• Tidak ada hasil yang ditemukan

Bab 9 Teori Relativitas Khusus

N/A
N/A
Protected

Academic year: 2017

Membagikan "Bab 9 Teori Relativitas Khusus"

Copied!
28
0
0

Teks penuh

(1)

memformulasikan teori relativitas khusus untuk waktu, panjang, dan massa, serta kesetaraan massa dengan energi yang diterapkan dalam teknologi

Setelah mempelajari bab ini, Anda harus mampu:

menganalisis berbagai besaran fisis pada gejala kuantum dan batas-batas berlakunya relativitas Einstein dalam paradigma Fisika Modern.

Hasil yang harus Anda capai:

Teori Relativitas Khusus

A. Semua Gerak

Bersifat Relatif

B. Teori Relativitas

Einstein

E6@6=C96H6=IB:C<6E6B6CIG>67:AIB7>G6B:C?:A6?6=>EA6C:H 96C7>CH6C<9>AI6FH6H6GIFM6.6A6=G6HI@:C96A6M6C<9>=696E6>696A6= ?IBA6= 76=6C 76@6F M6C< 9>7IHI=@6C G6C<6H 76CM6@ @6F:C6 ?6F6@ H:BEI=CM67>G67:FDF9:H6=IC6C86=6M66A6B;>AB ;>AB;>@G>>AB>6= E:F?6A6C6CG:E:FH>>HIB:FIE6@6C=6AM6C<7>6G6@6F:C6E:G6K6HM6C< 9><IC6@6CB:B>A>@>@:8:E6H6CM6C<G6C<6HH>C<<>(>G6ACM696A6B;>AB

)'' E:G6K6HM6C<7:FC6B6)'(%#)'%'(B6BEI7:F?6A6C9:C<6C @:8:E6H6CDF9:86=6M6/6=I@6=C966E6=I7IC<6C6CH6F6?6F6@9:C<6C @:8:E6H6C86=6M6%>@6GI6HI7:C967:F<:F6@9:C<6C@:8:E6H6C86=6M6 H:DF>F:A6H>J>H6G@=IGIG6@6C7:FA6@I.6A6=G6HI>BEA>@6G>96F>E:C:F6E6C H:DF>F:A6H>J>H6G@=IGIG696A6=H:F?69>CM6@DCHF6@G>E:CMIGIH6CE6C?6C< G:=>C<<6?6F6@H:BEI=CM6G:B6@>CE:C9:@

.:A6>C @DCHF6@G> E6C?6C< B6G>= 76CM6@ A6<> E:C<6FI= M6C< 9>6@>76H@6C DA:= 7:C96 M6C< 7:F<:F6@ 9:C<6C @:8:E6H6C B:C9:@6H> @:8:E6H6C86=6M66CM6@=6AM6C<H:F@:G6CH>96@B6GI@6@6A@6C H:H6E>?>@69>H>C?6I9:C<6CB:C<<IC6@6CH:DF>F:A6H>J>H6G@=IGIGH:FCM6H6 >AB>6=96C96E6H9>7I@H>@6C!:CDB:C6 ;:CDB:6B:C6F>@H:FG:7IH6@6C

Pesawat ruang angkasa Starship Enterprise dalam serial televisi Star Trek seringkali berjalan dengan kecepatan cahaya.

Bab

9

(2)

Gambar 9.1

Menurut pengamat di luar kereta api, penumpang sedang bergerak dengan kecepatan yang sama dengan kecepatan kereta api.

A. Semua Gerak Bersifat Relatif

.:BI67:C969>@6H6@6C7:F<:F6@?>@6@:9I9I@6C7:C96>HI7:FI76= H:F=696EH>H>@68I6C6H6I@:F6C<@668I6CM6C<9>H:H6E@6C.:DF6C<G>GK6 M6C<G:96C<9I9I@9>96A6B@:F:H66E>M6C<7:F<:F6@9>@6H6@6C9>6B H>96@7:F<:F6@?>@6@:F6C<@668I6CCM6@:F:H66E>@6CH:H6E>G:DF6C< E:C<6B6H9>AI6F@:F:H66E>B:C<6H6@6CG>GK6H:FG:7IH7:F<:F6@9:C<6C @:8:E6H6CM6C<G6B69:C<6C@:8:E6H6C@:F:H66E>.6B6=6ACM6<:F6@ G:7I6=E:F6=IH:FG:7IH6A>F6C6>FGIC<6>+:F6=I96C6FIGGIC<6>7:F<:F6@ H:F=696EIB>DCHD=9>6H6GB:CIC?I@@6C76=K6H>96@6967:C96 M6C<7:F<:F6@BIHA6@M6C<696=6CM6A6=<:F6@F:A6H>;

/:DF>):KHDCH:A6=7:F=6G>AB:C?:A6G@6CE:F>GH>K6G:7I6=7:C96M6C< 7:F<:F6@9:C<6C@:8:E6H6CF:C96=G:E:FH>8DCHD= 8DCHD=<:F6@H:FG:7IH @6CH:H6E>H:DF>CM6H>96@7:F=6G>AB:C?:A6G@6CE:F>GH>K67:C96M6C< 7:F<:F6@B:C9:@6H>@:8:E6H6C86=6M6G:E:FH>G:?IBA6=:A:@HFDCM6C< 9>E:F8:E6HB:A6AI>7:96EDH:CG>6A(:16@6CB:C86E6>@:8:E6H6C

(:CIFIHB:@6C>@6):KHDC76=K6@:8:E6H6C:A:@HFDC6@6CB:C?69> ?>@6 9>E:F8:E6H 9:C<6C EDH:CG>6A G:7:G6F (:1 &:CM6H66C B:CIC?I@@6C76=K6@:8:E6H6C:A:@HFDCH:H6EG6?6G:7:G6F%:A6GA6= B:@6C>@6):KHDCH>96@96E6H9>E6@6>ICHI@7:C96 7:C96M6C<7:F<:F6@ B:C9:@6H>@:8:E6H6C86=6M6

1. Transformasi Galileo

+F>CG>EF:A6H>J>H6G"6A>A:D9>@:C6A?I<6G:76<6>EF>CG>EF:A6H>J>H6G@A6G>@ @6F:C6 =6CM6 7:F@6>H6C 9:C<6C =I@IB =I@IB <:F6@ ):KHDC DCHD=CM6E:C<6B6H6CH:F=696EG:DF6C<G>GK6M6C<G:96C<9I9I@9> 96A6B@:F:H66E>M6C<7:F<:F6@DA:=9I6DF6C<E:C<6B6HG:76<6>9I6 @:F6C<@668I6C7:F7:96

DCHD=H:FG:7IH96E6H9><6B76F@6C9:C<6CB:C<<IC6@6CG>GH:B @DDF9>C6H@:F6C<@668I6C=6AH:FG:7IH9>AI@>G@6CG:E:FH> +! / 6A6BHF6CG;DFB6G>M6C<6@6C9>HIFIC@6C>C>G:A6C<K6@HIM6C<9>86H6H DA:=E:C<6B6H9>96C9>6C<<6EG6B6

+! / B:BE:FA>=6H@6C9I6@:F6C<@668I6C96C&:F6C<@6

68I6CH:F=696E68I6C7:F<:F6@@:@6C6CG:E6C?6C<GIB7I -9:C<6C @:8:E6H6C H:H6E + +696 @:F6C<@6 68I6C >C:FG>6A 7:FA6@I* *" !""#,)$#&:F6C<@668I6C>C:FG>6AH>96@B:C<6A6B>E:F8:E6H6C (>G6A@6C9I6DF6C<E:C<6B6H96C B6G>C< B6G>C<7:F69696A6B @:F6C<@668I6C.96C+:C<6B6HM6C<7:F6969>GH6G>IC9>6C<<6E 7:F696E696@:F6C<@668I6CM6C<9>6B96EICE:C<6B6H 7:F696

Y

S'

O' X' = X V t

Z

Y' S x

P

O Z'

x 8

Y'

S'

Z

O' t = 0 X

v

7 6

Z

Y

S

X O t = 0

$!$*2++$+.$* ( /')-,0$.$-/'$* 1'3'1 0&2020)$/( ) ,* &0- *0- *!$/')21# * +!2)2* 1'& ,

Tes Kompetensi Awal

&:H>@6C96B:A>=6HED=DC ED=DC96F>96A6BBD7>A M6C<G:96C<7:F<:F6@ED=DC ED=DCH:FA>=6H7:F<:F6@ @:6F6=M6C<7:FA6K6C6C96F>6F6=<:F6@BD7>A+D=DC H:FG:7IH9>@6H6@6C7:F<:F6@F:A6H>;H:F=696EC96 M6C<9>6B6F>>AIGHF6G>H:FG:7IH8D76C96G>BEIA@6C 6E6@6=<:F6@F:A6H>;>HI

%>@6C967:FA6F>9:C<6C@:8:E6H6C@B?6B@:6F6= 9:E6C9>96A6B@:F:H66E>M6C<G:96C<7:F<:F6@9:C<6C

@:8:E6H6C@B?6B7:F6E6@:8:E6H6CHDH6AC96 B:CIFIHE:C<6B6HM6C<9>6B9>E>C<<>FF:A@:F:H6 %>@6@:8:E6H6C86=6M69>H:B76@@6C96F>E:G6K6H

GIE:FGDC>@M6C<B:B>A>@>@:8:E6H6CG6B69:C<6C @:8:E6H6C7ICM>BIC<@>C@6=@:8:E6H6C86=6M6 H:FG:7IHA:7>=96F>PBGE66A6G6CCM6 E6M6C<9>B6@GI99:C<6C:H:F+:F8D766C6E6@6=

M6C<B:C<<I<IF@6CH:DF>696CM6:H:F

Gambar 9.2

(3)

E696@:F6C<@668I6CM6C<7:F<:F6@(IA6 BIA696C7:F>BE>H96C G:H:A6=)G:@DCGI96=B:C:BEI=?6F6@+)

.:7I6=7:C967:F<:F6@@:@6C6C9:C<6C@:8:E6H6C*+696G66H)

G:@DC7:C96H:F=696E@:F6C<@668I6CB:B>A>@>@DDF9>C6H-./96C H:F=696E@:F6C<@668I6CB:B>A>@>@DDF9>C6H-./G:=>C<<6

--0+)..// O

:C<6C6C<<6E6CK6@HIM6C<9>6B6H>DA:=E:C<6B6HE696@:F6C<@6 68I6CG6B69:C<6CK6@HIM6C<9>6B6H>DA:=E:C<6B6H96A6B@:F6C<@6 68I6CM6C<7:F<:F6@

)) O

$/0 + , 7 96C7 9>@:C6A 9:C<6C HF6CG;DFB6G> "6A>A:D /F6CG;DFB6G>@:76A>@6CCM6696A6=

--+)..//)) O *A:=@6F:C6))HIFIC6C-6H6I-H:F=696E)G6B69:C<6CHIFIC6C

-6H6I-H:F=696E)%>@6$/0 + ,79>HIFIC@6CH:F=696EK6@HI)

6@6C9>E:FDA:=@:8:E6H6C

- +) +)

-

-) ) ) ) )

%>@6 - *) -696A6=@:8:E6H6C7:C96H:F=696E - *) -696A6=

@:8:E6H6C7:C96H:F=696E96C) +) + 6@6C9>E:FDA:=G:7I6= 7:CHI@E:FG6B66C

*-*-0+ O

+696GIB7I .7:FA6@I..E696GIB7I /7:FA6@I//

. . / / ) ) ) ) *.*.*/*/

H6I *-*-O+*.*.*/*/ O

HF6CG;DFB6G>@:76A>@6CCM6696A6=

*-*-+*.*.*/*/ O &:H:F6C<6C

*-@:8:E6H6C7:C96G:?6?6F -*.@:8:E6H6C7:C96G:?6?6F. */@:8:E6H6C7:C96G:?6?6F/

&:8:E6H6C9>HIFIC@6CH:F=696EK6@HI6@6CB:C<=6G>A@6CE:F8:E6H6C

- *)- *)-

. *.

