usaha

1. Pada saat atlet angkat besi mengangkat beban, sebetulnya ia sedang
melakukan kerja pada beban yang disimpan sebagai energi potensial.
67
Bab
3
Usaha, Energi, dan Daya
A. Gaya Dapat
Melakukan Usaha
B. Energi dan Usaha
C. Gaya Konservatif dan
Hukum Kekekalan
Energi Mekanik
D. Daya
Hasil yang harus Anda capai:
menganalisis gejala alam dan keteraturan dalam cakupan mekanika benda titik.
Setelah mempelajari bab ini, Anda harus mampu:
5A79 B171C 492DCD8;1 =1DB91 411= =51;D;1 1;C9E9C1BH1
B581A9 81A9
1H1; 1;C9E9C1B 1;C9E9C1B @A9=5A =1DB91 H17 =5=2DCD8
;1 55A79 B5@5AC9 =5=1B1; =53D39 @1;191 41 B521719 BD=25A
@55A171 @141 =11= 81A9
,519 1;C9E9C1B @A9=5A 21H1; 1;C9E9C1B
19H1H17=5=2DCD8;155A79491C1A1H1?18A171
*141 71=21A 49
1C1B B5?A17 1C5C B5417 =5717;1C 2521 H17 B171C 25A1C
C5C
C5AB52DC 81ADB 41@1C =57D;DA 1@1;18 91 =1=@D 1C1D C941; =5717;1C
2521 C5AB52DC
,51=1 @A?B5B 1C981 1C5C C5AB52DC 81ADB =5789CD7
25A1@121H1;;1?A9H1781ADB91;?BD=B9BD@1H1 411=@5A?=21191
41@1C =5717;1C 2521 H17 49979;1
11= 212 99 1;1 492181B C5C17 DB181 55A79 41H1 41
8D2D71 1C1A1 ;5C971H1
%?B5@ 9B9;1 C5C17 DB181 55A79 41
41H1 99 21H1; B5;19 1@9;1B9H1 411= ;5894D@1 B581A9 81A9
Sumber: Fundamentals of Physics, 2001
• menganalisis hubungan antara usaha, perubahan energi dan hukum
kekekalan energi mekanik;
• menerapkan hukum kekekalan energi mekanik untuk menganalisis gerak
dalam kehidupan sehari-hari.

2. (%(.6//(/2(.$,$3+-104(24$*$0(3)+'$0$:$-(3,$-$0.$*41$.41$.%(3+-65'$.$/%6-6.$5+*$0
A. Gaya Dapat Melakukan Usaha
71A 41 5298 =5=181=9 @575AC91 DB181 411= ;5894D@1
B581A9 81A9 @51:1A9 =1C5A9 25A9;DC 99
1. Pengertian Usaha
*141B11C49;51B4125ADB181251:1A=1;B9=1DCD;=5=@5A?58
919C9779
%5C9;1251:1A41=577D1;1C517141@9;9A1
11=
;5894D@1 B581A9 81A9 DB181 4945699B9;1 B521719 @5;5A:11 H17
491;D;1 DCD; =5=@5A?58 CD:D1 H17 49979;1
'5DADC 41
1@1;18@575AC91DB181411=69B9;1B1=14571@575AC91DB181411=
;5894D@1 B581A9 81A9 C5AB52DC .B181 411= 69B9;1 B51D 25A8D2D71
4571 CA1B65A 55A79 41 71H1
,9=1;18 3?C?8 25A9;DC
,52D18 =?29
=?7?;494?A?7?58-?71A457171H1B589771=?2925A@9418C5=@1C
B5:1D8 4 41A9 @?B9B9 1F1H1
%5C9;1 -?71A =54?A?7 =?29 C5AB52DC
B589771=?2925A75A1;-?71A=51;D;1DB181H19CD=5CA1B65A55A79
=51D9 71H1 4?A?7 @141 =?29 B589771 =?29 25A75A1; 41 25A@9418
B5:1D8 4
5B1A DB181 H17 491;D;1 -?71A DCD; =54?A?7 =?29
?58 71H1 B1=1 4571 81B9 ;19 71H1 4571 @5A@94181 4
F
68 Mudah dan Aktif Belajar Fisika untuk Kelas XI
4 K
%5C5A171
DB181 :?D5
71H1 (
4 @5A@94181 =
.B181 14118 25B1A1 B;11A F11D@D 71H1 41 @5A@94181 4
=5AD@1;1 E5;C?A
'5DADC @5A;191 E5;C?A
81B9H1 81ADB 25AD@1
B;11A
.B181H17491;D;1?5871H1;?BC1H17=5=25CD;BD4DC
C5A8141@ 1A18 @5A@94181 2541 B5@5AC9 C5A981C @141 $/%$3
25B1A DB181H1 14118
,3?B K
/5;C?A 41@1C 49DA19;1 =5:149 4D1 ;?=@?5 71H1 H17 B197
C571;DADBH19CD;?=@?53?B H17B51A1845711A18@5A@94181
2541 41 B9 H17 C571; DADB 4571 1A18 @5A@94181
-5AH1C1
81H1;?=@?571H1H17B51A184571@5A@94181H17=5781B9;1
DB181 H19CD B525B1A , 3?B
5A9;DC 99 2525A1@1 ;51411 9BC9=5F1
H17 4981B9;1 (34$/$$0
;
1

3. J
.CD;

4. J 1A18 71H1 B51A18 4571 1A18 @5A@94181 B589771
49@5A?58
,3?B

5. J
, K
$51B;145712181B141B549A9@575AC91DB181
4155A79
@1;18 @141 B52D18 2?1 H17 1;1 49C5417
C5A41@1C55A79@?C5B91
Gambar 3.1
Togar melakukan usaha(W) dengan
mentransfer energi melalui gaya
dorong F sehingga mobil berpindah
sejauh s.
F
s
,52DC;1 3?C?8 3?C?8 @55A1@1 D;D=
%5;5;115A79H1714149B5;9C1A41
@1@5A2541141H14155A79
Tes Kompetensi Awal
Gambar 3.2
(a) Usaha oleh gaya F yang
membentuk sudut terhadap
perpindahan benda s.
(b) Penguraian vektor F menjadi
komponen-komponennya.
F sin
F cos
2
arah perpindahan
F
s
1

6. w
F
Usaha, Energi, dan Daya 69
,52D1871H1C5C1@B525B1A(25;5A:1@141B52D182541H1725A=1BB1;7
$9;1
BD4DCH174925CD;1C1A171H1412941741C1A14118J25A1@1DB181H17
491;D;171H19CDC5A8141@2541B51=145C9;
$8$%
9;5C18D9 (';7 J
), '
3?B
'
(3?B
;7
=B
2

7. J
.CD;

8. J 1A18 71H1 C571; DADB 4571 1A18 @5A@94181
B589771 49@5A?58
,3?B

9. J

10. K
$9;1

11. 25A1AC9 71H1 C5AB52DC C941; =51;D;1 DB181
571
;1C1 19 71H1 H17 C571; DADB 4571 1A18 @5A@94181 2541
1AC9H1 71H1 C5AB52DC C941; =51;D;1 DB181
3

12. J
%51411 99 =5H1C1;1 218F1 1A18 71H1 25A1F11 4571 1A18
@5A@94181 B589771 49@5A?58
,3?B

13. J
,K
4, K
?C?8 DB181 571C96 H19CD B5?A17 @57541A1 B5@541 H17 B5417
=5=13D B5@541H1 C921 C921 =575A5= B5@541H1
.B181 H17
491;D;1 ?58 71H1 75B5; H17 C5A:149 1C1A1 ;54D1 21 B5@541
4571 :11 25A919 571C96 ;1A51 71H1 75B5; 25A1F11 1A18
4571 1A18 @5A@94181 B5@541
5B1AH1 DB181 571C96 C5AB52DC
B521497457171H175B5;41@5A@94181H1749C5=@D8B5@541
B51=171H175B5;25;5A:1
57145=9;91B5@541=5711=975A1;
49@5A1=21C
4
*5A@94181 2541,

