4. modul praktikum fisika dasar i

Penuntun Praktikum Fisika Dasar I

1

CARA PENGGUNAAN ALAT UKUR

PRAKTIKUM FISIKA DASAR I

JANGKA SORONG

Jangka sorong adalah alat pengukur tebal suatu benda yang sangat kecil sekali,

kepekaannya mencapai 0,1 mm. Alat pengukur ini dapat pula digunakan untuk mengukur

jari-jari atau dalam dari sebuah tabung.

Sebelum menggunakan alat pengukur ini sebaiknya diteliti terlebih dahulu apakah

alat tersebut mempunyai kesalahan titik nol. Gambar alat jangka sorong ini dapat dilihat

seperti Gambar 1.

Gambar 1. Alat ukur Jangka Sorong

Kesalahan titik nol ini dapat dibaca bila A dan B diimpitkan ternyata titik nol

yang terdapat pada skala tambahan (nonius) tidak tepat berimpit dengan titik nol yang

terdapat pada skala dasar F, sedangkan untuk kesalahan pada titik nol bila keadaan

sebaliknya. Misalkan dalam pengukuran suatu benda skala dasar menunjukkan 1,49 cm,

sedangkan kesalahan titik nolnya –0,07 cm, maka jarak antara paruh A dan B adalah (

1,49 + 0,07 = 1,56 ) cm.

CARA PENGGUNAAN JANGKA SORONG

Bila mengukur garis tengah suatu tabung, letakkanlah tabung A dan B sehingga

tebal tabung tepat diantara paruh A dan B, dengan demikian dapat dibaca pembagian

skala beberapa jarak antara paruh A dan B ini.


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Jika jarak tidak tepat barulah bilangan bulat dalam nilai meter dibaca dalam skala

dasar, dengan nonius dapat dibaca pembagian skala telih teliti. Panjang skala pada nonius

9 mm dibagi menjadi 10 skala yang sama, jadi jarak dua garis kecil yang ada pada nonius

sebesar 0,09 cm.

Dalam suatu pengukuran (lihat Gambar 2) pada waktu paruh A dan B berimpit,

skala nol nonius terletak berimpit dengan skala nol, jadi berarti pada keadaan ini tidak

mempunyai kesalahan titik nol (Gambar 2a). Setelah benda yang hendak diukur

diletakkan diantara paruh A dan B ternyata titik nol nonius terletak diantara 8 dan 9 pada

skala dasar F (Gambar 2b).

Gambar 2. Keadaan titik nol Alat Jangka Sorong

Kemudian lihat garis manakah pada nonius yang berimpit dengan garis skala

dasar. Pada gambar diatas terlihat bahwa pada garis ke-6 nonius berimpit pada salah satu

pada skala dasar (disisi pada skala 14), jadi tebal benda tersebut adalah 8 mm + 0,6 mm

atau 8,6 mm, atau dapat juga dihitung demikian, garis ke-6 pada nonius berimpit pada

garis nol 14 pada skala dasar. Jadi jarak AB adalah 14-6x0,9 = 8,6 mm atau 8+0,6 = 8,6

mm.

PERHATIAN … !!!

Pada waktu pengukuran suatu benda agar jarak AB tidak berubah, sekrup R diatas

nonius diputar keras, bila terdapat kesalahan titik nol, pengukuran diatas harus dikurangi

atau ditambah dengan kesalahan titik nolnya. Untuk mengukur garis tegak tabung dapat

dipakai paruh CD yang terletak diatas paruh AB (lihat Gambar 1), sedang batang E

digunakan untuk mengukur dalamnya tabung.


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Pada waktu mengadakan pengukuran terhadap suatu benda, maka supaya jarak

AB tidak berubah hendaknya sekrup R diatas nonius diputar hingga keras. Jika terdapat

kesalahan titik nolnya, untuk mengukur garis tengah dari tabung dalam dapat dipakai

paruh CD yang berada diatas paruh A dan B (lihat Gambar 1), sedangkan batang E

digunakan untuk mengukur dalam tabung.

MIKROMETER SEKRUP

Alat lain untuk mengukur jarak yang sangat kecil dengan teliti adalah Mikrometer

Sekrup. Gambar alat mikrometer sekrup ini dapat dilihat seperti Gambar 3.

Gambar 3. Alat ukur Mikrometer Sekrup

Kalau sekrup D diputar, maka ujung B dapat bergeser mundur atau maju. Jika sekrup D

diputar satu putaran, jarak AB bergeser sejauh 0,5 mm. Disekeliling dari kiri C diberi

skala (yang merupakan nonius S) dan banyaknya skala 50 buah.

Pada sekrup D diberi skala yang melingkar dan sejajar dengan nonius C serta

mempunyai ukuran dan banyak skala sama dengan nonius C dan juga pada batang dasar

E ini terdapat skala yang memanjang yang merupakan skala dasar E.

CARA PENGGUNAAN MIKROMETER SEKRUP

Sebelum digunakan untuk mengukur benda, tentukan terlebih dahulu kesalahan

titik nolnya, apakah pada waktu ujung A dan B berimpit (jangan dipaksa waktu

menghimpitkannya), titik nol pada nonius C berimpit atau tidak pada titik nol nonius D.

Jika berimpit berarti tidak mempunyai kesalahan titik nol, jika mempunyai kesalahan

titik nol positif dan sebaliknya mempunyai kesalahan titik nol negatif.

Jika titik nol nonius C berimpit dengan skala 48 nonius D, berarti mempunyai

kesalahan titik nol negatif sebanyak 2 skala. Tetapi jika titik nol nonius C berimpit

dengan skala 2 nonius D berarti mempunyai kesalahan titik nol positif sebanyak 5 skala.


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Andai kata akan mengukur garis tengah sesuatu kawat dan pengukuran ini digunakan

mikrometer sekrup yang mempunyai kesalahan titik nol berbeda. Digunakan micrometer

sekrup X dengan kesalahan titik nol negatif dan micrometer sekrup Y dengan kesalahan

titik nol positif.

Jika kawat itu waktu diukur dengan micrometer sekrup X mempunyai dua

perputaran ditambah dengan 19 skala pada nonius D, dari data-data diatas kita dapat

membuat perhitungan sebagai berikut :

Mikrometer Sekrup X Mikrometer Sekrup Y

Jumlah skala pada nonius C 50 50

Jarak skala pada tiap-tiap Skala

nonius C mm

50

5,0 mm

50

5,0

Tabel dari kawat yang terbaca

Mikrometer Sekrup 2 putaran +

19 skala nonius C

2 putaran +

26 skala nonius D

Kesalahan titik nol Kurang 2 skala

Pada nonius D

Lebih 5 skala

Pada nonius D

Skala yang besarnya dipakai Oleh

micrometer sekrup 2 putaran +

21 skala nonius D

2 putaran +

21 skala nonius D

Garis tengah kawat 0,121 cm 0,121 cm

Pada percobaan mencari kelengkungan batang logam akan dijumpai suatu alat pengukur

lengkung yang kerjanya hampir menyerupai sekrup.


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TEORI KETIDAKPASTIAN PENGUKURAN DALAM PERCOBAAN

I. PENDAHULUAN

Pada percobaan Fisika hasil yang diperoleh biasanya tidak dapat langsung

diterima karena harus dipertanggungjawabkan keberhasilan dan kebenarannya.

Hal ini disebabkan oleh kemampuan manusia yang terbatas dan ketelitian alat-alat

yang digunakan serta mempunyai batas kemampuan tertentu. Dengan kata lain peralatan

dan sarana (termasuk waktu) yang tersedia bagi kita membatasi tujuan dan hasil yang

dapat dicapai.

Hasil percobaan baru dapat diterima apabila harga besaran yang diukur

dilengkapi dengan batas-batas penyimpangan dari hasil tersebut, yang disebut sesatan

(ketidakpastian). Jika hasil tersebut diketahui penyimpangan terlalu besar maka bila

diperlukan percobaan harus diulang kembali dengan berbagai cara misalnya :

Mengulang pengukuran beberapa kali yang lebih teliti atau mengganti alat-alat

percobaan dengan alat yang lebih baik ketelitiannya. Jadi jelaslah untuk keperluan ini

mutlak diperlukan teori sesatan (ketidakpastian). Dengan demikian dapat ditentukan

sesatan pada hasil percobaan agar dapat memberi penilaian yang baik.

II. KETIDAKPASTIAN PADA PENGUKURAN

Kesalahan atau Error dalam suatu percobaan dapat dibagi atau dua golongan yaitu

:

II.1. Kesalahan Bersistem (Systematic Error)

Kesalahan yang bersumber pada alat pengukuran yang dipakai besarannya,

kesalahan biasanya konstant sehingga sering sekali dinamakan sebagai kesalahan konstan

(Constant Error).

Kesalahan Bersistem ini dapat terjadi karena :

a. Kesalahan titik nol (Zero Error).

b. Kesalahan pada kalibrasi pengukuran.

c. Kesalahan orangnya (pengamat), kesalahan ini disebabkan oleh kebiasaan

seorang pengamat. Misalnya seorang pengamat sering kali membuat

kesalahan karena kedudukan matanya terlalu rendah atau terlalu tinggi

sewaktu membaca tinggi kolam air didalam pipa yang tegak. Kesalahan ini

disebut : Parallak.