) *).. O

/*/

) *) / /

Tantangan

untuk Anda

(4)

:F96G6F@6C$/0 + ,796E6H9>@6H6@6C76=K6E:F8:E6H6C 7:C9696A6B@:F6C<@668I6CG6B69:C<6CE:F8:E6H6C7:C9696A6B @:F6C<@668I6C(6GG67:C969>E6C96C<96F>@:F6C<@668I6C

96C9>6C<<6EH:H6EG6B6B6@6<6M6E696@:F6C<@668I6C96C B:C?69>G6B6EIA6M6>HI"96C"G:=>C<<6

6F>IF6>6CH:FG:7IH96E6H9>6B7>A@:G>BEIA6C76=K6* *",)$# )#)#' #%'("#' (*)*#))%("!"("*

'# *##'(!

.:7I6=@:F:H66E>7:F<:F6@9:C<6C@:8:E6H6C@B?6B.:DF6C<E:CIBE6C< 7:F?6A6C96A6B@:F:H69:C<6C@:8:E6H6C@B?6BG:6F6=9:C<6C@:F:H6:F6E6 @:8:E6H6CE:CIBE6C<H:FG:7IHH:F=696EDF6C<M6C<9>6B9>H:E>F:A

4 !

:C<6CB:C<<IC6@6C$/0 + ,7*-*-0+

*F6C<M6C<9>6B9>H:E>F:AG:76<6>@:F6C<@668I6C&:F:H66E>M6C<7:F<:F6@ H:F=696EDF6C<M6C<9>6BG:76<6>@:F6C<@668I6C&:8:E6H6CE:CIBE6C<H:F=696E @:F6C<@668I6C696A6=*-@B?6B:C<6C9:B>@>6C@:8:E6H6CE:CIBE6C<

*-H:F=696EM6C<9>6B696A6=

*-*-+@B?6B

Contoh

9.1

2. Percobaan Michelson–Morley

":?6A6M6C<H6BE6@E696<:ADB76C<H6A><:ADB76C<E:FBI@66C6>F 6H6I<:ADB76C<7ICM>B:CIC?I@@6C76=K6<:ADB76C<96E6HB:F6B76H B:A6AI>GI6HIB:9>IBM6C<B:C?6A6F@6C<:H6F6C96F>GI6HIH:BE6H@: H:BE6H A6>CCM6 *A:= @6F:C6 86=6M6 ?I<6 96E6H 9>6C<<6E G:76<6> <:ADB76C<6E6@6=M6C<B:BIC<@>C@6CB:F6B76HCM6<:ADB76C<86=6M6 96F>(6H6=6F>@:IB>G:96C<@6CG:76<>6C7:G6F96:F6=6CH6F6(6H6=6F> 96CIB>696A6=FI6C<=6BE6

0CHI@ B:C?6K67 E:FH6CM66C >C> E696 6769 @: E6F6 6=A> B:C<6?I@6CGI6HI=>EDH:G>GM6C<9>@:C6A9:C<6C%$)(()'(:CIFIH =>EDH:G>G>C><:ADB76C<86=6M696F>(6H6=6F>@:IB>96E6HB:F6B76H B:A6AI>GI6HIB:9>IBM6C<9>C6B6@6C:H:F(:9>IB>C>H:F96E6H9>B6C6 B6C69>6A6B>C>H:FB6GI@FI6C<=6BE6:C<6C696CM6=>EDH:G>G>C> ICHI@ G:B:CH6F6 96E6H B:C<=>C96F@6C @:GI@6F6C H:CH6C< B:9>IB E:F6B76H6C<:ADB76C<86=6M6

+696'"&$*0-,96C-/*$5B:A6@I@6C:@GE:F>B:C

ICHI@B:B7I@H>@6C@:7:F6966C:H:F @GE:F>B:C>C>9>A6@I@6C9:C<6C B:C<I@IFG:A>G>=K6@HI6CH6F6@:A6?I6C86=6M6@:H>@67:F<:F6@G:?6?6F 96CH:<6@AIFIG:H:F<6FC9696E6HB:B6=6B>:@GE:F>B:C(>8=:AGDC (DFA:M>C>E:F=6H>@6C>AIGHF6G>H:CH6C<<:F6@E:F6=IM6C<7:F<:F6@G:6F6= 9:C<6C 6A>F6C GIC<6> 96C <:F6@ E:F6=I M6C< 7:F<:F6@ B:CM:7:F6C<> GIC<6>H:<6@AIFIG9:C<6C6A>F6CGIC<6>+696 +! /E:F6=I 7:F<:F6@EIA6C<E:F<>B:CM:7:F6C<>GIC<6>96F>H>H>@(@:)96C@:B76A> @:(A6<>9:C<6C6F6=H:<6@AIFIG6A>F6CGIC<6>M6C<7:F<:F6@9:C<6C @:8:E6H6C+0CHI@B:A6@I@6CE:CM:7:F6C<6C>C>6F6=<:F6@6CCM6=6FIG 9>B>F>C<@6C@:@>F>ICHI@B:C<>B76C<>6FIGGIC<6>G:E:FH>9>E:FA>=6H@6C

E696 +! /:G6FF:GIAH6C96F>@:8:E6H6CE:F6=I96C@:8:E6H6C

6A>F6CGIC<6>+96E6H9>HIA>G@6CG:76<6>7:F>@IH

Gambar 9.3

Gerak perahu bolak-balik yang tegak lurus aliran sungai.

Gambar 9.4

Diagram arah kecepatan perahu dan aliran sungai.

N

v

c

M N

v

aliran sungai

c

M

(5)

v

c + v

cv

M O

aliran sungai

Gambar 9.5

Gerak perahu yang searah dan berlawanan dengan aliran sungai.

v’ c2v2 O

%>@6E6C?6C<A>CH6G6C(@:)696A6=!K6@HIM6C<9>E:FAI@6CICHI@ B:CM:7:F6C<>GIC<6>696A6= + %69>ICHI@EIA6C<E:F<>B:CM:7:F6C<>

GIC<6>9>7IHI=@6CK6@HI

)

+

+

O

.:@6F6C<E:F=6H>@6C +! /+:F6=I 7:F<:F6@7DA6@ 76A>@ 96F>H>H>@(@:*A6AI@:B76A>@:(A6<>+6C?6C<A>CH6G6C96F>(@:* G6B6 9:C<6C E6C?6C< A>CH6G6C 96F> ( @: ) M6>HI! +696 G:E6FI= E:F?6A6C6CCM6M6C<E:FH6B6@:8:E6H6CCM69>76CHIDA:=6A>F6CGIC<6> G:=>C<<6 ICHI@ B:C:BEI= G:?6I= 9>E:FAI@6C K6@HI

+ @6C

H:H6E>E696K6@HIG:E6FI=E:F?6A6C6CCM6ICHI@@:B76A><:F6@CM6?IGHFI B:A6K6C6FIGG:=>C<<69>E:FAI@6CK6@HI + ICHI@B:C:BEI=?6F6@ M6C<G6B6M6>HIG:E6C?6C<:C<6C9:B>@>6CG:AIFI=E:F?6A6C6C

E:F6=IEIA6C<E:F<>B:B:FAI@6CK6@HI

) + +

:CHI@H:FG:7IH96E6H9>HIA>G?I<69:C<6C

+ +

) + +

+ + )

+

+

+:FG6B66CH:FG:7IH96E6H?I<69>HIA>G@6C

)

+

)

+

O

0CHI@@6GIG<:F6@IB>9>96A6B:H:F9><IC6@6C6C6AD<>G:76<6> 7:F>@IH&:A6?I6CGIC<6>9>6C6AD<>@6CG:76<6>@:A6?I6C:H:F96C@:A6?I6C E:F6=I9>6C6AD<>@6CG:76<6>86=6M66A6B@DCH:@G>C>)7:F6FH>K6@HI M6C<9>H:BEI=86=6M6@:H>@6A>CH6G6CCM6H:<6@AIFIG9:C<6C6F6=@:A6?I6C :H:FG:96C<@6C)696A6=K6@HIM6C<9>H:BEI=86=6M6@:H>@6A>CH6G6CCM6 G:?6?6FH:F=696E6F6=@:A6?I6C:H:F.:A>G>=K6@HI6CH6F6)96C)696A6=

)O)

+

O

+

)O)

+

O

+

O

a2b2 = (a + b)(ab)

(6)

0CHI@B:CM:A:G6>@6CE:FG6B66CH:FG:7IH9><IC6@6C9:F:H7>CDB>6A M6>HI

-#

# - # - # - ## -#

96C

# # # # #

O

.I@I +

E696$/0 + ,796E6H9>HIA>G@6C96A6B7:CHI@

9:F:H7>CDB>C6A9:C<6CB:C<6C6AD<>@6C+G:76<6>-96CE6C<@6H

OG:76<6>#B6@66@6C9>96E6H@6C

+

#-##O

-

+

+

*A:=@6F:C6BG96C+7:FDF9:@:8>AC>A6>

+

G6C<6H@:8>AG:@6A>

G:=>C<<6+ %69>E:FG6B66C9:F:HCDB>C6AH:FG:7IH96E6H9>HIA>G@6C

+

+

:C<6C86F6M6C<G6B6B6@6 +

96E6H9>HIA>G@6C96A6B

7:CHI@9:F:HCDB>C6AG:76<6>7:F>@IH

+

+

B6@6

)O)

+

O

+

)O)

+ O

+

)O)

+

O

+696 E:F8D766C (>8=:AGDCO(DFA:M M6C< G@:B6CM6 H:FA>=6H E696

+! /E6C?6C<A>CH6G6CM6C<9><IC6@6C696A6=B96EIC

@:A6?I6C:H:F+696A6=@:A6?I6CFDH6G>IB>M6>HIPBG*A:=

@6F:C6>HIG:A>G>=K6@HI86=6M6M6C<G:?6?6F:H:F96CH:<6@AIFIG:H:F 96E6H9>=>HIC<

)O)

B

P BG

P BG P BG

POG

Tantangan

untuk Anda

Agar Anda lebih memahami tentang deret binomial. Kerjakan contoh-contoh berikut.