14. *141 $/%$3
149 B5417 25A49A9 B1=29 =57754?7 C1B
-1B
C5AB52DC =5=99;9 71H1 25A1C B525B1A 0 4571 1A18 ;5 21F18
5B1A
71H1 C1A9; C19 C1B ?58 @D77D7 149 B1=1 4571 25B1A 71H1
25A1C C1B 8 B589771 C1B 411= ;51411 B5C9=217
!1H1 A51;B9 ;5
1C1B?58@D77D7 149@141C19C1BC5AB52DCC941;4989CD7B521719
DB181;1A51C941;141@5A@94181@141C1B1;921C71H1A51;B9
1A9
(34$/$$0
; 4941@1C;1 218F1
,3?B

15. 3?B

16. ?C?81914118B5?A1711;H1725AB141A@14149497$/%$3
9497 C941; 25A75B5A ;1A51 71H1 H17 491;D;1H1 C941;
3D;D@ ;D1C DCD; =5775B5A 49497
571 45=9;91 DB181 H17
491;D;1 ?58 71H1 4?A?7H1 B1=1 4571 ?
*5AD 41 ;5C18D9 B1CD1 DB181 14118 :?D5 49B97;1C $ -.
$). # #(#,#%( ,!# ,+ ., 2(! #%.%( ) !2 ,,+ ,-.
(0-)( .(-.% ''#(%( ( ,$. ,-. '-+
F
Gambar 3.3
Fadli sedang menggendong tas.
Gambar 3.4
Seorang anak sedang bersandar
pada dinding.
Contoh 3.1
F
F cos
s

17. Contoh 3.2
,52D18254125A=1BB1;7C5A5C1;491C1B2941741C1A;1B1A4571;?569B95
75B5;;95C9;

18. 541C5AB52DC49C1A9;B5:1D8=5C5A45711:DC5C1@
5A1@1;18
DB181H174981B9;1?5871H1C1A9;C5AB52DC:9;1C1A9;1H1B5:1:1A45711C19
49;5C18D9!

19. =B
$8$%
9;5C18D9 ';7 , =
;

20. =B
5B1AH1DB181?5871H1C1A9;14118
4
3?B ,
)58;1A51

21. 3=1;125B1ADB18114118
,
5B1A71H1=1B9825D=49;5C18D9
)58;1A511:D2541C5C1@=1;125B1AA5BDC171H1

22. 14 %

23. @141BD=2D-1
41 240

24. @141BD=2D-2
B589771
3?B

25. J4 %
B9

26. J40
,D2BC9CDB9;1
;549@5A?58
4 % 0
% '!

27. ;7

28. =B
(
=1;1 ,
(=$
$149DB181H17491;D;171H1C5AB52DC14118$
Tokoh
James Prescott Joule
(1824–1907)
Sumber: Jendela Iptek, 1997
James Prescott Joule lahir di Salford,
Inggris. Ia adalah fisikawan kenamaan
Inggris yang berperan dalam
perumusan Hukum Kekekalan Energi.
Pada 1840, Joule mendeklarasikan
sebuah hukum, yang dikenal sebagai
Hukum Joule, yaitu tentang panas
yang diproduksi dalam konduktor
listrik. Untuk menghormati jasa-jasanya,
nama Joule digunakan
sebagai satuan energi dan usaha.
Contoh 3.3
70 Mudah dan Aktif Belajar Fisika untuk Kelas XI
F
N
fk
s
w
,
1
2 -
12
=BB

29. =
,3?B (

30. =

32. $
$149DB181H17491;D;171H114118

34. :?D5
/
'1BB1B5?A17@57541A1=?C?A41B5@541=?C?AH114118

36. ;7
,5@541=?C?A
99=5D3DA4571;51:D1

37. =B
%5=D491=?C?A49A5=8977125A85C9B5C518
45C9;
-5CD;1DB181H17491;D;1B51=1@575A5=125A17BD7
$8$%
9;5C18D9
'

39. ;7/

40. =B-45C9;

41. ,5@541=?C?A25A85C9/

42. C//-
C

43. =BB
K=B
,
-
-

44. =BB
K=BB

45. =K

46. =

47. =
, ;1A511A1871H1B5:1:1A4571@5A@941812541
',

49. ;7K=B

50. BK

54. $
$149DB181H17491;D;1B51=1@575A5=114118K

55. ;$

56. F = s F(t)
s1 s s2
F
Gambar 3.5
Pada besar F konstan, W = luas
daerah di bawah kurva F(t).
s1 s2 s
s
s
F d s
Usaha, Energi, dan Daya 71
,
, K
9=
,
K
,
9=
9=
,
,5@?C?7 21?; ;1HD H17 =1BB1H1 ;7
C5A5C1;491C1B2941741C1A
%5=D491
21?;;1HDC5AB52DC=5711=975A1;DADB
H1749B5212;1?5871H1H1725B1AH1
25AD218 D218C5A8141@;54D4D;121?;
B5@5AC9C1=@1;@14171=21A
-5CD;1C?C1
DB181 H17 491;D;1 71H1 @141 21?;
8977125A@9418B5:1D8=
$8$%
D1BCA1@5B9D=

57. 40

58. :?D5
D1B

59. !
D1BB579C971 !
!N!
NK

60. K

61. $
$149DB181C?C1DCD;

62. 114118
C?C1 !

63. K

64. $

65. $
Gambar 3.6
Grafik gaya (F) terhadap
perpindahan (s) dengan gaya (F)
tidak konstan atau berubah-ubah.
F (N)
B C
D E G
A 2 4 5 7 s
–40 F
Gambar 3.7
Usaha merupakan luas daerah
arsir di antara s1 dan s2 pada
kurva antara gaya F dan
perpindahan s.
2. Menentukan Usaha dari Grafik Gaya Terhadap
Perpindahan
*141DA191B525D=H171H1H17497D1;125A919;?BC1DCD;
=5781B9;1 DB181 @141 2541 H17 25A@9418 B5:1D8 ,
$9;1 41 =5=2D1C 7A169; C C5A8141@ , @5A@94181 @141 71H1
;?BC1 41 1;1 =5=@5A?58 7A169; B5@5AC9 @141 $/%$3

66. 5A41B1A;17A169;C5AB52DC25B1ADB181H174981B9;1?5871H1;?BC1
B589771254125A@9418B5:1D84B1=14571D1B415A184921F18
;DAE1 C
.CD; DB181 H17 4981B9;1 71H1 H17 25B1AH1 25AD218 D218
1;1 4941@1C;1 B52D18 7A169; B5@5AC9 @141 $/%$3
D1B 415A18
H17 491AB9A 25A141 49 1C1A1 71A9B BD=2D , 41 71A9B BD=2D
.B181C?C1H17C5A:149@141$/%$3
=5AD@1;1@5:D=181
B5C91@ DB181 41A9 ,
B1=@19 4571 ,
$149 41@1C 49CD9B;1
-)-
,
*545;1C1 C5A219; 14118 4571 31A1=5=@5A;539 , B1=@19
=545;1C9?1C1D

67. )58;1A519CDB531A1=1C5=1C9B(34$/$$0
; =5:149

68. ,
-)-
,
,
1C1D

69. ,
, ,
,
, ,
K
AC99C57A1@141(34$/$$0
;14118D1B415A18H17491AB9A
49 1C1A1 ;DAE1 25B1A 71H1 41 25B1A @5A@94181 ,
Contoh 3.4
s
F
Kata Kunci
• usaha negatif
• usaha nol
• usaha positif
s
s1 s2 s
F
2
1