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d. Terjadinya gesekan dan fatiqua (kesalahan) pada alat karena sering dipakai.

e. Kondisi percobaan, jika sebuah alat digunakan dengan kondisi percobaan

yang berbeda dengan kondisi sewaktu kalibrasi, akan menghasilkan

kesalahan.

f. Gangguan teknis : misalnya pada waktu pengukuran terjadi gangguan seperti

adanya kebocoran-kebocoran yang akan mengganggu system dan

menyebabkan kesalahan.

II.2. Kesalahan Random

Karena pengulangan pengukuran selalu memberikan hasil yang berbeda-beda,

maka harga tersebut juga akan berbeda dengan harga yang sebenarnya. Kesalahan ini

dinamakan kesalahan Random atau kesalahan kebetulan, yang terjadi atas :

a. Kesalahan penafsiran, kebanyakan alat pengukuran memerlukan suatu penafsiran

pada bagian skala tertentu dan penafsiran ini dapat berubah dari waktu kewaktu yang

lain.

b. Keadaan penyimpangan, seperti suhu, tekanan udara, atau tegangan listrik.

c. Gangguan, misalnya : adanya getaran mekanis atau pengaruh putaran motor dari alat

listrik.

d. Definisi, walaupun proses pengukuran telah sempurna, pengulangan pengukuran

yang sama selalu akan memberikan penyimpangan, besaran yang diamati tidak

didefinisikan secara tetap.

Misalnya :

Panjang suatu meja persegi bukanlah suatu besaran yang terdefinisi secara eksak. Hal

ini disebabkan bahwa kalau kita teliti, sisi meja tidaklah rata ataupun mungkin tidak

tepat sejajar.

Sehingga walaupun kita menggunakan alat ukur yang sangat baik untuk mengukur

meja tersebut, harga yang diperolah selalu berubah-ubah tergantung penampang

panjang yang kita ukur.

II.3. Kesalahan-Kesalahan Lain

Kesalahan lain yang tidak termasuk bahasan 1 dan 2 yang perlu diperhatikan

adalah :


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a. Kekeliruan membaca alat atau skala alat dan mengatur kondisi percobaan. Kesalahan

ini dapat diatasi dengan cara melakukan percobaan seteliti mungkin atau bila

memungkinkan mengulangi percobaan tersebut.

b. Kesalahan perhitungan, yaitu kesalahan memasukkan harga atau angka-angka

perhitungan, menggunakan kalkulator, menggunakan daftar logaritma dan

sebagainya.

III. PERHITUNGAN KESALAHAN

III.1. Sesatan Taksiran

Bila pengukuran dilakukan hanya satu kali biasanya sesatan diambil setengah kali

skala terkecil dari alat ukur yang digunakan.

Contoh :

Menggunakan mistar yang skala terkecil 1 mm, bila tebal plat diukur menghasilkan 50

mm, maka hasilnya dapat ditulis :

t = ( 50 0,5 ) mm atau

= ( 5,0 0,05 ) x 10 mm

t = 0,5 adalah sesatan mutlak (absolut), sedangkan sesatan relatifnya dapat dinyatakan

dengan :

= %100xt

t

= %10050

5,0x

= 1 %

III.2. Menentukan Harga Rata-rata (nilai terbaik) dan Sesatannya

Misalkan kita melakukan N kali pengukuran didapat hasil sebagai berikut :

X1, X2, X3, ……… , XN

Untuk mendapatkan nilai yang terbaik (benar) dari pengukuran tersebut adalah merata-

ratakan hasil pengukuran tersebut, yaitu :

N

X

N

XXXXX

NNN

...321 (III.2.1)

( NX = rata-rata = nilai terbaik), maka simpangan atau deviasi untuk :


8

X1 adalah X1 = X1 - X

X2 adalah X2 = X2 - X

XN adalah XN = XN - X

Harga sesatan rata-rata adalah :

N

XXXXXXXXX

N

...321

N

XXXX

N (III.2.2)

Persamaan (III.2.2) ini disebut deviasi rata-rata.

Sedangkan deviasi standar atau simpangan baku semesta X(x) : didefinisikan sebagai :

xx V

Dimana Vx adalah variasi yang didefinisikan

N

XXV NN

x

)(2

dengan N menuju tak hingga.

Sehingga x dapat dituliskan :

N

XXV

NN

xx

)(2

(III.2.3)

dengan N menuju tak hingga.

Harga x berada pada pengukuran tak terhingga yang tidak mungkin dilakukan dengan

menggunakan suatu pendekatan teori samping x dapat diganti dengan SN yang

dinamakan simpangan baku contoh (sample standard deviation). N memberikan

gambaran tentang simpangan X terhadap Xo.

Sedangkan SN menggambarkan simpangan X terhadap NX maka :

)1(

)(2

N

XXS N

N

yang dapat diubah menjadi,

)1(

)(22

N

XNXS N

N (III.2.4)

Dimana N 8 (untuk N = 1 SN tidak mempunyai arti).


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Menurut teori percobaan SN sebenarnya adalah NX

S yaitu ketidakpastian pada nilai rata-

rata contoh XN yang mempunyai harga

N

SS N

X N (III.2.5)

Penggantian SN menjadi SX hal ini disebabkan kurva sebaran nilai rata-rata contoh X

lebih sempit dari pada kurva sebaran pengukuran tunggal (X1) berarti Xx yaitu

kita mengulangi pengukuran N kali dengan hasil rata-rata, misalnya 1X maka ada

kepastian 66% 1X terletak dalam selang XX N didalam praktek percobaan tak

terhingga, tak mungkin kita lakukan, jadi X dan X

tidak dapat diketahui dan sebagai

pengganti terbaik dipakai SN dan NX

S seperti diatas.

Untuk pemakaian selanjutnya digunakan,

)1(

22

NN

XNX

N

SSX

NNN

X N (III.2.6)

dengan N 8.

Apabila X diukur N kali, ada kemungkinan 68% bahwa simpangan nilai rata-rata contoh

X terhadap nilai benar Xo tidak lebih dari NX

S dengan kata lain “ada jaminan 68%

bahwa Xo ada dalam interval NX

SX ” dengan demikian persoalan selesai.

Kita tidak dapat mengetahui nilai benar Xo dari eksperimen, tetapi dengan mengadakan

pengulangan cukup banyak, kita dapat menyodorkan sebagai penggantinya nilai contoh

X dan dapat memberikan pernyataan sampai berapa jauh X menyimpang dari Xo.

Contoh :

X = 10,0; 10,2; 10,0; 10,0; 9,8; 10,1; 9,8; 10,3; 9,8; 10,0

Maka nilai terbaik X dan sesatannya ( X X) dapat dicari sebagai berikut :

N XN 2

NX

1 10,0 100,00

2 10,2 104,04

3 10,0 100,00

4 10,0 100,00

5 9,8 96,04

6 10,1 102,01

7 9,8 96,04

8 10,3 106,09


10

9 9,8 96,04

10 10,0 100,00

XN = 100,0 2

NX = 1000,26

0,1010

0,100

N

XX

NN

0,100)0,10()( 22 NX

)1(

22

NN

XNXSX

NN

X N

)110(10

0,1001026,1000

x

05,090

26,0

maka nilai terbaik X = ( 10,00 0,05 )

III.3. Contoh Perhitungan

III.3.1. Ketelitian Pengukuran

Suatu amperemater mempunyai skala 0 – 5 A, dengan pembagian skala terkecil

0,1 A.

(a). Berapa ketelitian alat itu bila skala pada pengukuran, skala penuh ?

(b). Dan pada setengah skala ?

Jawab :

(a). I = ½ skala terkecil = ½ x 0,1 A, dan I = 5 A

Ketelitian %1%1005

05,0

x

I

I

(b). I = ½ skala terkecil = ½ x 0,1 A = 0,05 A, dan I = 2,5 A

Ketelitian %2%1005,2

05,0

x

I

I

III.3.2. Sesatan Yang Ditentukan Oleh Skala Alat

1. Tahanan sepotong kawat ditentukan menurut hokum ohm.

Hasilnya adalah V = ( 1,0 0,05 ) volt dan I = ( 5,0 0,05 ) mA atau I = ( 5,0 0,05

) x 10-3

A.


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Berapakah R ?

Jawab :

ohmxI

VR 200

100,5

0,13

I

I

V

V

R

R

5

05,0

0,1

05,0

200

R

ohmxR 12200)01,005,0(

Jadi R = ( 200 12 ) ohm

2. Pada percobaan tegangan permukaan air digunakan rumus : rg

h

2

Bila : r = ( 0,30 0,005 ) mm

g = ( 980 2% ) cm/det2

= 1,0 g/cm3 dan h = ( 50,0 0,05 ) mm

Tentukan : dan

Jawab :

rg

h

2

2

30,09800,10,50

2

xxxrgh

50,73

r

r

g

g

h

h

(tidak mempunyai sesatan)

0018,030,0

005,0

980

02,0

50

05,0

50,73

13,050,730018,0 x

Jadi )13,050,73( dyne.

