LAPORAN PRAKTIKUM FISIKA DASAR I AYUNAN DAN PERCEPATAN GRAVITASI (M.6)
Oleh:
Nama
: Ni Made Susita Pratiwi
NIM
: 1008105005
Dosen Pengaja
: I Ketut Sukarasa, S.Si, M.Si
Asisten dosen
: 1. Siska Rohani 2. Desak Putu Risky Vidika Apriyanthi
JURUSAN KIMIA FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM UNIVERSITAS UDAYANA 2010
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AYUNAN DAN PERCEPATAN GRAVITASI (M.6)
I. TUJUAN
1. Mempelajari sifat ayunan 2. Menentukan kecepatan gravitasi
II. DASAR TEORI 2.1
Pengertian Ge Getaran
Getaran adalah gerak bolak-balik secara periodik yang selalu melalui titik keseimbangan.
Satu getaran adalah gerakan dari titik mula-mula dan kembali ke titik tersebut.
Periode (waktu getar) adalah waktu yang digunakan untuk mencapai satu getaran penuh, dilambangkan T (sekon atau detik).
Frekuensi adalah banyaknya getaran tiap detik, dilambangkan f (Hertz).
Amplitudo
adal adalah ah
simp simpan ang gan
mak maksimu simum m
dari ari
suat suatu u
getar etaran an,,
dilambangkan A (meter).
Simpangan adalah jarak besarnya perpindahan dari titik keseimbangan ke suatu posisi, dilambangkan Y (meter).
Sudut fase getaran adalah sudut tempuh getaran dalam waktu tertentu, dilambangkan ϕ (radian).
adalah perban perbandin dingan gan antara antara lamany lamanyaa getara getaran n dengan dengan Fase Fase getaran getaran adalah periode, dilambangkan Φ .
Kecepatan sudut adalah sudut yang ditempuh tiap satuan waktu ω .
Getaran Harmonis
Gerak harmonik sederhana (GHS) adalah gerak periodik dengan lintasan yang yang ditemp ditempuh uh selalu selalu sama sama (tetap) (tetap).. GHS mempun mempunyai yai persam persamaan aan gerak gerak dalam dalam bentuk sinusiodal sinusiodal dan digunakan untuk menganalisis suatu gerak periodik tertentu
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Yang termasuk ke dalam Gerak Harmoni Sederhana Linier: penghisap dalam alam sili silin nder der gas, gas, gera gerak k osila silassi air air raks raksa/ a/ai airr dala dalam m
pipa ipa U, gerak erak
horisontal/vertikal dari pegas, dsb. •
Gerak Harmoni Sederhana Sederhana Anguler
Gera Gerak k band bandul ul term termas asuk uk ke dala dalam m sederhana , yaitu
sala salah h satu satu jenis jenis gerak gerak harmo harmoni niss
Contoh lainnya, lainnya, Gerak Harmoni Sederhana Anguler . Contoh
misalnya :osilasi ayunan Bandul Bandul sebenarnya sebenarnya ada dua jenis, yaitu bandul bandul mekanis mekanis dan bandul fisis. Bandul mekanis adalah disebut juga bandul sederhana merupakan sebuah bandul ideal yang terdiri dari sebuah partikel yang digantung pada seutas tali panjang yang ringan dan berayun dengan sudut simpangan kecil maka susunan ini disebut bandul matematis. Hukum-hukum (ayunan) Galilei tahun 1596, yaitu: •
Tempo ayunan tidak bergantung dari besarnya amplitude (jarak ayunan), asalkan amplitude tersebut tidak terlalu besar.
•
Tempo ayunan tidak bergantung dari beratnya bandulan ayunan
•
Tempo ayunan adalah sebanding laras dengan akar dari panjangnya bandulan (l )
•
Tempo ayunan adalah sebanding-balik dengan akar dari percepatan yang disebabkan oleh gaya berat.