1. (1 – x2)3 2. (1 + 2x)3

Gambar 9.6

Skema percobaan Michelson-Morley. cermin 2

cermin 1 perjalanan A

aliran eter

layar pengamat kaca

(7)

.:A>G>=K6@HI>C>G6C<6H@:8>A96CH>96@BIC<@>C9>6B6H>G:86F6 B6CI6A)6BIC?>@69><IC6@6C86F6 86F6DEH>@=6A>C>6@6CB:B7:F>@6C @:H:A>H>6CM6C<G6C<6HH>C<<>.6A6=G6HICM6B:A6AI>EDA6>CH:F;:F:CG> :F@6G 86=6M6 M6C< 9>E6CHIA@6C 96C 9>H:FIG@6C DA:= @686 G:H:C<6= 8:FB>CH:CHIB:B>A>@>;6G:M6C<7:F7:96G:=>C<<66@6CH:FA>=6HGI6HI EDA6 >CH:F;:F:CG> %>@6 9>6B6H> B:A6AI> A6M6F E:C<6B6H 6@6C B:BE:FA>=6H@6CE:F7:966CH:FG:7IH/:FCM6H6E:F8D766C(>8=:AGDC (DFA:MG6C<6HB:C<:?IH@6C@6F:C696F>=6G>AE:C<6B6H6CH:F=696EEDA6 >CH:F;:F:CG>H>96@H:FA>=6HE:F7:966C;6G:#6A>C>7:F6FH>76=K6H>96@ H:F96E6HE:F7:966C6CH6F6K6@HIM6C<9>E:FAI@6CDA:=86=6M6ICHI@ EIA6C<E:F<>96A6B6F6=G:?6?6F9:C<6C6A>F6C:H:F96C6F6=H:<6@AIFIG H:F=696E6A>F6C:H:F

I6=6AE:CH>C<M6C<96E6H9>G>BEIA@6C96F>E:F8D766C(>8=:AGDCO (DFA:MM6>HIG:76<6>7:F>@IH

6 #>EDH:G>GH:CH6C<B:9>IBM6C<9>G:7IH:H:FH>96@96E6H9>7I@H>@6C :C<6C@6H6A6>C:H:F>HIH>96@696

7 &:8:E6H6C86=6M6696A6=G6B6ICHI@G:<6A66F6=H>96@7:F<6CHIC< E696<:F6@IB>

B. Teori Relativitas Einstein

#6G>AE:F8D766C(>8=:AGDC (DFA:MB:B7I@H>@6C76=K6:H:FG:76<6> B:9>IBF6B76H6C86=6M6>HIH>96@696+696*!$/1 ',01$',

B:C<IGIA@6CGI6HIH:DF>H:CH6C<@:8:E6H6C86=6M6/:DF>>C>B:CM6H6@6C

76=K6(' %)#.!("*#)* ("*'#'! *

*#)* ("*)"%))'.###) '#)*#%' (*"' "*%*# %#")#. /:DF> >C> 9>G:7IH)$' '!)+)( *(*( >CGH:>CB:C<:BI@6@6C9I6EDGHIA6HCM6M6>HIG:76<6>7:F>@IH

&:A6?I6C86=6M69>FI6C<=6BE6@:G:<6A66F6=696A6=BIHA6@H>96@ 7:F<6CHIC<E696<:F6@GIB7:F86=6M6B6IEICE:C<6B6H

#I@IB =I@IB ;>G>@6 B:@6C>@6 ):KHDC B:B>A>@> 7:CHI@ M6C< G6B6E696G:BI6@:F6C<@668I6C>C:FG>6A

+DGHIA6HE:FH6B6BIC8IA6@>76H>BEA>@6G>7:G6F6C 7:G6F6C;>G>GM6C< G6C<6HAI6G9>B6C6#I@IB(:@6C>@6):KHDCG:E:FH>@:8:E6H6CH>96@ 7:FA6@IICHI@86=6M6(:CIFIH',01$',K6@HI)H>96@G6B69:C<6C)

G:=>C<<6 F:A6H>J>H6G ):KHDC 96C HF6CG;DFB6G> "6A>A:D H>96@ 96E6H 9><IC6@6C :G6F6C @:8:E6H6C K6@HI E6C?6C< 96C B6GG6 7:C96 G:BI6CM67:FG>;6HF:A6H>;

Tes Kompetensi

Subbab

A

$/( ) ,* &. # !2)2* 1'& ,

6<6>B6C6@6=E6C96C<6CB6CIG>6H:F=696E?6A6CCM6 E:F6B76H6C<:ADB76C<86=6M696F>(6H6=6F>G6BE6> 9> IB> E696 6769 @: 6<6>B6C6@6= EIA6 E:FB6G6A6=6CH:FG:7IH9>G:A:G6>@6CE6966K6A6769 @:

(:C<6E6G:BI6<:F6@7:C9696E6H9>@6H6@6C<:F6@ F:A6H>;96C76<6>B6C6@6=@:9I9I@6C6CH6F6<:F6@ F:A6H>;M6C<G6HI96CM6C<A6>CCM6%:A6G@6C

/:F6C<@6C @:H:F@6>H6C #I@IB ):KHDC 96C HF6CG;DFB6G>"6A>A:D

.:7IH@6CA6H6F7:A6@6C<E6F6;>G>@6K6C6769@: 96A6BB:M6@>C>696CM6:H:F

/:F6C<@6CB:HD9:E:F8D766C(DFA:M (>8=:AGDC96C @:G>BEIA6C6E6@6=M6C<96E6H9>E:FDA:=96F>E:F8D766C (DFA:M (>8=:AGDC

Kata Kunci

• transformasi Galileo • kerangka acuan • eter

(8)

Gambar 9.7

Dua kerangka acuan S dan S', dengan S' memiliki kecepatan (v) relatif terhadap S.

1. Transformasi Lorentz

6F>IF6>6CG:7:AIBCM69>@:H6=I>76=K6HF6CG;DFB6G>"6A>A:DH>96@ 96E6H9><IC6@6CICHI@B:C?:A6G@6CH:DF> >CGH:>C0CHI@B:C?:A6G@6C H:DF> >CGH:>C>C>9><IC6@6CHF6CG;DFB6G>'DF:CHN/F6CG;DFB6G>M6C< 9>@:BI@6@6CDA:=-/$,167:FA6@IIBIBFH>CM6HF6CG;DFB6G>>C>H>96@ =6CM67:FA6@IICHI@@:8:E6H6C @:8:E6H6CM6C<B:C9:@6H>@:8:E6H6C 86=6M6H:H6E>?I<67:FA6@IICHI@@:8:E6H6C @:8:E6H6CM6C<?6I=A:7>= @:8>A96F>@:8:E6H6C86=6M6

+:F=6H>@6C +! /(:CIFIHHF6CG;DFB6G>"6A>A:D9>96E6H@6C

--+)/>H>@96CB6G>C< B6G>C<B:FIE6@6CEIG6H@DDF9>C6H96F> G>@I G>@I-./96C-./+696)@:9I6GIB7I7:F>BE>H.IB7I-.

/7:F<:G:F@:@6C6CG:E6C?6C<GIB7I -9:C<6C@:8:E6H6CH:H6E+.:H:A6=

) G:@DC ?6F6@ 696A6= + ) 0CHI@ H>H>@ M6C< H:FA:H6@ E696

GIB7I -?>@6@DDF9>C6HCM69>CM6H6@6C9:C<6C-96C-6@6CB:B:CI=> =I7IC<6C

--

--+) O

6A6B=6A>C>E:C<6B6H9>96CB:C<<IC6@6CG:A6C<K6@HIM6C< 9>BIA6>E696G66H7:FG6B66C.:6C96>CM6H>H>@?I<67:F<:F6@@:@6C6C G:E6C?6C<GIB7I-9:C<6C@:8:E6H6CH:H6EH:F=696EE:C<6B6H@:9I69>

G:7:G6F+@:9I9I@6CH:F=696EGIB7I -96C-M6>HI ICHI@))--+)

ICHI@))

-+) O

ICHI@))--+)

%69> 76>@ E:C<6B6H E:FH6B6 B6IEIC E:C<6B6H @:9I6 B:C<<IC6@6C K6@HI))) )C @6C H:H6E> ?>@6 G:A6C< K6@HI

E:C<6B6HE:FH6B696CE:C<6B6H@:9I69>7:96@6C9:C<6C)96C)0CHI@ E:C<6B6HE:FH6B6696A6=))))C96CICHI@E:C<6B6H@:9I6696A6=

))))#$/0 + ,7E:FAI9>CM6H6@6C96A6B)=6A>C>

7:F6FH>C9696E6HB:C<6A>@6C9:C<6CGI6HI@DCGH6CH6M6C<9>G:7IH ))%#)'#($'"(:C<6C9:B>@>6C?>@6HF6CG;DFB6G>>C>9>6C<<6E A>C:6F$/0 + ,7B:C?69>

--+) O

%>@6@:F6C<@668I6CH:F=696E@:F6C<@668I6C7:F<:F6@@:@6C6C 9:C<6C@:8:E6H6CH:H6E+@:F6C<@668I6CH:F=696E96E6H9>6C<<6E 7:F<:F6@F:A6H>;@:@>F>9:C<6C@:8:E6H6C+#I7IC<6C-96C-B:C?69>

--0+) O

.I7GH>HIG>@6C$/0 + ,7@:96A6B$/0 + ,7G:=>C<<6

-4 -0+)+)5--0+)+)

) ) - +

O

z' z

P

X

vt

X'

y' y

v

(9)