70. Tes Kompetensi Subbab A
(3,$-$0.$*'$.$/%6-6.$5+*$0
4
–4
B. Energi dan Usaha
89CD718DB181
F (N)
2 4
7
6 8
x (cm)
*5A18;18 41 =5981C B55;?A ;D41 H17 B5417 =51A9; 75A?21;
H17@5D84571=D1C1%5C9;1;D41B5417=51A9;75A?21;411=
F1;CD H17 3D;D@ 1=1 291B1H1 1@1B ;D41 C5A981C C5AB571 B571
'571@1 45=9;91 %D41 C5AB52DC C518 =575D1A;1 55A79 H17 49
7D1;1 DCD; =51;D;1 DB181
571 45=9;91 (+!# ,.-.
%''*.( .(-.% '%.%( .,
1. Energi Kinetik dan Teori Usaha-Energi
-51841@51:1A9@141BD2212B525D=H1218F1DB18141@1CC5A:149
@14171H1;?BC11C1D71H1H1725AD218 D218%54D1:59BDB181C5AB52DC
=5=99;9 ;5B1=11 H19CD 141H1 71H1 H17 25;5A:1 @141 2541 B589771
2541 25A75A1; 1:DH1 ;?BC1 1C1D =5=99;9 @5A35@1C1
,5;1A17 1;1 492181B ;51411 4571 A5BDC1 71H1 ;?BC1
!1H1 C5AB52DC 25;5A:1 @141 2541 25A=1BB1 ' 41 1;1 =5781B9;1
@5A35@1C1
'5DADC D;D= ## (5FC? 25B1A @5A35@1C1 C5AB52DC
41@D @5AB1=11 25B1A @5A@94181H1 14118
14118
'
- , / /
.B181 H17 491;D;1 ?58 71H1 C5AB52DC 14118

71. 72 Mudah dan Aktif Belajar Fisika untuk Kelas XI
,',

72. - ' / /
'/
'/
-

73. K
,5?A17B9BF1=54?A?7B52D18=5:1457171H1

74. (
5A1@1;18 DB181 H17 491;D;1 ?58 71H1
4?A?7171A=5:125A@9418B5:1D8=
5A1@1;18DB181H17491;D;1DCD;=5717;1C
B52D18=5B9C9;H17=1BB1H1;789771;5C97791
=!=B
,52D182541H17=1BB1H1;7=5D3DA4571
;535@1C1

75. =B
)58;1A51141@571AD871H1
75B5;1C1A11C19412541254125A85C9B5C518
25A75A1;45C9;
-5CD;1DB181H17491;D;1?58
71H175B5;@1412541C5AB52DC
,52D18 2541 25A=1BB1 ;7 49C1A9; ;5 1C1B @141
29417=9A97;1B1A?5871H1

76. (B51A184571
29417
,D4DC;5=9A97129417C5A8141@8?A9I?C1
14118
C1
B589771 2541 25A@9418
B5:1D8 =
$9;1 ;?569B95 75B5;1 1C1A1 2541
457129417

77. 41
C1
H17491;D;1?5871H125A1C4171H175B5;;95C9;
,52D18 71H1 H17 25AD218 D218 25;5A:1 @141
B52D182541B5897712541=5711=9@5AD2181
B5@5AC97A169;@14171=21A25A9;DC
9CD7 DB181 H17 491;D;1 ?58 71H1 @141
2541DCD;:1A1;B5:1D8=

78. Vt V0
F
A s B
Gambar 3.8
Besar usaha yang dilakukan oleh
pengemudi becak sama dengan
besar gaya yang bekerja pada becak
dikalikan dengan besar
perpindahannya.
Usaha, Energi, dan Daya 73
41 C518 =575C18D9 218F1 DB181 14118 @A?B5B CA1B65A 55A79
=51D9 71H1 B589771 2541 25A75A1;
%5C9;1 2541 25A75A1; 2541
=5=99;9 ;535@1C1 41 =5781B9;1 55A79 ;95C9;
5A41B1A;1
(34$/$$0
; 55A79 ;95C9; 2541 49H1C1;1 4571
%
'/ K

79. %5C5A171
% 55A79 ;95C9; $
' =1BB1 2541 ;7
/ ;51:D1 2541 =B
571 45=9;91 ;4;
K
$149DB181H174981B9;171H1A5BDC1@141@1AC9;5C5AB52DCB1=1
4571 @5AD2181 55A79 ;95C9; @1AC9;5
; K
(34$/$$0
; 49;51 4571 C5?A5=1 DB181 55A79 DCD; @1AC9;5
Tugas Anda 3.1
Amatilah perubahan energi yang
terjadi di sekitar Anda. Diskusikanlah
hal tersebut bersama teman Anda,
apakah perubahan energi yang terjadi
akan memengaruhi usaha yang
dilakukan?
Contoh 3.5
,52D18;55A5725A=1BB1

80. 7
)58;1A51@571AD871H1;55A5725A75A1;4571
;51:D1C5C1@

81. 3=B
-5CD;155A79H1749=99;9;55A57C5AB52DC
$8$%
9;5C18D9
'N

82. K;7
/

83. 3=B

84. =B
%
'/
N

85. K;7

86. =B
N

87. K$
$14955A79;95C9;H1749=99;9;55A5714118
N

88. K$
Contoh 3.6
*1;D25A=1BB17C5A5@1B41A9C171B5?A17CD;17;1HD
%5C9;1@1;D=5H5CD8
C118 ;51:D1H1

89. =B
$9;1 71H1 75B5; @1;D C5A8141@ C118 B525B1A (
89CD718;5411=1@1;DH17=5131@411=C118
$8$%
9;5C18D9
' 7
/

90. =B
(
2 2
2 1
m / /
, K
N

91. K;7

92. K

93. =B
F
s
, ,

94. =
$149;5411=1@1;DH17=5131@411=C11814118

95. =

96. 2. Energi Potensial
(+!# *)-(,# (+!# 2(! -+,#'*( * ,.-. ( %#-
(-.%(2-%(2-.%((2($#%%(''.(!%#(%((+!#
-+,.-*-#'.(.%(
?C?8H1C192DBDAH17B541749C5717;1
*141 ;51411 99 C19 2DBDA =5=99;9 55A79 @?C5B91
$9;1 C19 2DBDA
495@1B;1 11; @118 41@1C C5A5=@1A 4571 :1A1; C5AC5CD
579CD
:D71 @141 ;1C1@5
5A79 @?C5B91=D3D ;5C9;1 ;1A5C ;1C1@5 49C5717
;1 ;5=D491 8917 ;5C9;1 ;1A5C ;1C1@5 495@1B;1
5CD; 55A79
@?C5B91 19 H17 C5A41@1C 49 11= 14118 55A79 @?C5B91 7A1E9C1B9 41
55A79 @?C5B91 @571B
a. Energi Potensial Gravitasi
5A79 C941; 41@1C 4939@C1;1 41 C941; 41@1C 49=DB18;1 C5C1@9
41@1C 25AD218 41A9 BD1CD 25CD; =5:149 25CD; H17 19
5=9;91
:D71 55A79 @?C5B91 7A1E9C1B9 H17 B5A97 49C5=D;1 411= ;5894D@1
B581A9 81A9
*5A81C9;1 3?C?8 25A9;DC
,52D18 21CD ;5A9;9 495=@1A;1 B531A1
E5AC9;1
5A79 @?C5B91 C5A25B1A H17 49=99;9 21CD 14118 ;5C9;1 21CD
=531@19 ;5C97791 =1;B9=D=
?C?8 19 B52D18 @5B9 H17 C5A5C1;
49 1C1B =5:1 =5=99;9 55A79 @?C5B91 7A1E9C1B9 H17 25B1AH1 B521497
4571 =1BB1 41 C5=@1C ;54D4D;1 @5B9 C5A8141@ 1C19
%5C9;1 @5B9
41B5CD84141291A;1:1CD8;51C1971H125A1C@5B9=51;D;1
DB181 B589771 @5B9 25A@9418 @?B9B9H1 41A9 1C1B =5:1 ;5 1C19
5B1A 55A79 @?C5B91 7A1E9C1B9 H17 49=99;9 2541 2541 @141
3?C?8 49 1C1B 25A71CD7 @141 ;54D4D;1 2541 C5AB52DC C5A8141@
13D1 C5AC5CD
*141 $/%$3
DCD; =5717;1C B55;?A 9;1 H17
25A1CH10B5C9779DB181H17491;D;1*1;,9=2??14118
1A18 71H1 B51A18 @5A@94181 2541 1C1D 49CD9B
F
h
mg
y2
74 Mudah dan Aktif Belajar Fisika untuk Kelas XI
'! K
%5C5A171
'
=1BB1 2541 ;7
!
25B1A @5A35@1C1 7A1E9C1B9 =B
C9779 2541 =
541H1725A141@141;5C9779141A9C9C9;13D1=5=99;955A79
@?C5B91 DCD; =51;D;1 DB181 B525B1A '!
$149 2541 =5=99;9
@?C5B91 7A1E9C1B9 H17 25B1AH1
*'! K
6%60)$0 $05$3$ (0(3)+ 215(04+$. )3$7+5$4+ '$0 64$*$
*5A81C9;1$/%$3
A18E5AC9;1;51C1BBD=2D-249C5C1@;1
B521719 1A18 @?B9C96 B5417;1 71H1 7A1E9C1B9 25A1A18 ;5 BD=2D-2 571C96
;5 21F18
%5C9;1 ;5 1C1B
C171
C1714
'!
'!2 4 2
Gambar 3.9
Menegangkan tali panah dan
katapel memunculkan energi
potensial.
Gambar 3.10
Usaha yang dibutuhkan Pak
Simbolon untuk mengangkat
ikan setinggi h adalah W = mgh.
Gambar 3.11
Sebuah benda yang diangkat oleh
gaya dorong Ftangan = mg dari posisi
y1 ke y2.
h
y1
s
'
Ftangan= mg
Fgravitasi=mg

