisika untuk Kelas XI

Tes Kompetensi Subbab

B

Kerjakanlah dalam buku latihan. I4

K4

B(.(8&*/(2/&)/(,-0&2")'(3(2&W&-)(8&-(*&aK&'(,&W&-)(8 FKB#@")(2&81."6/.&aK&R&VK&-U81.&'(,&#")(2&81."6/.&FK&R KX&-U81.4&E$2/,-.(%&3")#(,'$,-(,&",")-$&6$,"2$6&2)(,*.(*$ )(2(=)(2(& 6"'/(& 81."6/.& '(,& 3")#(,'$,-(,& (,2()( 6">"3(2(,&6"'/(&81."6/.&2")*"#/24 B/(&81.&-(*&16*$-",&2")'(3(2&3('(&*"#/(%&#"9(,( #")P1./8"&J&.$2")&'",-(,&2"6(,(,&J&(284&E$2/,-.(% ",")-$&6$,"2$6&2)(,*.(*$&)(2(=)(2(&'()$&81."6/.&16*$-", 3('(&61,'$*$&2")*"#/24

HQ(**(&81."6/.&16*$-",&('(.(%&Y0VI&^&IZMKJ&6-O PetunjukT E$2/,-&'/./&$&'",-(,&)/8/*&!"#R#()$0&6"8/'$(, V -/,(6(,&)/8/*&6/#R /$4&b(.(/3/,&16*$-",&('(.(% K V Y 81."6/.& '$(218$60& '$& *$,$& '$-/,(6(,& 0& #/6(,& K K 6()",(& +(,-& '$2(,+(6(,& ('(.(%& ",")-$& 6$,"2$6 2)(,*.(*$0&#/6(,&",")-$&81."6/.4

C. Kecepatan Efektif Partikel Gas D$6(&'(.(8&*/(2/&)/(,-&2")2/2/3&2")'(3(2&*"#(,+(6&NI&81."6/.&+(,#")-")(6& '",-(,& 6">"3(2(,& 1I0& NK& 81."6/.& +(,-& #")-")(6& '",-(,& 6">"= 3(2(,&1K0&'(,&*"2")/*,+(0&)(2(=)(2(&6/(')(2&6">"3(2(,&3()2$6".&-(*&1K&'(3(2 '$2/.$*& *"#(-($& #")$6/24 1K &R&

NI 1IK % N K 1KK % 444 % N 8 18 K # N 8 18 K $ , R& NI N K % 444 % N 8 N8

HLMKNO

S">"3(2(,&"<"62$<&3()2$6".&-(*&1)8*&H)8*&R#7oot#+e<(#sC;<7eO&'$'"<$,$= *$6(,& *"#(-($& (6()& '()$& )(2(=)(2(& 6/(')(2& 6">"3(2(,4 1)8*&R& 1K &(2(/&1)8*KR 1K

HLMVZO

A,2/6& 8",+(2(6(,& 6">"3(2(,& )(2(=)(2(& '()$& 3()2$6".& -(*0& 2$,9(/.(% %/#/,-(,& (,2()(& ",")-$& '(.(8& HAO& '(,& ",")-$& 6$,"2$6& )(2(=)(2(& 3()2$6". -(*& H6/O0& +($2/ V A I 66&R& &(2(/& +31)8*K&R& /$ K K N *"%$,--(& '$3")1."% 1)8*K&R& V/$ &&&(2(/&&&1)8*R V/$ +3 +3

HLMVIO

1."%& 6()",(

* ) +3&R& N &'(,&/&R& N 7 7 B",-(,&*&('(.(%&8(**(&81."6/.&)".(2$<0& N7&('(.(%&#$.(,-(,&7P1-(')10 '(,&)&('(.(%&61,*2(,2(&-(*4&Persamaan&(7–31)&'(3(2&'$2/.$*6(,&*"#(-($&#")$6/24 1)8*&R&

V)$ *

HLMVKO

D$6(& 3")*(8((,& !"& R& ()$& '$*/#*2$2/*$6(,& 6"& Persamaan (7–32)0 (6(,& '$'(3(26(,& 3")*(8((,& #")$6/24 1)8*&R&

V !" (*

HLMVVO

Teori Kinetik Gas

173

B",-(,&+&R&(*&*"#(-($&8(**(&212(.&-(*&'(,&8(**(&9",$*&-(*& " !

+ "

8(6(& Persamaan (7–33)& '(3(2& '$2/.$* 1)8*&R&

V! "

HLMVWO

;"),+(2((,&6">"3(2(,&"<"62$<&3('(&Persamaan (7–34)&8",/,9/66(, #(%G(&3('(&*/%/&2")2",2/0&81."6/.=81."6/.&-(*&+(,-&."#$%&)$,-(,&)(2(=)(2( #")-")(6&."#$%&>"3(24&C(*&%$')1-",&'",-(,&8(**(&81."6/.&K&-U81.&(6(,&#")= -")(6&"83(2&6(.$&."#$%&>"3(2&'()$3('(&-(*&16*$-",4&5(#".&#")$6/2&8"83")= .$%(26(,& 6">"3(2(,& "<"62$<& H1)8*O& #"#")(3(& 9",$*& -(*& 3('(& */%/& 2")2",2/4 Tabel 7.1 S">"3(2(,&c<"62$<&@"#")(3(&C(*&3('(&?/%/&KZ[\

Informasi untuk Anda Energi Matahari berasal dari reaksi fusi nuklir yang berasal dari penggabungan 2 buah proton. Sebenarnya, proton memiliki gaya tolak menolak dengan proton lainnya karena muatannya sejenis. Selain itu, proton tidak memiliki energi kinetik yang cukup besar untuk mengatasi gaya tolak-menolak tersebut. Akan tetapi, ada sebagian proton yang memiliki kecepatan tinggi sehingga memiliki energi kinetik yang cukup besar. Oleh karena itu, Matahari masih bersinar.

Information for You The suns energy is supplied by nuclear fusion process that starts with the merging of two protons. However, protons have a motion to repel each other because of their electrical charges and protons of average speed do not have enough kinetic energy to overcome the repulsion. Very fast protons with speed can do so, however and for that reason the sun can shine. Sumber: Fundamentals of Physics, 2001

Gas

Massa 1 mol gas (10–3 kg/mol)

vrms (m/s)

EK E" EKa F" FK&(2(/&\a Fa \aK ?aK

&&K0ZK &&W0Z IX KZ0I KX VZ WW WX

I4NZK I4VYK JVL JZV YII WNW WZX VNZ Sumber: Fundamental of Physics, 2001

Contoh 7.8 E$2/,-.(%&6">"3(2(,&"<"62$<&-(*&#")8(**(&9",$*&IZ&6-U8V&+(,-&#")('(&'(.(8&2(#/,#")2"6(,(,&IK&^&IZY&&;(4 Jawab: B$6"2(%/$T " &R&IZ&6-U8V_&!&R&IK&^&IZY&;( S">"3(2(,&"<"62$<&3()2$6".&-(*&'$%$2/,-&'",-(,&8",--/,(6(,&Persamaan (7–34)4 Y 1)8*&R& V! &R& VHIK " IZ ;(O &R& VJ "IZW &8U*R&JZZ&8U* " IZ&6-U8 V D('$0&6">"3(2(,&"<"62$<&-(*&('(.(%&JZZ&8U*4

Contoh 7.9 5",2/6(,&3")#(,'$,-(,&6">"3(2(,&"<"62$<&(,2()(&81."6/.=81."6/.&-(*&%$')1-", HQ)&R&K&-U81.O&'(,&-(*&16*$-",&H*)&R&VK&-U81.O&3('(&*/%/&2")2",2/4 Jawab:

V)$ * S">"3(2(,&"<"62$<&*"#(,'$,-&'",-(,&(6()&'()$&6"#(.$6(,&8(**(&81."6/.&)".(2$<,+(4 ?">()(&8(2"8(2$*0&'$2/.$*6(, 1)8*R&

I * # EK $ * #DK $ 1)8* # DK $ 1 #D $ VK&-U81. &R& &R& &R& &R& )8* K &R&&W4 K&-U81. 1)8* #EK $ 1)8* #EK $ I * # DK $ * # EK $

174

Mudah dan Aktif Belajar Fisika untuk Kelas XI

Tes Kompetensi Subbab

C

Kerjakanlah dalam buku latihan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

Y4 J4

L4

X4

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

Rangkuman I4

K4

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c,")-$&6$,"2$6&-(*T

K 6/&R &/$ V

V4

c,")-$& '(.(8& -(*& ('(.(%& 9/8.(%& *"./)/%& ",")-$ 6$,"2$6&3()2$6".&-(*&'(.(8&*/(2/&)/(,-&2")2/2/34

K A&R&N66&R& N#/#$ V @")$6/2&$,$0&",")-$&'(.(8&/,2/6&-(*&'$(218$64 (4 ;('(&*/%/&)",'(%&HeKYZ&SO_&>&R&V&H2$-(&'")(9(2 6"#"#(*(,O4

W4

V A&R&N66&R& N#/#$ K #4 ;('(&*/%/&*"'(,-&HeYZZ&SO_&>&R&Y&H.$8(&'")(9(2 6"#"#(*(,O4 Y A&R&N66&R& N#/#$ K >4 ;('(&*/%/&2$,--$&HeI4ZZZ&SO_&>&R&L&H2/9/% '")(9(2&6"#"#(*(,O4 L A&R&N66&R& N#/#$ K S">"3(2(,& "<"62$<& 3()2$6".& -(*& '(3(2& '$6"2(%/$ '",-(,&3")*(8((,T V! 1)8*&R& "

Teori Kinetik Gas

175

Peta Konsep

Teori Kinetik Gas 8"8#(%(*

C(*&f'"(. ;)$,*$3&c6/$3()2$*$&c,")-$

#").(6/

S">"3(2(,&c<"62$< ;()2$6".&C(*

8"8#(%(*

E/6/8&@1+."

E/6/8 @1+."=C(+&!/**(>

5"6(,(,&C(*&'(.(8 d/(,-&5")2/2/3 '(3(2& 8",>()$

!"&R&2"2(3 +&'(,& ( 2"2(3

!" $

R&61,*2(,2(

c,")-$&S$,"2$6&'(, c,")-$&B(.(8&C(* +&'(,& ( 2$'(6& 2"2(3

!" $

R#(#)

3('(

C(* Q1,1(218$6

C(* B$(218$6

Refleksi Setelah mempelajari bab ini, Anda tentu akan mengetahui bahwa gas ideal di alam tidak ada. Anda juga tentu menjadi paham tentang prinsip ekuipartisi energi, energi kinetik, dan energi dalam gas, serta kecepatan efektif dari gerak partikel gas. Dari materi yang dipelajari pada bab ini, bagian manakah yang

176

Mudah dan Aktif Belajar Fisika untuk Kelas XI

menurut Anda sulit dipahami? Coba diskusikan bersama teman atau guru Fisika Anda. Anda menjadi tahu alasan mengapa balon gas dapat mengapung merupakan manfaat mempelajari bab ini. Coba Anda cari manfaat lain mempelajari bab ini.

Tes Kompetensi Bab 7 A. Pilihlah salah satu jawaban yang paling tepat dan kerjakanlah pada buku latihan. I4

K4

;('(&E/6/8&@1+."0&!"&R&/0&&'",-(,&/&('(.(%&4444 (4 '(+( '4 */%/ #4 /*(%( "4 61,*2(,2(&-(* >4 818",2/8&.$,"() ;('(&-(8#()&#")$6/20&P1./8"&2(#/,-&@#*(8(&'",-(, K&6(.$&P1./8"&2(#/,-&74

V

>4

V

"4 V

p

V

V

W4

Y4

J4

#4

"4

p

p

T

p

T

3N

?$*2"8&2")*"#/2&'$$*$&'",-(,&-(*&$'"(.4&D/8.(%&81."6/. '(.(8&2(#/,-&7&*(8(&'",-(,&F&'(,&'(.(8&2(#/,-&@ ('(.(%&VF4&D$6(&-(*&'(.(8&2(#/,-&7&#")*/%/&VZZ&S0 */%/&-(*&'(.(8&2(#/,-&@&('(.(%&4444 (4 IZZ&S '4 WYZ&S #4 IYZ&S "4 JZZ&S >4 KZZ&S @1+."&8"8#/(2&*/(2/&%/#/,-(,&(,2()(&2"6(,(,&'(, P1./8"&'()$&*/(2/&-(*4&D$6(&'$,+(2(6(,&'(.(8&-)(<$60 (6(,&#")#",2/6&*"3")2$&-)(<$6&4444 p p (4 '4

p

T

B N

p

p

T

>4

A

#4

'4

p

T

kapiler

V4

(4

B(.(8&*(2/(,&*$*2"8&f,2"),(*$1,(.0&*(2/(,&2"6(,(,&-(* '$,+(2(6(,&'",-(,&4444 (4 (28 '4 &>8E#4 FU8 "4 &91/." >4 FU8K C(*&'(.(8&)/(,-&2")2/2/3&#")*/%/&WK[\&'(,&#")2"6(= ,(,&L&(280&*")2(&P1./8",+(&X&.$2")4&D$6(&-(*&'$3(,(*6(, *(83($&XL[\0&2"6(,(,&,($6&*"#"*()&I&(28&'(,&P1./8" -(*&(6(,&4444 (4 #")6/)(,-&IZg '4 #")2(8#(%&KZg #4 2"2(3 "4 #")2(8#(%&IKg >4 #")6/)(,-&KZg C)(<$6&(,2()(&2"6(,(,&-(*&H!O&+(,-&8(**(,+(&2")2",2/ 3('(&P1./8"&2"2(3&*"#(-($&
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email protected]`8(,&/&R&I0VX&^&IZMKV&D0&",")-$ 6$,"2$6&*"#/(%&(218&%".$/8&3('(&*/%/&KL[\&('(.(%&4444 (4 W0IW&^&IZMKI&D '4 J0KI&^&IZMKI&D MKI #4 K0ZL&^&IZ &D "4 IK0WK&^&IZMKI&D MKI >4 Y0JN&^&IZ &D

Teori Kinetik Gas

177

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

Jawablah pertanyaan berikut ini dengan tepat.

I4

B(.(8&*/(2/&2(#/,-&2")2/2/3&A0 gas 2")'(3(2& *"9",$*& -(*& $'"(.4& D$6( 2"6(,(,&/'()(&./()&LYZ&88E-0 P1./8"&-(*&YZ&>8V&'(,&*/%/,+( VZ[\0&&2",2/6(,&P1./8"&-(*&2")= raksa *"#/2&3('(&6"('((,&,1)8(.&HZ[\0 LJZ&88E-O4 ?/(2/&9",$*&-(*&8","83(2$&P1./8"&IZZ&>8V&3('(&*/%/ Z[\&'(,&2"6(,(,&I&(284&D$6(&*/%/,+(&8",9('$&YZ[\ '(,&2"6(,(,&8",9('$&K&(280&2",2/6(,&P1./8"&(6%$) -(*&2")*"#/24 Q(**(&9",$*&*/(2/&-(*&$'"(.&3('(&*/%/&8/2.(6&$&'(, 2"6(,(,&!&('(.(%&IV&-U>8V4&D$6(&2"6(,(,&-(*&2")*"#/2 '$9('$6(,& K!& '(,& */%/,+(& 2/)/,& 8",9('$& Z0Y& $0 2",2/6(,&8(**(&9",$*&-(*&2")*"#/24

IX4

IN4

KZ4

>4

W4

10 cm

B.

IL4

K4

V4

178

Mudah dan Aktif Belajar Fisika untuk Kelas XI

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aK&HQ7&R&VKO&8"8$.$6$&P1./8"&*"#"*()&4444 H)&R&X0VIW&DU681.S_&I&(28&R&IZ Y&FU8 KO (4 I0W&^&IZMJ&8V '4 K0X&8V MV V #4 K0X&^&IZ &8 "4 KK0W&8V MV V >4 KK0W&^&IZ &8 HUMPTN 1989O ?"#/(%&2(#/,-&-(*&'",-(,&P1./8"&2")2",2/&#")$*$&-(* $'"(.&'",-(,&2"6(,(,&!4&76()&,$.($&)(2(=)(2(&6/(')(2 .(9/&81."6/.&-(*&'$*"#/2&1)8*4&D$6(&6"&'(.(8&2(#/,2")*"#/2&'$3183(6(,&-(*&*"9",$*&*"%$,--(&2"6(,(,,+( 8",9('$&K!0&*"'(,-6(,&*/%/,+(&'$#/(2&2"2(30&1)8*=,+( (6(,&8",9('$&4444 1)8* (4 '4 K1)8* K #4 1)8* "4 W1)8*

Y4

J4

L4

K 1 )8*

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

Bab

8 Sumber: Physics for Scientists and Engineers, 2000

Kereta uap dapat berjalan dengan memanfaatkan energi uap yang diubah menjadi energi kinetik.

Termodinamika Hasil yang harus Anda capai: menerapkan konsep termodinamika dalam mesin kalor. Setelah mempelajari bab ini, Anda harus mampu: menganalisis perubahan keadaan gas ideal dengan menerapkan hukum termodinamika.

!"#$%$n ("n)$n *"+,"-.$n)$n /$-$n0 1$+$n$ t+$n1*3+t$1i 5$n) (i)6n$,$n -$n61i$ t"+61 ."+,"-.$n)7 8$-$n ($96%60 ,6($ ($n ,"+"t$ ,6($ -"n#$(i *+i-$(3n$ $n),6t$n ($+$t7 !$$t ini0 *"+$n$n ,6($ 1".$)$i $%$t t+$n1*3+t$1i ($+$t 16($9 t"+)$nti,$n 3%"9 ,"."+$($$n -3t3+0 -3.i%0 ($n ,"+"t$7 :"%".i9$n ($+i 1$+$n$ t+$n1*3+t$1i -3("+n ini $($%$9 t"n$)$ 5$n) (i9$1i%,$nn5$ %".i9 ."1$+ ($+i*$($ t"n$)$ ,6($7 ;%"9 ,$+"n$ it60 #6-%$9 *"n6-*$n) ($n .$+$n) 5$n) ($*$t (i$n),6t *6n 1"-$,in .$n5$,7 <$($ ($1$+n5$0 *"+,"-.$n)$n 1$+$n$ t+$n1*3+t$1i t"+1".6t ti($, %"*$1 ($+i ,"-$#6$n t",n3%3)i $*%i,$1i *+in1i* t"+-3(in$-i,$7 =$-*i+ 1"-6$ -"1in 5$n) $($ -"n))6n$,$n *+in1i* t"+-3(in$-i,$0 5$it6 -"n)6.$9 "n"+)i ,$%3+ -"n#$(i "n"+)i )"+$,7

A. Usaha pada Berbagai Proses Termodinamika B. Hukum I Termodinamika C. Kapasitas Kalor Gas dan Siklus Termodinamika D. Hukum II Termodinamika

179

Tes Kompetensi Awal S,b,lum&m,m6,la7ari&kon-,6&;,rmo&-oal?-oal&b,rikut&an( G7 ["n)$*$ )"%$1 ti*i1 5$n) .i$1$n5$ (i)6n$,$n 6nt6, L7 U*$,$9 5$n) (i-$,16( ("n)$n "Qi1i"n1i -"1inY -in6- "1 .i1$ *"J$9 ,"ti,$ (ii1i $i+ *$n$1Y Z7 ["n6+6t Un($0 $*$,$9 5$n) (i-$,16( ("n)$n "nt+3*iY M7 \"n)$n .$9$1$ 1"n(i+i0 #"%$1,$n J$+$ ,"+#$ t"+-31 1"9in))$ $i+ .i1$ t"t$* *$n$17

A. Usaha pada Berbagai Proses Termodinamika 1. Usaha yang Dilakukan Gas

ds

F = pA

>in#$6%$9 1".6$9 1i1t"- 5$n) (i%"n),$*i ("n)$n 1".6$9 t$.6n) ($n *"n)i1$* )$1 5$n) ($*$t ."+)"+$, .".$1 1"*"+ti t$-*$, *$($ !ambar& '()7 U1$9$ @!A 5$n) (i%$,6,$n 3%"9 )$1 1"96.6n)$n ("n)$n *"+6.$9$n B3%6-" )$1 $($%$9 1".$)$i ."+i,6t7 Ci,$ t",$n$n )$1 .","+#$ *$($ *"n)i1$*0 ,"-6(i$n *"n)i1$* ."+)"1"+ 1"#$69 @"A ," $t$1 ("n)$n %6$1 *"n$-*$n) *"n)i1$* @#A0 61$9$ @!A 5$n) (i%$,6,$n 3%"9 1i1t"- )$1 t"+9$($* %in),6n)$n $($%$9 (D E*F(" E @$#A@%"A E $@#%"A E $%& $ E G $t- E HI J-=) E GKG7LKK <$ Unt6, *+31"1 ($+i 'G ," 'M0 61$9$ @,"+#$A 5$n) (i%$,6,$n 3%"9 )$1 $($%$9 'M

!E Gambar 8.1 Sistem melakukan usaha terhadap lingkungannya.

p 1

ekspansi W > 0 luas = W 2

V1

@$A

V2

V

pemampatan W < 0 luas = W

p 1

2

V1

@.A

V2

V

Gambar 8.2 (a) Usaha yang dilakukan oleh sistem adalah positif (W = p " V ). (b) Usaha yang dilakukan oleh sistem adalah negatif (W = –p " V ).

180

! $%'

@NOGA

'G

! E $ @'M O 'GA E $ " '

@NOMA

:"t"+$n)$nP ! E 61$9$ 5$n) (i%$,6,$n 1i1t"- )$1 $ E t",$n$n )$1 @,3n1t$nA 'G E B3%6-" $D$% 'M E B3%6-" $,9i+ +,r-amaan& /'012 ."+%$,6 9$n5$ #i,$ t",$n$n @$A ,3n1t$n7 !"%$-$ *"+6.$9$n B3%6-" t"+1".6t0 61$9$ @!A ($*$t ."+ni%$i *31itiQ $t$6 n")$tiQ ("n)$n ,"t"nt6$n 1".$)$i ."+i,6t7 G7 Ci,$ )$1 -"%$,6,$n ",1*$n1i @*"n)"-.$n)$nA0 61$9$ @!A ."+ni%$i *31itiQ7 !i1t"- -"%$,6,$n 61$9$ 5$n) -"n5".$.,$n B3%6-"n5$ ."+t$-.$90 'M R 'G7 M7 Ci,$ )$1 (i-$-*$t,$n0 ! ."+ni%$i n")$tiQ7 <$($ 1i1t"- t"+1".6t (i%$,6,$n 61$9$ 3%"9 %in),6n)$n 5$n) -"n5".$.,$n B3%6-"n5$ ."+,6+$n)0 'M S 'G7 U1$9$ 5$n) (i%$,6,$n *$($ 1i1t"- (i1".6t (")*)+ ,()r7 T6$1 $+"$ (i .$D$9 ,6+B$ $($%$9 61$9$ 5$n) (i%$,6,$n 3%"9 1i1t"-7 <"+9$ti,$n !ambar& '(17

Contoh 8.1 !6$t6 )$1 ($%$- 1i%in("+ t"+t6t6* -"n)$%$-i *+31"1 1"*"+ti t$-*$, *$($ )$-.$+7 >"nt6,$n 61$9$ 5$n) (i%$,6,$n 3%"9 )$1 *$($P $7 *+31"1 #. @!UVAW .7 *+31"1 ./ @!VXAW J7 *+31"1 /# @!XUAW ($n (7 1"%6+69 *+31"1 @!t3t$%A7

Mudah dan Aktif Belajar Fisika untuk Kelas XI

p(kPa) 250

50

A

B

C E 25

D 75

V(L)

BaCab: $7 U1$9$ ($+i # ," . 1$-$ ("n)$n %6$1 #.67 ($n ."+ni%$i *31itiQ ,$+"n$ $+$9 *+31"1 ," ,$n$n @'V R 'UA !UV E %6$1 #.67 E #. _ .6 E @H` T O M` TA@M`K ,<$A !UV E @`K TA@M`K _ GKL <$A E GM0` ,C7 .7 U1$9$ ($+i . ," / 1$-$ ("n)$n %6$1 ./76 ($n ."+t$n($ n")$tiQ ,$+"n$ $+$9 *+31"1 ," ,i+i @'X R 'VA7 !VX E %6$1 ./76 E O G @/7 a .6A76 M E @O G A@`K ,<$ a M`K ,<$A@H` T O M` TA E OH0` ,C7 M J7 U1$9$ ($+i /# 1$-$ ("n)$n n3% ,$+"n$ /# ti($, -"-."nt6, .i($n) ("n)$n 16-.6 ' @%6$1n5$ E KA7 (7 U1$9$ ,"1"%6+69$n *+31"1 @!UVXUA $($%$9 !UVXU E !UV a !VX a !XU E @GM7`KK O H7`KK a K A C E ` ,C7 U1$9$ t3t$% ($*$t #6)$ (i9it6n) 1"J$+$ %$n)16n)7 G ! t3t$% E %6$1 #./# E @#/A@ A@UVA M E @ G A@M`K ,<$ O `K ,<$A@H` T O M` TA E ` ,C7 M

p

2. Usaha pada Proses yang Dialami Gas ]$1 5$n) ."+$($ ($%$- +6$n) t"+t6t6* ($*$t (i6.$9 ,"$($$nn5$ -"%$%6i ."."+$*$ *+31"10 5$it6 *+31"1 i13t"+-$%0 *+31"1 i13,93+i,0 *+31"1 i13.$+i,0 ($n *+31"1 $(i$.$ti,7 a.