Perioda Perioda yang mengalami mengalami gerak selaras sederhana, sederhana, termasuk bandul, tidak bergantung pada amplitudo. Galileo dikatakan sebagai yang pertama mencatat kenyat kenyataan aan ini, sementar sementaraa ia melihat melihat ayunan ayunan lampu lampu dalam
kateda katedalan lan di pissa. pissa.
Penemuan ini mengarah pada bandul jam yang pertama mirip dengan lonceng Periode dari bandul matematis dapat ditentukan dengan rumus :
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Dimana : T = periode ayunan (detik) L = panjang tali (m) g = percepatan gravitasi bumi (m/s 2) Periode Periode bandul atau ayunan ayunan adalah waktu yang yang dibutuhkan dibutuhkan untuk untuk 1 kali getaran. Satu kali getaran yang dimaksudkan adalah pergerakan dari titik A-B-CB-A, jadi, getaran yang dilakukan dimulai dari titik A hingga ke titik A lagi (kembali ke titik awal). Bila bandul ditarik kesamping dari posisi seimbangnya kemudian dilepas, maka bandul akan berayun karena pengaruh gravitasi atau bandul bergetar dengan ragam getaran selaras. Gaya pemulih yang bekerja pada m: F = -mg sin 0. karena gaya pemulihnya sebanding dengan sin 0 bukan dengan simpangannya. Gaya yang menyebabkan menyebabkan bandul bandul ke posisi posisi kesetimbang kesetimbangan an dinamakan dinamakan gaya pemulih yaitu mg sin θ dan panjang busur adalah s = l θ θ . Kesetimbangan gayanya adalah
Dan gaya-gaya yang bekerja pada bandul sederhana atau bandul matematis adalah seperti berikut ini
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Bandul juga berguna dalam bidang geologi dan sering kali diperlukan untuk mengukur percepatan gravitasi pada lapis tertentu dengan sangat teliti. Bandul fisis merupakan sembarang benda tegar yang digantung yang dapat beray berayun/ un/ber bergeta getar/b r/beris erisola olasi si dalam dalam bidang bidang vertic vertical al terhad terhadap ap sumbu sumbu terten tertentu. tu. Bandul Bandul fisis fisis sebena sebenarny rnyaa memili memiliki ki bentuk bentuk yang yang lebih lebih komple kompleks, ks, yaitu yaitu sebaga sebagaii benda tegar. Periode dari bandul fisis dapat ditentukan dengan rumus sebagai berikut :
Dimana : T = perioda ayunan (detik) k = radius girasi terhadap pusat massa (cm) a = jarak titik gantung terhadap pusat massa (m) g = percepatan gravitasi bumi (m/s 2)
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Keterangan gambar: m= massa benda (kg) g= percepatan gravitasi (m/s2 ) θ= sudut simpangan
PERCEPATAN GRAVITASI
HUKUM Newton tentang gravitasi bumi dapat diungkapkan sebagai berikut: Setiap partikel materi di jagat raya melakukan tarikan terhadap setiap
partikel lainnya dengan suatu gaya yang berbanding langsung dengan hasil kali massa partikel-partikel itu dan berbanding terbalik dengan kuadrat jarak yang memisahkan.
Gaya-gaya gravitasi yang bekerja pada partikel itu membentuk sepasang aksi-re aksi-reaks aksi. i. Walaup Walaupun un massa massa partik partikel-p el-parti artikel kel itu berbed berbeda, a, gaya gaya yang yang sama sama besarn besarnya ya bekerj bekerjaa pada pada masing masing-mas -masing ing partik partikel el itu dan garis garis kerja kerja keduan keduanya ya terletak di sepanjang garis yang menghubungkan partikel-partikel itu. Hukum Hukum Gravita Gravitasi si Newton Newton ialah ialah hukum hukum untuk untuk dua partik partikel. el. Faktan Faktanya ya bahwa gaya gravitasi yang dilakukan pada atau oleh suatu bola homogeny sama
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III. ALAT – ALAT
1. Ayun Ayunan an Sede Sederh rhan anaa 2. Ayunan Fi Fisis 3. Stopwatch 4. Pemb Pember erat at (140 (1400 0 gr) gr)
IV. CARA KERJA A. Ayun Ayunan an Sede Sederh rhan ana a
1.