97. N
mg
s
mg
2
h
F =mg sin
Usaha, Energi, dan Daya 75
.B181 C5AB52DC 4945699B9;1 B521719 @5AD2181 55A79 5;BC5A1 C171 * 5;B
*5;B
* 4 *
5;B ' !2 4 2
K
,11C ;5 21F18
7A1E9C1B9
7A1E9C1B9
'!2
4 2
4' !
.B181C5AB52DC4945699B9;1B521719@5AD218155A79@?C5B917A1E9C1B9
* 7A1E
* 7A1E
*4 *
47A1E ' !24 2
K
5A79 @?C5B91 7A1E9C1B9 @141 C9C9; 2 41A9 C9C9; 13D1 C5AC5CD 2

98. 49H1C1;1 4571 @5AB1=11
*
' ! 2 1C1D *
' ! K
4571 =5AD@1;1 C9779 2541 C5A8141@ 1C19
4$*$:$0)'+.$-6-$01.(*)$:$2$'$%(0'$2$'$-(5+0))+$0
*5A81C9;1$/%$3
$41$/%$3
%
1A9441,1=D5
B5417 =5=9418;1 21?; H17 25A=1BB1 B1=1 ;5 ;5C97791
1A94
=5=9418;1 21?; =577D1;1 29417 =9A97 B5417;1 ,1=D5
=5=9418;1 21?; =577D1;1 ;1CA?
'5DADC 41 B1=1;18
DB181 H17 491;D;1 1A94 41 ,1=D5 C5A8141@ 21?; C5AB52DC
*141 $/%$3
$ @1:17 9C1B1 H17 49C5=@D8 ,
=5=25CD;BD4DC C5A8141@294178?A9I?C1
57145=9;91DB181
@141 9C1B1 =9A97 H17 491;D;1 1A94 14118
O4
'!,B9

99. '! B9
B9
'! K
41@D DB181 H17 491;D;1 ,1=D5 DCD; =5=9418;1 21?;
;5 ;5C97791 =5781B9;1 9C1B1 E5AC9;1 B5@1:17
571
45=9;91 DB181 H17 491;D;1 ,1=D5 14118
'! K
5A41B1A;1;54D13?C?8C5AB52DC41@1C49B9=@D;1218F1DB181
H17 491;D;1 2541 25A71CD7 @141 ;5C97791 H17 4931@19 C941;
25A71CD7 @141 31A1 @5717;1C1 2541 C5AB52DC 1C1D 9C1B1 H17
49C5=@D8 B51=1 @5717;1C1
Contoh 3.7
1CD25A=1BB1;7:1CD82521B41A9;5C97791

100. =491C1BC118
-5CD;1@5AD2181
55A79@?C5B9141DB181H17491;D;171H125A1C21CDC5AB52DC@141B11C=531@19
;5C97791=491C1BC118
$8$%
9;5C18D9
'
;7

101. ==
Gambar 3.12
(a) Farid memindahkan balok ke
ketinggian h menggunakan
bidang miring, sedangkan
(b) Samuel menggunakan katrol
dengan lintasan vertikal.
Samakah usaha yang dilakukan
keduanya?
h
1
A
B

102. Tantangan
untuk Anda
Gambar 3.13
(a) Keadaan awal benda dalam
posisi seimbang.
(b) Pegas ditarik sejauh
simpangan y2.
(c) Posisi benda kembali ke titik
setimbang karena gaya
pegas F = –ky2.
1
*5AD218155A79@?C5B91
p E '!K;7

103. =B=K

104. =K

106. $
$149@5AD218155A79@?C5B91B525B1A

108. :?D5
2
.B181H17491;D;171H125A1C
K'!KK;7

109. =B=K

110. =

112. $
.B181@?B9C96;1A511A1871H125A1CB51A1845711A18@5A@94181
$149DB181H17491;D;171H125A1CB525B1A

114. :?D5
5A1@1;18 55A79 @?C5B91 H17 49=99;9 ?58

116. = 19A H17 25A141 @141
;5C97791

117. =:9;1=1BB1:59B19A

120. ;7=41@5A35@1C17A1E9C1B949C5=@1C
C5AB52DC

121. =B
$8$%
9AC5A:DC5AB52DC=5=99;9=1BB1
'

124. ;7=

126. =N

127. ;7
5A79@?C5B91H1749=99;919AC5A:D14118
* '!
N

128. ;7

129. =B

130. =N

131. $
$14955A79@?C5B91H1749=99;919AC5A:D14118N

132. :?D5
b. Energi Potensial Elastis Pegas
5A79 @?C5B91 51BC9B @571B 25A2541 4571 55A79 @?C5B91 @141
D=D=H1
5A79@?C5B91@571B1411855A79H1749=99;9@571B1;921C
141H1@5AD2181@1:171C1DA57171@571B
!1H1H1725;5A:1@141
@571B =5=D7;9;1 @571B DCD; =5A5717
*5A81C9;1$/%$3
*141$/%$3
$=D1 =D1@571B411=
;51411 B5C9=217 5A79 @?C5B91 @571B 41 55A79 ;95C9;H1 ?
*141
$/%$3
%41$/%$3
@571B=5=99;9B9=@171B5:1D82
41 2 @1:17 2
2
)58 ;1A51 141 C1A9;1 B525B1A %2 41
@571B =51A9; ;5=219 2541 B5BD19 D;D= ### (5FC? @571B K%
5B1AH1DB181H17491;D;1@571B41A9;514112

133. ;522B1=1
25B1A4571@5AD218155A79@?C5B91@571B1C1A12

134. 4122
@571B 4 ,25B1A@5A@94181@?B9B92541
76 Mudah dan Aktif Belajar Fisika untuk Kelas XI
2 2

135. 2
2
2

136. %2 2
%2
571 45=9;91 25B1AH1 DB181 H17 491;D;1 ?58 71H1 @571B
49H1C1;1 4571 @5AB1=11
@571B @ @571B
4571 @@571B
%2 K

137. %5C9;1 @571B 495@1B;1 @571B 1;1 =51;D;1 75A1; 81A=?9;
,51=1 @5A75A1;1H1 @571B =5711=9 @5AD2181 55A79 ;95C9;
=5:149 55A79 @?C5B91 @571B 1C1D B5219;H1
-941; B51=1H1 @571B
=51;D;1 75A1; 81A=?9; @571AD8 71H1 D1A 1;1 =5=2D1C @571B
25A85C9 @141 @?B9B9 ;5B5C9=2171
1 2 3
y2'
y2
y1=0
Contoh 3.8
Sumber: Fisika untuk Sains dan Teknik, 1998
Perhatikan gambar di atas. Jika
seorang ahli gizi menyatakan
bahwa pada pizza isi daging dan
keju tersebut mengandung energi
16 megajoule, bagaimana
pendapat Anda jika dikaitkan
dengan konsep Fisika? Bagaimana
cara mendapatkan angka tersebut?