Proses Isotermal <+31"1 i13t"+-$% $($%$9 *+31"1 *"+6.$9$n ,"$($$n 1i1t"- *$($ 1696 t"t$* @!ambar& '(AA7 <+31"1 t"+1".6t 1"16$i ("n)$n =6,6- V35%"0 5$it6 $' E ,3n1t$n7 >in#$6%$9 *"+1$-$$n )$1 i("$% $' E 01T3 ;%"9 ,$+"n$ 1696 @TA0 00 ($n 1 t"t$* -$,$ $G'G E $M'M @NOLA U1$9$ 5$n) (i%$,6,$n 1i1t"- ($*$t (it"nt6,$n -"n))6n$,$n *"+1$-$$n ."+i,6t7 01T ! E # $%'0 ("n)$n $ E ' 01T E # %' ' ^i%$i T0 00 ($n 1 ,3n1t$n 1"9in))$ ($*$t (i,"%6$+,$n ($+i *"+1$-$$n int")+$%7 %' & ! E 01T # E 01T !%n' "&M G ' E 01T @%n'4 O %n'5A C$(i0 61$9$ 5$n) (i%$,6,$n 3%"9 1i1t"- *$($ *+31"1 i13t"+-$% $($%$9

'M ! E +01T %n ' G

p1

p2

V1

V

V2

Gambar 8.3 Kurva p–V dengan T konstan pada proses isotermal.

@NOZA

Contoh 8.2 \6$ -3% )$1 $+)3n -"-6$i 1"J$+$ i13t"+-$% *$($ 1696 MHbX0 ($+i B3%6-" $D$% K0KM` -L -"n#$(i K0K` -L7 >"nt6,$n 61$9$ 5$n) (i%$,6,$n )$1 t"+1".6t @1 E N0LG Cc-3%:A7 BaCab: \i,"t$96iP 0 E M -3%W d3%6-" $D$% E 'G E K0KM` -L d3%6-" $,9i+ E 'M E K0K` -L

Termodinamika

181

Tantangan untuk Anda Menurut Anda, benarkah angin itu tidak mendinginkan suhu, melainkan menaikkan suhu di sekitarnya?

1 E N0LG Cc-3%:W T E @MH a MHLA ,+E LKK :7 U1$9$ 5$n) (i%$,6,$n )$1 *$($ *+31"1 i13t"+-$% ($*$t (i9it6n) ("n)$n +,r-amaan /'0E27 'M ! E 01 T %n ' 7 G % K0K` - L & E @M -3%A@N0LG Cc-3%:A@LKK :A %n ' E Z7fNI %n M E L7Z`I0KL #36%"7 L ( ) K0KM` - *

b. Proses Isokhorik <+31"1 i13,93+i, $($%$9 *+31"1 *"+6.$9$n ,"$($$n 1i1t"- *$($ B3%6-" t"t$* @!ambar& '(EA7 >in#$6%$9 ,"-.$%i *"+1$-$$n ,"$($$n )$1 i("$%0

p p1

$' E 01T0 B3%6-" @'A t"t$*0

p2 V

V1 = V2

1"%$%6 t"t$*7 U,i.$tn5$0

Gambar 8.4 Proses isokhorik pada grafik p–V.

01 $ E 6nt6, )$1 i("$% ("n)$n 0 ($n 1 T '

$ E ,3n1t$n $t$6 T $ $G E M TM TG

@NO`A

<$($ *+31"1 i13,93+i,0 1i1t"- ti($, -"n)$%$-i *"+6.$9$n B3%6-" @'G E 'MA 1"9in))$ 61$9$ 5$n) (i%$,6,$n 3%"9 )$1 1$-$ ("n)$n n3%0 5$it6 ! E $@ " 'A E K7 <"+6.$9$n t",$n$n *$($ )$1 $,$n -"n5".$.,$n *"+6.$9$n 1696 )$17 Ci,$ 1696 )$1 (in$i,,$n0 t",$n$n ($%$- )$1 $,$n ."+t$-.$90 1"*"+ti (it6n#6,,$n *$($ !ambar& '(F7 d3%6-" ti($, t"+e *"n)$+69 *"+6.$9$n t",$n$n )$17

p

Contoh 8.3

T

Gambar 8.5 Grafik p–T pada V konstan.

p(Pa)

!".6$9 t$.6n) ."+i1i GK %it"+ )$1 i("$% *$($ 1696 GMHbX ($n t",$n$n M _ GK` <$7 >$.6n) t"+1".6t (i*$n$1,$n 9in))$ -"nJ$*$i 1696 LMHbX7 Ci,$ B3%6-" t$.6n) (i.6$t t"t$*0 t"nt6,$n t",$n$n )$1 (i ($%$- t$.6n)7 BaCab: \i,"t$96iP TG E @GMH a MHLA : E ZKK :W $ E M0K _ GK` <$ TM E @LMH a MHLA : E IKK : <"+1$-$$n ,"$($$n )$1 *$($ *+31"1 i13,93+i,P ` $M $G $ $&$M E L _ GK` <$7 E M $ M # GK <$ E ZKK : 600 K TM TG

c.

V1

V2

V(L)

Gambar 8.6 Grafik p–V pada tekanan (p) konstan. V (volume)

T (suhu)

Gambar 8.7 Grafik V–T pada tekanan (p) konstan.

182

Proses Isobarik <+31"1 i13.$+i, $($%$9 *+31"1 *"+6.$9$n ,"$($$n 1i1t"- *$($ t",$n$n t"t$*7 <$($ !ambar& '(G t$-*$, .$9D$ *"+6.$9$n B3%6-" ti($, -"n)e 9$1i%,$n *"+6.$9$n t",$n$n7 !"16$i ("n)$n *"+1$-$$n )$1 i("$%0 $' E+01T0 01 ' t",$n$n @$A t"t$*0 ($n T E $ 7 ;%"9 ,$+"n$ 0 ($n 1 1"%$%6 t"t$* -$,$ 'G 'M ' E ,3n1t$n $t$6 T E T @NOIA T G M ]+$Qi, 96.6n)$n $nt$+$ ' ($n T 6nt6, *+31"1 i13.$+i, t$-*$, *$($ !ambar&'(H7 <$($ *+31"1 i13.$+i,0 t",$n$n )$1 (i61$9$,$n t"t$* 1"9in))$ *"+6.$9$n 1696 *$($ )$1 $,$n -"ni-.6%,$n *"+6.$9$n B3%6-" )$1 6nt6, -"-*"+t$9$n,$n $)$+ t",$n$n )$1 t"t$*7 U1$9$ 5$n) (i%$,6,$n )$1 *$($ *+31"1 i13.$+i, $($%$9 1"16$i ("n)$n *"+1$-$$n ."+i,6t7 ! E $@'M O 'GA E $ $ "' % @NOHA

Mudah dan Aktif Belajar Fisika untuk Kelas XI

Contoh 8.4 !"#6-%$9 )$1 ($%$- +6$n) t"+t6t6* B3%6-"n5$ L %it"+0 t",$n$n M $t-0 ($n 1696n5$ MHbX7 ]$1 t"+1".6t (i*$n$1,$n ("n)$n t",$n$n t"t$* 1"9in))$ -"nJ$*$i 1696 GHHbX7 >"nt6,$n B3%6-" )$1 ($n 61$9$ 5$n) (i%$,6,$n )$1 t"+1".6t7 BaCab: \i,"t$96iP $ E M $t-W TG E @MH a MHLA : E LKK : 'G E L %it"+W TM E @GHH a MHLA : E Z`K : ' ' $7 <"+1$-$$n )$1 *$($ t",$n$n t"t$* $($%$9 G E M TG TM 'M L %it"+ E $ 'M E Z0` %it"+7 LKK : Z`K : 1"9in))$ B3%6-" )$1 -"n#$(i Z0` %it"+7 .7 ! E $ @'M O 'GA E M @Z0` OLA E L #36%"7

d. Proses Adiabatik <+31"1 $(i$.$ti, $($%$9 *+31"1 *"+6.$9$n ,"$($$n 1i1t"- t$n*$ $($n5$ *"+t6,$+$n ,$%3+ ("n)$n %in),6n)$nn5$0 $t$6 ti($, $($ ,$%3+ 5$n) (i%"*$1 -$6*6n 5$n) (it"+i-$ 3%"9 )$1 t"+1".6t 1"9in))$ 8 E K7 ]+$Qi, *$($ !ambar&'(' -"n6n#6,,$n .$9D$ *$($ *+31"1 $(i$.$ti, t"+#$(i *"+6.$9$n 16960 t",$n$n0 ($n B3%6-"7 <+31"1 ini ."+($1$+,$n r(9(" :;i"";0 5$n) (it6%i1,$n $ '+ E ,3n1t$n0 $t$6 $G 'G+ E $M 'M+

@NONA

($n T ' $+ ,G% E t"t$*0 $t$6 TG 'G$+ ,G% E TM 'M$+ ,G%

@NOfA

\"n)$n + R G $($%$9 k;0">)0>)+ ?)$,)cA 5$n) -"+6*$,$n *"+.$ne (in)$n ,$*$1it$1 ,$%3+ )$1 *$($ t",$n$n t"t$* X* ($n ,$*$1it$1 ,$%3+ )$1 *$($ B3%6-" t"t$* XB7 !"J$+$ -$t"-$ti10 ."1$+$n t"+1".6t (it6%i1

+E

X* XB

p

proses adiabatik proses isotermik p1 p2 V1 V2

V

Gambar 8.8 Grafik p–V pada proses adiabatik lebih curam daripada proses isotermal.

@NeGKA

U,i.$t ti($, $($n5$ *"+t6,$+$n ,$%3+ ("n)$n %in),6n)$n0 61$9$ 5$n) (i%$,6,$n 3%"9 )$1 9$n5$ -"n)6.$9 "n"+)i ($%$-7 V"1$+n5$ 61$9$ t"+1".6t ($*$t (it"nt6,$n ("n)$n -"+6#6, +,r-amaan& /'012 1"9in))$ (i*"+3%"9 *"+1$-$$n G ! E + , G @$G'G O $M'MA @NOGGA $t$6

!E

L 0 1 @TG O TMA M

@NOGMA

U1$9$ 5$n) (i%$,6,$n 3%"9 )$1 *$($ *+31"1 $(i$.$ti, ($*$t (i*"+3%"9 ("n)$n -"n))6n$,$n +,r-amaan& /'0))2 ($n +,r-amaan& /'0)120 #i,$ ,"$($$n $D$% ($n ,"$($$n $,9i+ (i,"t$96i7 X3nt39 *+31"1 $(i$.$ti, ($%$,"9i(6*$n 1"9$+ie9$+i $($%$9 *"-6$i$n )$1 *$n$1 *$($ -"1in (i"1"% ($n -"1in *"n(in)in7

Contoh 8.5 ]$1 i("$% -"n)$%$-i ",1*$n1i 1"J$+$ $(i$.$ti,7 [6%$e-6%$0 ."1$+ t",$n$n )$1 $($%$9 M _ GK` <$7 !"t"%$9 ",1*$n1i t",$n$n )$1 -"n#$(i GK` <$7 >"nt6,$n B3%6-" )$1 $,9i+0 #i,$ B3%6-" )$1 -6%$e-6%$ K0G -L 1"+t$ ,3n1t$nt$ T$*%$J" ` 7 L

Termodinamika

183

BaCab: \i,"t$96iP $G E M _ GK` <$W $M E G _ GK` <$W 'G E K0G -L + + <"+1$-$$n )$1 *$($ *+31"1 $(i$.$ti, $($%$9 $G 'G & $M 'M `

`

`

`

@M # GK ` A@K0G - L A L E @G # GK ` A@ 'M A L $ @ 'M A L E @MA@K0GA L

:"(6$ +6$1 (i*$n),$t,$n L `

L 1"9in))$ (i*"+3%"9 ` L

` ` L . E @MA E /@K0GAL 0 $ 'M E @MA` @K0GA - L 'M 1 2 'M E K0G`G` -L 'G $ +'ME K0G` -L C$(i0 B3%6-" )$1 1"t"%$9 ",1*$n1i $($%$9 K0G` -L7 ` L

$ %

Tes Kompetensi Subbab

L `

A

K,r7akanla>&an( G7 !"#"ni1 )$1 ."+t",$n$n ` $t- ."+$($ ($%$- D$($9 5$n) -"-i%i,i B3%6-" `KK %it"+7 =it6n)%$9 61$9$ 5$n) (i%$,6,$n 3%"9 )$10 #i,$P $7 )$1 -"-6$i *$($ t",$n$n t"t$* 1"9in))$ B3%6-"n5$ M0` ,$%i B3%6-" 1"-6%$W ($n .7 )$1 (i-$-*$t,$n *$($ t",$n$n t"t$* 1"9in))$ B3%6-"n5$ -"n#$(i (6$ *"+ ti)$ ,$%i B3%6-" 1"-6%$7 @G $t- E GK` <$A7 M7 >"nt6,$n%$9 61$9$ 5$n) (i%$,6,$n 3%"9 )$1 6nt6, *+31"1 UV 1"16$i ("n)$n (i$)+$- $B' ."+i,6t7

0

Z7

p(Pa)

p(Pa) B

14

10

L7

B

70 60

`7 A 200

A V (dm3)

V (dm3) 10 500

@$A

0

200

p(Pa)

@.A

600 800

I7 50

B

20

A

0

200 400 600

V(dm3)

!".6$9 t$.6n) ("n)$n B3%6-" ` T ."+i1i )$1 i("$% ("n)$n 1696 GKKbX ($n t",$n$n G0K _ GK` <$7 >$.6n) t"+1".6t (i*$n$1,$n 9in))$ -"nJ$*$i 1696 MHKbX7 Ci,$ B3%6-" t$.6n) (i$n))$* t"t$*0 ."+$*$ t",$n$n )$1 ($%$- t$.6n)Y !6$t6 )$1 i("$% 5$n) B3%6-" $D$%n5$ K0LZZ - L (i",1*$n1i,$n 1"9in))$ B3%6-" $,9i+n5$ -"n#$(i K0ZMZ -L *$($ t",$n$n t"t$* GKG ,<$7 $7 >"nt6,$n%$9 61$9$ 5$n) (i%$,6,$n 3%"9 )$1 t"+1".6t ($+i ,"$($$n $D$% 9in))$ ,"$($$n $,9i+7 .7 Un($i,$n *+31"1 ($*$t (i.$%i, ($+i ,"$($$n $,9i+ ," ,"$($$n $D$%0 ."+$*$,$9 ."1$+ 61$9$ 5$n) (i%$,6,$n 3%"9 )$1Y Unt6, -"-*"+,"Ji% B3%6-" 1".6$9 )$1 -"n#$(i 1"t"n)$9n5$ 1"J$+$ i13t"+-$%0 (i*"+%6,$n 61$9$ `KK C7 V"+$*$,$9 61$9$ 5$n) (i*"+%6,$n 6nt6, -"-*"+,"Ji% B3%6-" )$1 t"+1".6t -"n#$(i 1"*"+1"*6%69 ($+i B3%6-" $D$%Y !".6$9 -"1in )$13%in -"-i%i,i +$1i3 ,3-*+"1i0 5$it6 +$1i3 B3%6-" $D$% t"+9$($* B3%6-" $,9i+ 1"."1$+ I0`7 Ci,$ 1696 J$-*6+$n .$9$n .$,$+ 6($+$ $($%$9 LKbX ($n *+31"1 ,3-*+"1i ."+%$n)16n) 1"J$+$ $(i$.$ti, ("n)$n + E G0M0 ."+$*$,$9 1696 J$-*6+$n .$9$n .$,$+ t"+1".6t *$($ ,3-*+"1i -$,1i-$%Y

@JA

B. Hukum I Termodinamika >$96,$9 Un($ t"nt$n) =6,6- g >"+-3(in$-i,$Y Unt6, -"n)"t$96in5$0 1i-$,%$9 6+$i$n ."+i,6t ini 1"J$+$ 1$,1$-$7

1. Pengertian Hukum I Termodinamika =6,6- g t"+-3(in$-i,$ -"n#"%$1,$n 96.6n)$n $nt$+$ ,$%3+ 5$n) (it"+i-$ $t$6 ,$%3+ 5$n) (i%"*$1,$n 3%"9 1i1t"- ," %in),6n)$n ($n 61$9$ 5$n) (i%$,6,$n 3%"9 1i1t"-0 1"+t$ *"+6.$9$n "n"+)i ($%$- 5$n) (iti-.6%e ,$nn5$7 [i1$%,$n 16$t6 1i1t"- -"n"+i-$ ,$%3+ 8 -$,$ ,$%3+ t"+1".6t ti($, 9$n5$ (i)6n$,$n 6nt6, -"n)6.$9 "n"+)i ($%$- @ " CA0 t"t$*i #6)$ (i*$,$i 6nt6, -"%$,6,$n 61$9$ @! A7 !"J$+$ ,"1"%6+69$n0 "n"+)i t"+1".6t ti($,

184

Mudah dan Aktif Belajar Fisika untuk Kelas XI

$($ 5$n) 9i%$n)7 hn"+)i ($*$t ."+6.$9 ."nt6, ," "n"+)i %$inn5$ ($n #6-%$9 "n"+)i t3t$% 1"%$%6 t"t$*7 V"+($1$+,$n 96,6- ,",",$%$n "n"+)i0 =6,6- g >"+-3(in$-i,$ (i+6-61,$n 1".$)$i ."+i,6t7 Dik)+ "AE(9,)*+ k),;r+ F)0G+ %iHArik)0+ kA$)%)+ "i">A9I+ %i$)k)i+ "AH)Gi)0+ ;,A* "i">A9+(0>(k+9A,)k(k)0+(")*)+!I+"A,i"i*+A0ArGi+8B!+")9)+%A0G)0+$Ar(H)*)0 A0ArGi+ %),)9+ @CA+ %)ri+ "i">A93

"C E CM O CG E 8 O ! $t$6 8 E "C a !

Q+

W + sistem

@NOGLA

Unt6, %".i9 -"-$9$-i =6,6- g >"+-3(in$-i,$ t"+1".6t0 *"+9$ti,$n !ambar& '(J7 <"+#$n#i$n t$n($ 6nt6, 8 ($n ! *$($ !ambar& '(J& $($%$9 1".$)$i ."+i,6t7 $7 Ci,$ 1i1t"- -"%$,6,$n 61$9$0 ni%$i ! ."+t$n($ *31itiQ @a!A .7 Ci,$ 1i1t"- -"n"+i-$ 61$9$0 ni%$i ! ."+t$n($ n")$tiQ @O!A J7 Ci,$ 1i1t"- -"n"+i-$ ,$%3+0 ni%$i 8 ."+t$n($ *31itiQ @a8A (7 Ci,$ 1i1t"- -"%"*$1 ,$%3+0 ni%$i 8 ."+t$n($ n")$tiQ @O8A hn"+)i ($%$- 16$t6 )$1 i("$% -"+6*$,$n 6,6+$n %$n)16n) ($+i 1696 ($n t",$n$n7 <"+6.$9$n "n"+)i ($%$- @ " CA 9$n5$ ."+)$nt6n) *$($ ,"$($$n $D$% ($n ,"$($$n $,9i+0 ti($, ."+)$nt6n) *$($ *+31"1 .$)$ie -$n$ ,"$($$n 1i1t"- ."+6.$97 Unt6, )$1 -3n3$t3-i, ("n)$n ("+$#$t ,".".$1$n @J E LA0 *"+6.$9$n "n"+)i ($%$- ($*$t (i9it6n) 1".$)$i ."+i,6t7

" C E CM O CG E L Kk @TM O TGA E L K k@ " TA M M L L " C E CM O CG E 0 1@TM O TGA E 0 1@ " TA M M L " C E CM O CG E @$M'M O $G'GA E L " @$'A M M

@$A

lingkungan

@.A

Q

W

–

– sistem lingkungan

@JA

W=0

Q +

sistem lingkungan

@(A

Q=0

W + sistem

lingkungan

Gambar 8.9

@NOGZA

Unt6, )$1 (i$t3-i, ($n *3%i$t3-i,0 Q$,t3+ L *$($ +,r-amaan& /'0)E2 (i)$nti ("n)$n ("+$#$t ,".".$1$n 5$n) (i-i%i,i )$1 t"+1".6t7

Contoh 8.6

Hubungan sistem dan lingkungan. (a) Sistem menerima kalor sambil melakukan usaha. (b) Sistem melepaskan kalor dan pada sistem dilakukan usaha. (c) Sistem menerima kalor, tetapi tidak melakukan kerja. (d) Sistem melakukan kerja, tetapi tidak ada kalor yang masuk ataupun keluar (adiabatik).

!6$t6 1i1t"- -"n5"+$* ,$%3+ 8 ($+i %in),6n)$n 1"."1$+ G7NKK C7 >"nt6,$n *"+6.$9$n "n"+)i ($%$- @ " CA0 #i,$P $7 1i1t"- -"%$,6,$n 61$9$ M7IKK C t"+9$($* %in),6n)$nW .7 %in),6n)$n -"%$,6,$n 61$9$ M7IKK C t"+9$($* 1i1t"-7 BaCab: $7 !i1t"- -"n"+i-$ ,$%3+ 8 E aG7NKK C ($n 1i1t"- -"%$,6,$n 61$9$ ! E a M7IKK C7 ["n6+6t =6,6- g >"+-3(in$-i,$0 8 E " C a ! " C E 8+O ! E @G7NKK C O M7IKK CAE ONKK C .7 !i1t"- -"n"+i-$ 61$9$ ($+i %in),6n)$n! E OM7IKK C -$,$ (i*"+3%"9 " C E 8+O ! E G7NKK C O @OM7IKK CA E Z7ZKK C >$n($ *31itiQ 6nt6, " C+-"n6n#6,,$n .$9D$ "n"+)i ($%$- 1i1t"- ."+t$-.$9 1"."1$+ Z7ZKK C7

2. Aplikasi Hukum I Termodinamika pada Proses-Proses Termodinamika !".$)$i-$n$ Un($ ,"t$96i0 $($ "-*$t #"ni1 *+31"1 ($%$- t"+-3(in$-i,$0 5$it6 *+31"1 i13t"+-$%0 i13,93+i,0 i13.$+i,0 ($n $(i$.$ti,7 \$%$- .$9$1$n ini $,$n (it"+$*,$n =6,6- g >"+-3(in$-i,$ *$($ *+31"1e*+31"1 t"+1".6t7

Termodinamika

185

a. Proses Isotermal <+31"1 i13t"+-$% $($%$9 *+31"1 5$n) ti($, -"n)$%$-i *"+6.$9$n 1696 @ " T E KA 1"9in))$ *"+6.$9$n "n"+)i ($%$-n5$0 " C E L 01+ @ " TA E K7 M 'M U1$9$ %6$+ 5$n) (i%$,6,$n 3%"9 )$10 5$it6 8 E ! E 01T+ %n ' -$,$ G *"n"+$*$n =6,6- g >"+-3(in$-i,$ $,$n -"n)9$1i%,$n 8 E "C a ! E K a ! E !