(>G6A@6C @:8:E6H6C H:F=696E @:F6C<@6 68I6C 96C 696A6= @:8:E6H6C86=6M6*-(:CIFIH >CGH:>C@:8:E6H6C86=6M6H:F=696E @:F6C<@668I6CE:C<6B6HE:FH6B69>G6B67:G6FCM6M6>HI*-6F> G>C>9>96E6H=I7IC<6C-)96C-)G:=>C<<6$/0 + ,7

B:C?69>

)-0+) O

:C<6CB:C<<6CH>)E696$/0 + ,79>E:FDA:=

) - + - +) 0CHI@B:C?:A6G@6CE:FG6B66CH:FG:7IH>@IH>A6C<@6= A6C<@6=7:F>@IH>C> &6A>@6CG:H>6EGI@IG:GI6>9:C<6CG>;6H@DBIH6H>; ) - + -+)

&IBEIA@6CGI@I GI@IM6C<B:B>A>@>J6F>67:A-9>FI6G@>F> 96CM6C<B:B>A>@>J6F>67:A)9>FI6G@6C6C

-+

O-O ) O+)

&6A>@6C9:C<6CO O- + ) +)

&:AI6F@6CJ6F>67:A-9>FI6G@>F>

- + ) +) .IGICE:FG6B66CG:=>C<<69>FI6G@>F>=6CM6696J6F>67:A -- ) +) + ) + + &6A>@6C9:C<6C -) + + + ) + +

.:E:FH>H:A6=9>76=6GG:7:AIBCM6B:CIFIH >CGH:>C-)*A:=@6F:C6 >HI96E6H9>HIA>G@6C )) + +

Tokoh

H.A. Lorentz (1853–1928)

Hendrik Antoon Lorentz (1853– 1928) adalah seorang fisikawan Belanda yang kali pertama me-ngemukakan tentang pemantulan dan pembiasan cahaya, ditinjau dari teori bahwa cahaya termasuk gelombang elektromagnetik. Teori ini dikembangkan oleh James Clerk Maxwell yang menyatakan bahwa cahaya terdiri atas gelombang listrik dan gelombang magnetik dengan sudut yang berbeda. Lorentz juga memprediksi keberadaan elektron. Beliau menerima hadiah Nobel tahun 1902 dalam bidang fisika atas penelitiannya mengenai medan magnet. Dalam bab teori relativitas,

Lorentz berjasa dalam teorinya mengenai "Transformasi Lorentz".

(10)

B6@6

+

+

+ +

+

O +

+

+

O

@=>FCM6=6G>AHF6CG;DFB6G>'DF:CHN96E6H9>HIA>GG:76<6>7:F>@IH

- -O+)

+

-O+)

- +) +

..// O

) )+-

)

+

+-)

+-)

+

O

$/0 + , 7 9>@:BI@6@6CDA:=$,#/') ,1--, -/$,16

G:DF6C<;>G>@6K6C:A6C96E696+:FG6B66CH:FG:7IH96E6H9>E6@6> ICHI@B:C<=>HIC<E6FH>@:A E6FH>@:AM6C<7:F<:F6@8:E6H/F6CG;DFB6G> 'DF:CHN>C>6@6CH:F:9I@G>B:C?69>HF6CG;DFB6G>"6A>A:D6E67>A6@:A6?I6C

+?6I=A:7>=@:8>A96F>@:A6?I6C86=6M6+

2. Transformasi Kecepatan dari Lorentz

+DGHIA6HF:A6H>J>H6G@=IGIGB:CM6H6@6C76=K6@:A6?I6C86=6M696A6B FI6C<=6BE6B:B>A>@>=6F<6M6C<G6B6ICHI@G:BI6E:C<6B6HH>96@ 7:F<6CHIC<E696<:F6@F:A6H>;CM6.:7:F@6G86=6M6M6C<9>E6C86F@6C 96A6B@:F6C<@668I6CE6966F6=<:F6@CM69:C<6C@:A6?I6C+F:A6H>; H:F=696E@:F6C<@66@6CB:B>A>@>@:A6?I6C+9>I@IF96F>

.:@6F6C< C96 H>C?6I G:GI6HI M6C< 7:F<:F6@ F:A6H>; H:F=696E @:9I6CM6M6>HI96C+:C<6B6H9>B:C<I@IF@:H><6@DBEDC:C @:8:E6H6C96A6BM6>HI

Tantangan

untuk Anda

Dengan cara yang sama seperti pada

(11)

- - . . / /

+ ) ) + )

96EICE:C<6B6H96A6BB:C96E6H +--) . .) +/ /)

:C<6CB:C9>;;:F:CG>6A@6C$/0 + ,7 9>E:FDA:=

- +)

- . . / /

+

+

)

-)

+

G:=>C<<6

-

-- +)

+ - +

- - +) )

) + + + +

-)

-) - )

+

6H6I

-

--

--

-+ -+ + +

+ + + + ++

O

:C<6C 86F6 M6C< G6B6 C96 ?I<6 6@6C B:C96E6H@6C HF6CG;DFB6G> @:8:E6H6CF:A6H>J>GH>@ICHI@GIB7I .96CGIB7I /

+.

.

-+

+

+ +

+.

.

-+ +

+ +

O

+/

/

-+

+

+ +

+/

/

-+ +

+ +

Tantangan

untuk Anda

(12)

Gambar 9.8

Sebuah meteran yang bergerak sebesar 87% dari kecepatan cahaya, panjangnya hanya terlihat setengahnya oleh pengamat yang diam.

3. Akibat Prinsip Relativitas Khusus

a. Kontraksi Lorentz

/:DF>F:A6H>J>H6GB:B76K6E:C<6FI=H:F=696EE:C<I@IF6CE6C?6C< GI6HI 7:C96 M6C< 7:F<:F6@ H:F=696E G:DF6C< E:C<6B6H +:FI76=6C E6C?6C<GI6HI7:C966@>76H<:F6@6CF:A6H>;E:C<6B6H6H6I7:C969>G:7IH

$#)' ($'#)/6H6I%#.*(*)#%##!#)$#)')$#

+6C?6C<6H6I?6F6@7I@6CA6=G:GI6HIM6C<BIHA6@H:H6E>G:GI6HI M6C<F:A6H>;+69696G6FCM6ICHI@B:C<I@IF?6F6@C96=6FIGB:A>=6H @:9I9I@6C 9I6 H>H>@ G:86F6 G:F:CH6@ #I7IC<6C ?6F6@ 6CH6F6 9I6 @:F6C<@668I6C96E6H9><6B76F@6C9:C<6C86F6G:9:F=6C6G:E:FH>7:F>@IH >C>

.:7I6=GIB7:F86=6M6E696@:F6C<@668I6C7:F<:F6@9:C<6C @:8:E6H6C+H:F=696E@:F6C<@668I6C.I6HI@:A>E86=6M69>E6C86F@6C 96F>GIB7:FH:FG:7IH96C9>E6CHIA@6CDA:=G:7I6=8:FB>CM6C<7:F?6F6@

96F>GIB7:F.:76<6>68I6C9>H:BE6H@6CG:7I6=B>GH6F9>6BM6C<

9><IC6@6CICHI@B:C6C96>?6F6@M6C<9>H:BEI=DA:=86=6M6EIA6C< 76A>@96F>GIB7:F@:8:FB>C96C@:B76A>@:GIB7:F26@HI )M6C<

9>E:FAI@6CICHI@EIA6C<E:F<>86=6M6H:FG:7IH696A6=G:76<6>7:F>@IH

)

O

C96>@6CE6C?6C<B>GH6FM6C<9>6B6H>96F>@:F6C<@6696A6=

96CK6@HIM6C<9>E:FAI@6CDA:=@:A>E86=6M67:F<:F6@96F>GIB7:F@: 8:FB>C696A6=)B6@6E6C?6C<A>CH6G6CHDH6A96F>GIB7:F@:8:FB>C

7I@6C

B:A6>C@6C696A6=

+)

O

*A:=@6F:C6@:A>E86=6M67:F<:F6@9:C<6C@:8:E6H6CB6@6

) O

.:7I6=E:G6K6H6C<@6G67:F@:A6?I6CH:F=696EIB>%>@6E:G6K6H6C<@6G6 B:A:K6H>9:C<6C@:A6?I6CF:A6H>;H:F=696EE:G6K6H7:F6E6@6=@:A6?I6C E:G6K6HH:F=696EIB>

4 !

:C<6CB:C<<IC6@6C$/0 + ,7 9>E:FDA:=

-+ + + + +

-

+

%69>@:A6?I6CE:G6K6H F:A6H>;H:F=696EIB>A:7>=@:8>A96F>@:8:E6H6C 86=6M6

(:CIFIHB:@6C>@6@:8:E6H6CE:G6K6H H:F=696EIB>>C> H>96@BIC<@>C

(13)

%>@6 @:9I6$/0 + ,7 96C $/0 + , 7 9><67IC< 9>E:FDA:=

)

J)

G:=>C<<6

) +

O

0CHI@@:B76A>@:GIB7:F?6F6@M6C<9>H:BEI=86=6M6A:7>=E:C9:@ @6F:C69>A>=6H96F>@:F6C<@6GIB7:F96C8:FB>CG6A>C<B:C9:@6H> %>@6K6@HIM6C<9>E:FAI@6CDA:=86=6M6ICHI@@:B76A>696A6=)B6@6

O+)

O

96C ) O

9:C<6C86F6M6C<G6B69>E:FDA:=

) + O

26@HIHDH6A)))ICHI@E:F?6A6C6CEIA6C<E:F<>@:A>E86=6M6

9>A>=6H96F>696A6=

) + +

)

+

O

.6BE6> E696 H6=6E >C> C96 =6FIG B:C<>C<6H @:B76A> E:B76=6G6C H:CH6C<HF6CG;DFB6G>'DF:CHNM6>HIGI6HI@DCGH6CH69>E:FAI@6CICHI@ B:CM:H6F6@6CE:C<6B6H6CE696@:F6C<@668I6CG96C@:F6C<@668I6CG

) )

) )

)

) +

*A:=@6F:C6)

6@6C9>96E6H@6C

+ +

+

O

6H6I

+

O

Gambar 9.9

Semakin besar kecepatan bola, ukuran bola akan semakin mengecil.

v = 0 v = 0,995 c

v = 0,999 c v = 0,87 c

v = c

Tantangan

untuk Anda

Perhatikan kembali Persamaan (9–26) dan Persamaan (9–29).

(14)

Gambar 9.10

(a) Sebuah bangunan yang dilihat oleh pengamat yang diam; (b) Bangunan yang dilihat oleh pengamat yang bergerak sangat cepat; (c) Diagram yang memperlihatkan bagaimana bagian sisi dinding dapat terlihat.