138. Kata Kunci
• energi kinetik
• energi potensial
x
m
v
m
v
m
k
1
2
3
licin
x1
x2
x = x2 – x1
licin
licin
Usaha, Energi, dan Daya 77
Contoh 3.9
*571B25AC1=218@1:17

139. 3=;5C9;14925A971H1

140. (
5A1@1;1855A79@?C5B91
@571B:9;171H1@141@571BC5AB52DC49:149;1;199@1C
$8$%
9;5C18D9

141. (1

142. 3=

143. =
F
F
Tes Kompetensi Subbab B
(3,$-$0.$*'$.$/%6-6.$5+*$0
,52D1821CD;53925A=1BB17495@1B;141A9;1C1@5
B58977125B1A55A79;95C9;H1749=99;9H114118

144. :?D5
9CD7;51:D121CDC5AB52DC
'?29 25A=1BB1

145. ;7 B5417 25A75A1; 4571
;535@1C1;=:1=C921 C92149A5=4125A85C9
B5C518=55=@D8:1A1;

146. =
-5CD;118
1
71H1A5=@141=?2941
2
DB181H1749@5A?5841A9@575A5=1
%5A5C1 =191 H17 =1BB1H1 ;7 495@1B;1 41A9
@D31;29417=9A979394571BD4DC;5=9A971

147. JC5A8141@8?A9I?C1
$9;1@1:179C1B129417
=9A97
=41!

148. =BC5CD;1@5AD218155A79
@?C5B914941;5A5C1B5C518=55=@D8:1A1;

149. =
54125A=1BB1

150. ;7495@1B;141A9;5C97791

152. 3=
1
9CD718DB181H17491;D;171H17A1E9C1B9
@1412541C5AB52DC
2
9CD71825A;DA17H155A79@?C5B917A1E9C1B9
2541C5AB52DC
541'25A=1BB1
;7:1CD8=5775939A41A91C1B
29417=9A974571BD4DC;5=9A971J
541
C5AB52DC=5D=2D;B52D18@571BH17C5A5C1;
=
41A9 5C1;' B5=D1
$9;1 %

154. (= 41 @571B
C5AC5;1=1;B9=D=B5:1D8

155. 3=89CD7;?569B95
75B5;1C1A121?;'457129417=9A97
%
1

156. (

157. =

159. (=
$9;1

160. ( (
1
%
(

162. (=

164. (=

165. =
*
%1

167. (=

168. =
$
$14925B1A55A79@?C5B9151BC9B@571B14118
$
C. Gaya Konservatif dan Hukum Kekekalan
Energi Mekanik
*5A81C9;1 $/%$3
$
,52D18 @571B 495C1;;1 49 1C1B 1C19
41 B118 B1CD D:D7H1 499;1C;1 @141 49497
%5=D491 B52D18 21?;
25A=1BB1'=5D3DA4571;535@1C1 C5@1C;51A18@571B
$9;11C19
41C1A41939B5AC1@571BH19451B9BC5=1;1=5=5D89D;D=??;5
K% 9 4571 14118 71H1 @141 @571B B11C D:D7 2521BH1 25A75B5A
B5:1D8
%51411 H17 49979;1 @141 B9BC5= C5AB52DC 14118 55A79
;95C9;C5A@DB1C@141=1BB121?;B58977155A79;95C9;@571B491219;1
;921CH1 =1BB1 @571B 491771@ B171C ;539 41A9@141 =1BB1 21?;
%5C9;121?;=5H5CD8@571B1:D21?;25A;DA17B1=@191;89AH1
25A85C9 ;1A51 71H1 @571B H17 =51F1 71H1 4?A?71 41A9 21?;
*5A81C9;1$/%$3
%
%5=D4911A1821?;25A219;1;921C71H1
@571B 25;5A:1
;921CH1 21?; =5=@5A?58 55A79 ;95C9;H1 ;5=219
B5@5AC9 B11C 21?; =5H5CD8 @571B F11D@D 1A18H1 25A2541
1?;
Gambar 3.14
Gaya pada pegas merupakan gaya
konservatif.

169. Gambar 3.15
Seseorang sedang melakukan
usaha memindahkan peti.
Tugas Anda 3.2
Sebutkan contoh-contoh gaya
konservatif yang ada di sekitar Anda.
;589171 55A79 ;95C9;H1 @141 B118 B1CD 1A18 75A1;H1 C5C1@9
=5=@5A?58 55A79 ;95C9;H1 ;5=219 @141 1A18 75A1; H17 19 H19CD
;5C9;1 21?; 25A219; ;5 @?B9B9 B5=D1 $/%$3
*141 @5A9BC9F1 C5AB52DC DB181 H17 491;D;1 71H1 @571B % 9
C941;=57D21855A79=5;19;B9BC5=@571B
!1H1H17491;D;1?58
@571BC5AB52DC25AB961C;?B5AE1C96
!1H17A1E9C1B9:D7125AB961C;?B5AE1C96
41@1C;1841=5:51B;1=571@171H17A1E9C1B925AB961C;?B5AE1C96
1A9BD4DC@1417H171971H1;?B5AE1C96:D71=5=99;939A9218F1
:D=18DB181H17491;D;171H1@141@1AC9;52541491771@B521719
@1AC9;5 14118 ?
*141 ;51411 B5C9=217 @?B9B9 1

170. 71H1 @571B
@ @141 3?C?8 C5AB52DC 49H1C1;1 4571 @5AB1=11
78 Mudah dan Aktif Belajar Fisika untuk Kelas XI
@
% 9 K
-18D;18 41 DB181 H17 491;D;1 ?58 71H1 @571B C5AB52DC
*5A81C9;1 ;5=219 $/%$3
;5C9;1 2541 25A@9418 41A9 @?B9B9
H17=5=99;9B9=@1711
;5@?B9B94571B9=@171125B1ADB181
H17491;D;171H1@571BC5A8141@254149H1C1;14571@5AB1=11
K* 1
K%1 1
-141 571C96 =5H1C1;1 218F1 1A18 71H1 @571B * 25A1F11
4571 1A18 @5A@94181 1 *.( ,#'*(!( G *- #*+) +#
(##+-+-+#,#'*(!(1
411
571 45=9;91 @5AB1=11 41@1C 49H1C1;1 4571
K%1 1
1 1
K%
1 1
%
1 1 1 1
%
1 1
5A41B1A;1 @5AB1=11 :51B18 218F1 DB181 H17 491;D;1
?58@571BC941;=57D21855A79=5;19;B9BC5=41C941;25A71CD7
@141@?B9B91F141@?B9B91;89A2541H1749;51971H1@571BC5AB52DC
*5A81C9;1$/%$3

171. ,52D18@5C949@9418;1;5C5=@1C19
B5C9779 .B181 H17 49@5AD;1 DCD; =5=9418;1 @5C9 14118
K'!-141571C96C9=2D;1A511A1871H125A1C25A1F11
4571 1A18 75A1; @5C9
.B181 ;5C9;1 =5=9418;1 @5C9 C941; 25A71CD7 @141 @1:17
9C1B1H17491D9@5C9C5C1@925A71CD7@14125B1A@5AD2181C9779
@5C941A9;54D4D;11;89A;5;54D4D;11F1H1
$9;1@5C949@9418;1
179;5@?B9B91F1H1DB181H17491;D;1H114118'!
,531A1
=1C5=1C9B DB181 C?C1 H17 491;D;1 DCD; =5=9418;1 @5C9 41A9
21F18 ;5 1C1B
1D 49@9418;1 179 ;5 21F18 14118
C?C
K'! '!