Pembahasan Soal Suatu sistem mengalami proses adiabatik. Pada sistem dilakukan usaha 100 J. Jika perubahan energi dalam sistem adalah " U dan kalor yang diserap sistem adalah Q, akan berlaku .... a. " U = –1.000 J b. " U = 100 J c. " U = 10 J d. Q = 0 e. " U + Q = – 100 J Soal UMPTN Tahun 1994 Pembahasan: Hukum I Termodinamika: Q = "U + W Pada proses adiabatik, tidak ada kalor yang diterima atau diserap sistem. Jadi, Q = 0. Pada sistem dilakukan usaha W = –100 J Jadi, Q = "U + W 0 = " U – 100 J " U =100 J Jawaban: b

'M @NOG`A 8 E ! E 01T %n ' G +,r-amaan&/'0)F2 -"n6n#6,,$n .$9D$ ,$%3+ 5$n) (i."+i,$n ,"*$($ 16$t6 1i1t"-0 1"%6+69n5$ (i)6n$,$n 6nt6, -"%$,6,$n 61$9$7 b. Proses Isokhorik <+31"1 i13,93+i, $($%$9 *+31"1 5$n) (i$%$-i 3%"9 1i1t"- t$n*$ $($n5$ *"+6.$9$n B3%6-" @' E KA 1"9in))$ 61$9$ 3%"9 1i1t"- )$1 $($%$9 ! E $@ " 'A E K7 <"+6.$9$n "n"+)i ($%$-n5$ 1"16$i ("n)$n *"+1$-$$n " C E

L 01@" TA7 <"n"+$*$n =6,6- g >"+-3(in$-i,$ -"n)9$1i%,$n i E " C+a j M E " C+a K E " C7 8 E " C E L 01@ " TA @NOGIA M Unt6, )$1 i("$%0 C+E L 01T -$,$ 8 E CM O CG E L 01 @TM O TGA7 M M

C$(i0 ,$%3+ 5$n) (i."+i,$n ,"*$($ 16$t6 1i1t"- *$($ B3%6-" t"t$*0 1"%6+69n5$ (i)6n$,$n 6nt6, -"n$i,,$n "n"+)i ($%$- 1i1t"-7 c.

Proses Isobarik <$($ *+31"1 i13.$+i,0 1i1t"- ti($, -"n)$%$-i *"+6.$9$n ."1$+ t",$n$n

@ "$ E KA7 V"1$+n5$ 61$9$ 5$n) (i%$,6,$n )$1 -"-"n69i *"+1$-$$n ! E $@" 'A E+$@'MO'GA7 <"n"+$*$n =6,6- g >"+-3(in$-i,$ *$($ *+31"1 i13.$+i, -"n)9$1i%,$n 8 E " C+a ! E " C+a $@ " 'A

Tugas Anda 8.1 Diskusikanlah bersama teman Anda, apakah ada proses adiabatik di alam ini?

@NOGHA

d. Proses Adiabatik <$($ *+31"1 $(i$.$ti,0 ti($, t"+#$(i *"+t6,$+$n ,$%3+ ($+i 1i1t"- ," %in),6n)$nn5$ @8 E KA7 <"+6.$9$n "n"+)i ($%$- 1"16$i ("n)$n *"+1$-$$n L " C+E+ 01@TMOTGA7 ;%"9 ,$+"n$ it60 *"n"+$*$n =6,6- g >"+-3(in$-i,$ M

*$($ *+31"1 $(i$.$ti, -"n)9$1i%,$n 8 E " C a ! $t$6 K E " C+a+! ! E O " C E O+ L 0 1@TMOTGAW $t$6 M

! E L 0 1@TGOTMA M

Kata Kunci • • • •

adiabatik isobarik isokhorik isotermal

186

@NOGNA

+,r-amaan& /'0)'2 -"n5$t$,$n .$9D$ ti($, $($ ,$%3+ 5$n) -$16, ," ($%$- 1i1t"- 1"9in))$ 61$9$ %6$+ 5$n) (i%$,6,$n 1i1t"- $,$n -"n)6+$n)i "n"+)i ($%$- 1i1t"-7 \$+i ,""-*$t *+31"1 5$n) ($*$t (i$%$-i 1i1t"-0 8 ."+ni%$i *31itiQ #i,$ 1i1t"- -"n"+i-$ ,$%3+ ($n n")$tiQ #i,$ 1i1t"- -"%"*$1,$n ,$%3+7 =6,6- g >"+-3(in$-i,$ ($*$t (i$*%i,$1i,$n *$($ 1"-6$ *+31"1 t"+-3(in$-i,$ 5$n) ."+96.6n)$n ("n)$n ,"ti)$ ."1$+$n0 5$it6 80 !0 ($n "C7

Mudah dan Aktif Belajar Fisika untuk Kelas XI

Tes Kompetensi Subbab

B

K,r7akanla>&an( G7

M7

L7

Z7

!6$t6 )$1 -"n5"+$* ,$%3+ `KK C ($n -"%$,6,$n 61$9$ `K C7 V"+$*$ *"+6.$9$n "n"+)i ($%$- 1i1t"- )$1 t"+1".6tY U*$,$9 )$1 t"+1".6t -"-6$i $t$6 (i-$-e *$t,$nY !6$t6 1i1t"- -"n"+i-$ ,$%3+ 1"."1$+ GK C ($n -"%$,6,$n 61$9$ %6$+ 1"."1$+ Z C *$($ 1696 t"t$* MHbX7 V"+$*$,$9 *"+6.$9$n "n"+)i ($%$- 1i1t"- t"+1".6tY !".$n5$, Z -3% )$1 i("$% -3n3$t3-i, ("n)$n 1696 $D$% MHbX (in$i,,$n 1696n5$ -"n#$(i GMHbX *$($ t",$n$n t"t$*7 V"+$*$,$9 ,$%3+ 5$n) (i*"+%6,$nY @1 E N0LG Cc-3%:A !6$t6 )$1 *$($ t",$n$n ,3n1t$n 1"."1$+ I0Z _ GKZ <$ (i-$-*$t,$n ($+i B3%6-" N %it"+ -"n#$(i M %it"+7 \$%$*+31"1 t"+1".6t0 )$1 -"%"*$1 ,$%3+ ZKK #36%"7 $7 V"+$*$,$9 61$9$ 5$n) (i%$,6,$n 3%"9 )$1Y .7 V"+$*$,$9 *"+6.$9$n "n"+)i ($%$-n5$Y

`7

I7

C"%$1,$n .$9D$ )$1 ($*$t (i*"+%$,6,$n -"n5"+6*$i ,"$($$n )$1 i("$% *$($ *+31"1 i13t"+-i,0 i13.$+i,0 ($n i13B3%6-"7 <"+9$ti,$n )+$Qi, ."+i,6t ini7 p (atm) D

2,0

1,5

N 0,3

J

U 0,8

V (liter)

Unt6, ,"ti)$ %int$1$n \^U0 \CU0 ($n \U ($%$)$-.$+0 9it6n)%$9P $7 61$9$ 5$n) (i%$,6,$n 3%"9 )$1W ($n .7 *"+*in($9$n ,$%3+ ($%$- *+31"17

C. Kapasitas Kalor Gas dan Siklus Termodinamika :$*$1it$1 ,$%3+ @/A ($+i 16$t6 /$t (i("Qini1i,$n 1".$)$i H)0F)k0F) k),;r i F)0G+ %i$Ar,(k)0+ (0>(k+ 9A0)ikk)0+ "(*(+ L)>+ >Ar"AH(>+ "AHA")r+ 5+ kA,&i0 )>)(+ ")>(+ %Ar)E)>+ cA,"i("7 !"J$+$ -$t"-$ti10 (it6%i1,$n

8 @NOGfA "T :$*$1it$1 ,$%3+ 6nt6, )$1 $($ (6$ -$J$-0 5$it6 6nt6, B3%6-" t"t$* @/BA ($n 6nt6, t",$n$n t"t$* @/*A0 ("n)$n /* O /d E 0 17 /E

1. Kapasitas Kalor untuk Proses Isokhorik (V = tetap) :$*$1it$1 ,$%3+ 6nt6, )$1 5$n) -"-i%i,i B3%6-" t"t$* ($*$t (i9it6n) 1".$)$i ."+i,6t7 L 0 1 "T " C M E E L 01 /'E M "T "T

Unt6, )$1 -3n3$t3-i,P /d E L 0 1

@NOMKA

/d E ` 01

@NOMGA

M

Unt6, )$1 (i$t3-i,P

M

2. Kapasitas Kalor untuk Proses Isobarik (p = tetap)

:$*$1it$1 ,$%3+ 6nt6, )$1 5$n) -"-i%i,i t",$n$n t"t$* ($*$t (i9it6n) 1".$)$i ."+i,6t7 8 E "U a $@ "V A E L 01 @ "T A a 01 @ "T A E ` 01 @ "T A M M Unt6, )$1 -3n3$t3-i,P

/*E ` 01

@NOMMA

Unt6, )$1 (i$t3-i,P

/* E

H 01 M

@NOMLA

M

Kata Kunci • kapasitas kalor tekanan tetap • kapasitas kalor volume tetap • konstanta Laplace

Tantangan untuk Anda Anda pasti tahu apa termos itu. Dapatkah Anda menjelaskan cara kerja termos sehingga air panas dapat tetap panas? Jelaskan hal tersebut dengan konsep termodinamika.

Termodinamika

187

;ab,l&'() >"t$*$n T$*%$J" + ]$1e]$1 >"+t"nt6 *$($ >",$n$n G $t($n !696 MMbX

M

!aN;0;)>;9ikO ="%i6- @="A U+)3n @U+A 6i)>;9ikO ^it+3)"n @^MA ;,1i)"n @;MA :$+.3n -3n3,1i($ @X;A

H 01 /* + k ]$1 (i$t3-i,P E E M E G0Z7 ` 01 /d M ;ab,l&'() -"n6n#6,,$n ni%$i ,3n1t$nt$ T$*%$J" 6nt6, ."."+$*$ )$1 *$($ t",$n$n G $t- ($n 1696 MMbX7

G0II G0IH G0ZK G0ZK

Contoh 8.7

G0ZK

Sumber: Fundamental of Physics, 2001

Tantangan untuk Anda Anda pasti pernah mendengar istilah mesin 4 tak dan mesin 2 tak. Selidikilah dan diskusikanlah, apa perbedaan di antara keduanya? Mengapa mesin 2 tak memiliki akselerasi lebih cepat daripada mesin 4 tak?

p A

Q1 B W D

T1 C

Q2

T2 V

Gambar 8.10 Satu siklus suatu mesin Carnot menggunakan suatu gas ideal sebagai fluida kerja. Grafik AB dan CD menampilkan proses isotermal, grafik BC dan DA menampilkan proses adiabatik.

188

:3n1t$nt$ T$*%$J" 1"J$+$ t"3+iti1 ($*$t (i9it6n) 1"16$i ("n)$n *"+e 1$-$$n ."+i,6t7 ` 01 /* k ]$1 -3n3$t3-i,P + E E M E G0IH7 L 01 /d

!696 M ,) )$1 nit+3)"n @."+$t -3%",6% E MN )c-3%A (in$i,,$n ($+i G`bX+-"n#$(i GKKbX -"%$%6i *+31"1 i13.$+i,7 =it6n) ,"n$i,$n "n"+)i ($%$- ($n 61$9$ 5$n) (i%$,6,$n 3%"9 )$17 BaCab: ]$1 ^M *$($ ,"$($$n ini ($*$t (i)3%3n),$n 1".$)$i )$1 (i$t3-i, 1696 1"($n) 1"9in))$ ,$*$1it$1 *$n$1 -3%$+ )$1 *$($ B3%6-" t"t$* ($n *$($ t",$n$n t"t$* $($%$9 ` ` /&+M+ 1+E M N0LG Cc-3%: E MK0N Cc-3%: M /$+M+ H 1+E H N0LG Cc-3%: E Mf0G Cc-3%: M M C6-%$9 -3% )$1 $($%$9 @1$t6$n -$11$n5$ 9$+61 (i6.$9 ($%$- )+$-AP 0 E 9 E M7KKK -3% E `KK -3% MN )c-3% .N H \i,"t$96iP `KK -3% 0E H /& E MK0N Cc-3%: /$ E Mf0G Cc-3%: T M E @GKK a MHLA : E LHL : T G E @G` a MHLA : E MNN : " T+E LHL : O MNN : E N` : `KK " C E++0/B " T+E -3% @MK0N Cc-3%:A@N` :A E G0MI _ GK` C H `KK -3%@Mf0G Cc-3%:A@N` :A E G0HH _ GK` C 8 E 0/* " T+E H ! E+8 O " T+E @G0HH _ GK`A C O @G0MI _ GK`A C E `0G _ GKZ C



%$

%$!"3+$n) i%-6D$n <+$nJi10 Sa
Mudah dan Aktif Belajar Fisika untuk Kelas XI

<+31"1 ($+i U ," V $($%$9 *+31"1 ",1*$n1i $t$6 *+31"1 *"n)"-.$n)$n i13t"+-$% *$($ 1696 TG7 <$($ *+31"1 ini0 )$1 -"n5"+$* ,$%3+ 8G ($+i +"1"+B3i+ ."+1696 tin))i TG ($n -"%$,6,$n 61$9$ !UV7 <+31"1 ($+i V ," X $($%$9 *+31"1 *"n)"-.$n)$n $(i$.$ti,7 !"%$-$ *+31"10 1696 )$1 t6+6n ($+i TG -"n#$(i TM 1$-.i% -"%$,6,$n 61$9$ !VX7 <+31"1 ($+i X ," \ $($%$9 *+31"1 *"-$-*$t$n i13t"+-$% *$($ 1696 TM7 \$%$- *+31"1 ini0 )$1 -"%"*$1 ,$%3+ 8M ," +"1"+B3i+ ."+1696 +"n($9 TM ($n -"%$,6,$n 61$9$ !X\7 <+31"1 $,9i+ ($+i \ ," U $($%$9 *+31"1 *"-$-*$t$n $(i$.$ti,7 !696 n$i, ($+i TM ," TG 1$-.i% -"%$,6,$n 61$9$ !\U7 !i,%61 X$+n3t $($%$9 ($1$+ ($+i -"1in (i"1"%0 5$it6 -"1in 5$n) *$%in) i("$%0 5$n) 1"%$n#6tn5$ (i1".6t -"1in X$+n3t7 !"%$-$ *+31"1 1i,%61 X$+n3t ."+%$n)16n)0 )$1 -"n"+i-$ ,$%3+ 8G ($+i +"1"+B3i+ ."+1696 tin))i ($n -"%"*$1 ,$%3+ 8M ," +"1"+B3i+ ."+1696 +"n($97 U1$9$ 5$n) (i%$,6,$n 3%"9 )$1 1"16$i ("n)$n =6,6- g >"+-3(in$-i,$ $($%$9 8 E " C a ! $t$6 8G O 8ME K a ! ! E 8G O 8M

T1

Q1

W (= Q1)

Q2 = 0

Gambar 8.11 Siklus mesin ideal Q1 dan suhu fungsi reservoir diubah seluruhnya menjadi usaha W dengan efisiensi 100%.

@NOMZA

:"t"+$n)$nP 8G E ,$%3+ 5$n) (i1"+$* ($+i +"1"+B3i+ 5$n) ."+1696 tin))i 8M E ,$%3+ 5$n) (i%"*$1 ," +"1"+B3i+ 5$n) ."+1696 +"n($9

3. Efisiensi Mesin <"+9$ti,$n !ambar&'()17 ]$-.$+ t"+1".6t -"n6n#6,,$n 1i,%61 ,$%3+ (i ($%$- 1".6$9 -"1in7 <"+.$n(in)$n $nt$+$ ."1$+n5$ 61$9$ @!A 5$n) ($*$t (i%$,6,$n 3%"9 1i1t"- t"+9$($* ,$%3+ @8GA 5$n) (i1"+$* ($*$t -"n"nt6,$n "Qi1i"n1i 16$t6 -"1in7 !"J$+$ -$t"-$ti10 "Qi1i"n1i -"1in ($*$t (it6%i1,$n 1".$)$i ."+i,6t7 3E

! _ GKKl 8G

Kata Kunci • efisiensi mesin

@NOM`A

a. Mesin Carnot hQi1i"n1i -"1in X$+n3t (i*"+3%"9 ("n)$n J$+$ -"n))$nti 61$9$ @!A ("n)$n +,r-amaan& /'01E2 1"9in))$ +,r-amaan& /'01F2 -"n#$(i 8G , 8M _GKKl 8G

% 8 & $t$6 3 E ' G , M ( _ GKKl @NOMIA 8G * ) >"%$9 (i.$9$1 .$9D$ 6nt6, 16$t6 )$1 i("$%0 "n"+)i ($%$- @CA 1".$n(in) ("n)$n 1696 -6t%$, @TA 1"9in))$ 6nt6, -"1in X$+n3t0 +,r-amaan& /'01G2 ($*$t (it6%i1 1".$)$i ."+i,6t7

3E

% T & 3 E ' G , M ( _ GKKl TG * )

:"t"+$n)$nP TG E 1696 +"1"+B3i+ tin))i @:A TM E 1696 +"1"+B3i+ +"n($9 @:A

Q1

W

@NOMHA

<"n))$nti$n ."1$+$n ,$%3+ @8A -"n#$(i 1696 -6t%$, @TA ($%$-"n"nt6,$n "Qi1i"n1i 1".6$9 -"1in0 ."+($1$+,$n *$($ "n"+)i ($%$1".$n(in) ("n)$n 16967 :"%Bin -"n6n#6,,$n .$9D$ 8M T E M 8G TG

T1

Q2 T2

Gambar 8.12

@NOMNA

Perubahan kalor menjadi kerja: Q1 = kalor masuk; Q2 = kalor dilepaskan; W = usaha yang dilakukan; T1 = suhu reservoir tinggi; dan T2 = suhu reservoir rendah.

Termodinamika

189

p A B

Q1 D

Q2 C V

Gambar 8.13

b. Mesin Otto ["1in ;tt3 -"+6*$,$n -"1in ,$%3+ 5$n) *+in1i* ,"+#$n5$ ."+($1$+,$n 1i,%61 ;tt37 <$($ 1i,%61 ;tt30 t"+($*$t (6$ *+31"1 $(i$.$ti, ($n (6$ *+31"1 i13,93+i,7 <"+9$ti,$n !ambar& '()A7 <$($ !ambar&'()A0 UOV ($n XO\ -"+6*$,$n *+31"1 $(i$.$ti,0 1"($n),$n VOX ($n \OU -"+6*$,$n *+31"1 i13,93+i,7 U($*6n 8G $($%$9 ,$%3+ 5$n) -$16, ($%$- 1i1t"-0 1"($n),$n 8M $($%$9 ,$%3+ 5$n) ,"%6$+ @(i%"*$1,$nA 3%"9 1i1t"-7 hQi1i"n1i ($+i 1i,%61 ;tt3 (in5$t$,$n ("n)$n *"+1$-$$n G,+

Dua proses adiabatik dan dua proses isokhorik pada siklus Otto.

%8 & 3 &G,' M ( ) 8G *

@NOMfA

!i,%61 ;tt3 .$n5$, (i$*%i,$1i,$n *$($ -"1in -3t3+ .$,$+7 c.

p A

D Q1

B Q2 C V

Gambar 8.14 Siklus diesel

Mesin Diesel ["1in (i"1"% -"+6*$,$n -"1in ,$%3+ 5$n) *+in1i* ,"+#$n5$ -"n))6n$,$n 1i,%61 (i"1"%7 <$($ 1i,%61 (i"1"% t"+($*$t (6$ *+31"1 $(i$.$ti,0 1$t6 *+31"1 i13.$+i,0 ($n 1$t6 *+31"1 i13,93+i,7 <"+9$ti,$n !ambar& '()E7 <+31"1 ($+i \ ," U -"+6*$,$n *+31"1 i13.$+i,0 UOV ($n XO\ -"+6*$,$n *+31"1 $(i$.$ti,0 ($n *+31"1 VOX -"+6*$,$n *+31"1 i13,93+i,7 <+in1i* ,"+#$ -"1in (i"1"% 9$-*i+ 1$-$ ("n)$n -"1in 3tt3 ,$+"n$ 1"-6$ *+31"1 *$($ -"1in (i"1"% 1$-$ ("n)$n -"1in 3tt30 ,"J6$%i *+31"1 i13.$+i,7 hQi1i"n1i ."."+$*$ -"1in (it6n#6,,$n *$($ ;ab,l& '(17 ;ab,l&'(1 hQi1i"n1i V"."+$*$ ["1in B,ni-&M,-in

Pembahasan Soal Sebuah mesin Carnot yang menggunakan reservoir suhu tinggi 800 K, memiliki efisiensi 40%. Agar efisiensinya naik menjadi 50%, suhu reservoir suhu tinggi dinaikkan menjadi .... a. 900 K d. 1.180 K b. 960 K e. 1.600 K c. 1.000 K Soal UMPTN Tahun 1990 Pembahasan: Keadaan 1: 3 = 40% T1 = 800 K T 3 = 1 – 2 $ 40% T1 T2 =1– 800 K T2 = 480 K

MK O M` MI O LN L` ZK

Contoh 8.8 !".6$9 -"1in X$+n3t -"-i%i,i "Qi1i"n1i ZKl7 Ci,$ 1696 +"1"+B3i+ tin))i NKK :0 t"nt6,$n%$9 ."1$+n5$ 1696 +"1"+B3i+ tin))i $)$+ "Qi1i"n1i -"1in -"n#$(i `Kl ("n)$n $n))$*$n 1696 +"1"+B3i+ +"n($9 ti($, -"n)$%$-i *"+6.$9$n7 BaCab: <"+t$-$0 t"nt6,$n 1696 +"1"+B3i+ +"n($9 @TMA *$($ 3 E ZKl7

3 EGO

TM TG

ZKl E G O

TM $ TM E ZNK : NKK :

:"(6$0 t"nt6,$n 1696 +"1"+B3i+ tin))i @TGA ("n)$n -"-*"+)6n$,$n TM 5$n) t"%$9 (i9it6n) t$(i 6nt6, E `Kl7

TM TG ZNK : `Kl E G O TG ZNK : ZNK : K0` E G O E K0` $ TG E fIK : $ TG TG

Keadaan 2: 3 = 50% T2 = 480 K T 3 = 1 – 2 $ 50% T1 480 K =1– T1 T1 = 960 K

3 EGO

Jawaban b

190

["1in -3.i% @."n1inA ["1in (i"1"% >6+.in 6$* *"-.$n),it n6,%i+ >6+.in 6$* *"-.$n),it .$t6.$+$

NOi-i,n-i&/P2

C$(i0 1696 +"1"+B3i+ tin))i 5$n) (i.6t69,$n $($%$9 fIK :7

Mudah dan Aktif Belajar Fisika untuk Kelas XI

Tes Kompetensi Subbab

C

K,r7akanla>&an( G7 !".6$9 -"1in X$+n3t 5$n) -"n))6n$,$n +"1"+B3i+ 1696 tin))i NKK :0 -"-i%i,i "Qi1i"n1i MKl7 Unt6, -"n$i,,$n "Qi1i"n1in5$ -"n#$(i LIl0 ."+$*$ ("+$#$t 1696 +"1"+B3i+ tin))i 9$+61 (in$i,,$nY M7 ["1in X$+n3t 5$n) ."+1696 +"1"+B3i+ tin))i HKbX -"-i%i,i "Qi1i"n1i ZKl7 hQi1i"n1i ($+i -"1in t"+1".6t (itin),$t,$n -"n#$(i `Kl7 V"+$*$ ("+$#$t 1696 +"1"+B3i+ tin))i 9$+61 (in$i,,$nY L7 ["1in X$+n3t -"n"+i-$ ,$%3+ ($+i +"1"+B3i+ 5$n) ."+1696 tin))i MMHbX ($n -"%"*$1,$nn5$ *$($ 1696 +"n($9 MHbX7 >"nt6,$n "Qi1i"n1i -"1in X$+n3t t"+1".6t7 Z7 ["1in *"n(in)in +6$n)$n -"n5"+$* ,$%3+ 1"."1$+ Z7KKK #36%" ($%$- D$,t6 G 1",3n7 Ci,$ 1696 +6$n)$n $,$n (i*"+t$9$n,$n 1"."1$+ M`bX0 1"($n),$n 1696

`7

I7

%in),6n)$n t"-*$t *"-.6$n)$n ,$%3+ $($%$9 LMbX7 V"+$*$,$9 ($5$ %i1t+i, 5$n) (i.6t69,$nY !".6$9 -"1in -"n5"+$* ,$%3+ 1"."1$+ `7KKK C36%" ($+i 1".6$9 +"1"+B3i+ ."+1696 `KK : ($n -"-.6$n)n5$ 1"."1$+ M7KKK #36%" *$($ 1696 MKK :7 \$+i ($t$ t"+1".6t0 t"nt6,$n%$9P $7 "Qi1i"n1i -"1inW ($n .7 61$9$ 5$n) ($*$t (i%$,6,$n7 !".6$9 -"1in X$+n3t -"-i%i,i "Qi1i"n1i LKl7 Ci,$ 1696 +"1"+B3i+ tin))i H`K :0 t"nt6,$n%$9 ."1$+n5$ 1696 +"1"+B3i+ tin))i $)$+ "Qi1i"n1i -"1in -"n#$(i `Kl0 ("n)$n $n))$*$n 1696 +"1"+B3i+ +"n($9 ti($, -"n)$%$-i *"+6.$9$n7