3. Sesatan yang paling mempengaruhi

Rumus lensa tipis (Gauss) : '

'

SS

SSf

Bila S = ( 8,0 0,05 ) cm dan S’ = ( 24,0 0,05 ) cm


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Berapakah ( f f ) ?

Jawab:

'

'

SS

SSf

'

111

SSf

0,24

1

0,8

11

f

0,6f cm

'

'

S

S

S

S

f

f

008678,0)0,24(

05,0

)0,8(

05,0

)0,6( 222

f

0312,0)0,6(008678,0 2 xf

Jadi )03,000,6( f cm.


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I. GERAK JATUH BEBAS

1.1. TUJUAN PERCOBAAN

► Dapat memahami dan menentukan percepatan benda pada gerak jatuh bebas.

1.2. ALAT DAN BAHAN BESERTA FUNGSINYA

1. Dasar Statif, A

........................................................................................................................................

2. Batang Statif

........................................................................................................................................

3. Magnet pemegang bola logam

........................................................................................................................................

4. Gerbang cahaya

........................................................................................................................................

5. Bola logam

........................................................................................................................................

6. Timer counter, AT-01

........................................................................................................................................

7. Bosshead, universal

........................................................................................................................................

8. Rol meter, 3m

........................................................................................................................................

9. Kabel penghubung

........................................................................................................................................

10. Plumb bob

........................................................................................................................................


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1.3. DASAR TEORI

Alat percobaan gerak jatuh bebas didesain untuk membantu mahasiswa

memahami gerak jatuh bebas, yaitu pengukuran waktu jatuh bola logam, memeriksa

hubungan ketinggian dan waktu tempuh, dan mengukur percepatan gravitasi g.

Dengan menggunakan pencacah waktu (Timer counter AT-01) memungkinkan

pengukuran waktu jatuh bebas sampai skala millisekon. Waktu jatuh bebas diukur

menggunakan dua sensor gerbang cahaya. Pada saat bola dilepaskan, Timer counter

secara otomatis segera memulai melakukan pengukuran waktu, timer counter akan

membaca waktu tempuh bola dari magnet pemegang bola ke masing-masing gerbang

cahaya infra merah pada gerbang cahaya kedua, timer counter otomatis akan

menghentikan pengukuran.

Tinjauan Teori:

Persamaan kinematika gerak untuk gerak benda dengan percepatan tetap a,

diberikan oleh:

2112ox v t at (1)

sehingga untuk sebuah benda jatuh bebas dengan percepatan adalah g (g adalah

percepatan gravitasi) dan kecepatan awal adalah nol (vo = 0) didapatkan persamaan:

212

h g t (2)

t adalah waktu yang diperlukan benda jatuh dari ketinggian h. Jika persamaan 2

digunakan untuk gerbang cahaya 1 dan gerbang cahaya 2 (Gambar 1) berikut


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Gambar 1. Skema Percobaan

maka diperoleh dua persamaan yang memberikan hubungan antara ketinggian dan waktu

tempuh yang diperlukan oleh suatu benda ke masing-masing gerbang cahaya. Persamaan

untuk masing-masing ketinggian diberikan oleh:

21

1 12h g t untuk gerbang cahaya 1 (3)

21

2 22h g t untuk gerbang cahaya 2 (4)

Dari persamaan 3 dan persamaan 4 dapat dilihat bahwa percepatan jatuh bebas pada

masing-masing ketinggian adalah sama dengan g.

Dengan mengurangkan persamaan 4 dengan pesamaan 3, maka dapat diperoleh

besaran percepatan gravitasi g, yaitu

2 1

2 2

2 1

2( )

( )

h hg

t t

(5)

Persamaan 5 di atas akan digunakan untuk menentukan besar percepatan jatuh bebas dan

memverifikasi bahwa percepatan pada gerak jatuh bebas adalah sama dengan percepatan

garvitasi.

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1.4. PROSEDUR PERCOBAAN

II. RANGKAIAN PERALATAN

1. Rangkai peralatan seperti pada Gambar 2. Pasang magnet pemegang bola pada

bagian atas statif, gerbang cahaya pertama di tengah batang, dan gerbang cahaya

kedua pada bagian paling bawah.

Gambar 2. Rangkaian Percobaan

2. Hubungkan magnet pemegang bola ke keluaran P1/E.MAGNET pada Timer

counter AT-01 menggunakan kabel penghubung.

3. Hubungkan gerbang cahaya satu dan gerbang cahaya dua secara berurutan pada

terminal P1 dan P2 pada Timer counter. Atur jarak kedua gerbang cahaya

sedemikian rupa sehingga jarak antara keduanya adalah 10 cm.

4. Hubungkan Timer counter AT-011ke soket jala listrik. Timer counter dalam kead

an mati (OFF).


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5. Hidupkan Timer counter AT-01. Tekan tombol pemilih fungsi pada timer counter

beberapa kali sedemikian rupa sehingga timer berada pada fungsi Gravity

Acceleration. Pada keadaan tersebut lampu LED pada fungsi tersebut dan pada

fungsi E.MAGNET akan menyala. LED pada fungsi E.MAGNET menunjukkan

bahwa sumber tegangan untuk magnet pemegang bola juga dalam keadaan hidup

(ON).

6. Atur kelurusan magnet pemegang bola, dan kedua gerbang cahaya sedemikian

rupa sehingga trayektori bola logam dari magnet pemegang bola menghalangi

berkas cahaya pada masing-masing gerbang cahaya. Untuk memudahkan

mengatur kelurusan, gunakan plumb bob.

II. PELAKSANAAN PENGAMBILAN DATA

1. Hidupkan Timer counter AT-01.

2. Tekan tombol FUNCTION pada Timer counter AT-01 sedemikian rupa beberapa

kali sehinggga pewaktu berada pada fungsi Gravity Acceleration. Timer counter

berada pada fungsi Gravity Acceleration ditunjukkan oleh nyala merah lampu

indicator LED. Pada keadaan ini, Timer counter juga akan menyalakan fungsi

E.MAGNET yang ditunjukkan oleh nyala merah indicator LED. Dengan

menghubungkan terminal E.MAGNET ke magnet pemegang bola logam

menggunakan kabel penghubung, maka pada kumparan magnet pemegang akan

timbul medan magnet sehingga dapat menarik benda-benda konduktor.

3. Pasang bola logam pada magnet pemegang bola logam. Mulailah melakukan

pengukuran dengan cara menekan tombol E.MAGNET pada Timer counter.

Setelah tombol E.MAGNET ditekan, maka fungsi E.MAGNET akan mati

sehingga medan magnet pada magnet pemegang bola juga akan hilang. Bola

logam akan jatuh melewati gerbang cahaya 1 dan gerbang cahaya 2 secara

berurutan.

4. Baca hasil pengukuran waktu pada Timer counter AT-01. Timer akan

menampilkan waktu tempuh bola ke gerbang cahaya 1 dan gerbang cahaya 2

secara berurutan. Catat hasil pengukuran waktu ini ke dalam Tabel Pengamatan.

5. Ubah ketinggian jatuh bebas bola h. Atur ulang Timer dengan menekan tombol

FUNCTION satu kali sedemikian rupa sehingga fungsi E.MAGNET kembali


19

aktif (ON) kembali. Ulangi langkah percobaan 1 s/d 4 untuk beberapa ketinggian

yang berbeda dengan menekan tombol E.MAGNET.

1.5. TUGAS PENDAHULUAN

1. Buktikan rumus 2v gh !

2. Jelaskan ketiga hukum Newton baik secara teoritis maupun matematis!

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21

1.6. DATA HASIL PENGAMATAN

Tabel Hasil Pengamatan

No

Massa

Peluru

(gram)

h1 (cm) h2 (cm) Waktu t1

(ms)

Waktu t2

(ms)

1 10 30

2 10 50


22

1.7. PENGOLAHAN DATA

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25

1.8. ANALISA

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26

1.9. TUGAS AKHIR

1. Hitung besarnya percepatan gerak jatuh bebas peluru tersebut menggunakan

persamaan (3), periksa hasilnya apakah besar percepatan jatuh bebas peluru

memiliki harga yang sama atau harga yang berbeda pada ketinggian jatuh yang

berbeda? Jelaskan jawaban Anda!

2. Berdasarkan pada hasil percobaan, benarkan dugaan prediksi teori bahwa

percepatan jatuh bebas sama dengan percepatan gravitasi? Jelaskan jawaban

Anda!

3. Analisa hasil percobaan dan perhitungan yang anda lakukan.

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1.10. KESIMPULAN

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30

LAMPIRAN GAMBAR


31

II. PRINSIP KERJA KATROL


1. Melakukan percobaan yang menunjukkan prinsip kerja katrol dapat memudahkan

mengangkat beban.

2. Mampu menunjukan melalui percobaan dan perhitungan perbedaan keuntungan

mekanik dengan menggunakan beberapa katrol.