.:7I6=76H6C<H:F>@6HE696G:7I6=FD@:HM6C<G:96C<B:AIC8IF9:C<6C@:A6?I6C (:CIFIH6K6@E:G6K6HE6C?6C<76H6C<696A6=B:H:F:F6E6@6=E6C?6C<76H6C<H:FG:7IH B:CIFIHE:C<6B6HM6C<9>6BH:F=696EIB>

4 !

>@:H6=I>B+

+ B:H:F

%69>E6C?6C<76H6C<B:CIFIHE:C<6B6HM6C<9>6BH:F=696EIB>696A6=B:H:F #6A>C>7:F6FH>76=K6E6C?6C<76H6C<>HIA:7>=E:C9:@?>@69>E6C96C<96F>IB> .:7I6=7:C9696A6B@:6966C9>6BE6C?6C<CM6B:H:F:C96>HI7:F<:F6@9:C<6C @:8:E6H6CG:6F6=9:C<6CE6C?6C<CM6#>HIC<A6=E6C?6C<7:C96G66H7:F<:F6@ 4 !

>@:H6=I>B:H:F+

:C<6CB:C<<IC6@6C$/0 + ,7 +

B:H:F

%69>E6C?6C<7:C96G66H7:F<:F6@696A6=B:H:F

$/0 + ,7B:CM6H6@6C76=K67:C96M6C<E6C?6C<CM6

?>@69>6B6H>DA:=E:C<6B6HM6C<7:F<:F6@G:?6?6FE6C?6C<CM69:C<6C @:8:E6H6C+7:C966@6CH:FA>=6HB:C<6A6B>E:FI76=6CE6C?6C<+6C?6C< M6C<H:FA>=6HDA:=E:C<6B6HM6C<7:F<:F6@696A6=

+@6F:C6 + B6@6

&:H:F6C<6C

E6C?6C<7:C967:F<:F6@M6C<9>6B6H>DA:=@:F6C<@6M6C<9>6B

E6C?6C<7:C96M6C<9>6BE696GI6HI@:F6C<@668I6C

+ @:8:E6H6C7:C96H:F=696E@:F6C<@69>6B

@:8:E6H6C86=6M6PBG

%69> E6C?6C< 7:C96 G:DA6= DA6= B:CMIGIH ":?6A6 >C> 9>G:7IH @DCHF6@G> E6C?6C< #6A >C> 9>@:BI@6@6C DA:=-/$,16 G:=>C<<6 @DCHF6@G>CM69>G:7IH $#)' ($'#)/

b. Dilatasi Waktu

',01$',B:CM6H6@6C76=K6K6@HI696A6=G:GI6HIM6C<F:A6H>;#6A

>C>96E6H9>>AIGHF6G>@6C9:C<6C<:F6@86=6M69>96A6BGI6HI@:F6C<@6 68I6C M6C< 7:F<:F6@ &:BI9>6C <:F6@ 86=6M6 H:FG:7IH 9>6B6H> 96F> @:F6C<@668I6CM6C<9>6BG:E:FH>E696 +! /

&:F6C<@668I6C7:F<:F6@9:C<6C@:8:E6H6CF:A6H>;H:F=696E@:F6C<@6

.:DF6C< E:C<6B6H E696 @:F6C<@6 B:C<6F6=@6C G:7I6= GIB7:F 86=6M6@:G:7I6=8:FB>CM6C<?6F6@CM6H:FA>=6HG:E:FH> +! /

Contoh

9.3

Contoh

9.4

6 7

8

A B

C

C

C’ D

v

B

B’ A

(15)

+696<6B76FH:FA>=6H76=K686=6M6M6C<9>E6C86F@6C9>9>E6CHIA@6C @:B76A>G:E6C?6C<<6F>GM6C<G6B6G:E:FH>M6C<9>6B6H>96A6B@:F6C<@6

26@HIEIA6C<E:F<>@:A>E86=6M69>96F>@:8:FB>C96C@:B76A> @:696A6=

6H6I )

)

O

&:?69>6C 9> ?>@6 9>E6C96C< DA:= E:C<6B6H M6C< 7:F696 E696 @:F6C<@696E6H9>A>=6HE696 +! /!M6C<B:BE:FA>=6H@6C76=K6 A>CH6G6C86=6M6K6@HIE:F<>H>96@A6=G6B69:C<6CK6@HIEIA6C<%>@6G:A6C< K6@HIEIA6C< E:F<>B:CIFIHE:C<6B6H9>696A6=)?6F6@6CH6F6

96C696A6=+ ) 96EICA>CH6G6C86=6M6696A6= 6F><6B76FH:FA>=6H

76=K6

9:C<6C + )

)

+ )

)

O

%>@6$/0 + , 7 9><67IC<@6C @: 96A6B$/0 + , 7 9>E:FDA:=

) + )

)

O

%>@6$/0 + ,79>@I69F6H@6C9>E:FDA:=

)

) + )

)

)+ )

)

O+ )

)

)

O

+

)

.:A6C?IHCM6 9>E:FDA:= =I7IC<6C 6CH6F6t 96C t

M6C< 96E6H

9>FIBIG@6CG:76<6>7:F>@IH

) )

+

O

&:H:F6C<6C

+ @:8:E6H6CF:A6H>;E:C<6B6HM6C<7:F<:F6@H:F=696EE:C<6B6HM6C< 9>6B

)

G:A6C<K6@HI9>I@IFDA:=E:C<6B6HM6C<F:A6H>;7:F<:F6@

)

G:A6C<K6@HI9>I@IFDA:=E:C<6B6HM6C<F:A6H>;9>6B

Gambar 9.11

(a) Kelip cahaya pulang balik dipancarkan di O dipandang oleh pengamat di S'; (b) Kelip cahaya di S' dipandang dari S.

cermin cermin

Dt0

Dt v Dt

c 6

7

d

d waktu

waktu

waktu 1 waktu 2

pengamat

O O'

(16)

.I6HIE6FH>@:AB:B>A>@>K6@HI=>9IEPOG:@DCM6>HIK6@HIE6FH>@:A>HIBIA6>

696=>C<<6BIGC6=G6B6G:@6A>:F6E6@6=K6@HI=>9IEE6FH>@:A>HI?>@6>67:F<:F6@ 9:C<6C@:A6?I6C

4 !

>@:H6=I>)POG:@DC+O

9:H>@

) )

+

5. Momentum dan Massa Relativistik

#I@IB):KHDCH:CH6C<<:F6@B:CM6H6@6C76=K6?>@6E696G:7I6= 7:C967:FB6GG6"7:@:F?6G:7I6=<6M6@DCGH6C7:C96H:FG:7IH6@6C 7:F<:F6@9>E:F8:E6H7:F6HIF6C:G6FCM6@:8:E6H6C7:C966@6C7:FH6B76= H:FIGG:GI6>K6@HI7:F96G6F@6C=I7IC<6C+ ")%>@6<6M67:@:F?6 8I@IEA6B6G:=>C<<6=6F<6)G6C<6H7:G6FH>96@A6=BIGH6=>AA6?I7:C96 B:C?69>G6C<6H7:G6F6F>=6G>AE:F8D766C76<6>B6C6EIC7:G6FCM6:C:F<> M6C<9><IC6@6C7:G6FCM6@:8:E6H6CG:7I6=7:C96H>96@E:FC6=B:C86E6> @:8:E6H6C 86=6M6 .:H>6E 7:C96 M6C< 7:FB6GG6" 7:F<:F6@ 9:C<6C @:8:E6H6C+B:B>A>@>BDB:CHIBA>C:6FM6C<B:CIFIHB:@6C>@6@A6G>@ 9>FIBIG@6C

%"+ O

%>@6@:8:E6H6C7:C96+GI6HIG66HB:C9:@6H>@:8:E6H6C86=6M6 B6GG67:C966@6C7:FI76= I76=+696G66H>HIBDB:CHIB7:C969>G:7IH BDB:CHIBF:A6H>J>GH>@

0CHI@<:F6@6C <:F6@6C7:C969:C<6C@:8:E6H6CM6C<F:A6H>;@:8>A H>96@ H:F?69> E:FI76=6C B6GG6 +:FI76=6C >HI 76FI H6BE6@ ?>@6 @:8:E6H6CCM6B:C9:@6H>@:8:E6H6C86=6M6*A:=#()#=I7IC<6C B6GG6 9>6B 96C B6GG6 7:F<:F6@ M6C< 9>H>C?6I 96F> GI6HI E:C<6B6H 9>FIBIG@6CG:76<6>7:F>@IH

" "

+

O

&:H:F6C<6C

" B6GG67:C9696A6B@:6966C7:F<:F6@@<

" B6GG67:C9696A6B@:6966C9>6B@<

+ @:8:E6H6C7:C96BG

@:8:E6H6C86=6M69>I96F6BG

Contoh

9.5

.6A6=G6HI7I@H>@:7:C6F6CH:DF>F:A6H>J>H6G696A6=;6@H6@:7:F6966C"*$#9>IB> 6F>A6=>C;DFB6G>H:CH6C<"*$#>C>96F>7:F76<6>GIB7:F96C7I6HA6=F:GIB:96F> >C;DFB6G>M6C<C9696E6H@6C&IBEIA@6CF:GIB:C96@:E696<IFI-:GIB: H:F76>@9>EF:G:CH6G>@6C96C9>9>G@IG>@6C9>9:E6C@:A6G

(17)

%>@6$/0 + ,79>GI7GH>HIG>@6C@:96A6B$/0 + ,7B6@6

" + %

+

O

#I@IB&:@:@6A6C(DB:CHIB7:FA6@I96A6BF:A6H>J>H6G@=IGIGG:E:FH> 96A6B;>G>@6@A6G>@)6BIC#I@IB$$):KHDCB:C<:C6><:F6@96A6B H:DF>F:A6H>J>H6G96E6H9>HIA>G@6CG:76<6>7:F>@IH

" + % "+

) ) ) +

O

+696E:FG6B66C ) " + " +) +") =6F<6 ") H>96@CDA?>@6B6GG6 7:C967:FI76=H:F=696EK6@HI"6M6F:GIAH6CE6967:C96G:A6AIG6B6 9:C<6CA6?IE:FI76=6CBDB:CHIBH:F=696EK6@HI

%>@6B6GG69>6B7:C96@<=>HIC<A6=B6GG67:C967:F<:F6@9:C<6C@:8:E6H6C

4 !