Tokoh

D. Hukum II Termodinamika =6,6- g >"+-3(in$-i,$ -"n5$t$,$n t"nt$n) ,",",$%$n "n"+)i0 5$it6 "n"+)i ti($, ($*$t (iJi*t$,$n $t$6 (i-61n$9,$n0 -"%$in,$n 9$n5$ ($*$t (i6.$9 ($+i 1$t6 ."nt6, "n"+)i ," ."nt6, "n"+)i %$inn5$7 =6,6- g >"+-3(in$-i,$ ti($, -"-.$t$1i .$)$i-$n$ *"+6.$9$n "n"+)i t"+1".6t ."+%$n)16n)7 T$in 9$%n5$ ("n)$n =6,6- gg >"+-3(in$-i,$ 5$n) -"-i%i,i .$t$1$ne.$t$1$n t"+t"nt67 !".6$9 -"1in ($*$t ."+)"+$, (i1".$.,$n $($n5$ "n"+)i ,$%3+ 5$n) (i."+i,$n *$($ -"1in t"+1".6t 1"J$+$ t"+61e-"n"+610 t"t$*i 1".$%i,n5$ ti($, -6n),in "n"+)i )"+$, @61$9$A ($*$t -"-."+i,$n ,$%3+ 1"J$+$ t"+61 -"n"+617 <$($ ,"n5$t$$nn5$0 ti($, $($ 1".6$9 -"1in *6n 5$n) .","+#$ -"n5"+$* "n"+)i ,$%3+ ($n -"n)6.$9 1"%6+69n5$ -"n#$(i 61$9$7 V"+i,6t ini 9$%e9$% 5$n) ."+,$it$n ("n)$n =6,6- gg >"+-3(in$-i,$ 5$n) -"+6*$,$n ,"1i-*6%$n ($+i *"n)$-$t$ne*"n)$-$t$n 5$n) (i%$,6,$n 3%"9 K,lQin0 +lanRk0 ($n Klau-iu-7 G7 ["n6+6t :"%Bin ($n <%$nJ,0 ti($, -6n),in -"-.6$t -"1in 5$n) .","+#$ ($%$- 16$t6 1i,%610 -"n"+i-$ ,$%3+ ($+i 1$t6 +"1"+B3i+ ($n -"n)6.$9 1"%6+69 ,$%3+ t"+1".6t -"n#$(i 61$9$7 M7 ["n6+6t X%$61i610 ti($, -6n),in -"-.6$t -"1in 5$n) .","+#$ ($%$1$t6 1i,%610 -"n)$-.i% ,$%3+ ($+i +"1"+B3i+ 5$n) -"-i%i,i 1696 +"n($9 ($n -"-."+i,$nn5$ *$($ +"1"+B3i+ 5$n) -"-i%i,i 1696 tin))i t$n*$ -"-"+%6,$n 61$9$ ($+i %6$+7 L7 ["1in X$+n3t 5$n) .","+#$ (i $nt$+$ +"1"+B3i+ 1696 TG ($n +"1"+B3i+ 5$n) ."+1696 TM @TG R TMA -"n)9$1i%,$n "Qi1i"n1i 5$n) tin))i7 C$(i0 -"n6+6t :"%Bin ($n <%$nJ, ti($, -6n),in 16$t6 -"1in 9$n5$ -"-i%i,i 1".6$9 +"1"+B3i+ ($n ti($, -6n),in 1".6$9 -"1in -"-i%i,i "Qi1i"n1i GKKl7 Ci,$ "Qi1i"n1i GKKl0 ,$%3+ 5$n) (i1"+$* ($+i %in),6n)$nn5$ $,$n (i6.$9 1"%6+69n5$ -"n#$(i 61$9$7 U1$9$ -"1in 1"-$J$- ini (i1".6t -"1in $rA$A>((9+9;Hi,A #"ni1 ,"(6$7 :"n5$t$$nn5$0 ti($, $($ -"1in 1"*"+ti it60 D$%$6*6n -$1i9 -"-"n69i =6,6- g >"+-3(in$-i,$7

Nikolaus Otto

Sumber: Jendela Iptek: Energi, 1997

Pada 1876, seorang warga negara Jerman, Nikolaus Otto menjadi orang pertama yang membuat dan menjual mesin 4 tak yang kemudian menjadi dasar pembuatan kebanyakan mesin. Ia menamakan mesinnya Silent Otto karena mesin tersebut mampu bekerja tanpa menimbulkan kebisingan. Salah satu ciri mesin 4 tak adalah tekanan kompresinya. Jika bahan bakar berupa gas yang dimampatkan, akan lebih banyak energi yang dilepaskan. Gagasan ini pertama kali dikembangkan oleh Alphone Beau de Rochas (1815– 1891) yang berkewarganegaraan Prancis, tetapi justru Otto yang menyukseskan ide tersebut.

Termodinamika

191

["n6+6t X%$61i610 -"1in 1"%$%6 -"-"+%6,$n 61$9$ %6$+ $)$+ ($*$t -"-in($9,$n ,$%3+ ($+i t"-*$t 5$n) ."+1696 +"n($9 ," t"-*$t 5$n) ."+1696 tin))i7 ["1in 1"*"+ti ini (i1".6t -"1in *"n(in)in0 -i1$%n5$ %"-$+i "1 ($n *"n(in)in +6$n)$n $t$6 UX @)ir+ c;0%i>i;0ArA7

1. Proses Reversibel dan Irreversibel <+31"1e*+31"1 *$($ -"1in ,$%3+ $($ 5$n) ."+1iQ$t rA&Ar"iHA,+($n $($ *6%$ 5$n) ."+1iQ$t irrA&Ar"iHA,+ @ti($, +"B"+1i."%A7 <+31"1 rA&Ar"iHA,+ -"+6*$,$n *+31"1 5$n) ."+%$n)16n) 1$n)$t %$-.$t 1"9in))$ *+31"1n5$ ($*$t (i$n))$* 1".$)$i +$n),$i$n ,"$($$n 1"ti-.$n)7 !"%6+69 *+31"1 t"+1".6t ($*$t (i,"+#$,$n 1"J$+$ ,".$%i,$n t$n*$ -"n)6.$9 ."1$+ 61$9$ 5$n) (i%$,6,$n $t$6 ,$%3+ 5$n) (i*in($9,$n7 <+31"1 +"B"+1i."% 1"-*6+n$ ti($, ($*$t (it"nt6,$n ($%$- ,"n5$t$$n ,$+"n$ *+31"1 ini t$, t"+.$t$17 <+31"1 ini #6)$ -"n)9"n($,i ti($, $($n5$ )"1",$n0 )$n))6$n $%i+$n 6($+$0 1"+t$ Q$,t3+ *"n)6.$9 ,$%3+ ($n 61$9$ %$inn5$7 <+31"1 5$n) $($ *$($ ,"n5$t$$nn5$ $($%$9 *+31"1 i++"B"+1i."%7 <$($ *+31"1 n5$t$0 -i1$%n5$ -$1i9 (it"-6,$n )"1",$n 5$n) -"n5".$.,$n $($n5$ *$n$1 5$n) 9i%$n) $t$6 $%i+$n )$1 5$n) ."+6.$97 T1

Q1

W

Q2 T2

Gambar 8.15 Perubahan kerja menjadi kalor.

Tantangan

2. Mesin Pendingin (Refrigerator) =6,6- gg >"+-3(in$-i,$ ."+*")$n) ,"*$($ ,"J"n("+6n)$n $%$-i$9 1iQ$t ,$%3+ 5$n) 1"%$%6 -"+$-.$t 1"J$+$ 1*3nt$n ($+i ."n($ ."+1696 tin))i ," ."n($ 5$n) ."+1696 +"n($90 ,"J6$%i #i,$ $($ 61$9$ %6$+ 5$n) -"-$,1$ -"-in($9,$n ,$%3+ ($+i 1i1t"- ."+1696 +"n($9 ," %in),6n)$n 5$n) ."+1696 %".i9 tin))i7 <$($ -"1in *"n(in)in0 1i1t"- -"n)$-.i% ,$%3+ 8M ($n -"%"*$1,$n ,$%3+ 8G7 U($*6n 61$9$ 5$n) (i%$,6,$n $($%$9 !7 !i,%61 -"1in *"n(in)in ($*$t (i%i9$t *$($ !ambar& '()F7 :"t"+$n)$n )$-.$+P 8G E ,$%3+ 5$n) (i%"*$1,$n *$($ 1696 tin))i TG 8M E ,$%3+ 5$n) (i1"+$* *$($ 1696 +"n($9 TM ! E 61$9$ 5$n) (i%$,6,$n ($+i %6$+ U,6+$n ($5$ 1".6$9 -"1in *"n(in)in (in5$t$,$n ("n)$n ,3"Qi1i"n ($5$ )6n$7 !"J$+$ -$t"-$ti10 ($*$t (it6%i1,$n 1".$)$i ."+i,6t7 PE

untuk Anda Mengapa AC menggunakan freon? Apakah freon dapat digantikan oleh gas lain?

8M 8M TM E E 8G , 8M ! TG , TM

@NOLKA

T"-$+i "1 ($n *"n(in)in +6$n)$n -"-i%i,i ,3"Qi1i"n ($5$ )6n$ ($%$#$n),$6$n M 1$-*$i ("n)$n I7 !"-$,in tin))i ni%$i P0 1"-$,in .$i, -"1in *"n(in)in t"+1".6t7

Contoh 8.9 >"-*"+$t6+ (i ($%$- 1".6$9 %"-$+i "1 $($%$9 OLbX7 m%6i($ ,"+#$ 5$n) (i-$-*$t,$n (i ($%$-n5$ -"n)"-.$n) *$($ t"-*"+$t6+ 1"."1$+ MHbX7 >"nt6,$n%$9 ,3"Qi1i"n ($5$ )6n$ %"-$+i "1 t"+1".6t7 BaCab: \i,"t$96iP TM E @OL a MHLA E MHK : TG E @MH a MHLA E LKK : \"n)$n -"n))6n$,$n *"+1$-$$n TM P E T ,T G M

192

Mudah dan Aktif Belajar Fisika untuk Kelas XI

(i*"+3%"9 MHK : MHK : P E LKK , MHK : E Ef $ % LK : C$(i0 ,3"Qi1i"n ($5$ )6n$ %"-$+i "1 t"+1".6t 1"."1$+ f7

Tes Kompetensi Subbab

D

K,r7akanla>&an( G7

M7

L7

!696 (i ($%$- 1".6$9 %"-$+i "1 $($%$9 O`bX7 m%6i($ ,"+#$ 5$n) (i-$-*$t,$n (i ($%$-n5$ -"n)"-.6n *$($ 1696 M`bX7 >"nt6,$n%$9 ,3"Qi1i"n ($5$ )6n$ %"-$+i "1 t"+1".6t7 !"#6-%$9 -$,$n$n ($%$- %"-$+i "1 -"n)9$1i%,$n ,$%3+ 1"."1$+ Z7MKK C7 Ci,$ ,3"Qi1i"n ($5$ )6n$ %"-$+i "1 t"+1".6t L0`7 >"nt6,$n%$9 "n"+)i %i1t+i, 5$n) (i*"+%6,$n %"-$+i "1 6nt6, -"-in($9,$n ,$%3+ 5$n) (i9$1i%,$n -$,$n$n7 ["1in *"n(in)in +6$n)$n -"n5"+$* ,$%3+ 1"."1$+ N7`ZK C ($%$- D$,t6 G 1",3n7 !696 +6$n)$n (i*"+t$9$n,$n 1"."1$+ GNbX0 1"($n),$n 1696

Z7

`7

%in),6n)$n t"-*$t *"-.6$n)$n ,$%3+ $($%$9 LMbX7 >"nt6,$n%$9 ($5$ %i1t+i, 5$n) (i.6t69,$n7 !6$t6 -"1in *"n(in)in ."+($5$ ,"+#$ MKK D$tt7 Ci,$ 1696 +6$n) *"n(in)in OZbX ($n 1696 6($+$ (i %6$+ M`bX @$n))$* -"1in i("$%A0 ."+$*$ ,$%3+ -$,1i-65$n) ($*$t (i1"+$* -"1in *"n(in)in ($+i +6$n) *"n(in)inn5$ 1"%$-$ GK -"nitY !6$t6 .$n)6n$n 9"n($, (i(in)in,$n ("n)$n 1".6$9 -"1in *"n(in)in i("$%7 !696 (i %6$+ .$n)6n$n MNbX ($n (i ($%$- .$n)6n$n G`bX7 Ci,$ $%$t *"n(in)in t"+1".6t ."+,",6$t$n GK *$+@G *$+E HZ` D$ttA0 ."+$*$ *$n$1 5$n) (i,"%6$+,$n ($+i .$n)6n$n t"+1".6t 1"ti$* #$-Y

Rangkuman G7 :$%3+ -"+6*$,$n 1$%$9 1$t6 ."nt6, "n"+)i 5$n) ($*$t ."+*in($9 ($+i 16$t6 %in),6n)$n ," 16$t6 1i1t"-0 $t$6 1".$%i,n5$7 :$%3+ ."+*in($9 ($+i 1696 tin))i ," 1696 5$n) %".i9 +"n($97 8+E+9c " T M7 <$($ ,"$($$n t",$n$n t"t$*0 61$9$ 5$n) (i%$,6,$n )$1 $($%$9 'M

!E

# $ %'

E $ @'M O 'GA E $ " '

'G

Ci,$ )$1 -"%$,6,$n ",1*$n1i @*"n)"-.$n)$nA0 61$9$ ."+ni%$i *31itiQ 5$n) -"n5".$.,$n B3%6-" ."+t$-.$9 $t$6 'M R 'G7 Ci,$ )$1 (i-$-*$t,$n0 61$9$ ."+ni%$i n")$tiQ7 Tin),6n)$n -"%$,6,$n 61$9$ *$($ 1i1t"- 1"9in))$ 'M S 'G7 L7 ]$1 5$n) ."+$($ ($%$- +6$n) t"+t6t6* ($*$t (i6.$9 ,"$($$nn5$ -"%$%6i ."."+$*$ *+31"17 $7 <+31"1 g13t"+-$%0 t"+#$(i *$($ 1696 t"t$*7 U1$9$ 'M 5$n) (i%$,6,$n )$1 $($%$9 ! E +0 1T %n ' 7 G .7 <+31"1 g13,93+i,0 t"+#$(i *$($ B3%6-" t"t$*7 U1$9$ 5$n) (i%$,6,$n )$1 $($%$9 ! E $@ " 'A E K7 J7 <+31"1 g13.$+i,0 t"+#$(i *$($ t",$n$n t"t$*7 U1$9$ 5$n) (i%$,6,$n )$1 $($%$9 ! E $@'M O 'GA E $ $ "' % 7 (7 <+31"1 U(i$.$ti,0 t"+#$(i *$($ ,"$($$n 1i1t"- @)$1A ti($, -"n)$%$-i *"+t6,$+$n ,$%3+ ("n)$n %in),6n)$n7 <$($ *+31"1 ini t"+#$(i *"+6.$9$n 16960

t",$n$n0 ($n B3%6-"7 U1$9$ 5$n) (i%$,6,$n )$1 L $($%$9 ! E 01 @TG O TMA7 M Z7 =6,6- g >"+-3(in$-i,$ (i+6-61,$n 1".$)$i ."+i,6t7 !"#6-%$9 ,$%3+ 5$n) (i."+i,$n ,"*$($ 1i1t"-0 (i*$,$i 1".$)i$n 3%"9 1i1t"- 6nt6, -"%$,6,$n 61$9$ !7 !"%i1i9 "n"+)i 8 O ! 1$-$ ("n)$n *"+6.$9$n "n"+)i ($%$- @CA ($+i 1i1t"-0 5$it6 8 E "C a ! `7 :$*$1it$1 ,$%3+ ($+i 16$t6 /$t (i("Qini1i,$n 1".$)$i .$n5$,n5$ ,$%3+ 5$n) (i*"+%6,$n 6nt6, -"n$i,,$n 1696 /$t t"+1".6t 1"."1$+ 1$t6 ,"%Bin $t$6 1$t6 ("+$#$t J"%1i617 8 /E "T :$*$1it$1 ,$%3+ 6nt6, *+31"1 i13,93+i, @& E t"t$*AP L /d E 01 M :$*$1it$1 ,$%3+ 6nt6, *+31"1 i13.$+i,P @$ E t"t$*A f /* E 01 M =6.6n)$n $nt$+$ /* ("n)$n /B $($%$9 /* O /d E 01 I7 <$($ 1i,%61 X$+n3t0 )$1 -"n"+i-$ ,$%3+ 8G ($+i +"1"+B3i+ ."+1696 tin))i ($n -"%"*$1 ,$%3+ 8M ," +"1"+B3i+ ."+1696 +"n($97 !i,%61 X$+n3t -"+6*$,$n ($1$+ ($+i -"1in (i"1"% @-"1in X$+n3tA0 5$it6 -"1in 5$n) *$%in) i("$%7 hQi1i"n1i -"1in -"+6*$,$n *"+.$n(in)$n $nt$+$ ."1$+ 61$9$ 5$n) ($*$t (i%$,6,$n 3%"9 1i1t"- t"+9$($* ,$%3+ 5$n) (i1"+$*7

Termodinamika

193

3E

H7 =6,6- gg >"+-3(in$-i,$ -"-i%i,i ,"1i-*6%$n 1".$)$i ."+i,6t7 $7 >i($, -6n),in -"-.6$t 16$t6 -"1in 5$n) ($*$t -"n)6.$9 ,$%3+ 5$n) (it"+i-$ -"n#$(i 61$9$ 1"%6+69n5$ ($%$- 1$t6 1i,%617 .7 :$%3+ ti($, *"+n$9 -"n)$%i+ 1*3nt$n ($+i ."n($ ."+1696 +"n($9 ," ."n($ ."+1696 tin))i7 J7 ["1in X$+n3t 5$n) .","+#$ (i $nt$+$ +"1"+B3i+ ."+1696 TG ($n +"1"+B3i+ 5$n) ."+1696 TM ("n)$n TG R TM -$,$ "Qi1i"n1in5$ tin))i7

! 8G _ GKKl

8M & ( _ GKKl ) 8G * % TM & 3 E ' G , ( _ GKKl ) TG * %

3 E 'G ,

Peta Konsep ;,rmo
<+31"1 g13t"+-

%$=6,6- g >"+-3(in$-i,$

:$*$1it$1 :$%3+

-"-.$9$1

*$($

<+31"1 g13,93+i,

<+31"1 g13.$+i,

<+31"1 U(i$.$ti,

>",$n$n >"t$*

!i,%61 >"+-3(in$-i,$

=6,6- gg >"+-3(in$-i,$

-"-.$9$1

-"-.$9$1

hQ"1i"n1i -"1in

<+31"1 n"B"+1i."%

*$($

d3%6-" >"t$*

<+31"1 g++"B"+1i."% J3nt39n5$

["1in X$+n3t

["1in ;tt3

["1in \i"1"%

["1in <"n(in)in

Refleksi Setelah mempelajari bab ini, Anda tentu telah memahami Hukum I Termodinamika dan proses-proses yang dapat terjadi di dalamnya. Adapun Hukum II Termodinamika mempelajari tentang perlunya usaha luar dan konsep kapasitas kalor pada proses-proses termodinamika. Dari keseluruhan materi bab ini, bagian

194

Mudah dan Aktif Belajar Fisika untuk Kelas XI

manakah yang menurut Anda sulit? Coba diskusikan dengan teman atau guru Fisika Anda. Dari pemahaman yang Anda peroleh, coba sebutkan beberapa manfaat yang dapat diterapkan dalam kehidupan sehari-hari.

Tes Kompetensi Bab 8 S( +ili>la>&-ala>&-atu&7aCaban&TanU&6alinU&t,6at&&6aan( G7

M7

L7

Z7

`7

I7

H7

=6,6- g >"+-3(in$-i,$ -"n5$t$,$n .$9D$ 7777 $7 ,$%3+ ti($, ($*$t -$16, ," ($%$- ($n ," %6$+ ($+i 16$t6 1i1t".7 "n"+)i $($%$9 ,",$% J7 "n"+)i ($%$- $($%$9 ,",$% (7 1696 $($%$9 t"t$* "7 1i1t"- ti($, -"n($*$t 61$9$ ($+i %6$+ !"#6-%$9 )$1 i("$% ("n)$n -$11$ t"+t"nt6 -"n)$%$-i *"-$-*$t$n 1"J$+$ $(i$.$ti,7 Ci,$ ! $($%$9 ,"+#$ 5$n) (i%$,6,$n 3%"9 1i1t"- @)$1A ($n T $($%$9 *"+6.$9$n 1696 ($+i 1i1t"-0 ."+%$,6 7777 $7 ! E K0 " T R K (7 ! S K0 " T R K .7 ! R K0 " T E K "7 ! E K0 " T E K J7 ! S K0 " T E K \6$ -3% )$1 $+)3n -"-6$i 1"J$+$ i13t"+-$% *$($ 1696 LKK :0 ($+i B3%6-" $D$% K0K`K -L ," B3%6-" $,9i+ K0KIK -L7 U1$9$ 5$n) (i%$,6,$n )$1 $+)3n $($%$9 7777 @1 E N0LG Cc,-3%:A $7 ffH0M #36%" (7 Zf0NI #36%" .7 fKf #36%" "7 ZZ0NH #36%" J7 ZfN0I #36%" !".$n5$, M - L )$1 9"%i6- 5$n) ."+1696 ZHbX (i*$n$1,$n 1"J$+$ i13.$+i, 1$-*$i GMHbX7 Ci,$ t",$n$n )$1 9"%i6- M0` _ GK` ^c-M0 61$9$ 5$n) (i%$,6,$n )$1 t"+1".6t $($%$9 7777 $7 G`K ,C (7 GM0` ,C .7 GM` ,C "7 M`K ,C J7 G` ,C !6$t6 )$1 5$n) B3%6-"n5$ K0` -L *"+%$9$ne%$9$n (i*$n$1,$n *$($ t",$n$n t"t$* 1"9in))$ B3%6-"n5$ -"n#$(i M -L7 Ci,$ 61$9$ %6$+ )$1 t"+1".6t L _ GK` #36%"0 t",$n$n )$1 $($%$9 7777 $7 I _ GK` ^c-M (7 M _ GK` ^c-M ` M .7 Z _ GK ^c"7 G0` _ GK` ^c-M ` M J7 L _ GK ^c<"+9$ti,$n *"+n5$t$$ne*"+n5$t$$n ."+i,6t7 @GA <$($ *+31"1 i13,93+i,0 )$1 ti($, -"%$,6,$n 61$9$7 @MA <$($ *+31"1 i13.$+i,0 )$1 1"%$%6 -"n)"-.$n)7 @LA <$($ *+31"1 $(i.$ti,0 )$1 1"%$%6 -"n)"-.$n)7 @ZA <$($ *+31"1 i13t"+-i,0 "n"+)i ($%$- )$1 t"t$*7 <"+n5$t$$n 5$n) 1"16$i ("n)$n ,3n1"* t"+-3(in$-i,$ $($%$9 7777 $7 @GA ($n @MA (7 @MA0 @LA0 ($n @ZA .7 @GA0 @MA0 ($n @LA "7 @LA ($n @ZA J7 @GA ($n @ZA /Nbtana-&)JJJ2 Ti-$ %it"+ )$1 i("$% ($%$- 1i%in("+ -"1in (i"1"% -"n)$%$-i *+31"1 $(i$.$ti, *$($ t",$n$n G0M $t-7 Ci,$ 1"t"%$9 *+31"1 ,3-*+"1i (i9$1i%,$n B3%6-" $,9i+ H0` T ("n)$n + E G0`0 ."1$+n5$ t",$n$n $,9i+ $($%$9 7777

$7 K0NI $t(7 K0II $t.7 K0NK $t"7 K0IK $tJ7 K0HI $tN7 !"#"ni1 )$1 i("$% B3%6-"n5$ L T7 <$($ 1696 MHbX0 )$1 t"+1".6t (i*$n$1,$n *$($ t",$n$n t"t$* M $t- 1$-*$i 1696e n5$ MMHbX7 U1$9$ 5$n) (i%$,6,$n )$1 t"+1".6t $($%$9 7777 $7 Z _ GKM C (7 K0Z _ GKL C .7 Z _ GKL C "7 Z _ GK` C J7 K0Z _ GKM C f7 Ci,$ B3%6-" )$1 i("$% (i*"+."1$+ (6$ ,$%i B3%6-" 1"-6%$ ($n t"+n5$t$ "n"+)i ($%$-n5$ -"n#$(i "-*$t ,$%i 1"-6%$0 t",$n$n )$1 t"+1".6t -"n#$(i 7777 G