1. Katrol tunggal dan katrol ganda

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2. Tali nilon

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3. Neraca pegas

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4. Statif

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5. Beban

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32

2.3. DASAR TEORI

Pesawat sederhana digunakan untuk melipatgandakan gaya atau mengubah arah

gaya. Jika peswat sederhana melipatgandakan gaya, maka gaya yang dikeluarkan lebih

kecil dibandingkan dengan gaya yang diperlukan untuk melakukan suatu pekerjaan tanpa

bantuan pesawat sederhana. Besaran yang menyatakan pelipatgandaan hasil dari suaru

peswat sederhana terhadap gaya atau jarak perpindahan disebut keuntungan mekanis.

Salah satu bentuk pesawat sederhana adalah katrol. Katrol adalah alat berupa roda

yang dapat berputar pada porosnya. Untuk menggunakan katrol diperlukan tali atau mata

rantai. Secara umum katrol dikelompokkan menjadi dua yaitu: katrol tetap dan katrol

bergerak. Dalam pemakaian seringkali digabungkan beberapa katrol yang selanjutnya

disebut sebagai sistem katrol.

Gambar 1. Macam-macam katrol

Tinjau gambar 1a, untuk mengangkat beban seberat FB dengan cara menarik tali

dengan gaya sebesar FK. Pada kontrol tetap (Gambar 1a) hanya terdapat satu penggal tali

yang menahan berat beban, maka besar gaya Fk , untuk menarik beban sama dengan berat

FB atau :

FB = Fk ...................................................................... (2.1)

Penggunaan satu katrol tetap hanya mengubah arah gaya kuasa, sehingga

keuntungan yang diperoleh saat menggunakan adalah memudahkan pengangkutan benda

saja. Pada pemakaian satu buah katrol bergerak, beban yang akan diangkat digantungkan

pada katrol seperti Gambar 1b. Gaya berat FB, ditahan oleh dua buah penggal tali, maka

FB = 2 Fk ..................................................................... (2.2)


33

Keuntungan mekanis dengan menggunakan katrol bergerak adalah perbandingan antara

besar gaya beban FB dan gaya kuasa Fk.

Keuntungan Mekanis = FB / Fk = 2 ............................ (2.4)

Jelas bahwa untuk mengangkat suatu benda dengan satu katrol bergerak, cukup

mengerjakan ½ gaya yang diperlukan untuk mengangkat benda tersebut jika tanpa

menggunakan bantuan katrol. Katrol bergerak (Gambar 1c) juga sering dipergunakan.

Gaya berat FB, di tahan oleh dua buah penggal tali, maka

FB = 2Fk

Keuntungan mekanis pada sistem katrol ini adalah perbandingan antara besar gaya beban

dan gaya kuasa.

Keuntungan Mekanik = FB / Fk = 2 ............................ (2.6)

Sehingga untuk mengangkat benda sistem katrol 4c cukup menggunakan ½ gaya

berat benda. Perbedaan antara sistem katrol ini dengan satu katrol bergerak adalah arah

tarik Fk. Gaya tarik pada sistem katrol ini mengarah ke bawah sehingga akan lebih

memudahkan pekerjaan, bila dibandingkan dengan penggunaan satu katrol bergerak saja

yang arah tariknya ke arah atas.

Seringkali berat beban yang kita pindahkan mencapai beberapa ton. Untuk

mengangkat nya kita gunakan katrol ganda/katrol majemuk (Gambar 1d).Katrol

majemuk merupakan gabungan dari beberapa katrol diam dan katrol bergerak.

Seperti tampak pada gambar 1d kita akan menarik tali dengan gaya Fk agar beban

berat FB dapat terangkat. Gaya berat FB besarnya sama dengan gaya – gaya bekerja pada

sejumlah penggal tali yang menahan berat beban .

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1. Tentukan berat dari beberapa beban yang digunakan dengan menggunakan

neraca pegas.

2. Gantungkan katrol tunggal ke peyangga (statif) (seperti Gambar 1.a)

3. Hubungkan seutas tali ke katrol dengan satu ujung tali diikatkan pada beban dan

ujung yang lainnya dipegang.

4. Tarik tali yang menghubungkan beban dan katrol tersebut hingga beban terangkat.

5. Catat berat beban sekarang.

6. Ulangi langkah 1 s/d 4 untuk katrol ganda. (seperti Gambar 1.c dan 1.d)

7. Lakukan juga untuk katrol digantungkan ke tali (seperti Gambar 1.b).

8. Lakukan dalam satu keadaan minimal 10 kali.


1. Sebutkan kegunaan katrol pada kehidupan kita.

2. Mengapa dalam mengangkat beban yang berat orang sering menggunakan katrol.

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37

2.6. TABEL HASIL PENGAMATAN

A. Massa Beban

Tabel 1. Tanpa Katrol Tabel 2. Katrol Tetap

No. Massa Beban (kg)


I II III I II III

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

Tabel 3. Katrol Bergerak Tabel 4. Katrol Ganda



I II III I II III

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

Tabel 5. Katrol Majemuk


I II III

1.

2.

3.

4.

5.


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B. Gaya

Tabel 1. Tanpa Katrol Tabel 2. Katrol Tetap

No. Gaya (N)

No. Gaya (N)

I II III I II III

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

Tabel 3. Katrol Bergerak Tabel 4. Katrol Ganda

No. Gaya (N)

No. Gaya (N)

I II III I II III

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

Tabel 5. Katrol Majemuk

No. Gaya (N)

I II III

1.

2.

3.

4.

5.


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2.8. ANALISA

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43

2.9. TUGAS AKHIR

1. Tentukan selisih berat beban setelah dengan sebelum menggunakan katrol dari

masing-masing beban.

2. Berapa persen selisih berat beban dengan menggunakan katrol tersebut.

3. Hitung Gaya yang kita berikan untuk menahan beban dengan menggunakan katrol

dari masing-masing percobaan secara teori.

4. Bandingkan hasil praktek dengan hasil perhitungan secara teori.

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2.10. KESIMPULAN

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46

LAMPIRAN GAMBAR


47

III. GERAK ROTASI


► Dapat memahami dan kecepatan sudut, percepatan sudut, momen gaya akibat

gesekan pada poros, dan momen inersia silinder.


1. Satu set alat gerak rotasi (bahan baja dan plexiglass: ukuran diameter 200 mm dan

berat 3 kg)

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2. Beban bercelah dan penggantung 250 gram

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3. Beban bercelah dan penggantung 5 x 5 gram

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4. Benang

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5. Stopwatch

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6. Meteran (alat ukur panjang)

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48

3.3. DASAR TEORI

Pendahuluan:

Alat gerak rotasi digunakan untuk mengamati gerak rotasi pada sumbu putar yang

tetap. Persamaan-persamaan gerak rotasi pada sumbu putar tetap banyak yang memiliki

kemiripan dengan persamaan gerak translasi (gerak lurus). Sebagai contoh, dalam gerak

translasi, gaya F dikaitkan dengan kecepatan linear benda. Analogi gaya untuk gerak

rotasi adalah besaran yang disebut dengan torka (momen gaya).

Alat gerak rotasi terdiri atas silinder baja pejal, silinder ringan plexiglass/hub,

poros baja dan klem pemegang (lihat Gambar 1). Poros baja didesain sedemikian rupa

sehingga gesekan pada sumbu putar dapat dibuat sekecil mungkin. Untuk memutar

cakram baja, seutas tali lemas dan ringan dililitkan keliling roda plexiglass ringan. Pada

tali ini digantung sebuah benda bermassa m.

Gambar 1. Peralatan percobaan Gerak Rotasi

Tinjauan Teori:

Analogi gerak Translasi dan gerak rotasi


49

Alat gerak rotasi digunakan untuk mengamati gerak rotasi pada sumbu putar yang

tetap. Persamaan-persamaan gerak rotasi pada sumbu putar tetap banyak yang memiliki

kemiripan dengan persamaan gerak translasi (gerak lurus). Sebagai contoh, dalam gerak

translasi, gaya F dikaitkan dengan kecepatan linier benda. Analogi gaya untuk gerak

rotasi adalah besaran yang disebut dengan torka ( momen gaya ).