:C<6CB:C<<IC6@6C$/0 + ,79>E:FDA:=

@<

" "

+

96=6AB:C6F>@M6C<7:F@6>H6C9:C<6CB6GG6F:A6H>J>GH>@>C>E6@6= C96E:F86M6696E6FH>@:AM6C<H>96@B:B>A>@>B6GG6H:H6E>B:B>A>@> :C:F<>(:CIFIH;>G>@6@A6G>@=6A>C>H>96@BIC<@>CH:F?69>?>@6"

"+ +

@6CH:H6E>?>@6=6A>C>9>H>C?6IB:CIFIHH:DF>F:A6H>J>H6G96E6H9>7I@H> @6CG:86F6B6H:B6H>G76=K6696E6FH>@:AM6C<H>96@7:FB6GG6H:H6E> B:B>A>@>:C:F<>(>G6A@6C696G:7I6=E6FH>@:AM6C<7:FB6GG6"96C 7:F<:F6@9:C<6C@:8:E6H6C+

" +

" +

" +

" +

(18)

6A6B B6H:B6H>@6 696A6=7:CHI@H>96@H:CHIG:=>C<<6C>A6>CM6 G:B76F6C<7:F6E6G6?6&:G>BEIA6CCM6696A6=696E6FH>@:AM6C<H>96@ 7:FB6GG6B6GG69>6BH:H6E>B:B>A>@>:C:F<>6A6B@:=>9IE6CG:=6F> =6F>E6FH>@:AM6C<B:B>A>@>@6F6@H:F>GH>@G:E:FH>H:FG:7IH696A6=;DHDC 96CC:IHF>CD

6. Kesetaraan Massa dan Energi

#I7IC<6C E6A>C< H:F@:C6A M6C< 9>E:FDA:= >CGH:>C 96F> EDGHIA6H F:A6H>J>H6G@=IGIG696A6=B:C<:C6>B6GG696C:C:F<>#I7IC<6CCM696E6H 9>HIFIC@6CG:86F6A6C<GIC<96F>9:;>C>G>:C:F<>@>C:H>@96F>GI6HI 7:C96M6C<7:F<:F6@

(

(

9:C<6C B:CM6H6@6C @DBEDC:C <6M6 M6C< 7:@:F?6 96A6B 6F6= E:FE>C96=6CG:FH6(96C(B:CM6H6@6C?6F6@M6C<9>H:BEI=:C<6C B:B6@6>7:CHI@F:A6H>J>GH>@=I@IB<:F6@@:9I69>E:FDA:=

"+

)

G:=>C<<6FIBIG6C:C:F<>@>C:H>@B:C?69>

( "+

) (

"+ + " +

+ "+ + +

:C<6CB:C<<IC6@6CFIBIG6C>CH:<F6AE6FG>6A6@6C9>E:FDA:=

"0"

O

#6G>A>C>B:CM6H6@6C76=K6:C:F<>@>C:H>@GI6HI7:C96G6B69:C<6C E:FH6B76=6CB6GG6CM66@>76H<:F6@F:A6H>;CM69>@6A>@6C9:C<6C@I69F6H @:A6?I6C86=6M6+:FG6B66C96E6H?I<69>HIA>G

"0"

O

%>@69>B>G6A@6C"G:76<6>:C:F<>HDH6A7:C967:C9696A6B@:6966C

9>6BH:H6E>7:C96H:H6EB:B>A>@>:C:F<>":C<6C9:B>@>6C

" 9>G:7IH :C:F<> 9>6B

96F> 7:C96 M6C< B6GG6 9>6BCM6"

$/0 + ,7B:C?69>

O

&:H:F6C<6C

:C:F<>9>6B?DIA:

%>@67:C967:F<:F6@:C:F<>HDH6ACM6696A6=

" "

+

O

Tantangan

untuk Anda

(19)

*A:=@6F:C6B6GG696C:C:F<>7I@6CB:FIE6@6C@I6CH>H6GM6C< 7:76G#I@IB&:@:@6A6C(6GG696C C:F<>G:7:C6FCM6B:C?69>G6HI M6>HI #I@IB &:@:@6A6C (6GG6 C:F<> (6GG6 96E6H H:F8>EH6@6C 96C H:FBIGC6=@6CH:H6E>?>@6=6A>C>H:F?69>G:?IBA6=:C:F<>M6C<G:H6F6=>A6C< 6H6IBIC8IA96CG:76A>@CM6%69>B6GG696C:C:F<>B:FIE6@6C6GE:@ M6C<7:F7:9696F>GI6HI@I6CH>H6G :F6E6@6=:C:F<>HDH6A:C:F<>@>C:H>@96CBDB:CHIBG:7I6=EFDHDC" (:1M6C<7:F<:F6@9:C<6C@:8:E6H6C+ 4 !

C:F<>HDH6A96E6H9>=>HIC<9:C<6CB:C<<IC6@6C$/0 + ,7

#6AM6C<B:C6F>@ICHI@9>76=6GB:C<:C6>:C:F<>F:A6H>J>GH>@696A6= 76<6>B6C6B:C<=>HIC<:C:F<>F:A6H>J>GH>@GI6HIE6FH>@:A?>@6B6GG6CM6 H>96@9>@:H6=I>6H6I?>@6E6FH>@:AH:FG:7IHH>96@7:FB6GG6+:F=6H>@6C @:B76A>E:B76=6G6CE696GI7767G:7:AIBCM6B:C<:C6>E6FH>@:AM6C< H>96@7:FB6GG6H:H6E>B:B>A>@>:C:F<>+:FG6B66C:C:F<>96CBDB:C HIBF:A6H>J>GH>@96E6H9>HIA>G@6CG:76<6>7:F>@IH " % " + + %>@6@:9I6E:FG6B66CH:FG:7IH9>@I69F6H@6C6@6C9>96E6H@6C

" O

% " + + O

Contoh

9.7

6

(:1 (:1 " +

HDHP:1PO?DIA::1

PO?DIA:

7 C:F<>@>C:H>@CM6O"

O(:1(:1 8 (DB:CHIBCM6

(:1 ?DIA:(:1 BG "

PO@<

G:=>C<<6 " + % +

@< BG @<BG %

%69>BDB:CHIBCM6696A6=PO@<BG

Perumusan integral parsial adalah:

x dy xy y dx

Ingatlah

Pembahasan Soal

Agar energi kinetik benda bernilai 25% dari energi diamnya dan c adalah kelajuan cahaya ruang hampa, benda harus bergerak dengan kelajuan ....

a.

4

c d. 3

4 c

b.

2

c e. 4

5 c

c. 35c

UMPTN 1998 Pembahasan:

Energi kinetik relativitas adalah

Ek = m0c2

2 2 1 1 1 v c

Dengan menggunakan Ek =

1 4m0c

2 = m 0c 2 2 2 1 1 1 v c Jadi, 2 2 1 1 1 v c

= 14; atau

22 1 1 v

c

= 5

4

22 1 v

c =

16 25 v2 =

9 25 c2

v = 35 c

(20)

m01 m02 v2 v1

6 7

m0

Gambar 9.12

(a) Sebuah benda yang memiliki massa diam m0; (b) Benda tersebut pecah menjadi

&6A>@6C$/0 + ,79:C<6C9>E:FDA:=

%

" + +

&IF6C<@6C$/0 + ,79:C<6C$/0 + ,7G:=>C<<6

O%"O

" + +

*A:=@6F:C6"

" +

B6@6

" " + %

+ +

+ "

%

+

O%"

"

% O

:C<6C B:C<<IC6@6C$/0 + , 7 C96 96E6H B:C<=>HIC< 7:F6E6:C:F<>F:A6H>J>GH>@GI6HIE6FH>@:AM6C<H>96@7:FB6GG6M6>HI

%8

% O

7. Hukum Kekekalan Energi dan Momentum Relativistik

>&:A6G3$C96H:A6=B:BE:A6?6F>H:CH6C<#I@IB&:@:@6A6C C:F<>96C#I@IB&:@:@6A6C(DB:CHIB#I@IB&:@:@6A6C C:F<> B:CM6H6@6C76=K6:C:F<>H>96@96E6H9>8>EH6@6C6H6I9>BIGC6=@6C H:H6E>:C:F<>96E6H7:FI76=7:CHI@B:C?69>:C:F<>A6>C:C<6C@6H6 A6>CE696GI6HIG>GH:B:C:F<>6K6ACM6G6B69:C<6C:C:F<>6@=>FCM6 :<>HI?I<6#I@IB&:@:@6A6C(DB:CHIB?>@6E696GI6HIG>GH:BH>96@ 7:@:F?6<6M6AI6FBDB:CHIB6K6AG6B69:C<6CBDB:CHIB6@=>F
(21)

+! / B:CIC?I@@6CG:7I6=7:C96M6C<B:B>A>@>B6GG69>6B

"G:86F6GEDCH6CE:86=B:C?69>9I676<>6C"96C"&:9I6E686=6C >C>7:F<:F6@9:C<6C@:8:E6H6CM6C<7:F7:96M6>HI+96C+0CHI@ B:C<<6B76F@6C@DCG:E>C>9:C<6CA:7>=?:A6G7:G6F6C 7:G6F6C""

+96C+6@6C9>7:F>C>A6>M6>HIB6GG6"@<7:F<:F6@9:C<6C

@:8:E6H6C+96CB6GG6"@<7:F<:F6@9:C<6C@:8:E6H6C

+:F96G6F@6C#I@IB&:@:@6A6C C:F<>7:FA6@I C:F<>6K6A C:F<>6@=>F

"

" +

O

" +

O

%>@6$/0 + ,79>76<>9:C<6C9>E:FDA:=

"

" +

O

" +

O

%69>96F>$/0 + ,7 C9696E6HB:C<:H6=I>B6GG69>6B96F> 7:C96G:7:AIBE:86=

"

c

" @<

6F>=6G>AE:F=>HIC<6CH:FG:7IH6E6@6=C96B:C:BI@6CG:GI6HIM6C< B:C6F>@#6G>AE:F=>HIC<6CB:CIC?I@@6CB6GG69>6BE696@:6966C6K6A "@<7:F7:969:C<6CB6GG69>6BE696@:6966C6@=>F@< #6A>C>G:?6A6C9:C<6C>BEA>@6G>H:DF>F:A6H>J>H6G@=IGIGM6C<B:CM:767@6C E:BI6>6CB6GG6E6967:C96M6C<7:F<:F6@B:C9:@6H>@:8:E6H6C86=6M6

&:BI9>6C 76<6>B6C6 9:C<6C BDB:CHIBCM6 .:A6B6 H>96@ 696 E:C<6FI=<6M6AI6F6@6C7:FA6@I#I@IB&:@:@6A6C(DB:CHIB

(DB:CHIB6K6ABDB:CHIB6@=>F

" + +

" + +

" + +

O

8. Aplikasi Kesetaraan Massa dan Energi pada Reaksi Fisi dan

Fusi Nuklir

E6M6C<96E6HC96G>BEIA@6C96F>E:B76=6G6CH:CH6C<#I@IB &:@:@6A6C C:F<>96C(DB:CHIB-:A6H>J>GH>@&:G>BEIA6C96F>#I@IB &:@:@6A6C C:F<>-:A6H>J>GH>@696A6=B6GG69>6BH>96@@:@6A