$7 .7

Z ,$%i (7 Z ,$%i M ,$%i "7 ,3n1t$n G J7 ,$%i M GK7 !"#6-%$9 )$1 -"n)$%$-i 1i,%61 1"*"+ti *$($ )$-.$+ p (N/m2) ."+i,6t7 5

2

A

B

D

C

2

4

V (m3)

!696 (i titi, X $($%$9 ZKK :0 ($n 1696 (i titi, U $($%$9 7777 $7 LKK : (7 `KK : .7 ZKK : "7 IKK : J7 Z`K : GG7 <"+9$ti,$n )+$Qi, ."+i,6t ini7 p (N/m2)

2

1

2

V (m3)

]+$Qi, t"+1".6t -"n6n#6,,$n 96.6n)$n t",$n$n @$A t"+9$($* B3%6-" @'A0 ($+i 1"#6-%$9 -$11$ )$1 i("$%7 U1$9$ 5$n) (i%$,6,$n )$1 1"%$-$ *+31"1 t"+1".6t $($%$9 7777 $7 I0` C (7 M C . ZC "7 G0` C J7 L0` C GM7 <"+9$ti,$n )+$Qi, ."+i,6t7 p (N/m2) 3

1 0

C

B

A 1

2

V (m3)

Termodinamika

195

GL7

GZ7

G`7

GI7

V( G7

M7

L7

Z7

`7

196

<$($ )+$Qi, t"+1".6t0 16$t6 )$1 -"n)$%$-i *+31"1 UeVeX7 :$%3+ 5$n) (i.6t69,$n 6nt6, *+31"1 t"+1".6t $($%$9 7777 $7 L #36%" (7 Z0` #36%" .7 H0` #36%" "7 GM #36%" J7 GK0` #36%" !6$t6 1i1t"- -"n)$%$-i *+31"1 $(i$.$ti,7 <$($ 1i1t"(i%$,6,$n 61$9$ GKK C7 Ci,$ *"+6.$9$n "n"+)i ($%$1i1t"- $($%$9 C ($n ,$%3+ 5$n) (i1"+$* 1i1t"- $($%$9 i0 (i*"+3%"9 7777 $7 " C E OG7KKK C (7 i E GK C .7 " C E GKK C "7 " C a i E GKK C J7 " C E K /WM+;X&)JJE2 <$($ )$1 i("$% -3n3$t3-i,0 *+31"1 5$n) t"+#$(i *$($ ."1$+$ne."1$+$n Qi1i1 1"J$+$ i13.$+i, $($%$9 7777 L $7 8 E " ' ($n " ' E 0 1 " T M .7 8 E ! ($n " C E K J7 8 E K ($n " C E K L (7 8 E 0+/$+ " T ($n " C E 0 1 " T M "7 8 E 0+/$+ " T ($n " C E K Unt6, *+31"1 $(i$.$ti,0 61$9$ 5$n) t"+#$(i *$($ )$1 i("$% -3n3$t3-i, $($%$9 7777 L $7 K (7 !+M+ 0 1 " T M L .7 !+M+8 "7 ! E O 0 1 " T M J7 !+M+$+ " ' !".6$9 -"1in X$+n3t 1"ti$* 1i,%61n5$ -"n"+i-$ "n"+)i ($+i +"1"+B3i+ 1696 tin))i 1"."1$+ GM ,C ($n -"-.6$n) "n"+)i Z7KKK ,C ," +"1"+B3i+ 1696 +"n($97 V"1$+ "Qi1i"n1i -"1in t"+1".6t $($%$9 7777 $7 GH l (7 IH l .7 LL l "7 ff l J7 `K l /Nbtana-&&1LLL2 BaCabla>&6,rtanTaan&b,rikut&ini&<,nUan&t,6at( !"#6-%$9 )$1 i("$% -"n"-*$ti +6$n) ."+B3%6-" G J-L0 -$11$ )$1 t"+1".6t GMZ )0 ($n ."+$t -3%",6%n5$ IM7 >"nt6,$n%$9 t",$n$n )$1 t"+1".6t *$($ 1696 MHbX7 ]$1 i("$% -"n)$%$-i *"-$nt$*$n 1"J$+$ $(i$.$ti, 1"9in))$ B3%6-"n5$ ."+,6+$n) K0` %it"+7 Ci,$ B3%6-" $D$%n5$ M0` %it"+ ($n t",$n$nn5$ Z $t-31Q"+0 t"nt6,$n%$9 t",$n$n )$1 t"+1".6t 1"t"%$9 -"n)$%$-i *"-$-*$t$n @t"t$*$n T$*%$J" E G0HA7 \$%$- 16$t6 *+31"10 16$t6 )$1 -"n"+i-$ ,$%3+ N7KKK ,$%3+i7 >"+n5$t$0 )$1 ($*$t -"%$,6,$n 61$9$ 1"."1$+ GM7KKK #36%"7 =it6n)%$9 *"+6.$9$n "n"+)i ($%$- )$17 ]$1 -"%$,6,$n 61$9$ 1"."1$+ LfH0G #36%" *$($ *+31"1 $(i$.$ti,7 V"+$*$ ,$%3+i ."1$+ *"+6.$9$n "n"+)i ($%$)$1Y @G ,$%3+i E Z0GN CA ]$1 -"n"+i-$ ,$%3+ Z7KKK ,$%3+i0 -"n)9$1i%,$n 61$9$ 1"."1$+ H7KKK #36%"7 V"+$*$ *"+6.$9$n "n"+)i ($%$)$1 @G ,$%3+i E Z0GN CAY

Mudah dan Aktif Belajar Fisika untuk Kelas XI

GH7 <"+9$ti,$n )+$Qi, $B' -"1in X$+n3t ."+i,6t ini7 p

A Q1 B D

C

Q2

V

\i,"t$96i ! E I ,C7 V$n5$,n5$ ,$%3+ 5$n) (i%"*$1 3%"9 -"1in 1"ti$* 1i,%61 $($%$9 7777 $7 M7M`K C (7 I7KKK C .7 L7IKK C "7 f7IKK C J7 L7H`K C /Nbtana-&)JJ'2 GN7 !".6$9 -"1in X$+n3t 5$n) +"1"+B3i+ 1696 +"n($9n5$ MHbX -"-i%i,i "Qi1i"n1i ZKl7 Ci,$ "Qi1i"n1i (i*"+."1$+ -"n#$(i `Kl0 +"1"+B3i+ 1696 tin))in5$ 9$+61 (in$i,,$n 1"."1$+ 7777 $7 M` : (7 GKK : .7 `K : "7 G`K : J7 H` : Gf7 n"1"+B3i+ ."+1696 tin))i *$($ -"1in X$+n3t $($%$9 NKK : ($n +"1"+B3i+ 1696 +"n($9n5$ LKK :7 :$%3+ 5$n) (i1"+$* 3%"9 -"1in ($+i +"1"+B3i+ 1696 tin))i 1"."1$+ GI7KKK #36%"7 V"1$+ 61$9$ 5$n) (i9$1i%,$n -"1in X$+n3t t"+1".6t $($%$9 7777 $7 I7KKK C (7 GM7KKK C .7 N7KKK C "7 GZ7KKK C J7 GK7KKK C MK7 U1$9$ 5$n) (i%$,6,$n 3%"9 )$1 i("$% 5$n) -"n)$%$-i *+31"1 i13,93+i, ($+i t",$n$n $G 1$-*$i $M $($%$9 7777 $7 K (7 $MdM

I7

.7

$GdG

"7

J7

@$G a $MA@dG a dMA

\i$)+$- $O' ."+i,6t -"n6n#6,,$n *+31"1 16$t6 )$1 ($%$- 1$t6 1i,%610 (i-6%$i ($+i ) ($n ."+$,9i+ (i )7 4 × 105

1 × 105

p (N/m2) a

b

d

c 1

H7

% $G $M & ''' ( ) G M*

3

V(m3)

\$+i )$-.$+ t"+1".6t0 ."+$*$,$9P $7 61$9$ *$($ 1"ti$* *+31"1W .7 61$9$ t3t$% )$17 !".$n5$, Z -3% )$1 -"-6$i 1"J$+$ i13t"+-$% *$($ 1696 H : 1"9in))$ B3%6-"n5$ ."+6.$9 ($+i Z J-L -"n#$(i IK J-L7 V"+$*$ 61$9$ 5$n) (i%$,6,$n )$1Y

N7

]$1 ($%$- 16$t6 +6$n) t"+t6t6* -"n)$%$-i *+31"1 ($%$- 1$t6 1i,%610 ($+i UOVOXO\OU0 1"*"+ti (i$)+$$B' ."+i,6t7 p (N/m2)

B

4 × 105

1 × 105

C

D

A 1

4

5

V"+($1$+,$n )+$Qi, 1i,%61 t"+1".6t0 ."+$*$ 61$9$ 5$n) (i%$,6,$n 3%"9 )$1Y f7 =it6n)%$9 "Qi1i"n1i ($+i 16$t6 -"1in 5$n) .","+#$ *$($ +"1"+B3i+ 1696 +"n($9 HbX ($n +"1"+B3i+ 1696 tin))i ZMHbX7 GK7 !".6$9 -"1in X$+n3t .","+#$ (i $nt$+$ +"1"+B3i+ *$n$1 GNHbX ($n +"1"+B3i+ (in)in T7 Ci,$ -"1in t"+1".6t -"n5"+$* ,$%3+ G7KKK #36%" ($n ($*$t -"%$,6,$n 61$9$ IKK #36%"0 ."+$*$ 1696 +"1"+B3i+ (in)inn5$Y

V(m3)

Termodinamika

197

Proyek Semester 2 !"*"+ti *$($ 1"-"1t"+ *"+t$-$ 5$n) %$%60 *$($ 1"-"1t"+ ini Un($ #6)$ (it6)$1,$n 6nt6, -"%$,6,$n ,")i$t$n 1"-"1t"+ $)$+ *"-$9$-$n ,3n1"* mi1i,$ Un($ 1"-$,in -"nin),$t7 U($*6n ,")i$t$n 1"-"1t"+ ini -"n)"n$i Q%6i($ ($n +$n),$i$n ,")i$t$n 5$n) 9$+61 Un($ %$,6,$n ."+1$-$ t"-$n 1","%3-*3, $,$n (i6+$i,$n ."+i,6t ini7 <$($ $,9i+ ,")i$t$n0 Un($ *6n 9$+61 -"n5616n %$*3+$n $,9i+ *"+J3.$$n ($n -"-*+"1"nt$1i,$nn5$ (i 9$($*$n ,"%3-*3, %$in ($n )6+6 mi1i,$ Un($7

Viskositas ;u7uan&K,Uiatan ["n"nt6,$n ,3"Qi1i"n ,","nt$%$n /$t J$i+ ("n)$n -"n))6n$,$n =6,6- !t3,"17 Slat&an G7 >$.6n) !t3,"1 @tin))i IK J-0 (i$-"t"+ Z J-0 *"n5$+in)0 M )"%$n) *"-.$t$1A M7 [i1t$+ @GKK J-A L7 [i,+3-"t"+ 1",+6* @KOM` --W K0KG --A Z7 ^"+$J$ ;9$611 @>ri$,A+HA)90 LGG )0 K0KG )A `7 ;$R)>c* N7 #rA;9A>Ar+@-$11$ #"ni1 SG )J-LA f7 >"+-3-"t"+ GK7 T6* +ro-, E J@FA7 $7 U,6+%$9 ($n J$t$t 1696 /$t J$i+ ($%$- t$.6n) 1t3,"1 ("n)$n -"n))6n$,$n t"+-3-"t"+0 )6n$,$n %6* $)$+ *"n)6,6+$n ($*$t (i%$,6,$n ("n)$n %".i9 t"%iti7 .7 U,6+ ($n J$t$t -$11$ #"ni1 /$t J$i+ ("n)$n -"n))6n$,$n $+"3-"t"+0 )6n$e ,$n %6* $)$+ *"n)6,6+$n ($*$t (i%$,6,$n ("n)$n %".i9 t"%iti7 J7 i-.$n) -$11$ .3%$ *"#$% 5$n) $,$n (i)6n$,$n J6,6* 1$t6 ,$%i *"n)6,6+$n7 <"+9$ti,$n *31i1i 1,$%$ n3% 1"."%6- $%$t 6,6+ (i*"+)6n$,$n7 "7 [$16,,$n .3%$ ," ($%$- t$.6n) 1t3,"1 5$n) t"%$9 (i."+i /$t J$i+ 5$n) $,$n (i6,6+ Bi1,31it$1n5$0 ,"-6(i$n $-$ti )"+$, .3%$ 9in))$ .3%$ (i$n))$* ."+)"+$, %6+61 ."+$t6+$n7 Q7 V"+i%$9 t$n($ .$t$1 ("n)$n )"%$n) ,$D$t *"+t$-$ ,"ti,$ .3%$ (i$n))$* t"%$9 -"n)$%$-i )"+$, %6+61 ."+$t6+$n @o ` J- (i $t$1 *"+-6,$$n /$t J$i+A7 )7 U,6+ #$+$, 5$n) $,$n (i$-$ti @FA ("n)$n -"-."+i,$n t$n($ ("n)$n )"%$n) ,"(6$7 97 U-.i% .3%$ 5$n) t"%$9 (i-$16,,$n0 ti+i1,$n0 %$%6 -$16,,$n ,"-.$%i ," ($%$- t$.6n) 1t3,"17 U-$ti ($n J$t$t D$,t6 5$n) (it"-*69 .3%$ ,"ti,$ ."+)"+$, %6+61 ."+$t6+$n 1"*$n#$n) F7 i7 T$,6,$n %$n),$9 )O9 6nt6, GK ,$%i *"+J3.$$n *$($ #$+$, F 5$n) ."+."($e ."($ ("n)$n J$+$ -"n)6.$9 ,"(6(6,$n *31i1i )"%$n) ,"(6$7 M7 +,rRobaan&1P ["n"nt6,$n 9$+)$ Bi1,31it$1 /$t J$i+ ."+($1$+,$n )+$Qi, Q6n)1i G

> E J@ M A7 r $7
198

Mudah dan Aktif Belajar Fisika untuk Kelas XI

.7 J7 (7

U,6+%$9 -$11$ ($n #$+ie#$+i 1"ti$* .3%$ @-$1in)e-$1in) J6,6* 1$t6 ,$%i *"n)6,6+$nA7 >"nt6,$n ($n 6,6+%$9 #$+$, $nt$+$ (6$ )"%$n) *"-.$t$1 *$($ t$.6n) !t3,"17 U,6+%$9 D$,t6 5$n) (i*"+%6,$n 1"ti$* .3%$ *"#$% 6nt6, -"n"-*69 #$+$, $nt$+$ ,"(6$ )"%$n) *"-.$t$1 5$n) 16($9 (it"nt6,$n t"+1".6t7

+,nUola>an&Yata G7 \"n)$n -"n))6n$,$n ($t$ *"+J3.$$n *"+t$-$0 .6$t )+$Qi, > E J@FA7 :"-6(i$n0 t"nt6,$n ,3"Qi1i"n ,","nt$%$n /$t J$i+ ."+($1$+,$n )+$Qi, t"+1".6t7 M7 L7

G

\"n)$n ($t$ *"+J3.$$n ,"(6$0 .6$t )+$Qi, > E J@ M A7 :"-6(i$n0 t"nt6,$n r ,3"Qi1i"n ,","nt$%$n /$t J$i+ ."+($1$+,$n )+$Qi, t"+1".6t7 V$n(in),$n 9$1i% ,"(6$ *"+J3.$$n t"+1".6t0 ,"-6(i$n ."+i,$n *"n#"%$1$n Un($ -"n)"n$i ,"(6$ 9$1i% t"+1".6t7

± 5 cm gelang satu

y

gelang dua

Tabung Stokes

Proyek Semester 2

199

Tes Kompetensi Fisika Semester 2

S( +ili>la>&-ala>&-atu&7aCaban&TanU&6alinU&t,6at&&6aan( G7

<"+9$ti,$n 1i1t"- ,"1"ti-.$n)$n *$($ )$-.$+ ."+i,6t7 @,$t+3% %iJinA

`7

<"+9$ti,$n )$-.$+ ."+i,6t7 45°

37°

53°

T2 T1

m2

T3

m1

w = 300 N

m3

M7

L7

<"+.$n(in)$n -$11$ ."n($ 9M ($n 9G $($%$9 7777 $7 M P ` (7 Z P L .7 L P Z "7 ` P L J7 L P ` !".6$9 ."n($ -"-i%i,i ."+$t NKK ^ ($n (i)$nt6n) ($%$- ,"$($$n (i$- 1"*"+ti t$-*$, *$($ )$-.$+ ."+i,6t7 V"1$+ t")$n)$n t$%i TM $($%$9 7777 $7 MKK ^ 30° 60° .7 LKK ^ T2 O T1 J7 ZKK ^ T3 (7 ZKK L ^ w "7 MKK L ^

I7

60°

y

F2 = 12 N

F1 = 8 N

–1 0

<"+9$ti,$n )$-.$+ ."+i,6t ini7 H7

T1

V"1$+ t")$n)$n t$%i TG $($%$9 7777 $7 GKK ^ (7 ZKK ^ .7 MKK ^ "7 `KK ^ J7 LKK ^ <"+9$ti,$n )$-.$+ ."+i,6t7

1 2 3

x (m)

n"16%t$n ($+i ,"(6$ )$5$ *$($ )$-.$+ t"+1".6t t"+%"t$, (i 7777 $7 S E OM0N (7 S E G0Z .7 S E K0I "7 S E M0G J7 S E G0M <"+9$ti,$n )$-.$+ ."+i,6t7 C

60°

T2

T

w

Ci,$ t$%i J6,6* ,6$t 6nt6, -"n$9$n t")$n)$n -$,e 1i-6- IK 3 ^0 ."1$+ R 5$n) -$1i9 ($*$t (it$9$n 3%"9 t$%i t"+1".6t $($%$9 7777 $7 `K ^ (7 `K L ^ .7 IK ^ "7 GKK ^ J7 IK L ^ Z7

T1

T1

T3

N7 60°

T2 m2

V"1$+ 9GEG` L ,) ($n ,3"Qi1i"n )"1", 1t$ti1 $nt$+$ 9G ($n -"#$ $($%$9 K0M7 [$11$ 9M $($%$9 7777 $7 Z0` ,) (7 GM ,) .7 J7

200

w = 30 N

!i1t"- *$($ )$-.$+ ."+i,6t ."+$($ ($%$- ,"$($$n 1"ti-.$n)7 m1

GM L ,) f ,)

"7

L

L ,)

Mudah dan Aktif Belajar Fisika untuk Kelas XI

B

A

V$t$n) UV 5$n) *$n#$n)n5$ NK J- (i."+i .".$n (i 6#6n)e n5$ 1"."1$+ LK ^7 Ci,$ *$n#$n) UX E IK J- ($n -$11$ .$t$n) (i$.$i,$n0 ."1$+ t")$n)$n t$%i T $($%$9 7777 $7 LI ^ (7 I` ^ .7 ZN ^ "7 NK ^ J7 `K ^ <"+9$ti,$n )$-.$+ ."+i,6t7 2 m 1m 3m Ci,$ 1".6$9 .$t$n) #. 5$n) ."+$tn5$ (i$.$i,$n0 ($n ,"e B A C D (6$ 6#6n)n5$ (i)$nt6n)e w1 w2 ,$n ("n)$n t$%i0 ,"-6(i$n ($n (i."+i .".$n -$1in)e-$1in) RG E LKK ^ ($n RM E IKK ^7 \i,"t$96i #/ E M -0 /6 E G -0 ($n 6. E L -0 ."1$+ t")$n)$n t$%i (i # ($n (i . $($%$9 7777 $7 IKK ^ ($n LKK ^ (7 `KK ^ ($n ZKK ^ .7 Z`K ^ ($n Z`K ^ "7 LKK ^ ($n IKK ^ J7 ZKK ^ ($n `KK ^

f7 n$*$t -$11$ 1")6-*$% "1 $($%$9 fGH ,)c-L7 ]6-*$%$n "1 5$n) t"+$*6n) ($%$- $i+ $,$n -6nJ6% (i $t$1 *"+e -6,$$n $i+ ("n)$n B3%6-" 7777 $ K0KNLK -L .7 K0KfGH -L J7 K0G -L (7 G -L "7 G0` -L GK7 !".6$9 *i*$ .$+3-"t"+ (i)$nti ("n)$n *i*$ 5$n) %6$1 *"n$-*$n)n5$ (6$ ,$%in5$7 <$($ t",$n$n 6($+$ %6$+ G $t-31Q"+0 tin))i +$,1$ ($%$- *i*$ $($%$9 7777 $7 Gf J.7 LK JJ7 HI J(7 GGZ J"7 G`M JGG7 !".6$9 *i*$ 1i%in("+ %6+61 -"-i%i,i %6$1 *"n$-*$n) MKK --M ($n GKK --M7
G`7 \i,"t$96i -$11$ #"ni1 $i+ %$6t G0KL )cJ-L ($n t",$n$n 6($+$ %6$+ E GK` ^c-M7 Ci,$ ,$*$% 1"%$- ."+$($ (i ,"($%$-$n GMK -0 t",$n$n 5$n) (i$%$-i ,$*$% 1"%$t"+1".6t $($%$9 7777 $7 G0`K [*$ .7 G0Z` [*$ J7 G0ZG [*$ (7 G0LG [*$ "7 G0M` [*$ GI7 <"+9$ti,$n )$-.$+ ."+i,6t ini7 1 5m 2

Ci,$ (i$-"t"+ %6.$n) L J-0 B3%6-" $i+ 5$n) ,"%6$+ ($+i %6.$n) (i titi, M 1"ti$* -"nit $($%$9 7777 $7 K0ZM -L *"+ -"nit .7 K0`M -L *"+ -"nit J7 K0IN -L *"+ -"nit (7 K0HM -L *"+ -"nit "7 K0H` -L *"+ -"nit GH7 !"t"%$9 (i6,6+ ("n)$n 1".6$9 -$n3-"t"+0 (i,"t$96i t",$n$n $i+ (i ($%$- 1".6$9 t$n),i $($%$9 `KK ,<$7 1 2 <"+9$ti,$n )$-.$+ (i 1$-*in)7 Ci,$ t"+#$(i ,".3J3+$n (i titi, M0 ,"J"*$t$n $i+ 5$n) ,"%6$+ ($+i titi, t"+1".6t $($%$9 7777 $7 LM -c1 .7 LI -c1 J7 ZK -c1 (7 ZM -c1 "7 Z` -c1 GN7 \6$ t$.6n) (ii1i ("n)$n )$1 ."+."($0 t"t$*i ,"(6$n5$ ."+$($ *$($ 1696 5$n) 1$-$7 \i,"t$96i N# ($n N. $($%$9 ."+$t -3%",6% ,"(6$ )$1 t"+1".6t7 \"n)$n ("-i,i$n0 ."1$+ -3-"nt6- +$t$e+$t$ -3%",6% ,"(6$ )$1 t"+1".6t0 5$it6 $# ($n $. $,$n ."+,$it$n 1$t6 1$-$ %$in -"n6+6t +6-61 7777 $7

$# E $.

.7

$# E

J7

$# E+ ' N# (:. ) .*

(7

$# E+ ' N ( :.

"7

$# E

N# N. :.