Panjang tali tertentu diambil.
2.
Waktu ayunan diukur dengan cara mengukur waktu yang diperlukan untuk 20 kali ayunan.
3.
Percob Percobaan aan ini diulan diulang g sekura sekurangng-kur kurang angny nyaa 5 kali kali dengan dengan mengam mengambil bil panjang tali yang beralainan.
B. Ayunan Fisis
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3.
Percob Percobaan aan B1 diul diulang ang untu untuk k 5 sumbu sumbu pada pada sisi B (bali (bali ayun ayunan an fisis) fisis) yang yang setangkup dengan titik sumbu 2. Letak pemberat satu atau lubang kesebelah dan ulangi percobaan B2 dan
4.
B3. Ambil masing-masing 5 sumbu, tidak perlu setangkup.
V. DATA PENGAMATAN A. AYUNAN SEDERHANA 0
ϴ = 10
Pecobaan I
Pengukuran Panjang tali (m) I II 0,71 I II IV V Pengukuran II
t (sekon) 36,11 35,78 34,92 35,77 35,11
Pengukuran Panjang ta tali (c (cm) I II 0,60 I II IV V Pengukuran III
t (s (sekon) 32,68 32,68 32,61 32,74 32,70
Pengukuran I II I II IV V
Panjang ta tali (c (cm)
0,50
t (s (sekon) 29,54 29,51 29,74 29,50 29,64
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IV V Pengukuran II
0,64
Pengukuran Panjang tali (m) I II 0,50 I II IV V Pengukuran III Pengukuran I II I II IV V
Panjang tali (m)
0,47
35,26 34,92 t (sekon) 34,19 34,13 34,41 34,23 34,23 t (sekon) 33,95 33,80 34,20 34,26 33,06
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= 1,8055 s Π2
•
= 9,87
Ditanya : g…………………….?
•
Jawab : T
L
2π
=
T2
=
g
=
4π
2
L
=
2
2
2
4π ⋅ 0,71 1,81
g
g
4π L T
g
g
= 8,59 m
=
2
s
2
4π
⋅
0,71
3,262
2
Dengan cara yang sama diperoleh data : 2
L (m)
T dalam 20 kali getaran 36,11
2
T (s)
T (s)
g (m/s )
1,806
3,262
8,59
1,789
3,200
8,76
1,746
3,048
9,12
1,788
3,197
8,77
1 756
3 084
9 09
35,78 0,71 34,92 35,77 35,11
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0,60
32,68 1,634
2,670
8,87
1,630
2,657
8,92
1,637
2,679
8,84
1,635
2,673 2 T =2,67
8,86
32,61 32,74 32,70
0 Pecobaan III 2
L (m)
T dalam 20 kali getaran 29,54
2
T (s)
T (s)
g (m/s )
1,477
2,182
9,05
1,476
2,179
9,06
1,487
2,211
8,93
1,475
2,176
9,07
1,482
2,196 2 T =2,18
8,99
29,51 0,50 29,74 29,50 29,64
9 Grafik data untuk ayunan sederhana
L (m) 0,71
2 T (s) T 2 =3,15
8 T =2,67 2
0,60
0
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B. Menentukan Percepatan Gravitasi (g) dengan Ayunan Fisis Percobaan I
a. Untuk L = 64 cm = 0,64 m Diketahui : •
Panjang tali (L) = 64 cm
= 0,64 m
•
T untuk 20 kali getaran
= 35,36
•
T untuk 1 kali getaran
= 1,768 s
•
Π
= 9,87
Ditanya : •
g…………………?