Pada gerak translasi, benda akan bergerak dengan percepatan a jika padanya

diberikan gaya sebesar F, dan dengan menggunakan hukum Newton kedua tentang gerak

F = ma (1)

m adalah massa benda. Untuk gerak rotasi, benda akan bergerak dengan percepatan sudut

jika padanya diberikan momen gaya sebesar , dengan menggunakan analogi hukum

Newton kedua tentang gerak :

I

(2)

I adalah momen inersia benda. Momen inersia benda bergantung pada distribusi massa

dan bentuk benda. Sebagai contoh, momen inersia silinder pejal ITeori dengan jari-jari R

dan massa M berputar pada sumbunya adalah sebesar :

21

2TeoriI MR (3)

Kecepatan dan percepatan pada gerak translasi dan gerak rotasi

Ketika silinder pejal berjari-jari r yang terpasang pada sumbu putarnya dan beban

m digantung menggunakan tali melingkari cakram dan beban m berada pada ketinggian h

dari lantai, maka kecepatan translasi dan percepatan translasi benda sapat diperoleh

dengan mengukur waktu yang diperlukan beban untuk bergerak dari keadaan diam

sampai menyentuh lantai. Besar kecepatan rata-rata beban diberikan oleh :

hv

t

(4)

Menggunakan persamaan kinematika gerak benda untuk kecepatan rata-rata pada

kecepatan tetap :

2

ov vv

(5)

Besar kecepatan akhir v dengan kecepatan awal sama dengan nol ( vo = 0 ) diberikan oleh


50

2

vv atau

22

hv

t (6)

Dan kecepata rotasi

2v v

r r

(7)

Di mana r adalah jari-jari sumbu. Percepatan translasi a :

va

t

(8)

Masaa beban yang digantung memiliki percepatan linier sebesar a. Hubungan

antara percepatan translasi dan percepatan rotasi adalah :

a

r

(9)

Gambar 2. Sistem gerak benda

Momen Inersia Silinder Pejal

Dari Gambar (2) dan dengan menggunakan hukum kedua Newton tentang gerak

diperoleh :

F ma

(10)


51

mg – T = ma

atau

T = mg – ma (11)

Momen gaya T pada silinder yang disebabkan oleh tegangan tali T adalah :

T = rT (12)

r tegak lurus terhadap jarak sumbu rotasi ke garis kerja gaya (tegangan tali). Momen

gaya netto pada sistem gambar 2 adalah :

T g I

(13)

g adalah momen gaya akibat adanya gaya gesekan pada sumbu cakram yang arahnya

berlawanan dengan arah gerak rotasi cakram.

Persamaan (13) dapat disederhanakan menjadi :

T gI

(14)

Persamaan (14) memiliki analogi dengan persamaan garis lurus y = mx + c.

Dengan membuat kurva antara momen gaya dan percepatan rotasi benda, dapat dihitung

besar momen inersia benda I.

Percepatan sudut silinder akan ditentukan dengan cara mengukur terlebih dahulu

waktu tempuh beban tetentu dari ketinggian h ke lantai. Nilai ini akan dibandingkan

dengan nilai yang akan didapat dari hasil percobaan. Perpotongan kurva pada sumbu

vertikal (sumbu y) menunjukkan momen gaya akibat gesekan pada sumbu rotasi g .

Momen gaya akibat adanya gaya gesekan g pada poros silinder dapat juga

ditentukan dengan cara menggerakkan silinder pada kecepatan sudut tetap.

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53


III. RANGKAIAN PERALATAN

1. Set up peralatan seperti pada Gambar (1).

2. Pasang klem dudukan alat gerak rotasi pada ketinggian 150 cm dari lantai

laboratorium dengan paku dinding. Pastikan klem dudukan cakram terpasang

kokoh pada dinding tempat alat dipasang.

3. Pasang silinder baja pejal pada klem. Atur baut pengencang sedemikian rupa

sehingga cakram terpasang dengan kokoh pada klem.

Periksa putaran cakram pada porosnya, jika diperlukan, kendurkan baut

pengencang sehingga cakram berputar dengan bebas pada porosnya.

4. Potong benang 200 cm dan ikat benang pada lubang yang terdapat cakram

plexiglass.

5. Lilitkan benang pada disk plexiglass/hub sedemikian rupa sehingga benang

melilit merata pada sisi pinggir disk.

Usahakan benang tidak menumpuk pada satu alur lilitan.

6. Pasang penggantung beban pada ujung benang.

II. PELAKSANAAN PENGAMBILAN DATA

A. Menentukan momen gaya akibat adanya gaya gesekan pada sumbu putar

cakram g

1. Gantung pengait beban 5 gram pada ujung tali alat gerak rotasi.

2. Periksa putaran silinder sedemikian rupa sehingga silinder berputar dengan

kecepatan sudut tetap dengan cara melepaskan beban sehingga beban

bergerak ke bawah.

3. Jika dengan menggunakan beban 5 g masih tetap diam, tambahkan beban

yang tidak terlalu berat ke beban 5 g. Jika perlu gunakan beban yang cukup

ringan, misalkan penjepit kertas sebagai beban tambahan. Tambahkan

penjepit kertas sedemikian rupa sehingga diperoleh gerak rotasi cakram

dengan kecepatan sudut tetap. Misalkan massa beban itu adalah mo.

Catatan : jika silinder bergerak rotasi dengan kecepatan sudut tetap, maka

0 . Menggunakan persamaan (14) diperoleh )( 0 gmrrTTg .

4. Jika massa beban mo tidak diketahui, ukur berat beban menggunakan

timbangan dan catat hasil pengukuran pada hasil pengamatan di bawah.


54

B. Menentukan Kecepatan Sudut dan Percepatan Sudut

1. Ganti beban yang lebih berat dari beban yang digunakan pada percobaan

bagian pertama. Misalkan digunakan beban bermassa 50 gram

2. Gantung beban tersebut pada ujung tali dan atur posisi beban sedemikian rupa

sehingga ujung bawah beban berada pada ketinggian h cm di atas lantai. Ukur

ketinggian h tersebut menggunakan meteran dan catat hasil pengukuran pada

tabel hasil pengamatan. Tahan beban pada ketinggian tersebut.

3. Lepaskan beban dan segera hidupkan stopwatch setelah beban dilepaskan.

4. Matikan stopwatch ketika beban menyentuh lantai.

5. Baca waktu yang terukur pada stopwatch dan catat hasilnya pada Tabel hasil

pengamatan.

6. Ulangi langkah 5 sampai 9 di atas sebanyak 5 kali dan catat hasilnya pada

tabel hasil pengamatan.

7. Tambahkan beban 10 gram pada penggantung beban dan ulangi langkah 5

sampai 5 kali.


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1. Jelaskan apa yang dimaksud dengan Gerak Rotasi!

2. Jelaskan perbedaan gerak translasi dengan gerak rotasi!

3. Buktikan persamaan (7)!

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- Jari-jari cakram baja, R : 0,2 m

- Jari-jari cakram plexiglass, r : 2,5 cm = 0,025 m

- Massa total cakram M : 3 kg

Tabel . Hasil Pengamatan

No Jarak/Tinggi,

h (meter)

Massa Beban,

m (gram)

Waktu Tempuh

Beban, t (detik)

1. 50

2. 100

3. 150

4. 200

5. 250

Catatan:

1. Kecepatan Linier: h

vt

2. Percepatan Linier: v

at

3. Kecepatan sudut: v

t

4. Percepatan Sudut: a

t

5. Momen Inersi Benda: 21

2I MR 6. Momen Gaya: I


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3.8. ANALISA

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62

3.9. TUGAS AKHIR

Percobaan A:

2. Hitung momen gaya yang diakibatkan oleh gaya gesekan menggunakan

persamaan )( 0 gmrrTTg .

3. Bandingkan dengan hasil yang diperoleh pada percobaan (B).

4. Analisa hasil pengukuran dan perhitungan yang ada lakukan.

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Percobaan B:

1. Hitung waktu tempuh rata-rata untuk masing-masing berat beban dengan

persamaan 1 2 3 .... nt t t tt

n

2. Hitung kecepatan gerak translasi beban menggunakan persamaan (5).

3. Dari data jawaban soal nomor (2), hitung percepatan translasi menggunakan

persamaan (6).

4. Dari data jawaban soal nomor (3), hitung percepatan rotasi menggunakan

persamaan (8).

5. Hitung besar momen gaya untuk masing-masing beban menggunakan persamaan

rTt .

6. Buat grafik antara momen gaya dan percepatan rotasi pada kertas grafik.

Tentukan persamaan garis untuk kurva momen gaya vs percepatan rotasi.

7. Tentukan gradien grafik untuk mendapatkan momen inersia silinder, misalkan

nilai ini sebagai IPercobaan.

8. Tentukan juga perpotongan grafik pada sumbu y untuk mendapatkan nilai momen

gaya akibat adanya gaya gesekan g .

9. Hitung momen inersia silinder pejal menggunakan persamaan (3), misalkan nilai

ini sebagai ITeori.

10. Bandingkan nilai momen inersia silinder hasil percobaan IPercobaan (jawaban no.7)

dengan momen inersia silinder dari perhitungan teori ITeori (jawaban no.9).

11. Hitung persentase perbedaan kedua nilai momen inersia yang didapatkan

menggunakan persamaan :

%100

)(2

1x

II

II

PercobaanTeori

PercobaanTeori

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12. Analisa hasil pengukuran dan perhitungan yang ada lakukan.

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68

3.10. KESIMPULAN

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69

LAMPIRAN GAMBAR


70

IV. MOMEN INERSIA


1. Memahami konsep momen inersia pada beberapa bentuk benda

2. Dapat menentukan benda momen inersia pada beberapa bentuk benda


1. Alat momen inersia

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2. Bola pejal

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3. Silinder pejal

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4. Silinder berongga

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5. Disc 213

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6. Disc 174

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7. Kerucut pejal

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8. Venier caliper atau penggaris

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9. Timbangan

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10. Photo gate (sensor)

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11. Timer counter AT-01

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71

4.3. DASAR TEORI

Momen Inersia Benda

Suatu sistem yang terdiri dari tiga partikel yang masing-amsing mempunyai

massa 1m , 2m dan 3m , mengubah bentuk benda pejal seperti terlihat pada Gambar (1).