%N &

% N. & ) #*

N. : N# .

Gf7 <$+ti,"%e*$+ti,"% )$1 i("$% -"-i%i,i 1iQ$t $nt$+$ %$inP @GA 1"%$%6 ."+)"+$,0 @MA ti($, 1$%in) t$+i, -"n$+i,0 @LA ."+t6-.6,$n %"ntin) 1"-*6+n$0 ($n @ZA ti($, -"n)i,6ti =6,6- ^"Dt3n t"nt$n) )"+$,7

Tes Kompetensi Fisika Semester 2

201

MK7

MG7

MM7

ML7

MZ7

202

<"+n5$t$$n 5$n) ."n$+ $($%$9 7777 $7 @GA0 @MA0 ($n @LA .7 @GA ($n @LA J7 @MA ($n @ZA (7 @ZA "7 1"-6$ ."n$+ <$($ 16$t6 1$$t0 ."1$+ t",$n$n 6($+$ %6$+ E HI J-=)7 U%$t 6,6+ t",$n$n @-$n3-"t"+ t"+.6,$A -"n6n#6,e ,$n .$9D$ t",$n$n (i ($%$- t$n),i $($%$9 ZKK J-=)7 !696 )$1 ($%$- t$n),i fbX7 :"-6(i$n0 ,$+"n$ *"-$e n$1$n0 1696 t$n),i n$i, -"n#$(i LGbX7 >",$n$n 5$n) (it6n#6,,$n -$n3-"t"+ $($%$9 7777 $7 `GL J-=) .7 ZHI J-=) J7 ZLH J-=) (7 `G0L J-=) "7 ZL0H J-=) !".6$9 t$n),i ."+B3%6-" L T )$1 3,1i)"n *$($ 1696 MKbX ($n t",$n$n t$n),i M` _ GK` <$7 Ci,$ (i,"t$96i 9 3,1i)"n E LM ,)c-3%0 t",$n$n 6($+$ %6$+ G _ GK` <$0 ($n 1 E N0LGZ Cc,-3%:0 -$11$ 3,1i)"n ($%$- t$n),i t"+1".6t $($%$9 7777 $7 K0KfN ,) .7 K0GKM ,) J7 K0G`K ,) (7 K0GNK ,) "7 K0MKK ,) d3%6-" Z0K ) )$1 3,1i)"n @N E LM ,)c-3%A *$($ ,"$($$n n3+-$% $($%$9 7777 $7 M0N _ GKO` -L .7 M0N _ GKOZ -L J7 M0N _ GKOL -L (7 M0N _ GKOM -L "7 M0N _ GKOG -L !".6$9 t$.6n) +"$,1i 5$n) *$n#$n)n5$ G` J- ("n)$n *"n$-*$n) ."+$t6+$n $,$n (it6+6n,$n ("n)$n 6#6n) t"+.6,$ ," ($%$- ($n$6 $i+ t$D$+7 U)$+ t$.6n) t"+i1i $i+ 1"*"+"-*$t .$)i$n0 t$.6n) t"+1".6t 9$+61 (it"-*$t,$n (i ,"($%$-$n 7777 @t",$n$n $t-31Q"+ E GKK ,<$A7 $7 L .7 Z J7 ` (7 I "7 H !".6$9 -"1in X$+n3t 5$n) -"n))6n$,$n +"1"+B3i+ 1696 tin))i ."+1696 NKK : ($n -"-i%i,i "Qi1i"n1i ZKl7 U)$+ "Qi1i"n1in5$ -"n#$(i `Kl0 1696 +"1"+B3i+ 1696 tin))i 9$+61 (in$i,,$n -"n#$(i 7777 $7 fKK : .7 fIK : J7 G7KKK : (7 G7GNK : "7 G7IKK :

Mudah dan Aktif Belajar Fisika untuk Kelas XI

M`7 !i,%61 X$+n3t (i.$t$1i 3%"9 (6$ )$+i10 5$it6 @GA i13.$+i, @MA $(i$.$ti, @LA i13B3%6-" @ZA i13t"+-i, <"+n5$t$$n 5$n) ."n$+ $($%$9 7777 $7 @GA0 @MA0 ($n @LA .7 @GA ($n @LA J7 @MA ($n @ZA (7 @ZA "7 1"-6$ ."n$+ MI7 hQi1i"n1i -"1in X$+n3t 5$n) ."+3*"+$1i ("n)$n 1696 +"n($9 G T ,"%Bin ($n ."+1696 tin))i T ,"%Bin $($%$9 7777 M $7 M` l (7 II l .7 LL l "7 H` l J7 `N l MH7 ["1in X$+n3t (i3*"+$1i,$n $nt$+$ (6$ +"1"+B3i+ ,$%3+ -$1in)e-$1in) ."+1696 TG ($n TM0 ("n)$n TM R TG7 hQi1i"n1i -"1in t"+1".6t ZK l ($n ."1$+n5$ TG E MGbX7 U)$+ "Qi1i"n1in5$ n$i, IK l0 ."1$+ *"+6.$9$n TM $($%$9 7777 $7 M`K : .7 LKK : J7 L`K : (7 ZKK : "7 `KK : /WM+;X&1LLL2 MN7 !".6$9 -"1in t6+.in -"-$,$i 6$* ("n)$n 1696 $D$% ``KbX ($n -"-.6$n)n5$ *$($ 1696 L`bX7 hQi1i"n1i -$,1i-6- -"1in t6+.in t"+1".6t $($%$9 7777 $7 LL l .7 ZL l J7 `L l (7 IL l "7 HL l Mf7 <$($ 16$t6 *+31"10 ,$%3+ 1".$n5$, N7KKK ,$%3+i (i9$nt$+,$n *$($ 1i1t"-0 1"($n),$n 1i1t"- -"%$,6e ,$n 61$9$ I7KKK #36%"7 V"1$+ "n"+)i 5$n) ."+6.$9 ($%$- 1i1t"- t"+1".6t $($%$9 7777 $7 LL0` ,C .7 MH0` ,C J7 MK ,C (7 GN ,C "7 G` ,C LK7 !".6$9 -"1in *"n)$(6, ."+($5$ GKK D$tt (i*$,$i 6nt6, -"n)$(6, ` ,) $i+7 :"-6(i$n0 1696 $i+ n$i, $,i.$t $($n5$ )"1",$n (i ($%$- $i+7 \"n)$n -"n)$n))$* 1"-6$ 61$9$ -"n#$(i ,$%3+0 D$,t6 5$n) (i.6t69,$n -"1in 6nt6, .","+#$ $)$+ 1696 $i+ n$i, IbX $($%$9 7777 $7 MG -"nit .7 MK -"nit J7 Gf -"nit (7 GN -"nit "7 GH -"nit

V(

BaCabla>&6,rtanTaan&b,rikut&ini&<,nUan&t,6at(

G7

!".6$9 +3($ 5$n) -3-"n in"+1i$n5$ K0KKM ,)-M ($*$t ."+*6t$+ .".$1 *$($ 16-.6 ($t$+7 >$%i (i%i%it,$n *$($ t"*i +3($ t"+1".6t ($n *$($ 6#6n) t$%i (i)$nt6n),$n .".$n NKK )7 C$+ie#$+i 16-.6 +3($ t"+1".6t $($%$9 M J-7 V")it6 .".$n (i%"*$10 +3($ -6%$i ."+*6t$+7 V"+$*$ #$69,$9 ."n($ t"+1".6t 9$+61 #$t69 $)$+ +3($ ."+,"J"*$t$n L *6t$+$nc1",3nY !".6$9 .3%$ .$1,"t -"n))"%in(in) t$n*$ 1"%i* *$($ .i($n) -i+in) 5$n) *$n#$n)n5$ ` - ("n)$n 16(6t ,"-i+in)$n LKb7 Ci,$ r.3%$ EMK J-0 9 E M ,)0 ($n .3%$ (i%"*$1,$n t$n*$ ,"J"*$t$n $D$% ($+i 6#6n) $t$1 .i($n)0 ."+$*$,$9 ,"J"*$t$n %in"$+ .3%$ 1$$t ti.$ (i 6#6n) .$D$9 .i($n)Y !".6$9 .3%$ *"#$% -"n))"%in(in) (i %$nt$i ($t$+ ("n)$n & E MK -c17 :"-6(i$n0 .3%$ t"+1".6t -"%"D$ti t$n#$,$n ("n)$n 16(6t LKb t"+9$($* .i($n) 93+i/3nt$%7 Ci,$ )$5$ )"1", .3%$ ($n %$nt$i (i$.$i,$n0 ."+$*$,$9 ,"tin))i$n 5$n) ($*$t (iJ$*$i .3%$ t"+1".6t ($+i ($1$+ %$nt$iY U($+$ 5$n) ."+-$11$ #"ni1 G0LI ,)c-L (i%"D$t,$n *$($ 1".6$9 *i*$ 5$n) -"-i%i,i %6$1 *"n$-*$n) G`K J-M7 Ci,$ (i6,6+ ("n)$n *i*$ *it3t0 *"+."($$n tin))i +$,1$ (i ($%$- -$n3-"t"+ $($%$9 K0N --7 >"nt6,$n B3%6-" 6($+$ 5$n) -"n)$%i+ ($%$- D$,t6 G -"nit7

M7

L7

Z7

`7 !"*3t3n) $%6-ini6- ($%$- 6($+$ ."+$tn5$ N0L` ) @ 4 $%6-ini6- E M0HK )cJ-LA7 Ci,$ ."n($ t"+1".6t (i)$ne t6n),$n *$($ 1"6t$1 t$%i0 ($n (iJ"%6*,$n ($%$- -in5$, @ 4 -in5$, E K0H` )cJ-LA0 ."+$*$,$9 t")$n)$n t$%i t"+1".6tY I7 !".6$9 .$, $i+ -"-i%i,i tin))i Z -7 !".6$9 %6.$n) *$($ .$, t"+1".6t -"-$nJ$+,$n $i+ 1"#$69 Z J-7 Ci,$ *"+J"*$t$n )+$Bit$1i G EGK -c1M0 t"nt6,$n ,"tin))i$n $i+ (i ($%$- .$, $i+ t"+1".6t7 H7 >"nt6,$n%$9 +$*$t -$11$ )$1 -"t$n @N E GI ,)c-3%A *$($ 1696 MKbX ($n t",$n$n ` $t-7 N7 >"nt6,$n &+-1 ($+i 16$t6 )$1 5$n) ."+$($ (i ($%$1".6$9 t$.6n) t"+t6t6* ("n)$n B3%6-" G %it"+ ($n t",$n$n 1"."1$+ L _ GK` <$ #i,$ +$*$t -$11$ )$1 t"+1".6t GKOM )cJ-L7 f7 ]$1 9i(+3)"n @N E M ,)c-3%A ($n )$1 nit+3)"n TN E MN ,)c-3%A ."+$($ *$($ 1696 5$n) 1$-$7 >"nt6,$n%$9 *"+.$n(in)$nP $7 @7kA= P@7kA^W ($n .7 @&+-1A= P @&+-1A^7 GK7 !".6$9 *"1$D$t *"n(in)in -"-i%i,i ,3"Qi1i"n ($5$ )6n$ 1"."1$+ I0`7 Ci,$ t"-*"+$t6+ +"1"+B3i+ 1696 tin))i $($%$9 LKbX0 9it6n)%$9 t"-*"+$t6+ +"1"+B3i+ 1696 +"n($9n5$7

Tes Kompetensi Fisika Semester 2

203

Tes Kompetensi Akhir S( +ili>la>&-ala>&-atu&7aCaban&TanU&6alinU&t,6at&&6aan( G7

M7

>"+9$($* ,33+(in$t+S+93+i/3nt$% ($n F+B"+ti,$%0 1".6$9 ."n($ 5$n) ."+)"+$, -"n)i,6ti )"+$, *"%6+6 -"-e *6n5$i ,3-*3n"ne,3-*3n"n ,"J"*$t$n 5$n) 7777 $7 ."1$+n5$ t"t$* *$($ $+$9 S ($n ."+6.$9 ."+$t6+$n *$($ $+$9 F .7 ."1$+n5$ t"t$* *$($ $+$9 F+($n ."+6.$9 ."+$t6+$n *$($ $+$9 S J7 ."1$+n5$ t"t$*0 .$i, *$($ $+$9 S -$6*6n *$($ $+$9 F (7 ."1$+n5$ ."+6.$9 ."+$t6+$n0 .$i, *$($ $+$9 S -$6*6n *$($ $+$9 F "7 ."1$+ ($n $+$9n5$ t"+61e-"n"+61 ."+6.$9 t"+9$($* D$,t6 <31i1i 1".6$9 ."n($ (in5$t$,$n ("n)$n *"+1$-$$n r E pG`t L i a @G`t O `tMA7q -7 !"t"%$9 ."n($ ."+)"+$, 1"%$-$ G0` 1",3n0 ,"%$#6$nn5$ $($%$9 7777 $7 K (7 MM0` -c1 .7 G` -c1 "7 G` L -c1 J7 GG0` L -c1 @WSX& 1LL1A

L7

Z7

`7

<"+n5$t$$n 5$n) ti($, ."n$+ -"n)"n$i 96.6n)$n $nt$+$ *"+J"*$t$n t$n)"n1i$%0 )"+$, +3t$1i 16$t6 *$+ti,"%0 ($n ."1$+$ne."1$+$n 16(6tn5$ $($%$9 7777 $7 *"+J"*$t$n t$n)"n1i$% -"n6n#6,,$n *"+6.$9$n ."1$+ ,"%$#6$n %in"$+ ($+i *$+ti,"% .7 *"+J"*$t$n t$n)"n1i$% 1"%$%6 -"-i%i,i *$+ti,"% 5$n) ."+)"+$, -"%in),$+ J7 *"+J"*$t$n t$n)"n1i$% -"-i%i,i *$+ti,"% 5$n) ."+)"+$, ("n)$n %$#6 %in"$+ t"t$* (7 *"+J"*$t$n t$n)"n1i$% 1".$n(in) ("n)$n *"+J"*$t$n 16(6t ($n #$+ie#$+i "7 *"+J"*$t$n t$n)"n1i$% 1"%$%6 -"n)$+$9 ," *61$t %int$1$n -"%in),$+n5$ <31i1i 1".6$9 ."n($ 5$n) (i%"-*$+,$n B"+ti,$% ," $t$1 (in5$t$,$n ("n)$n *"+1$-$$n F E@ M> a f>MA -0 ("n)$n >+($%$- 1",3n7 :"J"*$t$n $D$% ."n($ $($%$9 7777 $7 G -c1 (7 Z -c1 .7 M -c1 "7 ` -c1 J7 L -c1 !".6$9 ."n($ 5$n) ."+$tn5$ R -"%6nJ6+ ," .$D$9 ("n)$n ,"J"*$t$n t"t$* *$($ 16$t6 .i($n) -i+in) 5$n) ,$1$+7 Vi($n) -i+in) t"+1".6t -"-."nt6, 16(6t LKb t"+9$($* 93+i/3nt$%7 :3"Qi1i"n )"1",$n $nt$+$ ."n($ ($n .i($n) t"+1".6t $($%$9 7777 $7 .7 J7

204

GR L M G L M G M

(7 "7

G R M G L L

Mudah dan Aktif Belajar Fisika untuk Kelas XI

I7 !".6$9 ."n($ ."+-$11$ M` ,) (i(3+3n) ("n)$n )$5$ `K ^ $+$9 -"n($t$+7 :3"Qi1i"n )"1",$n ,"ti,$ ."n($ t"*$t $,$n ."+)"+$, $($%$9 7777 $7 K0G (7 K0Z .7 K0M "7 K0` J7 K0L H7 Ci,$ *"+J"*$t$n )+$Bit$1i (i *"+-6,$$n V6-i G0 ($n #$+ie#$+i V6-i 1 -$,$ *"+J"*$t$n )+$Bit$1i (i 16$t6 titi, 5$n) ."+#$+$, 1 ($+i *"+-6,$$n V6-i $($%$9 7777

G (7 M G G Z G .7 "7 Z G G M J7 G N7 !".6$9 *")$1 ("n)$n t"t$*$n ZKK ^c- (i."+i .".$n Z ,) ($n (it$+i, ," $t$1 ("n)$n *"+J"*$t$n M -c1M7 Ci,$ G E GK -c1M -$,$ *"+t$-.$9$n *$n#$n) *")$1 t"+1".6t $($%$9 7777 $7 K0GM (7 K0ZM .7 K0MZ "7 K0ZN J7 K0LI f7 !"3+$n) *"%$#$+ 5$n) -$11$n5$ `K ,)0 ."+)$nt6n) *$($ 6#6n) 1".6$9 *")$10 1"9in))$ *")$1 ."+t$-.$9 *$n#$n) GK J-7 \"n)$n ("-i,i$n0 ,3n1t$nt$ *")$1 ."+ni%$i 7777 $7 `KK ^c(7 MK ^c.7 ` ^c"7 `7KKK ^cJ7 `K ^c$7

@WM+;X& )JJJA

GK7 <")$1 (i1616n 1"J$+$ 1"+i ($n *$+$%"% 1"*"+ti )$-.$+ ."+i,6t ini7

k1

k4

k3

k2 M M

U#6n) *")$1 (i)$nt6n)i .".$n 5$n) 1$-$ ."1$+7 Ci,$ ,3n1t$nt$ *")$1 kG E kM E kL E kZ E k0 *"+.$n(in)$n *"+i3(" 1616n$n 1"+i ($n *$+$%"% $($%$9 7777 $7 ` P Z (7 G P M .7 M P G "7 M P L J7 L P M @WM+;X& )JJ'A

GG7 ]+$Qi, ."+i,6t -"n6n#6,,$n )"+$,$n 1".6$9 ."n($ ."+-$11$ GK ,) *$($ .i($n) ($t$+ t$n*$ )"1",$n ,$+"n$ *"n)$+69 )$5$ 5$n) ."+6.$9e6.$97 F (N)

GI7 \i $nt$+$ ."n($ ."+)"+$, ."+i,6t ini0 ."n($ 5$n) $,$n -"n)$%$-i )$5$ *$%in) ."1$+ #i,$ -"n6-.6, t"-.3, 9in))$ ."+9"nti $($%$9 7777 $7 ."n($ ."+-$11$ ZK ,) ("n)$n %$#6 M` -c1 .7 ."n($ ."+-$11$ `K ,) ("n)$n %$#6 G` -c1 J7 ."n($ ."+-$11$ GKK ,) ("n)$n %$#6 GK -c1 (7 ."n($ ."+-$11$ G`K ,) ("n)$n %$#6 H -c1 "7 ."n($ ."+-$11$ MKK ,) ("n)$n %$#6 ` -c1 GH7 balok

s (m)

Ci,$ ,"J"*$t$n ."n($ 1$$t " E K $($%$9 f -c10 -$,$P @GA ,"J"*$t$n ."n($ 1$$t " E H - $($%$9 GK -c1 @MA *"+6.$9$n "n"+)i ,in"ti, ($+i " E K 1$-*$i ("n)$n " E H - $($%$9 f` #36%" @LA ."1$+ 61$9$ ($+i " E K 1$-*$i ("n)$n " E H $($%$9 f` #36%" <"+n5$t$$n (i $t$1 5$n) ."n$+ $($%$9 7777 $7 @GA0 @MA0 ($n @LA (7 @GA 1$#$ .7 @GA ($n @LA "7 @GA ($n @MA J7 @MA ($n @LA @WSX& 1LLA2

GM7 V"n($ ."+-$11$ ` ,) (i%"-*$+ B"+ti,$% ," $t$1 ("n)$n ,"J"*$t$n $D$% GK -c17 V"1$+n5$ "n"+)i *3t"n1i$% (i titi, t"+tin))i 5$n) (iJ$*$i ."n($ $($%$9 7777 $7 MKK C (7 L`K C .7 M`K C "7 ZKK C J7 LKK C GL7 !".6$9 *")$1 5$n) ,3n1t$nt$n5$ k (i."+i .".$n ."+-$11$ 97 V".$n (i)"t$+,$n ("n)$n $-*%it6(3 #7 hn"+)i *3t"n1i$% .".$n it6 *$($ 1$$t ,"J"*$t$nn5$ K0N ,$%i ,"J"*$t$n -$,1i-6- $($%$9 7777 $7 K0GI k#M (7 K0LI k#M .7 K0GN k#M "7 K0`K k#M J7 K0LM k#M @WSX& 1LLE2

GZ7 !".6$9 .$%3, ."+-$11$ GK ,) (i(3+3n) ($+i ($1$+ 16$t6 .i($n) -i+in) 5$n) *$n#$n)n5$ ` -"t"+ ($n *6nJ$, .i($n) -i+in) ."+$($ L - ($+i t$n$97 Ci,$ .i($n) -i+in) (i$n))$* %iJin ($n *"+J"*$t$n )+$Bit$1i V6-i E GK -c1M0 61$9$ 5$n) 9$+61 (i%$,6,$n 6nt6, -"n(3+3n) .$%3, $($%$9 7777 $7 LKK #36%" (7 L7`KK #36%" .7 G7`KK #36%" "7 Z7KKK #36%" J7 L7KKK #36%" G`7 !".6$9 -3.i% ("n)$n -$11$ G t3n ."+)"+$, ($+i ,"$($$n (i$-7 !"1$$t ,"-6(i$n0 ,"J"*$t$nn5$ -"n#$(i I -c17 V"1$+ 61$9$ 5$n) (i%$,6,$n 3%"9 -"1in -3.i% t"+1".6t $($%$9 7777 $7 f7KKK C (7 G`7KKK C .7 GK7KKK C "7 GN7KKK C J7 GM7KKK C

peluru

<"%6+6 ("n)$n -$11$ GK )+$- ($n ,"J"*$t$n G7KKK -c1 -"n)"n$i ($n -"n6-.6, 1".6$9 .$%3, ("n)$n -$11$ GKK ,) 5$n) (i$- (i $t$1 .i($n) ($t$+ t$n*$ )"1",$n7 :"J"*$t$n *"%6+6 1"t"%$9 -"n"-.61 .$%3, $($%$9 GKK -c17 :"J"*$t$n .$%3, ,$+"n$ t"+t"-.61 *"%6+6 $($%$9 7777 $7 fKK -c1 (7 K0f -c1 .7 fK -c1 "7 K0Kf -c1 J7 f -c1 GN7 V3%$ ."+-$11$ N ,) #$t69 t$n*$ ,"J"*$t$n $D$% ," %$nt$i ($+i ,"tin))i$n * -"t"+7 Ci,$ *"+J"*$t$n )+$Bit$1i G+($n ,3"Qi1"n "%$1ti1it$1 .3%$ t"+9$($* %$nt$i $($%$9 ! -$,$ *"+n5$t$$ne*"+n5$t$$n t"nt$n) .3%$ ."+i,6t ini ."n$+0 kAc(),i 7777 $7 ."1$+ ,"J"*$t$n *$nt6%$n 5$n) *"+t$-$ E ! ! G* -c1 .7 ."1$+ ,"J"*$t$n *$nt6%$n 5$n) ,"(6$ E !M MG* -c1 J7 tin))i -$,1i-$% *$nt6%$n *"+t$-$ E ! +*+(7 tin))i -$,1i-$% *$nt6%$n ,"(6$ E ! 4 *+"7

,"J"*$t$n .3%$ 1$$t -"n6-.6, %$nt$i E MG* -c1 Gf7 !".6$9 *"%6+6 ."+-$11$ M` )+$- (it"-.$,,$n ($+i 1".6$9 1"n$*$n ," $+$9 1".6$9 .$%3, ."+-$11$ H0` ,) 1"9in))$ *"%6+6 ."+1$+$n) (i ($%$- .$%3, ,$56 t"+1".6t7 V$%3, ."+$56n ($n n$i, 1"tin))i `K J- ($+i ,"$($$n 1"-6%$7 Ci,$ *"+J"*$t$n )+$Bit$1i GK -c1M0 ,"J"*$t$n *"%6+6 1"t"%$9 -"n)"n$i .$%3, $($%$9 7777 $7 GKG GK -c1 (7 GKK M -c1 .7 GKM GK -c1 "7 GKG M -c1 J7 GKL GK -c1 MK7 !".6$9 .3%$ ,$1ti ."+-$11$ K0L ,) ($%$- ,"$($$n (i$-0 ,"-6(i$n (i*6,6% 1"9in))$ .3%$ -"%6nJ6+ ("n)$n %$#6 GKK -c1 ($n *"-6,6% .3%$ -"n5"nt69 .3%$ 1"%$-$ K0G 1",3n7 V"1$+ )$5$ *"-6,6% $($%$9 7777 $7 GMK ^ (7 G`K ^ .7 GLK ^ "7 GIK ^ J7 GZK ^ MG7 !".6$9 ."n($ ."+3t$1i ($+i ,"$($$n (i$- 1"9in))$ ($%$- D$,t6 G 1",3n -"-i%i,i ,"J"*$t$n GK +$(c17 !".6$9 titi, < ."+$($ *$($ ."n($ ($n ."+#$+$, ` J($+i 16-.6 +3t$1in5$7 <"+J"*$t$n t$n)"n1i$% +$t$e+$t$ 5$n) (i-i%i,i titi, < t"+1".6t $($%$9 7777