172. 5B1A DB181 @5=94181 B52D18 @5C9 41A9 ;54D4D;1 1F1 89771
;5=219 ;5 ;54D4D;1 1;89AH1 25A919 ?
$149 41@1C 49B9=@D;1
218F1 DB181 H17 491;D;1 ?58 71H1 ;?B5AE1C96 1;1 25A919 ?
:9;1 ;54D4D;1 1;89A 2541 ;5=219 ;5 ;54D4D;1 1F1H1

173. v 1 1
v2 2
h mg 2
h1
Usaha, Energi, dan Daya 79
1. Perumusan Hukum Kekekalan Energi Mekanik
11= =541 7A1E9C1B9 :D=18 55A79 @?C5B91 41 55A79 ;95C9;
BD1CD2541C5C1@:9;181H114171H17A1E9C1B9
*5AH1C11C5AB52DC49;51
B521719 D;D= %5;5;11 5A79 '5;19;
*5A81C9;1 $/%$3
,52D18 2541 25A=1BB1 ' :1CD8 2521B
*141 @?B9B9
;5C97791H1
C5A8141@ 13D1 1C19
,5B11C ;5=D491 2541 25A141 @141 @?B9B9
4571 ;5C97791 C5A8141@ 13D1
9;1C1;1 218F1 @141 2541
C5A:149 @57DA171 55A79 @?C5B91 H17 25B1AH1 B1=1 4571 DB181
H17 491;D;1 71H1 25A1C
K@4@
K
*141 @?B9B9
;535@1C1 2541 /
;5=D491 2541 CDAD 89771
@141 @?B9B9 4571 ;535@1C1 / *141 ;51411 C5AB52DC ;535@1C1
2541 25AC1=218 ;1A51 @571AD8 @5A35@1C1 7A1E9C1B9 B589771 DB181
H17 491;D;1 2541 B1=1 4571 @5AD2181 55A79 ;95C9; H19CD
;4;
K
5A41B1A;1 (34$/$$0
; 41 (34$/$$0
;
49@5A?58
@
K@;K;
1C1D @
;
@; K
Gambar 3.16
Balok dijatuhkan dari ketinggian
tertentu.
Contoh 3.10
,52D182?125A=1BB1'495=@1A;1E5AC9;1;51C1B4571;535@1C11F1B525B1A

174. -5CD;1
1
C9779=1;B9=D=H174931@1941
2
;535@1C1;5C9;12?1=531@19C9779B5C5718=1;B9=D=
$8$%
1
*
%
*%
'!
'/ '!
'/

175. '/
'!

176. )58;1A51//=1;1

177. '/ '!

178. /
!
$149C9779=1;B9=D=H174931@1914118

179. /
!
2
*
%
*%

180. '/ '!
'/
'%,

181. '/ '!
/

182. !
'/

183. '/ '

184. /
'/

185. '/
'/
/

186. /
/

187. /
$149;535@1C12?1;5C9;1=531@19C9779B5C5718C9779=1;B9=D=14118
/

188. /
h
m
v2 = 0
h2 = h
h1 = 0
v1 = v0
Ek2 ; Ep2
Ek1 ; Ep1

189. ,52D1821CD25A=1BB1'C5A71CD7@141B5DC1BC19H17@1:17H1 4925A971H1
=541C1A
1CD=D1925A75A1;4571;51:D11F1/

190. B5@5AC9@14171=21A;5C9;1
21CD=5H9=@174571BD4DC C9779H174931@192?141A9C9C9;B5C9=217H1
14118
-5CD;1
1
C9779=1;B9=D=H174931@1921CD41
2
25B1A;535@1C11F121CD/

191. $8$%
1
*%*%
'!
/2
A m '!
80 Mudah dan Aktif Belajar Fisika untuk Kelas XI
'/

192. /2
0 m '!

193. /

194. !

195. /
!
$149C9779=1;B9=D=H174931@1921CD

196. /
!
2
3?B
K

197. 3?B
/
!
K

198. 3?B
/
!
/

199. !
3?B
h
v0
1?;H1725A=1BB1;7=5775939A41A91C1BB52D1829417=9A97H17BD4DC
=9A97H1

200. J
1?;C5AB52DC;5=D491=5D=2D;@571BH17C5A5C1;=41A9
@?B9B9B5=D1
$9;1;?569B9575B5;1C1A121?;457129417=9A97

201. 25A1@1
=5C5A@571BC5AC5;19;5C18D9;?BC1C1@571B

203. (=
$8$%
.B181H17491;D;171H1@571B14118571C96;1A51@571B=51F171H1C5;1
21?;
AC9H1;5C9;1@571BC5AC5;1@571B=51F171H1C5;1B58977171H1
@571B411A18@5A@9418125A1F111A18
*5A81C9;171=21A25A9;DC
@571B
%1K
%
7A1E
4 *
4'!3K1
'!,B9

204. J

205. '!,
.B181?5875B5;125A919571C96
;1A511A1821?;25A1F11
45711A1871H175B5;
!,%
4 ;,
k'!3?B

206. J,
'!, ;
ha
hb hc
A
B
b
C
s
30°
Contoh 3.11
Contoh 3.12
Tugas Anda 3.3
Apakah Anda tahu olahraga bungee
jumping? Selidikilah Hukum Kekekalan
Energi yang bekerja saat orang
melakukan bungee jumping.

207. Pembahasan Soal
32
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 ....
a. mv2 d. 1
2 mv2
b. mv2 e. 1
4 mv2
c. 3
4 mv2
Soal UMPTN Tahun 1989
Pembahasan:
hB = 2hA
Berarti, EpB = 2 EpA
Sesuai dengan Hukum Kekekalan
Energi Mekanik maka
EpB – EpA = EkA – EkB
EkB = 2 EkA
= 2 1
2
mv2
= mv2
Jawaban: b
Usaha, Energi, dan Daya 81
'5AD:D;@A9B9@55A7949;5C18D9218F1
-)-
% B58977149@5A?58
*!,!+/!,%
'/
4/
K
%
'!,K
3'!, k
'

208. K

209. K
%
'!

210. k
4

211. ,
3 k ,

212. 4141@1C=5H55B19;1@5AB1=11;D14A1CC5AB52DC4571=5789CD741A9
'
;7%

214. (=,
= k

215. 41!

216. =B
N/m =K

218. ;7

219. =B

220. 4

221. =
3

222. =

223. =4

224. =K=

225. K

226. =C941;C5A@1;19

227. =
$149@571BC5AC5;1B5:1D8

228. =
?141@1C25A75A1;C1@175B5;1@1419C1B1B5@5AC971=21A25A9;DC
,11C49C9C9;
2?125A;535@1C1

230. 3=B
5A1@11:D49C9C9;41
A
$8$%
*141B9BC5=25A1;D%5;5;115A79'5;19;B589771
1
'!
'/
'!
'/

231. =B

232. =
=B

233. /
/

234. =B=B
$149;51:D12?149C9C9;14118=B
2
'!
'/
'!
'/

235. =B

236. =
=B

237. =B

238. =
/
/

239. =B
=B
$149;51:D12?149C9C9;14118
=B
C
B
80 cm
50 cm
Contoh 3.13

240. B
A
lintasan loop
Gambar 3.17
Lintasan roller coaster.
2. Analisis Gerak pada Roller Coaster
1=@9A B5=D1 C5;??79 49 C1=1 892DA1 B5@5AC9 #,(2 ( #,(2
)+1C1DD91 1C1B9B171C;1H11;1;?B5@69B9;1
91C1A1B5:D=18
@5A=191 H17 141 +)+ ),-+ 1C1D H17 291B1 49B52DC 8199C1A 41@1C
=54?A?741DCD;=5=181=95298411=;?B5@69B9;1C5C1775A1;
*5A81C9;1 $/%$3
%541A11 C1@1 =5B9 =577D1;1 21
25A:11)(/2)+-DCD;19;;5@D31;2D;9C=51D99C1B1H17
C941; C5A1D 3DA1=
*D31; 2D;9C B571:1 49A1317 5298 C9779 41A9@141 @D31;
??@ 81 C5AB52DC =5=D7;9;1 55A79 @?C5B91 ;541A11 49
H17 5298 25B1A B589771 =1=@D 25A:11 =51D9 9C1B1 =5D:D
@D31; 4571 219;
9C1B1 ??@ B571:1 492D1C B5@5AC9 C5C5B1 19A
C5A219;
$9;1??@25AD@197;1A1@5D81;149@5A?582?2?C@5D=
@1751=;192?2?C?A=1H1B11C;541A1149@?B9B9C5A5418;?49B9
99 41@1C =5H5212;1 @DB97 1D @97B1
9C1B1 ??@ H17 B5@5AC9
C5C5B1 19A 81H1 =5=25A9;1 2?2?C =1;B9=D= ;19 2?2?C ?A=1
H1 @141 2?2?C C5AB52DC @5D=@17 =1B98 =5A1B1;1 ;5H1=11
%5C9;1 +)+ ),-+ 25A141 49 C9C9; C5AC9779 41A9 9C1B1 ??@ H19CD
49C9C9;B5@5AC9H1741981C@141$/%$3
71H1B5CA9@5C1H1
14118 A5BDC1 41A9 71H1 C5;1 41 25B1A 71H1 25A1C @5D=@17
'! B589771
B
C
82 Mudah dan Aktif Belajar Fisika untuk Kelas XI
B3'!
/
'
,H1A1C ;51:D1 =99=1 49 C9C9; 14118