"@<

"@<

"

"O"O@<@<

+:C<IF6C<6CB6GG6>C>:@>J6A:C9:C<6C:C:F<>

"

(22)

&:BI9>6C76<6>B6C69:C<6C:C:F<>@>C:H>@CM6 C:F<>@>C:H>@E696 @:6966C6K6A96C@:6966C6@=>F96E6H9>HIA>G@6CG:76<6>7:F>@IH

6K6A

6@=>F

" +

O" "

+

Gambar 9.13

Tumbukan foton dan elektron (a) sebelum tumbukan; (b) sesudah tumbukan. foton dengan, p

6

7

', p'

foton terhambur

elektron

pe v

Menurut Planck, energi pada foton adalah E = hf. Jadi, hf = pc

P = hfc = h

Ingatlah

8

"

+

8

%69>6@=>FG:=>C<<6

6@=>FO6K6A

E6M6C<96E6HC96G>BEIA@6C96F>E:F=>HIC<6CG:A>G>=B6GG69>6B 96CG:A>G>=:C:F<>@>C:H>@H:FG:7IH/:FCM6H6G:A>G>=:C:F<>@>C:H>@M6C< 9>=6G>A@6CG6B69:C<6C:C:F<>9>6B6@>76HG:A>G>=B6GG69>6BH:FG:7IH $C>7:F6FH>696@DCJ:FG>:C:F<>9>6B6@>76HE:C<IF6C<6CB6GG69>6B B:C?69>:C:F<>@>C:H>@M6C<9>7:76G@6C6H6IE:C<IF6C<6C:C:F<>@>C:H>@ 6@6CB:C<6@>76H@6CE:C6B76=6CB6GG69>6B.:86F6B6H:B6H>G=6A >C>96E6H9>HIA>G@6CG:76<6>7:F>@IH

" O

&DCG:E@:G:H6F66CB6GG696C:C:F<>>C>H:F?69>E696F:6@G>;>G>96C ;IG>6@=>F+696F:6@G>;>G>CI@A>FG:7I6=>CH>7:F6H9>HIB7I@DA:=G:7I6= E6FH>@:AG:=>C<<6B:B7:A6=B:C?69>9I67I6=>CH>&:9I6>CH>>C>B:B>A>@> B6GG69>6BA:7>=F>C<6C96F>B6GG69>6B>CH>>C9I@CM6@6F:C6G:76<>6C B6GG69>6BCM67:FI76=B:C?69>:C:F<>@>C:H>@96EICE696F:6@G>;IG> CI@A>F9I67I6=>CH>F>C<6C7:F<67IC<B:B7:CHI@G:7I6=>CH>M6C<A:7>= 7:F6H(6GG69>6B9I6>CH>E:B7:CHI@CM6A:7>=7:F6H96F>E696B6GG6 >CH>=6G>AE:C<<67IC<6C@6F:C6G:76<>6CB6GG6CM67:FI76=B:C?69>:C:F<> @>C:H>@

9. Penerapan Prinsip Relativitas dalam Efek Compton

+69667C96H:A6=7:A6?6FH:CH6C<86=6M6M6C<9>6C<<6EG:76<6> E6FH>@:AM6>HI86=6M6B:FIE6@6CE:CM:76F6CE6@:H E6@:H:C:F<>M6C<9>G:7IH ;DHDC.6A6=G6HI=6AM6C<B:C9I@IC<@DCG:E>C>696A6=:;:@DBEHDC &:H>@6G:7I6=;DHDCB:CIB7I@G:7I6=:A:@HFDC9>6BB6@6;DHDCH:FG:7IH 6@6CH:F=6B7IF9:C<6CB:B7:CHI@GI9IHH:FH:CHI0CHI@B:C<>C<6H@6C C96H:CH6C<:;:@DBEHDCE:F=6H>@6C +! /7:F>@IH

+! /B:CIC?I@@6CG:7I6=;DHDC9:C<6CE6C?6C<<:ADB76C<

B:CIB7I@G:7I6=:A:@HFDC9>6B9:C<6CB6GG6"@>76HHIB7I@6C

H:FG:7IH;DHDCH:F=6B7IF9:C<6CGI9IHH:F=696E=DF>NDCH6A.:H:A6=

(23)

<:ADB76C<;DHDCG:GI96=HIB7I@6C6H6IGI9IH=6B7IF6C;DHDCCM696E6H 9>@:H6=I>96F>#I@IB&:@:@6A6C(DB:CHIBE696E:F>GH>K6HIB7I@6C H:FG:7IH

(DB:CHIB6K6A(DB:CHIB6@=>F +696GIB7I -9>96E6H@6C

8DG %8DG O

+696GIB7I .9>96E6H@6C

G>C %G>C

G>C%G>C O

&6A>@6C$/0 + ,796C79:C<6C8G:=>C<<69>E:FDA:=

O8DG %8DG O

G>C %G>C O

&I69F6H@6C$/0 + ,796C7G:=>C<<69>E:FDA:=

8DG O8DG %8DG O

G>C%G>C O

A>B>C6G>@6C$/0 + ,796C7G:=>C<<69>96E6H@6C 8DGG>C O8DG%8DG G>C

O8DG %

+696GI7767B:C<:C6>@:G:H6F66CB6GG696C:C:F<>C96H:A6=7:A6?6F 76=K6

"

96C

"

% O

6F>@:9I6E:FG6B66CH:CH6C<:C:F<>F:A6H>J>H6GH:FG:7IH9>96E6H@6C ""

%

"""%

%"

O

.:E:FH> H:A6= 9>76=6G G:7:AIBCM6 :A:@HFDC E696 BIA6CM6 9>6B G:H:A6=9>HIB7I@DA:=;DHDC:A:@HFDC7:F<:F6@9:C<6C:C:F<>@>C:H>@ H:FH:CHI:C<6C@6H6A6>CG:76<>6C:C:F<>;DHDCH:A6=7:FI76=B:C?69> :C:F<>@>C:H>@:A:@HFDC

O

(6@6$/0 + ,7 96E6H9>HIA>G@6CB:C?69>

%OO"

O O

.I7GH>HIG>@6C$/0 + ,7@:$/0 + ,7

O"OO

sin2 + cos 2 = 1

(24)

I6E:G6K6H6A;696C7:H67:F<:F6@9:C<6C6F6= 7:FA6K6C6C&:A6?I6CE:G6K6H6A;6G:7:G6F96C @:A6?I6CE:G6K6H7:H6696A6=/:CHI@6CA6= @:A6?I6CE:G6K6H6A;6F:A6H>;H:F=696EE:G6K6H7:H6 .:7I6=E:G6K6HFI6C<6C<@6G67:F<:F6@B:C?6I=>

IB> 9:C<6C @:8:E6H6C +:G6K6H H:FG:7IH B:C:B76@@6CG:7I6=E:AIFIM6C<6F6=CM6G6B6 9:C<6C<:F6@CM6%>@6@:8:E6H6CE:AIFIF:A6H>; H:F=696EE:G6K6H>HIH:CHI@6CA6=@:8:E6H6CF:A6H>; E:AIFI>HIH:F=696EIB>

.:DF6C<E:C<6B6H9>IA6CB:A>=6H9I6E:G6K6H 6C<@6G6AI6F96CB:C9:@6H>IA6C96A6B6F6= M6C<7:FA6K6C6CB6G>C< B6G>C<9:C<6C@:A6?I6C

96C

6 :F6E6@6=@:A6?I6CIA6CB:C9:@6H>E:G6K6H

B:CIFIHE:C<6B6H96A6BE:G6K6H 7 :F6E6@6= @:A6?I6C H:F=696E B:CIFIH

E:C<6B6H96A6BE:G6K6H

8 :F6E6@6=@:A6?I6CIA6CB:C9:@6H>E:G6K6H B:CIFIHE:C<6B6H96A6BE:G6K6H 9 :F6E6@6=@:A6?I6CH:F=696E B:CIFIH

E:C<6B6H96A6BE:G6K6H

:F6E6 @:8:E6H6C FD@:H E696 G66H E6C?6C<CM6 B:B:C9:@

.:7I6=E:G6K6H6CH6F>@G6B:A:K6H>IB>9:C<6C@:A6?I6C

+.:7I6=HDC<@6HM6C<E6C?6C<CM6B9>I@IF9> IB>7:F69696A6BE:G6K6H9:C<6CEDG>G>G:?6?6F9:C<6C 6F6=<:F6@E:G6K6H/:CHI@6CE6C?6C<HDC<@6H 6 B:CIFIHE:CIBE6C<96A6BE:G6K6H 7 B:CIFIHE:C<6B6HM6C<9>6B9>IB> .:7I6=E:G6K6HH:F76C<7:F<:F6@9:C<6C@:8:E6H6C

BG.:H:A6=7:F6E6=6F>@6=B:CIFIH?6B9>IB> @:9I6?6B9>IB>96C9>E:G6K6H7:F7:96O

G:@DC"IC6@6CE:C9:@6H6CO-#O#-

I6DF6C<@:B76F96C7:FIBIFH6=IC9>IB> 7:F6C<@6H@:7>CH6C<A;6:CH6IF>M6C<?6I=CM6 @6A>H6=IC86=6M6H6=IC86=6M6?6F6@M6C< 9>H:BEI=86=6M6G:A6B6H6=IC9:C<6C@:8:E6H6C .:H:A6=>HI@:B76A>@:IB>:F6E6@6=IBIF @:9I6DF6C<>HIG:H:A6=B:F:@67:FH:BI

.I6HI:A:@HFDC9>E:F8:E6H9:C<6C7:96EDH:CG>6A (:1 :F6E6@6= @:8:E6H6C M6C< 9>E:FDA:=CM6 BI6H6C:A:@HFDC&PO8DIADB796CB6GG6

:A:@HFDC"PO@<

Tes Kompetensi

Subbab

B

$/( ) ,* &. # !2)2* 1'& ,

8DG"OO8DG O

6<>$/0 + ,79:C<6CG:=>C<<69>E:FDA:=

"

O

O8DG

*A:=@6F:C6 B6@6

" O8DG

6H6I

" O8DG O

%69>E:F>GH>K6:;:@DBEHDCB:FIE6@6CG6A6=G6HI7I@H>H:CH6C<@DCG:E 9I6A>GB:<:ADB76C<E6FH>@:A96CH:DF>F:A6H>J>H6G@=IGIG

Kata Kunci

• relativitas khusus • transformasi Lorentz • kontraksi Lorentz • dilatasi Lorentz • dilatasi waktu • momentum relativitas • massa diam