Hitung : T = 2π
a2
K 2
+
ag
2
; K
2
=
L
12
Penentuan percepatan gravitasi (g) dengan melenyapkan K, maka K kita abaikan dalam penggunaan rumus. T= 2
a2
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35,26 1,763
3,108
8,13
1,746
3,049 T 2 =3,09
8,29
34,92
8 Percobaan II 2
L (m)
T dalam 20 kali getaran 34,19
0,50
2
T (s)
T (s)
g (m/s )
1,710
2,924
6,75
1,707
2,914
6,77
1,720
2,956
6,68
1,712
2,931
6,73
1,712
2,931 T 2 =2,93
6,73
34,13 34,41 34,23 34,23
1 Percobaan III 2
2
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VI. RALAT a. Ralat Ralat Per Percep cepat atan an Gravi Gravita tasi si (g) (g) Ayunan sederhana •
g untuk panjang tali 0,71 m
No 1
- 0,28
0,078
- 0,11
0,012
0,25
0,062
8,59 2 8,76 3
8,87
9,12 4
- 0,1
0,01
8,77 5
0,22 9,09 ∑ g =44,33
0,048
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No 1
8,87
0
0,036
8,87
0
0,036
8,87
0,05
0,0025
8,87
- 0,03
0,0009
8,87 2 8,87 3 8,92 4 8,84 5
8,87
-
0,01
0,0001
8,86 ∑ g =44,36 = 0,076
∆ g =
∆ g =
∆ g = ∆ g =
∑( g − g ) n ( n −1) 0,076 5( 5 −1) 0,076 20 0,0038
∆ g = 0,06 m
g ± ∆ g = (8,87 ± 0,06 ) m / s 2
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∆ g =
∆ g = ∆ g = ∆ g =
∑( g − g ) n ( n −1) 0,014 5( 5 −1) 0,014 20 0,0007
∆ g = 0,03 m
g ± ∆ g = ( 9,02 ± 0,03 ) m / s 2
Ralat nisbi =
∆ g
g
×100 % =
0,03 9,02
x 100% = 0,33%
Ralat kebenaran = 100% - 0,33% = 99,67 %
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Ayunan Fisis g untuk panjang tali 0,64 m
No 1
0,64
0,4100
0 01
0 0001
8,08 2
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g untuk panjang tali 0,50 m
No 1
0,02 6,75
0,0004
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g untuk panjang tali 0,47 m
No 1
-
0,04
0,0016
6,44 2 6,50 3
6,48
0,02
0,0004
- 0, 0 ,14
0,0196
6,34 4
-
0,16
0,0256
6,32 5
0,31
0,0961
6,79 ∑ g =32,39 = 0,143
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a.
Ralat Keraguan Waktu ( T ) Ayunan Sederhana Untuk panjang tali 0,71 m
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Ralat kebenaran = 100% - 0,62% = 99,38 % Untuk panjang tali 0,60 m
No 1
T ( sekon )
T ( sekon
)
(T −T )( sekon )
(T −T ) 2 ( sekon )
0
0
0
0
1,634 2 1,634 3
1,634
0,004
1,6 x 10 -5
0,003
0,9 x 10 -5
0,001
0,1 x 10 -5
1,630 4 1,637 5 1,635 ∑ g =8,17
2 ∑ (T −T ) = 2,6 x
10-5
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5
0,003 1,482 ∑ g =7,397
0,9 x 10 -5 2 ∑ (T −T ) = 10,2 x
10-5
∆T =
∑(T −T ) n ( n −1)
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∆T =
∆T =
∆T =
∑(T −T ) n ( n −1) 0,000286 5(5 −1) 0,000286 20
∆T = 14 ,3 x10
−6
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Ralat nisbi =
∆T
T
100 % ×100
=
1,14 .10 1,634
− 3
x 100% 100% = 0,0698 %
Ralat kebenaran = 100% - 0,0698 % = 99,93%
Untuk panjang tali 0,47 m
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bes besar ar resu result ltan an gaya gaya seba seband ndin ing g deng dengan an jara jarak k titi titik k semb sembar aran ang g keti ketiti tik k kesetimbangan tersebut. Rumus yang dipergunakan untuk mencari gravitasi pada percobaan kali ini adalah T = 2π
l g
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