241. B589771 49@5A?58

242. '!
/
'
/
Cmin !+
%5C9;1 +)+ ),-+ 25A141 49 C9C9; C5A5418 H19CD C9C9;
*

243. %*
%3*3
'/
'!
'!
'/
%19;1 ;54D1 AD1B @5AB1=11 C5AB52DC 4571
'
B589771 49@5A?58
!/
!/
)58;1A51

244. 41/
!=1;1
@5AB1=11 =5:149
!!

245. /
=9 / ! K
%5C97791 1F1 =99=1 D3DA1 49 C9C9; 41@1C 41 89CD7
=51D9 @55A1@1 D;D= %5;5;11 5A79 '5;19; 49 C9C9; 41
171A +)+ ),-+ =1=@D =55F1C9 ??@ 4571 1=1
Gambar 3.18
Lintasan roller coaster dengan
loop berbentuk lingkaran.
A
Sumber: Dokumentasi Penerbit
Nc mg

246. Usaha, Energi, dan Daya 83
Contoh 3.14
,5@?C?721?;25A=1BB1'=5D3DA@141BD1CDC11797;1A1411=B5@5AC9
C5A981C@14171=21A
$9;171H175B5;1C1A121?;41C117491219;1
1
25A1@1;18;5C97791=99=D=21?;H1781ADB495@1B171A75A1;1H141@1C
=531@19@D31;97;1A1C9C9;41
2
C5CD;11825B1A@5A35@1C121?;49C9C9;
$8$%
1
!D1;1AD=DB;51:D1=99=D=@141C9C9;C5A5418(34$/$$0
;

247. $149;51:D1=99=D=49C9C9;25B1AH1/=9 ! B5897711C1A1C9C9;
414571=577D1;18D;D=;5;5;1155A79=5;19;
*%*%
' !
' /
' !
' /
' !

248. '!
$149;5C97791=99=D=171A21?;=531@19C9C9;14118
2
5B1A@5A35@1C149C9C9;14118@5A35@1C1B5CA9@5C1
5A41B1A;171=21A
49C9C9;
B'!
',
'!49=11

249. ,!
$149@5A35@1C121?;49C9C9;14118,!
Kata Kunci
• energi mekanik
• gaya konservatif
• gaya sentripetal
• kelajuan minimal
• konstanta pegas
Tes Kompetensi Subbab C
(3,$-$0.$*'$.$/%6-6.$5+*$0
@1;18H1741;5C18D9C5C1771H1;?B5AE1C96
4171H1C941;;?B5AE1C96
@1;188D;D=;5;5;1155A79=5;19;25A1;D
@141B52D182541:9;171H1;?B5AE1C9625;5A:1@141
2541C5AB52DC
D12D18254141H1725A=1BB1=1B97 =1B97
':1CD82521B41A9;5C97791=5C5A41=5C5A
$9;1=5H5CD8 C118 4571 ;535@1C1 /=B
C5CD;118 55A79 ;95C9; 2541 B11C 1;1
=5H5CD8C118
,52D1821?;25A=1BB1;7=D1 =D1491=
1?;
C5AB52DC;5=D49149:1CD8;141A9BD1CD;5C97791
3=@141B52D18@571BH17;?BC1C171H1H1

251. (=
$9;1!=B25A1@1=5C5A@571BC5AC5;1
-?5 =5=9418;1 2D;D 41A9 1C19 ;5 1C1B =5:1
5A1@1DB181C?C1H1749C5A9=1?582D;DC5AB52DC
-97121CD21C1H17C521H13=495C1;;1491C1B
B52D18 =5:1
9CD718 DB181 DCD; =5D=@D;
;5C97121CD21C1C5AB52DC411=B1CDCD=@D;1:9;1
=1BB1B5C91@21CD21C1
;7
A
v
B
NB mg
R
hA
C

252. ,52D18;51@1:1CD82521B41A9;5C97791=5C5A
$9;1 =1BB1 2D18 ;51@1 ;7 41 !

253. =B
C5CD;118;535@1C12D18;51@1B11C=531@19
;5C97791=5C5A41A9C1184155A79;95C9;2D18
;51@1B5B11CB525D==531@19C118
,52D18;5A5C1=55F1C99C1B1+)+),-+4571
491=5C5A

254. =
71A;5A5C141@1C=59C1B4571
1=1 C5CD;118 ;535@1C1 =99=D= ;5A5C1
C5AB52DC
84 Mudah dan Aktif Belajar Fisika untuk Kelas XI
,52D18 2541 25A=1BB1

255. ;7 :1CD8 2521B 41A9
;5C97791 =5C5A 49 1C1B C118
$9;1!

256. =B
C5CD;118
1
;535@1C12541B11CC92149C11841
2
DB181?5871H125A1CB51=1@5A@94181

257. ,52D18@5DAD49C5=21;;1=9A97;51C1B4571
BD4DC55E1B9J4155A79;95C9;B525B1A

258. $
$9;1!

259. =BC5CD;11855A79;95C9;4155A79
@?C5B912541@141B11C=531@19C9C9;C5AC9779
D. Daya
41 C518 251:1A C5C17 31A1 =5789CD7 DB181 41A9 71H1 H17
491;D;1
921497;1 =575C18D9 25B1A DB181 5298 =51A9; =575
C18D9 B525A1@1 1:D DB181 C5AB52DC 49;5A:1;1
-5CDH1 25B1A1 F1;CD 49
411= 2181B1 99 =5:149 B171C 25A@5A1
,11C DB181 @5A B1CD1 F1;CD
4945699B9;1 =D3D18 9BC918 41H1
*5AD41971C218F141H1C941;49C5CD;1?5825B1A55A79H17
49=99;9 BD1CD 2541
.CD; 5298 =5=181=9H1 @5A81C9;1 3?C?8
25A9;DC
.3?; 41 DC5C 25A=1BB1 B1=1 H19CD

260. ;7 =519;9 1C19 4D1
B5;?18H1 B5C9779 =5C5A
%54D1H1 =5=99;9 55A79 B1=1 25B1A DCD;
=51;D;1DB181

262. :?D5
5A79@?C5B91H1749=99;9=5A5;1B1=1
F11D@D;5H1C11H1.3?;B1=@19491C194D1529835@1C
1A9DA191
3?C?8 C5AB52DC 49;5C18D9 218F1 1AC9H1 DB181 25D= 41@1C =5=25A9;1
96?A=1B9529857;1@C5C17@5A@941811;921C@571AD871H1
11=
@5A9BC9F1 99 41@1C 49;1C1;1 218F1 .3?; =5=99;9 41H1 5298 25B1A
41A9@141 DC5C F11D@D ;54D1H1 =5=99;9 ;5=1=@D1 DCD; =57
81B9;1 55A79 H17 B1=1
$149 41H1 14118 25B1A1 69B9;1 H17 =5H1C1;1 DB181 H17
491;D;1 ?58 2541 B5C91@ B5;?H1 1C1D 1:D 55A79 H17 492DCD8;1
2541 B5C91@ B5;?H1
1H1 A1C1 A1C1
DB181
B517F1;CD
-
1C1D ,
/
-
K
%5C5A171
DB181 H17 491;D;1 :?D5
- F1;CD H17 49@5AD;1 B5;?
/ ;51:D1 A1C1 A1C1 =B
11=B9BC5=,#B1CD141H149CDAD;141A9B1CD1DB181H19CD$B
,1CD1 C5AB52DC B5A97 49B52DC F1CC 49C5C1@;1 B521719 @5781A711
C5A8141@ 9=DF1 ,;?C1491 H19CD $/(4#$55
K
,1CD1 41H1 411= ;5=1=@D1 B52D18 =5B9 291B1 =577D1;1
B1CD1 )+, *)0+ * 1C1D 41H1 ;D41
8@F1CC

263. ;0
;08
;0
:1=N

264. $
Tugas Anda 3.4
Sebutkan contoh alat-alat yang
mencantumkan besaran daya yang ada
di sekitar Anda.