Gambar 1 . Sistem perubahan benda pejal pada tiga partikel

yang berputar dengan sumbu pada 0.

Jika 1m pada posisi 1r dan bergerak berotasi pada kecepatan sudut , memiliki

kecepatan linier 1 1v x r , disebut momentum sudut

1 1 1 1 1 1L r p m r v

1 1 1 1( )L m r r

atau

2

1 1 1L m r (1)

Dengan cara yang sama untuk 1m dan 2m

2

2 2 2L m r

2

3 3 3L m r

Total momentum sudut dapat ditulis sebagai berikut:

1 2 3L L L L

2 2 2

1 1 2 2 3 3( )L m r m r m r


72

L I (2)

dimana

2 2 2

1 1 2 2 3 3I m r m r m r

I dapat pula dituliskan sebagai berikut

32

1

i i

i

I m r

Persamaan (2) menyatakan hubungan antara L, I, dan ω. Hubungan ini seperti hubungan

antara momentum linear p, m, dan v pada gerak translasi, p = m v. Dimana disini I sama

dengan m pada gerak translasi dan ini disebut momen inersia.

Untuk sebuah sistem dengan N partikel mengubah benda pejal, ini adalah momen

inersia.

2

1

N

i i

i

I m r

Jika distribusi massa berlangsung terus menerus, maka elemen massa ∆mi yang berjaraj

ir dari porosnya, momen inersia dapat ditulis juga sebagai berikut:

2

1

N

i i

i

I r m

Jika ∆mi adalah sangat kecil, momen inersia ditulis:

2I r dm (3)

Dimana dm adalah bagian dari massa.

Dari persamaan di atas kita dapat membedakan macam-macam benda momen

inersia, seperti ditunjukkan pada Tabel (1) dibawah ini.


73

Tabel 1. Momen Inersia beberapa benda

No. Benda Posisi poros Momen inersia

1. Silinder pejal Poros silinder

2. Silinder pejal Pusat diameter

3. Silinder berongga Poros silinder

4. Bola pejal Diameter bola

5. Bola berongga Diamater bola

Jika sebuah benda diletakkan pada alat momen inersia dan kemudian bergetar, itu disebut

perioda getaran

2

2 4( )oT I I

(4)

dimana T adalah perioda getaran dan I adalah momen inersia benda ditempatkan pada

peralatan inersia.

Dari persamaan 2

24o oI T

dan persamaan (4), momen inersia benda, dapat

ditentukan dengan

2

21 o

o

TI I

T

(5)

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75


1. Susun peralatan seperti Gambar (2) berikut

Gambar 2. Set up peralatan percobaan

2. Ukur massa setiap benda.

3. Ukur dimensi setiap benda. Catat hasil pada Tabel (2).

4. Letakkan bola pejal pada sebuah alat momen inersia.

5. Hubungkan photo gate ke timer counter AT-01.

6. Hubungkan timer counter AT-01 pada tegangan 220V AC. Kemudian nyalakan.

Pilih fungsi cycle dengan menekan tombol FUNCTION. Tekan tombol CH.

OVER sebanyak 10 kali untuk batas 10 osilasi, yang akan ditinjau.

7. Putar posisi benda uji sampai 180o, dan kemudian lepaskan. Catat waktu dari 10

osilasi dilihat dari timer counter pada Tabel 3 untuk t1.

8. Tekan tombol FUNCTION satu kali untuk pengulangan.

9. Ulangi langkah 7 dan 8 sebanyak 10 kali. Catat hasilnya pada Tabel 3.

10. Gantilah bola pejal dengan benda yang tersedia pada Tabel 3. Ulangi langkah 7

sampai 9 untuk masing-masing benda.


76


1. Jelaskan apa yang anda ketahui tentang momen inersia?

2. Jelaskan penerapan momen inersia pada kehidupan sehari-hari?

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78


Tabel 2. Dimensi pada benda uji

No. Benda

Out-

diameter

(m)

In-diameter

(m)

Tinggi

(m)

Massa

(kg)

1. Bola pejal

2. Silinder pejal

3. Silinder berongga

4. Disc 213

5. Disc 174

6. Kerucut

Tabel 3. Perioda benda

Benda Waktu untuk 10 kali Osilasi, t (detik) trata-rata

(detik) 1 2 3 4 5 6 7 8 9 10

Bola Pejal

Silinder pejal

Silinder berongga

Disc 213

Disc 174

Kerucut padat


79


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82

4.8. ANALISA

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83

4.9. TUGAS AKHIR

1. Dari waktu rata-rata osilasi, hitunglah periodanya.

2. Hitunglah secara teori momen inersia dari masing-masing benda?

3. Hitung momen inersia dari setiap benda dengan persamaan (5)?

4. Analisa hasil jawaban dari soal no 1 dan 2?

5. Masukkan hasil perhitungan ke dalam Tabel (4) dan hitung kesalahan relatif

terhadap teori?

To = ......... s Io = ......... kgm2

Tabel 4. Momen Inersia beberapa benda hasil eksperimen dan

kesalahan terhadap teori

Benda ITeori

(kg m2)

T (s) I (kg m2)

Error

(%)

Bola Pejal

Silinder pejal

Silinder berongga

Disc 213

Disc 174

Kerucut padat

Catatan :

To dan Io dari sebelum melakukan percobaan

100%eksperimen Teori

Teori

I IError x

I

5. Pada percobaan di atas, massa dari benda yang di uji sama (tepat sama).

Bagaimana dengan momen inersianya, sama atau berbeda? Jelaskan! Mengapa!

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85

4.10. KESIMPULAN

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86

LAMPIRAN GAMBAR


87

V. PESAWAT ATWOOD


1. Dapat menyelidiki keberlakuan hukum-hukum Newton.

2. Dapat menghitung kecepatan dan percepatan suatu benda.

3. Dapat menghitung momen inersia sebuah katrol.


1. Type Atwood bertiang ganda.

Tinggi tiang: 150 cm.

Katrol: diameter 12 cm, bahan plexiglas.

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2. Tali penggantung : bahan nylon

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3. Dua beban berbentkuk silinder M1 dan M2 yang massanya sama M= 100 gram

diikatkan pada ujung-ujung tali penggantung. Bahan kuningan.

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4. Beban tambahan m dengan massa 20 gram . Bahan : alumunium

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5. Penahan beban berlubang dan tanpa lubang . bahan : steel.

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6. Pemegang beban dengan pegas.

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7. Timer counter AT-01

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8. Gerbang cahaya

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9. Jika peralatan No.8 dan 9 tidak tersedia dapat diganti dengan stopwatch (secara

manual).

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88

5.3. DASAR TEORI

Pendahuluan

Pesawat atwood terdiri dari dua buah massa M1 dan M2 yang digantungkan pada

ujung-ujung seutas tali yang dilewatkan melalui katrol atau sistem katrol. Tali sebagai

penghubung dan katrol cukup ringan dan massanya dapat di abaikan. Alat ini digunakan

untuk mempelajari gerak sebuah benda. Diantaranya menguji Hukum Newton dan

mengukur besar percepatan gravitasi g. Biasanya M1 di buat sama dengan M2, misalkan

M (lihat Gambat 1).

Gambar 1. Peralatan percobaan Pesawat Atwood

Pada pesawat ini dapat diamati dua jenis gerak, yaitu gerak linier dan gerak

rotasi. Gerak linier yang diamati adalah Gerak Lurus Beraturan (GLB) dan gerak lurus


89

berubah beraturan (GLBB). Gerak rotasi adalah gerak katro melalui porosnya. Untuk

gerak rotasi katrol, Momen inersia katrol perlu di perhitungkan. Akan tetapi dalam hal

massa benda-benda yang tergantung pada tali jauh lebih besar di bandingkan massa

katrol. Momen inersia katrol dapat di abaikan . Dalam hal yang demikian, persamaan

gerak sistem menjadi lebih sederhana.

Dalam hal momen inersia katrol tidak dapat diabaikan, momen inersia katrol

harus masuk ke dalam massa suatu sistem dalam bentuk “massa ekivalen” katrol. Bila r

jari-jari efektif katrol bisa massa ekivalen mk katrol sama dengan I/r2 sehingga pada

gerak sistem ini akan berlaku gerak yang ekivalen dengan persamaan gerak linier.

Hukum Newton II

Dengan mengabaikan massa tali dan momen inersia katrol dengan massa beban

M1 dan M2 dengan beban tambahan m , massa M1 bergerak naik dan M2 + m bergerak

turun. Dengan menggunakan Hukum Newton II, gerak pada beban M1 adalah :

1 1F T M g M a (1)

dan gerak pada beban M2 :

2 2( ) ( )F M m g T M m a (2)

Di mana gesekan dan momen inersia dari katrol di abaikan. Jika persamaan 1 dan

2 di umlahkan untuk mengeliminasi tegangan tali T, di dapatkan :

Gambar 2. Gaya-gaya yang bekerja pada M1 dan M2

2 1 1 2{( ) } ( )M m M g M M m a

atau :

M2

M1

W2

W1

T2

T1


90

1 2

2 1

( )

( )

M M m ag

M m M

(3)

Massa M1 sama dengan massa M2, Misalkan M, sehingga persamaan (3) dapat di

tuliskan sebagai:

(2 )M m ag

m

(4)

Karena percepatan gravitasi adalah tetap , maka a juga harus tetap . Presamaan s

= ½ a t 2 Memberikan dasar hubungan antara jarak tempuh s, percepatan a, dan waktu t.