Tes Kompetensi Akhir

205

MM7

ML7

MZ7

M`7

MI7

(7 K0G -c1M $7 K0M` -c1M .7 K0` -c1M "7 K0GM` -c1M J7 K0H` -c1M <"+9$ti,$n )$-.$+ (i 1$-*in)7 !".6$9 *i+in)$n 93-3)"n 5$n) -"-i%i,i -$11$ 9 ($n #$+ie#$+i r (i*6t$+ *$($ 1$%$9 1$t6 titi, (i )$+i1 1in))6n)n5$7 [3-"n in"+1i$ ($+i *i+in)$n 5$n) (i*6t$+ t"+1".6t $($%$9 7777 L M M M $7 9r (7 9r M ` G M M M .7 9r "7 9r M L J7 9rM !".6$9 .3%$ *"#$% ."+-$11$ ` ,) ($n ."+#$+ie#$+i ` J-7 V3%$ t"+1".6t -"n))"%in(in) (i *"+-6,$$n #$%$n 5$n) ,$1$+ $,i.$t 1".6$9 )$5$ (3+3n) U E MK ^7 Ci,$ .3%$ -"n))"%in(in) 1"-*6+n$ -$,$ *"+J"*$t$n 5$n) (i$%$-i .3%$ *"#$% t"+1".6t $($%$9 7777 $7 Z -c1M (7 `0Z -c1M .7 G0L -c1M "7 M0H -c1M J7 N -c1M <"+9$ti,$n 1i1t"- *$($ )$-.$+ ."+i,6t7 ]$5$e)$5$ 5$n) .","+#$ *$($ ."n($ ($%$- ,"$($$n 1"ti-.$n)7 Ci,$ G E GK -c1M0 t")$n)$n T ($n 1in 5 -$1in)e-$1in) $($%$9 7777 Z L $7 IK ^ ($n (7 `K ^ ($n ` I L L .7 IK ^ ($n H "7 ZK ^ ($n ` Z J7 IK ^ ($n ` !".6$9 *i+in)$n ."+."nt6, 1i%in("+ 93-3)"n ."+*6t$+ r *$($ *3+31n5$ ("n)$n ,"J"*$t$n $D$% GK +$(c17 Vi($n) *i+in)$n 1"#$#$+ .i($n) 93+i/3nt$%7 [$11$ piringan sumbu *i+in)$n E K0f ,) ($n #$+ie putar #$+i *i+in)$n E K0Z -7 Ci,$ (i $t$1 *i+in)$n (i%"t$,,$n JinJin ."+-$11$ K0` ,)0 ."+#$+ie#$+i K0G -0 ($n *61$t JinJin t"*$t (i $t$1 *61$t *i+in)$n -$,$ ,"J"*$t$n 16(6t *i+in)$n ($n JinJin ,"ti,$ ."+*6t$+ $($%$9 7777 $7 GI +$(c1 (7 GI0N +$(c1 .7 GN +$(c1 "7 GN0I +$(c1 J7 G`0I +$(c1 !".6$9 .$, -$n(i ."+."nt6, .$%3, -"-i%i,i *$n#$n) M -0 %".$+ G -0 ($n tin))i K0` -7 V$, -$n(i t"+1".6t

."+i1i `K %it"+ $i+ @ 4)ir E GKL ,)c-LA7 Ci,$ G E GK -c1M0 t",$n$n 9i(+31t$ti, *$($ ($1$+ .$, $($%$9 7777 $7 GKK <$ (7 M`K <$ .7 G`K <$ "7 LKK <$ J7 MKK <$ MH7 !".6$9 *3-*$ 9i(+3%i, -"-i%i,i (6$ *"n)9i1$* 5$n) ."+#$+ie#$+i -$1in)e-$1in) GK J- ($n `K J-7 <$($ *"n)9i1$* ,"Ji%0 (i,"+#$,$n )$5$ 1"."1$+ GKK ^7 ]$5$ 5$n) (i9$1i%,$n *$($ *"n)9i1$* ."1$+ $($%$9 7777

206

Mudah dan Aktif Belajar Fisika untuk Kelas XI

MN7

Mf7

LK7

LG7

LM7

LL7

LZ7

T $7 M7`KK ^ 5 30 N .7 L7KKK ^ J7 L7`KK ^ (7 Z7KKK ^ 4 kg "7 Z7`KK ^ V"+i,6t J3nt39 *"n"+$*$n =6,6- V"+n36%%i ($%$,"9i(6*$n 1"9$+ie9$+i0 kAc(),i 7777 $7 )$5$ $n),$t *"1$D$t t"+.$n) .7 ,$+.6+$t3+ -3.i% ($n -3t3+ J7 *"n5"-*+3t J$i+$n n5$-6, (7 B"nt6+i-"t"+ "7 +"- 9i(+3%i, !".6$9 %3)$- ."+."nt6, .3%$ ."+#$+ie#$+i Z J- ($n -$11$ #"ni1n5$ M )cJ-L7 T3)$- t"+1".6t #$t69 .".$1 (i ($%$- .$, ."+i1i /$t J$i+ 5$n) -"-i%i,i ,3"Qi1i"n Bi1,31it$1 GKL ^1c-M7 Ci,$ -$11$ #"ni1 /$t J$i+ G )cJ-L ($n *"+J"*$t$n )+$Bit$1i V6-i GK -c1M -$,$ ,"J"*$t$n t"+e -in$% .3%$ %3)$- $($%$9 7777 $7 G0IHI -c1 (7 G0IIH -c1 .7 G0MNI -c1 "7 G0MIH -c1 J7 G0LIH -c1 !".6$9 *i*$ 5$n) %6+61 -"-*6n5$i (6$ *"n$-*$n)0 ("n)$n %6$1 *"+-6,$$n -$1in)e-$1in) GKK -M ($n `K -M 5$n) (i%"t$,,$n 1"J$+$ 93+i/3nt$%7 Ui+ -"n)$%i+ ($+i *"n$-*$n) ."1$+ ," *"n$-*$n) ,"Ji%7 Ci,$ ,"J"*$t$n $+61 *$($ *"n$-*$n) ."1$+ Z -c10 ,"J"*$t$n $+61 $i+ *$($ *"n$-*$n) ,"Ji% $($%$9 7777 $7 ` -c1 (7 N -c1 .7 I -c1 "7 f -c1 J7 H -c1 Ci,$ 16$t6 )$1 5$n) -"-"n69i =6,6- V35%" (i#$(i,$n 1"t"n)$9n5$ -$,$ t",$n$n -"n#$(i (6$ ,$%in5$7 =$% ini (i1".$.,$n ,$+"n$ 7777 $7 -3%",6%e-3%",6% -"+$*$t 1"9in))$ ,"J"*$t$nn5$ -"n#$(i (6$ ,$%i .7 -3%",6%e-3%",6% ."+)"t$+ (6$ ,$%i %".i9 J"*$t J7 -3%",6%e-3%",6% ."1$+n5$ -"n#$(i (6$ ,$%i (7 .$n5$,n5$ -3%",6% -"n#$(i (6$ ,$%i "7 "n"+)i ,in"ti, -3%",6%e-3%",6% -"n#$(i (6$ ,$%i Ci,$ ,3n1t$nt$ V3%t/-$n k E G0LN _ GKOML Cc, -$,$ "n"+)i ,in"ti, 1".6$9 $t3- )$1 9"%i6- *$($ 1696 MHbX $($%$9 7777 $7 Z0GZ _ GKOMG C (7 I0MG _ GKOMG C OMG .7 M0KH _ GK C "7 GM0ZM _ GKOMG C OMG J7 `0`f _ GK C \i ($%$- +6$n) ."+B3%6-" M T0 t"+($*$t GKK -) )$1 ."+t",$n$n M $t-7 Ci,$ G $t- E GK` ^c-M0 ,"%$#6$n +$t$e+$t$ *$+ti,"% )$1 t"+1".6t $($%$9 7777 $7 (7 Z M -c1 Z L -c1 .7 M L -c1 "7 M M -c1 J7 L M -c1 [$11$ 1".6$9 -3%",6% nit+3)"n $($%$9 GK ,$%i -$11$ -3%",6% 9i(+3)"n7 Ci,$ -3%",6% nit+3)"n *$($ 1696 MNZ : -"-i%i,i %$#6 +$t$e+$t$ 5$n) 1$-$ ("n)$n %$#6 +$t$e+$t$ -3%",6% 9i(+3)"n -$,$ ($*$t (i*"+,i+$,$n 1696 9i(+3)"n t"+1".6t $($%$9 7777

$7 MK0L : (7 `K0L : .7 LK0L : "7 IK0L : J7 ZK0L : L`7 \i,"t$96i )$1 =" 1".$n5$% G -3% ($n 1696n5$ GMKbX7 hn"+)i ($%$- )$1n5$ $($%$9 7777 $7 Z7`KN #36%" (7 M7IH` #36%" .7 L7IH` #36%" "7 L7KIH #36%" J7 Z7fKG #36%" LI7 !".6$9 t$.6n) ."+i1i ` T )$1 i("$% *$($ 1696 G`KbX7 :"-6(i$n0 )$1 t"+1".6t (i*$n$1,$n 1"9in))$ 1696n5$ -"n#$(i LKKbX7 Ci,$ t",$n$n -6%$e-6%$ )$1 $($%$9 L _ GKM <$ ($n B3%6-" t$.6n) t"t$*0 t",$n$n )$1 *$($ t$.6n) $($%$9 7777 $7 Z _ GKL <$ (7 Z _ GKM <$ .7 ` _ GKL <$ "7 ` _ GKM <$ J7 I _ GKL <$ LH7 =$+)$ "Qi1i"n1i 16$t6 -"1in 5$n) .","+#$ *$($ +"1"+B3i+ 1696 +"n($9 LHbX ($n 1696 tin))i LLLbX $($%$9 7777 $7 ZI0` l (7 Zf0K l .7 ZH0I l "7 Zf0I l J7 ZN0N l V(

BaCabla>&6,rtanTaan&b,rikut&<,nUan&t,6at(

G7

!".6$9 *$+ti,"% ."+)"+$, ($+i *31i1i $D$% @Mi a Z7&a LkA -"t"+ ("n)$n ,"J"*$t$n t"t$* 5$n) ."1$+n5$ GM0` -c17 Ci,$ %int$1$n *$+ti,"% -"%$%6i @MM -0 GI -0 OI -A0 9it6n)e %$9 B",t3+ ,"J"*$t$n *$+ti,"% t"+1".6t7 Ci,$ *"+J"*$t$n )+$Bit$1i (i *"+-6,$$n V6-i f0N -c1M ($n V E I0IH _ GK OGG ^-Mc,)M0 t"nt6,$n%$9 -$11$ V6-i 5$n) ."+."nt6, .3%$ ("n)$n #$+ie#$+i I7LHK ,-7 !".6$9 *")$1 ."+)"t$+ 9$+-3ni1 ("n)$n $-*%it6(3 Z J-7 =it6n)%$9 1i-*$n)$n )"t$+ 1$$t "n"+)i ,in"ti, (6$ ,$%i "n"+)i *3t"n1i$%7 !".6$9 *"%6+6 5$n) -$11$n5$ `K )+$- (it"-.$,,$n ($n -"n)"n$i .$%3, ,$56 ."+-$11$ G0H` ,)0 5$n) t"+%"t$, (i *"+-6,$$n .i($n) ($t$+ ,$1$+ ("n)$n 'k EK0`7 Ci,$ *"%6+6 ."+1$+$n) (i ($%$- .$%3, 5$n) -"n)$,i.$t,$n .$%3, ."+)"1"+ 1"#$69 GK -"t"+0 t"nt6,$n%$9 ,"J"*$t$n *"%6+6 1"1$$t 1"."%6-"n"-.61 .$%3, @) E GK -c1MA7

M7 L7 Z7

@WSX& 1LLE2

`7

H7 m%6i($ i("$% ("n)$n ,"J"*$t$n L -c1 (i ($%$- *i*$ ."+)$+i1 t"n)$9 Z J- -$16, ," ($%$- *i*$ ."+)$+i1 t"n)$9 N J-7 >"nt6,$n%$9 ,"J"*$t$n $%i+ Q%6i($ *$($ *i*$ 5$n) ."1$+7 N7 \$%$- 1".6$9 +6$n) t"+t6t6* ."+B3%6-" G %it"+0 t"+($*$t G -3% )$1 ."+t",$n$n GKL <$7 Ci,$ *$+ti,"% )$1 -"-i%i,i ,"%$#6$n +$t$e+$t$ G7KKK -c10 t"nt6,$n -$11$ )$1 ($n "n"+)i ,in"ti, +$t$e+$t$ )$1 t"+1".6t7 f7 ]$1 3,1i)"n ."+$($ ($%$- +6$n) t"+t6t6* ."+1696 LHbX ($n t",$n$n GK $t-0 1"+t$ B3%6-"n5$ GK T7 :"-6(i$n0 )$1 3,1i)"n t"+1".6t (i*$n$1,$n 1$-*$i `KbX 1"9in))$ t",$n$nn5$ n$i, GM $t-7 >"nt6,$n B3%6-" )$1 1",$+$n)7 GK7 !6$t6 )$1 ($%$- 1i%in("+ t"+t6t6* -"n)$%$-i *+31"1 1"*"+ti *$($ )+$Qi, ."+i,6t7 p (N/m2) 100

A

\6$ .6$9 ."n($ 5$n) -"-i%i,i -$11$ 9G E 9M E M ,) ."+)"+$, 1$%in) -"n(",$ti 1"*"+ti *$($ )$-.$+ ."+i,6t7 m1

I7

LN7 !".6$9 %"-$+i "1 ."+1696 O`bX7 m%6i($ 5$n) (i-$-*$te ,$n (i ($%$-n5$ -"n)"-.6n *$($ 1696 M`bX7 :3"Qi1i"n ($5$ )6n$ %"-$+i "1 t"+1".6t $($%$9 7777 $7 H : (7 GK : .7 N : "7 GG : J7 f : Lf7 !".6$9 -"1in X$+n3+ -"n))6n$,$n +"1"+B3i+ 1696 tin))i HKK : ($n -"-i%i,i "Qi1i"n1i M`l7 U)$+ "Qi1i"n1i n$i, -"n#$(i H`l0 1696 +"1"+B3i+ tin))i 9$+61 (in$i,,$n 1"."1$+ 7777 $7 ZH` : (7 IM` : .7 `KK : "7 `M` : J7 ``K : ZK7 !".6$9 -"1in *"n(in)in +6$n)$n @UXA -"-i%i,i ($5$ G7KKK D$tt7 Ci,$ 1696 +6$n)$n GKbX ($n 1696 6($+$ MNbX0 .$n5$,n5$ ,$%3+ 5$n) (i1"+$* -"1in *"n(in)in 1"%$-$ GK -"nit $($%$9 7777 (7 N0NZ _ GKI C $7 f0ZM _ GKI C I .7 f0MZ _ GK C "7 H0`K _ GKI C I J7 N0ZN _ GK C

v1 = 10 m/s v2 = 20 m/s

25 m2

Ci,$ ,"(6$ ."n($ ."+t6-.6,,$n %"ntin) 1"-*6+n$0 t"nt6,$n%$9 ,"J"*$t$n -$1in)e-$1in) ."n($ 1"t"%$9 ."+t6-.6,,$n ($n t"nt6,$n *6%$ $+$9n5$7 !".6$9 .$t$n) "nt6,$n -3-"n )$5$ 5$n) .","+#$ *$($ .$t$n) #i,$P $7 *61$t -3-"n )$5$ (i <W .7 *61$t -3-"n )$5$ (i !7

C F 10

B E

V(m3)

60

>"nt6,$n 61$9$ 5$n) (i%$,6,$n )$1 *$($P $7 *+31"1 UV @!UVAW .7 *+31"1 VX @!VXAW J7 *+31"1 X\ @!XUAW (7 1"%6+69 *+31"1 @!t3t$%A7

Tes Kompetensi Akhir

207

Kunci Jawaban Bab 1

Analisis Gerak

Tes Kompetensi Awal G7 $7 LSM O IS O ` .7 MSF O ISFL O ` G S L ( ` S M , LS ( X J7 L M G S L F ( `SF ( G S M ( X (7 L M L7 :"J"*$t$n %in"$+ -"-i%i,i *"+*in($9$n %in"$+0 1"($n),$n ,"J"*$t$n 16(6t -"-i%i,i *"+*in($9$n +$(i$%7 Tes Kompetensi Subbab A G7 $7 Ii a GK7 .7 GG0I L7 $7 K0I -c1M .7 G0` -c1 J7 L -c1M `7 $7 OZ -c1M .7 GM0` Tes Kompetensi Subbab B G7 $7 G0I 1 .7 Z0HN J7 f0I L7 $7 K @titi, t"+tin))iA .7 N0I -c1 `7 G0Z 1 H7 M`0N -c1 Tes Kompetensi Subbab C G7 O@Z -c1Ai0 N-c1M L7 $7 GN0H -c1 .7 K0I *6t$+$n *"+ ("ti, J7 G0I 1 Tes Kompetensi Bab 1 A. Pilihan Ganda G7 $ GG7 $ L7 . GL7 " `7 . G`7 $ H7 J GH7 J f7 . Gf7 $ B. G7 L7 `7

208

Soal Uraian $7 G`0` -c1 .7 OM -c1M J7 ZL -c1M $7 GI0Nf -c1 .7 `I0Nf -c1 K0HG -

Mudah dan Aktif Belajar Fisika untuk Kelas XI

Bab 2

Gaya

Tes Kompetensi Awal G7 :$+"n$ ti($, $($ 9$-.$t$n @)"1",$nA 6($+$7 L7

Unt6, 1"+iP

G G G G G & ( ( ( 777 ( k" kG kM kL k0

Unt6, *$+$%"%P k* E kG a kM a kL a 777 a k0 Tes Kompetensi Subbab A G7 MK ^ L7 L -c1M `7 M`f0HM H7 G -c1M f7 $7 N0`L -c1M .7 HK0MZl Tes Kompetensi Subbab B G7 $7 MK ^ .7 K0GHI - ($+i .3%$ *"+t$-$ L7 `0` _ GKL ,)c-L `7 ML0L 1 H7 M7`KK ^ f7 GM0ZN _ GKGK ^ Tes Kompetensi Subbab C G7 @IL0If _ GKI ^c-MA0 @Z _ GKOZA0 @G`0f _GKGK ^c-MA L7 I0I _ GKL ^c`7 K0G -0 GKK ^cTes Kompetensi Subbab D G7 K0LH` ^ L7 K0`I ,) `7

Tes Kompetensi Bab 2 A. Pilihan Ganda G7 ( G`7 J L7 " GH7 J `7 $ Gf7 $ H7 " MG7 J f7 $ ML7 J GG7 ( M`7 J GL7 J

B. 1. 3. 5. 7. 9.

Soal Uraian 6 m/s2 2,5 m/s2; 30 N a. 4,17 × 1023 N b. 1,31 × 104 m/s 1,96 m/s2 0,6 cm

Bab 3

Usaha, Energi, dan Daya

Tes Kompetensi Awal 1. • Usaha adalah proses transfer energi dengan melibatkan gaya yang menyebabkan terjadinya perpindahan. • Energi adalah suatu kemampuan untuk melakukan usaha. 3. Sebuah benda yang dilemparkan ke atas, kemudian jatuh ke permukaan Bumi. Tes Kompetensi Subbab A 1. 160 J 3. 100 J 5. 12 J Tes Kompetensi Subbab B 1. 300 m/s 3. 200 J 5. 0,638 Tes Kompetensi Subbab C 1. • Gaya konservatif adalah gaya di mana usaha akibat gaya tersebut tidak mengubah energi mekanik sistem. • Gaya tidak konservatif adalah gaya di mana usaha oleh gaya tersebut dapat mengubah energi mekanik sistem. 3. !"2 5. !#h 7. 21,9 m/s dan 150 J 8. a. 12,7 m/s b. 60 J Tes Kompetensi Subbab D 1. 0,67 hp 3. 0 5. 83,3 watt 7. 20 m/s Tes Kompetensi Bab 3 A. Pilihan Ganda 1. c 11. c 3. a 13. d 5. b 15. c 7. b 17. e 9. e 19. b B. 1. 3. 5.

Soal Uraian 100 joule 976,48 joule 55,67 m/s

7.

9.

a. 20 joule b. 480 joule c. 500 joule d. 50 m/s 375 N/m

Bab 4

Momentum, Impuls, dan Tumbukan

Tes Kompetensi Awal 1. Ya 3. Ukuran elastisitas benda-benda yang bertumbukan. Tes Kompetensi Subbab A 1. a. 103 N b. 2 × 104 N Tes Kompetensi Subbab B 1. a. 6,67 m/s b. 26,67 m/s c. "p&' = 16,67 m/s "p&( = 10 m/s Tes Kompetensi Subbab C 1. 2p 3. a. 42 m/s, 18 m/s, 0 b. (20,4 m/s), (3,6 m/s), (10.886,4 J) c. 6 m/s, 6 m/s, 12.960 J 5. a. 3,5 m/s b. 10,5 J c. 0,4 7. 201 m/s 9. (3,33 m/s), (33,34 J) Tes Kompetensi Subbab D 1. 3,6 m 3. 15,8 m Tes Kompetensi Subbab E 1. 1,22 m 3. 1,42 m/s Tes Kompetensi Subbab F 1. 10.000 N Tes Kompetensi Bab 4 A. Pilihan Ganda 1. a 11. d 3. d 13. d 5. a 15. d 7. d 17. e 9. b 19. b B. 1. 3. 5. 7. 9.

Soal Uraian 140 kg m/s a. 0,7 m/s b. "1' = 2,5 m/s dan "2' = 2 m/s –33,33 m/s (vertikal ke bawah) 268,7 m/s a. 1 meter b. 0,16 meter c. 0

Kunci Jawaban

209

Tes Kompetensi Fisika Semester 1 A. 1. 3. 5. 7. 9. 11. 13. 15.

Pilihan c b d c a d b b

B. 1. 3. 5.

Soal Uraian 1 m/s2 4,625 m/s2; 45 N a. 4,17 × 1023 N b. 13.084 m/s 7.746 m/s 756,77 m

7. 9.

Bab 5

Ganda 17. d 19. c 21. a 23. d 25. b 27. e 29. a

Gerak Rotasi dan Kesetimbangan Benda Tegar

Tes Kompetensi Awal 1. • Momen gaya atau torsi merupakan besaran yang menyebabkan sebuah benda tegar (benda yang tidak dapat berubah bentuk) cenderung untuk berotasi terhadap porosnya. • Momen inersia merupakan sifat kecenderungan suatu benda untuk tetap mempertahankan gerak rotasinya. 3. Kesetimbangan pada benda yang digantung melalui katrol dan benda yang bergerak menggelinding. Tes Kompetensi Subbab A 1. a. 8 rad, 64 rad 460°, 3.670° b. 16,8 m c. 28 rad/s d. 24 rad/s 3. 24 rad/s2, 80 rad/s2 Tes Kompetensi Subbab B 1. 3,55 Nm 3. a. 120 Nm b. 120 Nm 5. a. 2,7 rad/s2 b. (20,412 N), (17,32 N) Tes Kompetensi Subbab C 1. 0,8 m 3. 213,3 N 5. 163,8 N; 140 N; 42,2° Tes Kompetensi Bab 5 A. Pilihan Ganda 1. d 9. d 5. e 13. a 7. c 15. a

210

Mudah dan Aktif Belajar Fisika untuk Kelas XI

B. 1. 3. 5. 7. 9.

Soal Uraian 0,26 Nm 1,025 kg m2 a. 12/5 m/s2 b. 0,36 N rad c. 4,8 m 41,8 Nm 50,2 sekon

Bab 6

Fluida

Tes Kompetensi Awal 1. Hukum Pascal. Cara kerjanya dengan menggunakan konsep tekanan hidrostatik. 3. Karena terdapat tegangan permukaan zat cair. Tes Kompetensi Subbab A 1. a. 12.160 N/m2 b. 20.160 N/m2 3. a. 34 cm b. 6,25 cm3 5. a. mengapung b. 3 m3 c. 24.000 N Tes Kompetensi Subbab B 1. 1,2 × 10 –3 mm Tes Kompetensi Subbab C 1. 87,46 m/s 3. 9.075 N 5. 22,13 m/s Tes Kompetensi Bab 6 A. Pilihan Ganda 1. e 11. b 3. b 13. c 5. e 15. c 7. d 17. d 9. b 19. a B. 1. 3. 5.

Soal Uraian 490 k Pa a. 4 m b. 4 × 104 N c. 2 × 104 N 1.250 sekon

Bab 7

Teori Kinetik Gas

Tes Kompetensi Awal 1. Nitrogen, oksigen, dan karbondioksida. Pada keadaan STP, gas tersebut bukan merupakan gas ideal. 3. Balon udara terbang dengan memanfaatkan massa jenis udara panas yang lebih ringan daripada udara bebas. Tes Kompetensi Subbab A 1. 16.628 Pa 3. 13,4 mL

Tes Kompetensi Subbab B 1. )k (O2) : )k (N2) = 7 : 8 "(O2) : "(N2) = 7 : 8 Tes Kompetensi Subbab C 1. "0 2 3. 0,89 atm 5. 3,74 kJ 7. 1,05 × 1023 molekul; 1,32 × 10–10 m/s; 42,74 m/s Tes Kompetensi Bab 7 A. Pilihan Ganda 1. b 11. d 3. c 13. c 5. b 15. a 7. e 17. e 9. a 19. d

Tes Kompetensi Bab 8 A. Pilihan Ganda 1. b 11. d 3. b 13. d 5. d 15. e 7. d 17. b 9. a 19. c B. 1. 3. 5. 7. 9.