• kesetaraan massa dan energi • reaksi fusi

• reaksi fisi

Rangkuman

+F>CG>EF:A6H>J>H6G"6A>A:D7:F96G6F@6C9I6EDGHIA6H G:76<6>7:F>@IH

6 26@HI696A6=7:G6F6CBIHA6@

7 =I@IB<:F6@):KHDCH>96@7:FI76=7:CHI@ >CJ6F>6C

+F>CG>EF:A6H>J>H6G >CGH:>C7:F96G6F@6C9I6EDGHIA6H 7:F>@IH

6 @:A6?I6C9>96A6BFI6C<=6BE6696A6=GI6HI 7:G6F6CBIHA6@

7 =I@IB B:@6C>@6 ):KHDC 96C :A:@HFD B6<C:H>@(6LK:AA>CJ6F>6C96A6B7:F76<6> @:F6C<@6>C:FG>6A

+:F8D766C(>8=:AGDC (DFA:MB:B7I@H>@6C76=K6 6 :H:FH>96@696

7 @:8:E6H6C86=6M6H>96@7:F<6CHIC<E6966F6= 96CH:BE6H

/F6CG;DFB6G>@:8:E6H6CF:A6H>;@=IGIGB:CIFIH B:@6C>@6F:A6H>J>GH>@9>FIBIG@6CG:76<6>7:F>@IH

6H6I

-

--

--

-+ + + + + ++ + + +

/F6CG;DFB6G>'DF:CHN9>FIBIG@6C9:C<6C

-+ - +)

- . . / / ) ) + +

(25)

&DCHF6@G>'DF:CHN9>FIBIG@6C9:C<6C

+

>A6H6G>K6@HI9>FIBIG@6C9:C<6C

) )

+

9>B6C6))

(6GG6F:A6H>J>GH>@9>FIBIG@6C9:C<6C

" "

+

(DB:CHIB96CB6GG6F:A6H>J>GH>@9>FIBIG@6C9:C<6C

" + %

+

C:F<>@>C:H>@9>FIBIG@6C9:C<6C

"

" " " +

B:B76=6G

B:B76=6G

M6>HI

Peta Konsep

$-/'$* 1'3'1 0&2020

/F6CG;DFB6G>"6A>A:D +DGHIA6H-:A6H>J>H6G >CGH:>C

/F6CG;DFB6G>

'DF:CHN /F6CG;DFB6G>&:8:E6H6C-:A6H>J>H6G&=IGIG -:A6H>J>H6G&=IGIG+F>CG>E

&DCHF6@G>+6C?6C<

>A6H6G>26@HI

@GE:F>B:C (>8=:AGDC (DFA:M

@:G>BEIA6CCM6

H:FH>96@696 9>6A6B>C>

(DB:CHIB-:A6H>J>GH>@

(6GG6-:A6H>J>GH>@

C:F<>>6B

"

C:F<>/DH6A

"

C:F<>&>C:H>@:C96

O

Setelah mempelajari bab ini, tentu Anda telah memahami bahwa gerak bersifat relatif. Anda juga tentu telah memahami teori relativitas Einstein dan pengaruh-nya terhadap besaran panjang, waktu, kecepatan dan massa benda. Dari keseluruhan materi yang ada pada bab ini, bagian manakah yang menurut Anda sulit

Refleksi

dipahami? Coba Anda diskusikan bersama teman atau guru Fisika Anda.

(26)

Tes Kompetensi

Bab 9

'*'&* &0 * &0 12( 4 ! ,5 ,%. *',%!$, / 6F>7:G6F6C 7:G6F6C7:F>@IH>C>M6C<=6F<6CM6G:A6AI

G6B6ICHI@G:BI6@:F6C<@668I6CE:C<6B6H6C696A6=

6 @:8:E6H6C7:C96 7 @:A6?I6C7:C96 8 @:8:E6H6C86=6M6 9 E6C?6C<7:C96 : B6GG67:C96

.6A6=G6HIEDGHIA6H >CGH:>C96A6BH:DF>F:A6H>J>H6G696A6=

6 =I@IB =I@IB):KHDCH:H6E7:FA6@IICHI@ 7:C96 M6C< B:B>A>@> @:8:E6H6C B:C9:@6H> @:8:E6H6C86=6M6

7 @:8:E6H6C7:C9696E6HA:7>=7:G6F96F>@:8:E6H6C 86=6M6

8 @:8:E6H6C 7:C96 7:G6FCM6 BIHA6@ H>96@ 7:F<6CHIC<E696E:C<6B6HCM6

9 @:8:E6H6C 86=6M6 7:G6FCM6 BIHA6@ H>96@ 7:F<6CHIC<E696E:C<6B6HCM6

: @:8:E6H6C7:C96B:C:CHI@6C7:G6FCM6B6GG6 7:C96

%>@6A6?IE6FH>@:AE:F76C9>C<6CF:A6H>J>GH>@ H:F=696EB6GG69>6BCM6696A6=

6 9

7 :

8

&:8:E6H6CE:G6K6HBG96C@:8:E6H6CE:G6K6H BG7:F<:F6@G:6F6=9:C<6C&:8:E6H6C H:F=696E@:8:E6H6CB:CIFIH):KHDC96CB:CIFIH >CGH:>C696A6=BG

6 96C 9 96C 7 96C : 96C 8 96C

I6E:G6K6H96C7:FE6E6G6CB6G>C< B6G>C< 9:C<6C @:8:E6H6C @:8:E6H6C 86=6M6 &:8:E6H6CE:G6K6HH:F=696EE:G6K6H696A6= 6 9

7 :

8

.:7I6=FD@:H@:H>@69>6B9>IB>B:B>A>@>E6C?6C< B&:BI9>6CFD@:HH:FG:7IH7:F<:F6@9:C<6C @:8:E6H6C@:8:E6H6C86=6M696A6BFI6C< =6BE6(:CIFIHDF6C<9>IB>E6C?6C<FD@:HH:FG:7IH G:A6B67:F<:F6@696A6=

6 B 7 B 8 B 9 B : B

+:G6K6H7:F<:F6@9:C<6C@:8:E6H6CH:F=696E IB>*F6C<9>IB>B:A>=6HCM6A6A6BEIG:A6B6 G:@DC96F>E:G6K6H>HI)M6A6A6BEIB:CIFIHDF6C< M6C<7:F6969>96A6BE:G6K6H696A6=

6 G 9 G 7 G : G 8 G

.:7I6=FD@:HM6C<B:B>A>@>E6C?6C<B:H:F96C B6GG6HDC7:F<:F6@9:C<6C@:8:E6H6C(:CIFIH E:C<6B6H9>IB>

6 B6GG6FD@:HHDCE6C?6C<FD@:HB 7 B6GG6FD@:HHDCE6C?6C<FD@:HB 8 B6GG6FD@:HHDCE6C?6C<FD@:HB 9 B6GG6FD@:HHDCE6C?6C<FD@:HB : B6GG6FD@:HHDCE6C?6C<FD@:HB .:7I6=:A:@HFDCM6C<B:B>A>@>B6GG69>6B"7:F<:F6@

9:C<6C@:8:E6H6CB6@6:C:F<>@>C:H>@CM6 696A6=

6 "

7 "

8 "

9 "

: "

.:7I6=HDC<@6HM6C<E6C?6C<CM6BB:B7:CHI@ GI9IHG:7:G6F

H6C

H:F=696E6F6=H>BIF%>@6

HDC<@6H7:F<:F6@@:H>BIF9:C<6C@:8:E6H6C E6C?6C<HDC<@6HG66H7:F<:F6@696A6=

6 B 9 B 7 B : B 8 B

+696IA6C<H6=IC9I6DF6C<@:B76F96C M6C< @: B:C<:B76F6@:6C<@6G6AI6F9:C<6CE:G6K6H M6C<7:F@:8:E6H6C G:96C<@6C H:H6E9>IB> (:CIFIH@6A:C9:F9>IB>@:B76A>G:H:A6=H6=IC G:=>C<<6IBIFB6G>C< B6G>C<E696G66H>HIB:CIFIH

696A6=H6=IC 6 96C 7 96C 8 96C 9 96C : 96C

.:7I6=E:FG:<>E6C?6C<9:C<6CG>G>B:H:F96C B:H:F7:F<:F6@G:6F6=E6C?6C<CM69:C<6C@:8:E6H6C 'I6G7>96C<H:FG:7IH696A6=

6 B 9 B

7 B : B

(27)

.:7I6=7:C9696A6B@:6966C9>6BE6C?6C<CM6- +:FCM6H66CM6C<7:C6F696A6=

6 96C 7 96C 8 96C 9 =6CM6 : G:BI6CM67:C6F

+:FCM6H66CM6C<7:C6FB:CIFIHH:DF>F:A6H>J>H6G >CGH:>C 696

Gambar

Gambar 9.5Gerak perahu yang searah dan
Gambar 9.6Skema percobaan Michelson-
Gambar 9.12(a) Sebuah benda yang memiliki
Gambar 9.13Tumbukan foton dan elektron

Referensi

Dokumen terkait

Sehubungan dengan butir 1 (satu) tersebut diatas, apabila peserta pengadaan berkeberatan atas keputusan ini, dapat menyampaikan sanggahan secara elektronik di aplikasi

Hasil uji antimikroba dengan metode difusi menggunakan sumuran menunjukkan isolat 3 bersifat fungisid terhadap Candida albicans tetapi tidak bersifat bakterisid

Hasil penelitian ini menunjukkan pengetahuan dan budaya modernisasi penggunaan susu formula yang masih menyebabkan rendahnya pemberian ASI Eksklusif, tetapi dengan

Metode FMEA adalah metode yang bertujuan untuk mengidentifikasi, memprioritaskan, dan mengurangi permasalahan dari suatu proses, sedangkan KPI adalah metode

Universitas

Docking dengan metode GADock terhadap kurkumin dan turunannya dengan sepuluh kali replikasi pada masing-masing senyawa menun- jukkan bahwa nilai  G ( score ) terendah

Mengetahui dasar teknik tegangan tinggi yang meliputi teori dasar medan elektrostatika, teori tembus denyar, phenomena transien tegangan tinggi, serta pembangkitan, pengukuran dan

bahwa dalam rangka menampung, menyalurkan dan menindaklanjuti aspirasi masyarakat pada Pemerintahan Desa dan untuk melaksanakan ketentuan Pasal 209 Undang-undang Nomor