Pada percobaan dengan membuat kurva antara s dan t dapat di gunakan untuk

menentukan besar percepatan gerak a, selanjutnya harga percepatan gravitasi dapat di

tentukan dengan menggunakan persamaan (4).

Jika massa katrol dan momen inersia I di perhitungkan dalam percobaan, maka

dalam menentukan harga g, persamaan (4) menjadi:

2(2 )I

RM m

gm

(5)

Dalam gerak translasi murni, sifat benda tegar mempertahankan keadaan

geraknya disebut sebagai sifat kelembaman atau inersial. Sifat kelembaman atau inersial

itu dinyatakan oleh massa kelembaman atau massa inersial yang biasa disebut secara

singkat sebagai massa. Dalam gerak rotasi murni, peran massa kelembaman benda tegar

digantikan oleh momen kelembaman benda tegar atau momen inersia benda tegar.

Momen inersia benda tegar adalah sifat benda tegar mempertahankan keadaan geraknya

atau berarti sama dengan kemalasan benda tegar untuk mengubah keadaan geraknya.

Momen inersia sebuah benda tegar bergantung kepada bentuk geometris, distribusi massa

dan letak sumbu rotasinya. Dalam kegiatan belajar ini anda dapat mempelajari momen

inersia dari sebuah katrol. Momen inersia sebuah katrol merupakan ukuran kelembaman

sebuah katrol untuk berotasi atau berubah keadaan gerak rotasinya bila ada resultan

momen gaya yang bekerja padanya. Momen inersia katrol ini dapat ditentukan pertama

dengan menggunakan pendekatan konsep dan matematis melalui penjabaran dengan

menggunakan teknik differensial dan integral, dan kedua adalah dengan pendekatan

empiris melalui percobaan. Dalam modul ini, momen inersia sebuah katrol akan

ditentukan dengan menggunakan pendekatan empiris melalui percobaan. Untuk itu dalam


91

kegiatan belajar 1 ini anda dapat mempelajari penerapan konsep kecepatan, percepatan

dan hukum-hukum Newton pada sebuah sistem katrol yang kemudian disebut sebagai

pesawat Atwood. Dalam kinematika translasi telah diketahui bahwa percepatan adalah

perubahan kecepatan.

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93


1. Susun peralatan seperti Gambar (1)

2. Pastikan bahwa pesawat Atwood telah benar-benar siap untuk digunakan dengan

cara :

a. Memeriksa dan mengusahakan agar posisi tiang vertikal berskala benar-benar

vertikal. (bila-benar-benar tegak atau vertikal, ia pasti sejajar dengan tali

penggantung beban).

b. Memeriksa dan mengusahakan agar katrol dapat bebas berotasi pada sumbunya.

3. Timbang dan catat massa silinder M1, M2, dan beban tambahan m.

4. Ukur dengan jangka sorong jari-jari katrol dan tinggi silinder yang digunakan.

5. Gantungkan M1 pada salah satu ujung tali dan M2 pada ujung lainnya, pasangkan tali

pada katrol dengan posisi M1 di atas klem pemegang, berikan beban tambahan m di

atas M2.

6. Pasang dan tahan M1 pada klem pemegang, atur tinggi posisi klem pemegang agar

posisi beban tambahan m tepat di titik nol skala vertikal dan tandai itu sebagai titik

A.

7. Pasang klem pembatas berlubang sedemikian rupa agar posisi jatuhnya beban M2

nanti benar-benar di tengah-tengah lubangnya. Tandai posisi klem pembatas

berlubang sebagai titik B.

8. Pasangkan klem pembatas tak berlubang di titik C sedemikian rupa sehingga BC <

AB.

9. Lepaskan M1 dari klem pemegang agar M2 bergerak turun melewati klem pembatas

berlubang dan beban tambahan m tertinggal di sana. Catat waktu (tAB) yang

dibutuhkan (M2 + m) untuk menempuh jarak AB dan waktu (tBC) yang dibutuhkan

M2 untuk menempuh jarak BC.

10. Lakukan perulangan sebanyak 5 kali.

11. Ulangi langkah 9 dan 10 dengan menambahkan beban tambahan m.


94


1. Apa yang kamu ketahui tentang hukum Newton pada percobaan pesawat Atwood?

(Jelaskan)

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96


- Massa, M1 = ........... gram

- Massa, M2 = ........... gram

Tabel 1. Hasil Pengamatan dengan variasi beban tambahan m.

No. Massa tambahan

m (gram)

Jarak AB

(cm)

Jarak BC

(cm)

Waktu

tAB (detik)

(1)

Waktu

tBC (detik)

(2-1)

Waktu

tAC (detik)

(2)

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5


97


Massa tambahan = .......... gram

Jarak AB = .......... cm

No. tAB t t

1.

2.

3.

4.

5.

ABt =

n

t AB

t = t t

n

NilaiTerbaik = AB

t t

Kesalahan Mutlak = t

Kesalahan Relatif = 100%AB

tx

t

Jarak BC = .......... cm

No. tBC t t

1.

2.

3.

4.

5.

BCt =

n

tBC

t = t t

n

NilaiTerbaik = BC

t t


Kesalahan Relatif = 100%BC

tx

t

dimana:

AC

AC

tt

n

S AB BC

AC

AC

Sv

t

ACAC

AC

va

t


98

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101

5.8. ANALISA

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102

5.9. TUGAS AKHIR

1. Berdasarkan data percobaan yang anda peroleh buatlah jarak sebagai fungsi kelajuan

untuk M2 ketika :

a. masih ada beban tambahan di atasnya !

b. sudah tidak ada beban tambahan di atasnya !

2. Bagaimanakah gerak M2 menurut grafik itu ?

3. Bagaimanakah keberlakuan hukum Newton pada M2 itu ? Sebutkan hukum Newton

yang mana !

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104

5.10. KESIMPULAN

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105

LAMPIRAN GAMBAR


106

VI. BANDUL GABUNGAN


1. Memahami teori bandul gabungan secara lebih mendalam.

2. Menentukan harga percepatan gravitasi pada suatu tempat dengan cara bandul fisis.


1. Tripod.

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2. Batang logam dengan beberapa lobang

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3. Sekrup penyangga yang bersisi tajam beserta bautnya.

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4. Mistar ukur.

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5. Busur derajat.

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6. Stop Watch.

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107

6.3. DASAR TEORI

Skema gambar alat percobaan bandul gabungan seperti Gambar (1) berikut:

Gambar 1. Skema bandul gabungan

Skema diatas menggambarkan suatu benda tegar yang tergantung pada sumbu

horizontal melalui titik 0. Persamaan gerak dengan kecil untuk benda tersebut adalah :

Ihgm

dimana :

I = momen inersia benda untuk sumbu melalui titik 0

h = jarak 0G

yang dinyatakan melalui persamaan diatas merupakan gerak harmonik dengan perioda :

hgm

IT 2

menggunakan teorema dengan sumbu sejajar maka :

g

h

kh

T

2

2

dimana :

h

k 2

= jarak dan k dinamakan jari-jari gyrasi untuk titik pusat massa G.

h G

0


108

Untuk bandul sederhana berlaku 2l

Tg

sehingga h

kh

2

dapat dianggap

sebagai panjang bandul ekuivalen sederhana. Panjang h dapat diketahui dengan grafik T

terhadap d, yaitu jarak pusat gantungan pada ujung benda.

Jarak T tertentu, panjang l adalah sama dengan jarak antara titik potong pertama

dan atau titik potong kedua dan keempat. Sedangkan percepatan gravitasi dapat diketahui

dengan rumus :

2

2

4 lG

T

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110


1. Letakkan dengan bantuan waterpas dan atur tripod hingga atas horizontal.

2. Masukkan sekrup penyangga kelubang pertama pada batang logam dan

kencangkan dengan baut.

3. Letakkan dan gantungkan batang logam yang akan disekrup pada tripod dengan

sisi tajam pada sekrup penyangga yang menempel pada tripod.

4. Berikan simpangan awal 5o dan biarkan batang g berayun.

5. Catat waktu yang diperlukan oleh batang dalam melakukan ayunan berapa kali

(tergantung instruksi). Lakukan sampai beberapa kali pengamatan untuk satu

keadaan.

6. Ukur dengan mistar jarak lubang yang diberi sekrup terhadap ujung batang.

7. Ulangi butir (4) hingga (6), untuk lubang berikutnya. Lakukan untuk semua

lubang.

8. Ulangi butir (4) hingga (7), untuk besar simpangan awal 15o.


1. Apa manfaat mempelajari teori bandul gabungan?

2. Bagaimana menentukan harga percepatan gravitasi pada suatu tempat dengan cara

bandul fisis?