Soal Uraian 49,8 atm –4.000 J 9.720 J 3,44 × 10–3 J 60%

Tes Kompetensi Fisika Semester 2 A. 1. 3. 5. 7. 9. 11. 13. 15.

Pilihan d b c c a e c b

Tes Kompetensi Awal 1. Gelas tersebut dapat pecah karena ketika diisi air panas, permukaan gelas akan mengalami pemuaian akibat perubahan suhu yang tidak merata. 3. Efisiensi, dalam kaitannya dengan kinerja mesin adalah perbandingan antara usaha yang dilakukan dengan kerja yang dihasilkan.

B. 1. 3. 5. 7. 9.

Soal Uraian 5,25 cm 28,6 m 0,059 N 3,32 kg/m3 a. 1 b. 3,74

Tes Kompetensi Subbab A 1. a. –375 kJ b. 85 kJ 3. 145,524 kPa 5. 1.660,96 J

Tes Kompetensi Akhir

B. 1. 3. 5. 7.

Soal Uraian 44,37 cm3 52 g/cm3 30 liter 132 liter

Bab 8

Termodinamika

Ganda 17. a 19. a 21. b 23. c 25. c 27. a 29. b

A. 1. 3. 5. 7. 9. 11. 13. 15. 17. 19.

Pilihan a e e a d a b e e a

Tes Kompetensi Subbab C 1. 1.000 K 3. 40 % 5. a. 60 % b. 3.000 J

B. 1.

Tes Kompetensi Subbab D 1. 8,93 3. 410,86 watt 5. 6,21 × 108 J

7.

Soal Uraian ! = 10" + 6 # – 4,5 $ 4 3 cm 3 "2' = +10 m/s (ke kiri); "1' = –20 m/s (ke kanan) 3 m/s 4 8,68 L

Tes Kompetensi Subbab B 1. 450 J 3. 3.324 J 5. Gas ideal dapat terjadi jika tidak terdapat perpindahan panas. Perpindahan panas tidak akan terjadi jika suhu tetap (isotermal), tekanan tetap (isobar), dan volume tetap (isokhorik).

3. 5. 9.

Ganda 21. b 23. e 25. d 27. a 29. e 31. a 33. b 35. c 37. c 39. d

Kunci Jawaban

211

Apendiks Simbol-Simbol Matematika = ! " # $ > > >> < < <<

: : : : : : : : : : :

sama dengan tidak sama dengan hampir sama dengan dalam orde sebanding dengan lebih besar dari pada lebih besar sama dengan jauh lebih besar dari pada lebih kecil lebih kecil sama dengan jauh lebih kecil dari pada

%' |'| +, & lim %t ' 0 .' .t (' (t

: : : : : :

)

: integral

perubahan ' nilai absolut ' +(+ – 1)(+ – 2) ... 1 jumlah limit %t mendekati nol

: turunan ' terhadap t : turunan parsial ' terhadap t

Rumus Trigonometri tan 2* ! 2tan *2 1 + tan *

sin 2 * " cos2 * ! 1 sec 2 * + tan 2 * ! 1 csc 2 * + cot 2 * ! 1 sin 2* ! 2 sin * cos * 2 2 cos 2* = cos * + sin *

sin 1 * ! 1 + cos* cos 1 * 2 2 2 ! 1 " cos* tan 1 * 2 2 ! 1 + cos * 1 " cos*

= 2cos2 * + 1 = 1 + 2sin 2 * Turunan Fungsi-Fungsi Tertentu

./ ! 0 dengan / adalah konstanta .t . # t + $ ! +t + +1 .t . sin ,t ! , cos ,t .t . cos ,t ! +, sin ,t .t

. tan , t ! , sec 2 , t .t . ebt ! bebt .t . ln bt ! 1 .t t

Rumus-Rumus Integrasi

1

) 2t.t ! 2 2t

2 + "1

) 2t .t ! 2 +t " 1 +

) 2t

212

+1

.t ! 1 ebt 2t b 1 ) cos ,t.t ! , sin ,t 1 ) sin ,t.t ! + , cos ,t

)e

) 2.t ! 2t + ! +1

.t ! 2 ln t

Mudah dan Aktif Belajar Fisika untuk Kelas XI

bt

Satuan-Satuan Dasar Panjang

Waktu

Massa

Meter (m) adalah jarak yang ditempuh oleh cahaya di ruang vakum dalam waktu

Arus

1 sekon 299.792.458

Sekon (s) adalah waktu yang diperlukan untuk 9.192.631.770 siklus pada radiasi yang berhubungan dengan transisi antara dua tingkat hiperfin dengan keadaan dasar pada atom 133 Cs Kilogram (kg) adalah massa pada Standar Internasional untuk bobot dan ukuran yang disimpan di Sevres, Prancis

Ampere (A) adalah arus pada dua kawat panjang paralel yang terpisah sejauh 1 m dan menimbulkan gaya magnetik persatuan panjang sebesar 2 × 10–7 N/m 1

Temperatur Kelvin (K) adalah 273,16 dari temperatur termodinamika pada tr4ple po4+t a4r Intensitas Candela (cd) adalah intensitas cahaya dalam cahaya arah tegak lurus permukaan benda hitam seluas 1/600.000 m pada temperatur beku platinum dengan tekanan 1 atm

Satuan-Satuan Turunan Gaya Kerja, Energi Daya Frekuensi Muatan listrik Potensial listrik

newton (N) joule (J) watt (W) hertz (Hz) coulomb (C) volt (V)

1 N = 1 kg m/s2 1 J = 1 Nm 1 W = 1 J/s 1 Hz = 1/s 1 C = 1 As 1 V = 1 J/C

Hambatan listrik Kapasitas listrik Medan magnet Fluks magnet Induktansi

9,80665 m/s2 5,98 × 1024 kg 6,37 × 106 m 3.960 mil 1,12 × 104 m/s 1,35 kW/m2

Tekanan

ohm ( - ) farad (F) tesla (T) weber (Wb) henry (H)

1 - = 1 V/A 1 F = 1 C/V 1 T = 1 N/A m 1Wb = 1 Tm2 1 H = 1 J/A2

Data Terestrial Percepatan gravitasi # Massa Bumi M9 Jari-jari Bumi, :9, rata-rata Kecepatan lepas 2:9 # Konstanta Matahari* Suhu dan tekanan standar (STP): Temperatur *

101,325 kPa 1,00 atm Massa molar udara 28,97 g/mol Massa jenis udara (STP), .udara 1,293 kg/m3 Kecepatan suara (STP) 331 m/s Kalor didih air (0°C, 1 atm) 333,5 kJ/kg Kalor penguapan air (100°C, 1 atm) 2,257 MJ/kg

273,15 K

Daya rata-rata yang terjadi pada 1 m2 di luar atmosfer Bumi pada jarak rata-rata antara Bumi dan Matahari.

Data Astronomi %u'" Jarak ke Bulan* Jarak ke Matahari, rata-rata* Kecepatan orbit, rata-rata ()t)+)," Massa Jari-jari *

3,844 × 108 m 2,389 × 105 mil 1,496 × 1011 m 1,00 AU 2,98 × 104 m/s

%u-). Massa Jari-jari Periode Percepatan gravitasi pada permukaan

7,35 × 1022 kg 1,738 × 106 m 27,32 hari 1,62 m/s2

7,35 × 1022 kg 1,738 × 106 m

pusat ke pusat

Apendiks

213

Konstanta Fisika Konstanta gravitasi Kecepatan cahaya Muatan elektron Konstanta Avogadro Konstanta gas Konstanta Boltzmann Unit massa terpadu Konstanta Coulomb

; < e =2 : > ? >

6,672 × 10–11 Nm2/kg2 2,998 × 108 m/s 1,602 × 10–19 C 6,002 × 1023 partikel/mol 8,314 J/molK 1,381 × 10–23 J/K 1,661 × 10–24 g 8,988 × 109 Nm2/C2

Permitivitas ruang hampa / 0 Permeabilitas ruang hampa %0 Konstanta Planck h ! Massa elektron !e Massa proton !p Massa neutron !n

8,854 × 10–12 C2/Nm2 4 × 10–7 N/A2 6,626 × 10–34 Js 1,055 × 10–34 Js 9,109 × 10–31 kg 1,672 × 10–27 kg 1,675 × 10–27 kg

Faktor-Faktor Konversi /).#).0 1 km = 0,6215 mil 1 mil = 1,609 km 1 m = 1,0396 yd = 3,281 ft = 39,37 inci 1 inci = 2,54 cm 1 ft = 12 inci =30,48 cm 1 yd = 3ft = 91,44 cm 1 tahun cahaya = 1c tahun = 9,461 × 1015 m o 1 A = 0,1 nm 1u)s 1 m2 = 104 cm2 1 km2 = 0,3851 mil2 = 247,1 ha 1 inci2 = 6,5416 cm2 1 ft2 = 9,29 × 10–2 m2 1 m2 = 10,76 ft2 1 ha = 43,560 ft2 I mil2 = 640 ha2 = 590 km2 34-u'e 1 m3 = 106 cm3 1 L = 1.000 cm3 = 10–3 m3 1 gal = 3,786 L 1 gal = 4 qt = 8 pt = 128 oz = 231 inci3 1 inci3 = 16,39 cm3 1 ft3 = 1.728 inci3 = 28,32 L = 2,832 × 104 cm3 6)$tu 1 jam = 60 menit = 3,6 ks 1 hari = 24 jam = 1.440 menit = 86,4 ks 1 tahun = 365,24 hari = 31,56 Ms 7e8e9)t). 1 km/jam = 0,2778 m/s = 0,6215 mil/jam 1 mil/jam = 0,4470 m/s = 1,609 km/jam 1 mil/jam = 1,467 ft/s :u;ut<;).<7e8e9)t).<:u;ut 1 rad = 180° 1 rad = 57,30° 1° = 1,745 × 10–2 rad 1 rev/menit = 0,1047 rad/s 1 rad/s = 9,549 rev/menit

214

Mudah dan Aktif Belajar Fisika untuk Kelas XI

()ss) 1 kg = 1.000 g 1 ton = 1.000 kg = 1 Mg 1 u = 1,6606 × 10–27 kg 1 kg = 6,022 × 1023 u 1 slug = 14,59 kg 1 kg = 6,852 × 10–2 slug 1 u =931,50 MeV/<2 ()ss)<=e."s 1 g/cm3 = 10.000 kg/m3 = 1 kg/L (1 g/cm3)# = 62,4 lb/ft3 >)?) 1 N = 0,2248 lb = 105 dyne 1 lb = 4,4482 N (1 kg)# = 2,2046 lb @e$).). 1 Pa =1 N/m2 1 atm = 101,325 kPa =1,01325 bar 1 atm = 14,7 lb/inci2 = 760 mmHg 1 torr = 1 mmHg = 133,32 Pa 1 bar = 100 kPa A.e,0" 1 kWh = 3,6 MJ 1 kal = 4,184 J 1 Latm = 101,325 J = 24,217 kal 1 Btu = 778 ft lb = 252 kal = 1.054,35 J 1 eV = 1,602 × 10–19 J 1 u <2 = 931,50 MeV 1 erg = 10–7 J B)?) 1 daya kuda = 550 ft lb/s = 745,7 W 1 Btu/menit = 17,58 W 1 W = 1,341 × 10–3 daya kuda = 0,7376 ft lb/s (e;).<()0.et 1 G = 10–4 T 1 T = 104 G 74.;u$t"!"t)s<@e,')1 W/m K = 6,938 Btu inci/jam ft2 °F 1 Btu inci/jam ft2 °F = 0,1441 W/mK

Senarai A C'9-"tu;4D simpangan terjauh pada suatu osilasi/ayunan Cst,4.4'"D ilmu perbintangan. C?u.).<E)-"st"$D ayunan yang berfungsi untuk mengukur kecepatan gerak peluru.

B %e.;)<;"s$,"tD benda yang bentuk dan ukurannya diabaikan %e.;)
E AF"s"e.s"<'es".D ukuran kinerja sebuah mesin yang merupakan perbandingan antara energi yang dihasilkan terhadap energi yang diberikan. A-)st"s"t)sD kemampuan yang dimiliki oleh benda untuk kembali ke bentuk semula setelah mengalami gangguan bentuk. A.e,0"<$".et"$D energi yang dimiliki benda karena gerakannya. A.e,0"<'e$)."$D total energi kinetik dan energi potensial dari benda. A.e,0"< 94te.s")-D energi yang dimiliki benda karena kedudukannya.

F G,e$ue.s"D jumlah ayunan/osilasi yang terjadi pada jangka waktu satu detik.

G >)?)<);+es"D gaya tarik-menarik antara partikel tidak sejenis. >)?)<0ese$<$".et"$D gaya gesek yang timbul pada saat benda telah bergerak. >)?)< 0ese$< st)t"sD gaya gesek yang timbul pada saat benda masih diam. >)?)<$4+es"D gaya tarik-menarik antara partikel sejenis. >)?)<$4.se,!)t"FD gaya yang hasil usahanya hanya memperhatikan kedudukan awal dan akhir. >e#)-)<$)9"-),"t)sD gejala naiknya zat cair pada pipa-pipa kapiler.

H He-"4se.t,"sD pandangan yang menganggap bahwa Matahari adalah pusat dari peredaran benda langit.

K 7),Eu,)t4,D tabung pencampur bahan bakar pada kendaraan bermotor.

7e8e9)t).
M ().4'ete,D alat untuk mengukur selisih tekanan zat cair. (e."s$us< 8e$u.0D bentuk permukaan zat cair yang cekung ketika berada dalam suatu wadah. (e."s$us< 8e'Eu.0D bentuk permukaan zat cair yang cembung ketika berada dalam suatu wadah.

P /e,"4;e<4,E"t<s)te-"tD waktu yang dibutuhkan oleh satelit untuk beredar pada orbitnya sebanyak satu kali putaran. /,4ses<);")E)t"$D proses yang terjadi pada keadaan kalor sistem tetap. /,4ses< "s4E),"$D proses yang terjadi pada keadaan tekanan tetap. /,4ses< "s4$+4,"$D proses yang terjadi pada keadaan volume tetap. /,4ses<"s4te,')-D proses yang terjadi pada keadaan suhu tetap.

R IeF,"0e,)t4,D mesin pendingin. Iesu-t).< 0)?)D gaya total hasil penjumlahan dari beberapa gaya. !"##$% '"()*$%D kereta mainan yang memanfaatkan prinsip kekekalan energi mekanik benda. I4t)s"D perputaran benda pada porosnya.

S :"ste'
T @e$).).<+";,4st)t"$D tekanan yang dialami zat cair pada kedalaman tertentu. @"t"$< F4$us< e-"9sD titik pada jarak setengah jari-jari terpanjang pada elips. @4,s"D besaran yang menyebabkan benda tegar cenderung untuk berotasi pada porosnya. @,).s-)s"D pergeseran.

V 3e.tu,"'ete,D alat untuk mengukur kecepatan aliran gas. 3"s$4s"t)sD kekentalan zat cair.

215

Indeks aphelion 45 benda tegar 117, 118, 119, 121, 124, 132, 134, 135, 137,138 berat 31, 32, 33, 41, 42, 43, 46, 71, 73, 76, 80, 82, 83, 85, 86, 88, 92, 99, 114, 116, 118, 122, 127, 132, 133, 134, 136, 137, 142, 145, 146, 147, 148, 149, 151, 152, 153, 154, 158, 162, 163, 166, 177, 193, 202, 203, 204 daya kuda 89 derajat kebebasan 174, 175, 176, 179, 190 efisiensi 30, 194, 195, 196, 197, 201, 202, 205 elips 45, 124, 125 energi kinetik 76, 77, 80, 81, 82, 83, 85, 88, 90, 91, 92, 93, 94, 96, 100, 101, 102, 103, 104, 107, 109, 110, 111, 115, 116, 119, 129, 130, 131, 137, 138, 140, 167, 173, 174, 175, 176, 177, 178, 179, 181, 182, 204 energi potensial 71, 72, 78, 79, 80, 81, 83, 85, 86, 88, 90, 91, 92, 93, 94, 100, 107, 111, 115, 175 entropi 184 frekuensi 139 gas ideal 167, 168, 169, 170, 171, 173, 174, 176, 179, 180, 181, 182, 183, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 200, 201, 202, 204 gaya gesek 29, 30, 31, 32, 33, 35, 36, 38, 73, 76, 85, 127, 133 gaya kohesi 149, 150, 151 gaya konservatif 71, 82, 83, 91 gaya sentripetal 27, 35, 36, 37, 41, 46, 47 Hukum Boyle 168, 169, 180, 181, 185, 204 Hukum II Termodinamika 197 Hukum Kekekalan Energi 71, 74, 81, 83, 85, 87, 91, 100, 106, 107, 109, 130, 189 Hukum Kekekalan Energi Mekanik 71, 83, 85, 87, 91, 100, 106 Hukum Kekekalan Momentum 45, 97, 99, 100, 102, 103, 107, 106, 109, 111, 118, 123, 124, 125, 138 Hukum Kekekalan Momentum Sudut 45, 118, 123, 124, 125, 138

216

Mudah dan Aktif Belajar Fisika untuk Kelas XI

Hukum I Termodinamika 189, 197 impuls 95, 96, 97, 98, 99, 103, 109, 110, 111, 123, 124 integrasi 7, 11, 23, 119 jatuh bebas 12, 14, 18, 80, 83, 85, 88, 92, 93, 95, 98, 105, 111, 115 joule 72, 73, 74, 75, 80, 81, 85, 88, 92, 93, 103, 116, 129, 130, 150, 173, 174, 180, 186, 187, 190, 192, 197, 200, 201, 202, 205 kalori 71, 202, 205 kapasitas panas 193 kapilaritas 151, 163, 164, 166 kecepatan rata-rata 4, 5, 14, 23, 25, 27, 166, 177, 179 kecepatan sesaat 5, 6, 10, 14, 23, 25, 27 kecepatan terminal 154, 155, 163, 165 kelajuan rata-rata 4, 5, 88, 181 kelajuan sesaat 5, 6 kelembaman 124 kemiringan 1, 7, 10, 11, 21, 29, 32, 33, 36, 37, 38, 39, 76, 81, 88, 127, 131, 136, 139, 140, 206 kerja 71, 89, 108, 121, 135, 142, 144, 145, 163, 167, 184, 190, 193, 194, 195, 196, 198, 199, 200 koefesien restitusi 96, 109 konstanta gravitasi universal 40, 43, 47 laju aliran 156, 161, 166 lengan 117, 118, 121, 132, 133, 134, 137 massa 27, 34, 36, 39, 40, 41, 42, 46, 47, 48, 77, 78, 79, 80, 82, 83, 85, 88, 90, 92, 94, 96, 99, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 119, 120, 122, 123, 124, 126, 128, 131, 134, 136, 137, 138, 139, 140, 142, 143, 146, 147, 148, 149, 151, 152, 153, 154, 155, 158, 159, 160, 161, 162, 164, 165, 166, 167, 169, 170, 171, 173, 174, 175, 177, 178, 179, 181, 182, 200, 202, 203, 204, 205, 206 medan gravitasi 42, 43, 44, 78, 83, 85, 137 mesin Carnot 194, 195, 196, 197, 199, 201, 202, 205

momen inersia 117, 118, 119, 120, 122, 124, 125, 126, 128, 129, 131, 137, 138, 139, 140 momentum sudut 45, 117, 118, 120,123, 124, 125, 137, 138 panas 74, 94, 100, 102, 103, 104, 106, 109, 115, 116, 167, 184, 188, 193, 198, 199, 202 partikel 2, 3, 5, 7, 9, 10, 11, 12, 14, 20, 21, 22, 23, 25, 26, 27, 77, 82, 96, 97, 113, 119, 121, 122, 123, 124, 132, 139, 149, 150, 151, 153, 155, 167, 168, 170, 171, 172, 173, 174, 175, 177, 178, 179, 181, 182, 204 Pascal 142, 144, 145, 163, 164, 165, 166 percepatan angular 26 percepatan rata-rata 9, 10, 11, 14, 23, 25, 27 percepatan sentripetal 39, 46, 87 percepatan sesaat 9, 10, 11, 14, 23, 25 perihelion 45 periode 23, 42, 45, 46, 48, 103, 114, 138, 139 perkalian vektor 118 perpindahan 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 20, 23, 39, 72, 73, 74, 75, 77, 78, 80, 85, 88, 91, 150, 192 Persamaan Bernoulli 141, 157, 158, 160, 161, 164 Persamaan Kontinuitas 155, 156, 159, 160, 161, 163, 164 Prinsip Pascal 145 proses adiabatik 181, 185, 186, 187, 188, 189, 191, 194, 195, 196, 199, 200, 201 pusat berat 137

pusat massa 120, 134, 137, 174, 175 refrigerator 198 regangan 80, 166 Siklus Carnot 183, 194, 199, 205 skalar 2, 5, 72, 76, 77, 99, 123 tegangan permukaan 149, 150, 151, 152, 163, 164, 165, 166 tekanan 136, 142, 143, 144, 145, 152, 153, 155, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 177, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 196, 197, 199, 200, 201, 202, 204, 205, 206 temperatur 153, 169, 170, 171, 174, 189, 198, 202, 206 Teori Kinetik Gas 167, 168, 181 Termodinamika 167, 183, 184, 189, 190, 191, 192, 193, 194, 197, 198, 199, 200 torsi 40, 117, 118, 121, 123, 124, 132, 133, 137, 140 vektor 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 15, 18, 23, 25, 40, 44, 72, 92, 96, 97, 109, 113, 118, 120, 123, 124, 132, 134, 172 vektor kecepatan rata-rata 4, 5 vektor perpindahan 2, 3, 6 vektor posisi 2, 5, 8, 12, 14, 23, 25 vektor satuan 2, 4, 6, 92 watt 88, 89, 90, 94, 199, 204, 205

Indeks

217

Daftar Pustaka Allonso, M. and Finn 1980. Fundamental Physics, Vol 1and 2. New York: Addision-Wesley Publishing Company Inc. Biryam, M 1992. Hukum-Hukum Kekekalan dalam Mekanika. Jakarta: Departemen Pendidikan dan Kebudayaan. Bueche, Fredrick 1982. Introduction to Physics for Scientist and Insights. New York: Mc Grow Hill Book Company Inc. Dorling Kindsley 1995. Jendela IPTEK, seri 1-4. Jakarta: Balai Pustaka Jakarta. Giancoli, Douglas C. 2000. Physics, 3rd Edition. USA: PrenticeHall International. Grolier International Inc. 1995. Oxford Ensiklopedi Pelajar. Jakarta: PT. Widyadara. Haliday, D, R. Resnick, J. Waker. 2001. Fundamental of Physics, Sixth Edition. USA: John Willey and Sons Inc. Harsanto. 1980. Motor Bakar. Jakarta: Djambatan. Hermawan Edi. 2004. Radar Atmosfer Khatulistiwa. Surakarta: Pabelan. Hewwit, Paul G. 1993. Conceptual Physics, 6th Edition. USA: Harper Collins College Publisher. Hewwit, Paul G. 1998. Conceptual Physics, 8th Edition. USA: Addison Wesley Publishing Company Inc. Kamus Besar Bahasa Indonesia, cetakan ketiga. 2005. Jakarta: PT. Balai Pustaka. Kamus Fisika, cetakan kedua. 2003. Jakarta: PT. Balai Pustaka. Sears, F.W. et.al. 1993. University Physics. USA: Addison Wesley Publishing Company Inc. Tipler, Paul. 1998. Fisika untuk Sains dan Teknik, Jilid 1 (alih bahasa: Prasetyo dan Rahmad W. Adi). Jakarta: Erlangga. Tipler, Paul. 2001. Fisika untuk Sains dan Teknik, Jilid 2 (alih bahasa: Bambang Soegijono). Jakarta: Erlangga. Young, Hugh D. dan Freadman, Roger A. 2001. Fisika Universitas, edisi X. Jakarta: Erlangga.

218

Mudah dan Aktif Belajar Fisika untuk Kelas XI

ISBN 978-979-068-816-2 (No. Jld lengkap) ISBN 978-979-068-818-6

Harga Eceran Tertinggi (HET) Rp.14.468,-

PUSAT PERBUKUAN Departemen Pendidikan Nasional