265. Usaha, Energi, dan Daya 85
;08 14118 B1CD1 DB181 1C1D 55A79 2D;1 B1CD1 41H1
,1CD1
C5AB52DC 21H1; 497D1;1 DCD;=5H1C1;1 55A79 9BCA9;
$9;1 B5CA9;1
9BCA9; =5=99;9 41H1

267. F1CC 55=5 B5CA9;1 C5AB52DC 55A79 9BCA9;
=51;D;1 ;5A:1 1C1D DB181

269. :?D5 B5C91@ B5;?H1
Contoh 3.15
+9C?H1725A=1BB1

270. ;7=519;9C1771;51C19C971B5C9779
=B51=1

271. =59C
5A1@1;1841H1A1C1 A1C1H17491;D;1+9C?
$8$%
9;5C18D9
'

272. ;7
=
-

273. =59C
'!
- -

274. ;7

275. =B
=

277. F1CC

278. B
$149+9C?=575D1A;141H1B525B1A

280. F1CC
Contoh 3.16
,52D18=5B9@?=@1B5CA96D7141@1C=5=9418;1

282. ;719A;521;H17C9779H1
=5C5AB51=1=59C
$9;1569B95B9=5B9@?=@1C5AB52DC81H1

283. 25A1@1;18
41H1A1C1 A1C19BCA9;H1749@5AD;1
$8$%
9;5C18D9 '

285. ;7
=
- =59C

286. B
1H1H1749@5AD;1DCD;=5=9418;119A14118
'!
- -

288. ;7

289. =B =

290. F1CC

291. B
1H1H1749@5AD;1@?=@1DCD;=5=@5A?58DB181B525B1A

292. F1CC4571
569B95B9=5B9

293. 14118

294. F1CC

295. F1CC

297. F1CC
$14941H1@?=@1171A569B95B9H1

298. 81ADBB525B1A

300. F1CC

301. Tes Kompetensi Subbab D
(3,$-$0.$*'$.$/%6-6.$5+*$0
+9?=519;9C1771H17C9779H1=411=F1;CD
45C9;
9CD71841H1A1C1 A1C1+9?411=B1CD1
*:9;1=1BB1H1

302. ;7
!=B
,52D18@?=@1=5B94975A1;;1?58=?C?A9BCA9;H17
=5=99;941H1*
'5B9C5AB52DC1;1=519;;1
2521;7;5C5=@1CH17C9779H1
=
9CD718
F1;CD H17 492DCD8;1 DCD; =519;;1 2521
C5AB52DC
,52D18=?29=577D1;1=5B9

303. *
5A1@171H1
A1C1 A1C1H174925A9;1=5B9=?29C5AB52DC171A41@1C
25A75A1;4571;535@1C1;?BC1

304. ;=:1=
,52D1821?;25A=1BB1;725A141411=;51411
491=491C1B29417=9A97
1?;C5AB52DC=541@1C
71H1B525B1A
(B51A1829417=9A97;51C1B
1
-5CD;1;535@1C121?;B5C518=55=@D8
:1A1;,

305. =B5@1:1729417=9A97
2
9CD741H1H174925A9;1?5871H1
,

306. =!

307. =BBD4DC29417=9A97

308. J
W1
F
86 Mudah dan Aktif Belajar Fisika untuk Kelas XI
,52D18=5B9@?=@141@1C=5=9418;1

310. ;719A
;5B52D1821;H17C9779H1
=B51=1
=59C
$9;1569B95B9=5B9@?=@199

311. 25A1@1;1841H1
9BCA9;H1749@5AD;1
$?125A=19@1@1D3DA49;5C97791=5C5A41A9
1C19
$9;1;535@1C1$?1@1411F1@5D3DA1=B
25A1@1;18;535@1C1H1;5C9;1=5H5CD81C19
1A9;5C97791

312. =B52D18;51@1H17=5=99;9
=1BB1

313. ;7 :1CD8 41A9 @?8?
5A1@1;18 55A79
;95C9; H17 49=99;9 ;51@1 @141 B11C =531@19
;5C97791

314. =491C1BC118!

315. =B
,52D182541H17=1BB1H1;725A75A1;4571
;535@1C1C5C1@=B
%5=D4912541C5AB52DC4925A9
71H1 B589771 2541 =5711=9 @5A1=21C1
;5=D491 25A85C9 B5C518 =55=@D8 :1A1;
=
-5CD;1
1
25B1A71H1@575A5=1H1725;5A:1@1412541
2
DB181H17491;D;125418977125A85C9
F m = 2 kg
30°
Rangkuman
.B181 14118 25B1AH1 71H1 B51A18 @5A
@94181B49;19457125B1AH1@5A@94181
3?B ,1C1D,3?B
4571 14118 BD4DC 1C1A1 71H1 41
@5A@94181
.B18125A81A71571C96=5D:D;;1218F171H1
H1725;5A:125A1F1145711A18@5A@94181
*1417A169;71H1C5A8141@@5A@9418125B1ADB181
=5AD@1;1D1B415A18H17491AB9A
5A79 14118 ;5=1=@D1 DCD; =51;D;1
DB181
5A79;95C9;1411855A79H1749=99;9
?58B5C91@2541H1725A75A1;
%
'/
5A79@?C5B911411855A79H1749=99;9?58
B5C91@2541;1A51;54D4D;1H1
$9;1;51411
=5=D7;9;155A79C5AB52DC41@1C49=D3D;1
*'!DCD;55A79@?C5B917A1E9C1B9
*51BC9B
%1DCD;55A79@?C5B91@571B
.B181 =5AD@1;1 @5AD2181 55A79 41A9 BD1CD
2541
%4%
DCD;55A79;95C9;
*4*
DCD;55A79@?C5B91
D;D= %5;5;11 5A79 '5;19; L$9;1 @141
BD1CD B9BC5= H17 25;5A:1 81H1 71H1 71H1
;?B5AE1C9655A79=5;19;B9BC5=B51DC5C1@
M
*4%
;?BC1
*
%
*%
Wtotal = W1+W2
s
W2

316. .B181 5A79 1H1
Usaha, Energi, dan Daya 87

317. .B181C?C1H17491;D;1?5871H1;?B5AE1C96
81H1=5=@5A81C9;1;514111F141;51411
1;89A@?B9B925419C1B1C941;=5=571AD89
1H1 14118 DB181 H17 491;D;1 ?58 2541
B5C91@B5;?1C1D1:D55A79H1725AD218=5:149
55A7925CD;19
Refleksi
4$*$0(3)+'$0$:$
.B181*5AD21815A79
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.
Peta Konsep
5A79%95C9; 5A79*?C5B91
D;D=%5;5;11
5A79'5;19;
5A79*?C5B91
!A1E9C1B9
5A79*?C5B91
*571B
=5=2181B
8D2D71H1
=5=2181B
=5=2181B

318. Tes Kompetensi Bab 3
A. Pilihlah salah satu jawaban yang paling tepat dan kerjakanlah pada buku latihan.
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88 Mudah dan Aktif Belajar Fisika untuk Kelas XI
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363. ;535@1C1
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436. 90 Mudah dan Aktif Belajar Fisika untuk Kelas XI
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