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112


Sudut, = 5o Sudut, = 15

o

Lubang

ke-

Jarak,

l (cm)

Waktu, t (detik)

Lubang

ke-

Jarak

l (cm)

Waktu (detik)

1 2 3 4 5 1 2 3 4 5

1 5 1 5

2 10 2 10

3 15 3 15

4 20 4 20

5 25 5 25

6 30 6 30

7 35 7 35

8 40 8 40

9 45 9 45

10 50 10 50

11 55 11 55

12 60 12 60

13 65 13 65

14 70 14 70

15 75 15 75

16 80 16 80

17 85 17 85

18 90 18 90

19 95 19 95


113


Sudut = 5o

Lubang ke-n dan ke-n

No. Waktu, t (detik) t t

1

2

3

4

5

t = t

n

t = t t

n

NilaiTerbaik = t t


Kesalahan Relatif = 100%t

xt

Sudut = 15o

Lubang ke-n dan ke-n

No. Waktu, t (detik) t t

1

2

3

4

5

t = t

n

t = t t

n

NilaiTerbaik = t t

Kesalahan Mutlak = t Kesalahan Relatif = 100%

tx

t


114

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117

6.8. ANALISA

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118

6.9. TUGAS AKHIR

1. Sebutkan minimal 5 contoh bandul gabungan !

2. Buatlah Grafik jarak terhadap waktu berdasarkan untuk sudut 50

dan 15 0

nilai

pengolahan data yang didapat.

3. Buktikan persamaan berikut :

g

lT 2

4. Buat grafik T (perioda) terhadap l (jarak), tentukan 2T

l untuk minimal 8

(delapan) T yang berbeda lalu hitunglah nilai g nya. Beri penjelasan anda

mengenai pengaruh besar sudut terhadap perhitungan g.

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LAMPIRAN GAMBAR


122

VII. VISKOSITAS ZAT CAIR


1. Memahami penerapan Hukum Stokes.

2. Menentukan harga viskositas zat cair, dengan cara Stokes.


1. Gelas ukur yang berisi zat cair

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2. Peluru-peluru kecil

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3. Stopwatch

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4. Mistar

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5. Jangka sorong

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6. Mikrometer skrup

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7. Pinset

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8. Kain lap/tissue

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9. Sendok saringan atau Magnet

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10. Neraca torsi/neraca analitis

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11. Gelas ukur

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7.3. DASAR TEORI

Fluida dapat didefinisikan sebagai zat yang dapat mengalir, yang berubah bentuk

secara terus menerus bila terkena tegangan geser walau sangat kecil. Cairan dan gas

adalah wujud fisik zat yang mudah berubah sesuai dengan wadahnya dan juga dapat

mengalir dari tempat yang bertekanan tinggi ke tempat yang bertekanan lebih rendah,

jadi cairan dan gas adalah fluida.

Pada fluida statik tekanannya hanya akan dipengaruhi oleh rapat massa dan

posisinya. Untuk fluida yang bergerak kekentalan atau viskositas merupakan faktor yang

penting, karena viskositas berpengaruh pada sifat alirnya.

Viskositas

Viskositas atau kekentalan dapat dianggap sebagai gesekan dibagian dalam suatu

fluida. Karena adanya viskositas maka untuk menggerakkan satu bagian terhadap

bagian lain dalam fluida haruslah dilakukan gaya pada permukaan lapisan-lapisan fluida.

Gambar.1 memperlihatkan sebagian lapisan fluida cair (cairan) pada dinding atas

yang bergerak dengan dinding bawah yang diam

Gambar 1. Lapisan fluida kental antar dua dinding

Cairan yang bersentuhan dengan dinding atas yang bergerak ternyata mempunyai

kecepatan yang sama dengan kecepatan gerak dinding, sedang cairan disebelah dinding

yang tak bergerak adalah diam. Atau dengan kata lain kecepatan lapisan-lapisan cairan

semakin cepat bila semakin dekat dengan dinding yang bergerak (sehingga timbul

gradien kecepatan), seperti ditunjukkan oleh anak-anak panah. Lapisan-lapisan cairan

tersebut saling meluncuri, bagian cairan yang suatu ketika berbentuk abcd pada saat yang

lain menjadi abc’d’.

Hukum Stokes

Bila sebuah bola bergerak di dalam suatu fluida statik tak viskos, maka garis-

garis arusnya akan membentuk suatu pola simetris sempurna disekeliling bola itu. Sesuai

l

F

F v

a b

d c d’ c’


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dengan prinsip Pascal maka tekanan terhadap sembarang titik pada permukaan bola yang

menghadap arah aliran datang tepat sama dengan tekanan terhadap titik berlawanan pada

permukaan bola tersebut, dan gaya resultan terhadap bola itu nol. Tetapi bila fluida itu

viskos maka akan ada seretan kekentalan atau hambatan terhadap bola, yang dirumuskan

sebagai:

2

v ρA CF

2

DD …………………………………. (1)

dengan CD adalah koefisien hambat, A adalah luas bola dan v adalah kecepatan relatif

bola terhadap fluida.

Dalam hal aliran fluida viskos disekitar bola yang mempunyai bilangan Reynold

lebih kecil dari satu telah dirumuskan oleh Stokes. Stokes mengambil nilai CD = 24/Re.

Jika CD = 24/Re disubstitusikan ke persamaan 1, dan mengganti Re dengan vd/η, serta

A dengan d2/4, maka diperoleh:

FD = 3 η d v = 6 η r v …………………………… (2)

Persamaan 2 dikenal sebagai hukum Stokes, yang dikemukanan oleh Sir George Stokes

pada tahun 1845.

Kecepatan Terminal

Sebuah bola yang jatuh melalui suatu fluida yang viskos (lihat Gambar 2) akan

mengalami gaya berat Fg, gaya apung Fa dan gaya seretan Fs. Jika hukum Stokes berlaku

maka gaya seretan akan sama degan persamaan 2 (FD = Fs).

Gambar 2 Gaya-gaya yang bekerja pada sebuah bola

yang jatuh dalam suatu fluida viskos

Menurut hukum kedua Newton bila bola ini bergerak dari keadaan diam dan arah

z positip adalah arah ke bawah, maka:

Fz = Fg – Fa – Fs = m a ………………………….. (3)

Pada awal gerak, disaat v = 0, gaya Stokes adalah nol dan percepatan awal ao adalah :

m

FFa

ag

o

……………………………………. (4)

Fg

Fa Fs

v


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Setelah beberapa lama, apabila v menjadi cukup besar, maka gaya Stokes sama dengan

gaya berat dikurangi gaya apung dan tidak ada gaya resultan yang bekerja pada bola.

Pada saat ini percepatan bola sama dengan nol dan lajunya konstan. Karena itu laju

maksimum atau laju akhir (terminal velocity) vT dapat dihitung dengan membuat a = 0,

sehingga persamaan 3 dapat ditulis menjadi:

Fg – Fa – k vT = 0

atau:

)/kF(Fv agT …………………………………… (5)

dengan k = 6 η r.

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1. Ukurlah jarak S antara dua karet gelang (tanda) yang terdapat pada tabung yang

berisi zat cair.

2. Ukurlah diameter peluru yang digunakan (lakukan pengukuran 10 kali untuk masing-

masing peluru).

3. Timbanglah berat peluru yang digunakan.

4. Tentukan massa jenis zat cair yang digunakan.

5. Dengan menggunakan pinset, jatuhkan peluru tepat pada permukaan atas zat cair, dan

waktu untuk menempuh jarak S dicatat dan diukur dengan menggunakan stopwatch.

6. Dengan menggunakan magnet, ambil peluru pada dasar tabung, kemudian tunggu

sampai tidak ada lagi gelembung-gelembung udara di dalamnya.

7. Ulangi langkah 5 dan 6 sebanyak 10 kali.

8. Kemudian ulangi langkah 5, 6, dan 7 untuk peluru yang lain.

9. Selanjutnya lakukan percobaan untuk zat cair yang lain.


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1. Apakah satuan viskositas dalam SI dan dalam CGS.?

2. Pada saat dilepaskan dalam zat cair dengan kecepatan awal nol, gaya apa saja yang

dialami peluru (tuliskan juga persamaannya).

3. Turunkan persamaan viskositas zat cair adalah : )(9

2 2

ov

gr

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No.

Jarak AB Diameter bola Waktu (t)

Oli, SAE 40

Waktu (t)

Minyak Sayur

Oli,

SAE

40

M.

Sayur I II III I II III I II III

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.


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7.8. ANALISA

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7.9. TUGAS AKHIR

1. Larutan yang digunakan dalam percobaan ini kental, untuk mencari kecepatan peluru,

apakah bisa dipakai rumus benda jatuh bebas?, Berikan alasannya!

2. Hitunglah masing-masing kecepatan peluru (v) dan massa jenis dari hasil percobaan

yang telah dilakukan dan sertakan simpangan (kesalahannya) !.

3. Dengan menggunakan rumusan seperti soal No.3 pada tugas pendahuluan dan

menganggap percepatan gravitasi (g = 10 m/det2) maka hitunglah viskositas zat cair

() yang digunakan dalam percobaan ini dimana (o = air = 103 kg/cm

3).

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LAMPIRAN GAMBAR

4. modul praktikum fisika dasar i

Education

Transcript of 4. modul praktikum fisika dasar i