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Sebuah benda bermassa m = 2 kg digantung seperti tampak pada gambar. Sistem dalam keadaan seimbang statik. Berapa besar tegangan tali ,  dan  ?

Pertanyaan

Sebuah benda bermassa m = 2 kg digantung seperti tampak pada gambar. Sistem dalam keadaan seimbang statik. Berapa besar tegangan tali begin mathsize 14px style T subscript 1 end stylebegin mathsize 14px style T subscript 2 end style dan begin mathsize 14px style T subscript 3 end style ?

Pembahasan Video:

Pembahasan Soal:

Diketahui :

m = 2 kg

 

Pembahasan :

Mencari sudut A, B, dan C

begin mathsize 14px style theta subscript A equals 45 degree plus 90 degree equals 135 degree theta subscript B equals 60 degree plus 90 degree equals 150 degree theta subscript C equals 180 degree minus sign 45 degree minus sign 60 degree equals 75 degree end style 

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin 75 degree end cell equals cell sin left parenthesis 30 degree plus 45 degree right parenthesis end cell row blank equals cell sin 30 degree cos 45 degree plus sin 45 degree cos 30 degree end cell row blank equals cell begin inline style bevelled 1 fourth end style left parenthesis square root of 2 plus square root of 6 right parenthesis end cell end table end style 

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sum F subscript italic y end cell equals cell 0 space space left parenthesis sistem space pada space beban right parenthesis end cell row cell W bond T subscript 1 end cell equals 0 row cell T subscript 1 end cell equals W row cell T subscript 1 end cell equals mg row cell T subscript 1 end cell equals cell left parenthesis 2 right parenthesis left parenthesis 10 right parenthesis end cell row cell T subscript 1 end cell equals cell 20 space N end cell end table end style 

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell T subscript 1 over sinC end cell equals cell T subscript 2 over sinB end cell row cell fraction numerator 20 over denominator sin 75 degree end fraction end cell equals cell fraction numerator T subscript 2 over denominator sin 150 degree end fraction end cell row cell fraction numerator 20 over denominator bevelled 1 fourth left parenthesis square root of 2 plus square root of 6 right parenthesis end root end fraction end cell equals cell fraction numerator T subscript 2 over denominator bevelled 1 half end fraction end cell row cell T subscript 2 end cell equals cell fraction numerator 40 over denominator square root of 2 plus square root of 6 end fraction end cell row cell T subscript 2 end cell equals cell 10 left parenthesis square root of 6 minus sign square root of 2 right parenthesis space N end cell end table end style  

 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight T subscript 3 over sinA end cell equals cell straight T subscript 2 over sinB end cell row cell fraction numerator straight T subscript 3 over denominator sin 135 degree end fraction end cell equals cell fraction numerator straight T subscript 2 over denominator sin 150 degree end fraction space end cell row cell fraction numerator straight T subscript 3 over denominator bevelled 1 half square root of 2 end fraction end cell equals cell fraction numerator 10 left parenthesis square root of 6 minus square root of 2 right parenthesis over denominator bevelled 1 half end fraction end cell row cell straight T subscript 3 end cell equals cell 20 left parenthesis square root of 3 minus 1 right parenthesis space straight N end cell end table    

Jadi, tegangan tali pada sistem sebesar

table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight T end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank subscript 1 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 20 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight N end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight T end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank subscript 2 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 10 left parenthesis square root of 6 minus square root of 2 right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight N end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell T subscript 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 20 left parenthesis square root of 3 minus 1 right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight N end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

F. Afrianto

Mahasiswa/Alumni Institut Teknologi Bandung

Terakhir diupdate 18 September 2021

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Pertanyaan yang serupa

Perhatikan gambar di bawah ini! Suatu sistem kesetimbangan yang terdiri atas 3 buah beban ,  dan  dipasang pada dua katrol tetap. Bila sistem dalam keadaan setimbang, maka perbandingan  dengan  a...

Pembahasan Soal:

Diketahui :

begin mathsize 14px style theta subscript 1 equals 60 degree theta subscript 2 equals 30 degree end style 

Pembahasan :

Menggunakan aturan sinus

Maka sudut seberang kedua tegangan tali :

begin mathsize 14px style theta subscript 1 equals 90 degree plus 30 degree equals 120 degree theta subscript 2 equals 90 degree plus 60 degree equals 150 degree end style 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight T subscript 1 over denominator sin space 120 degree end fraction end cell equals cell fraction numerator straight T subscript 2 over denominator sin space 150 degree end fraction end cell row cell fraction numerator straight T subscript 1 over denominator bevelled 1 half square root of 3 end fraction end cell equals cell fraction numerator straight T subscript 2 over denominator bevelled 1 half end fraction end cell row cell straight T subscript 2 over straight T subscript 1 end cell equals cell fraction numerator bevelled 1 half over denominator bevelled 1 half square root of 3 end fraction end cell row cell straight T subscript 2 over straight T subscript 1 end cell equals cell fraction numerator 1 over denominator square root of 3 end fraction end cell end table  

Jadi, jawaban yang tepat adalah A

Roboguru

Tentukan besar masing-masing tegangan tali pada gambar berikut!

Pembahasan Soal:

Gunakan kesetimbangan tiga gaya dan pastikan jawaban Anda benar!undefined 

Diket: begin mathsize 14px style m subscript 3 end style = 10 kg; g = 10 begin mathsize 14px style bevelled straight m over straight s squared end stylebegin mathsize 14px style T subscript 3 equals W subscript 3 end style

Ditanya: begin mathsize 14px style T subscript 1 comma space T subscript 2 comma space T subscript 3 end style = ...?

Mencari T3

begin mathsize 14px style T subscript 3 equals W subscript 3 T subscript 3 equals 10 left parenthesis 10 right parenthesis equals 100 space straight N end style 

Mencari T1

begin mathsize 14px style fraction numerator T subscript 3 over denominator sin space 120 degree end fraction equals fraction numerator T subscript 1 over denominator sin space 150 degree end fraction fraction numerator 100 over denominator 0 comma 5 square root of 3 end fraction equals fraction numerator T subscript 1 over denominator 0 comma 5 end fraction T subscript 1 equals fraction numerator 100 square root of 3 over denominator 3 end fraction space straight N end style 

Mencari T2

begin mathsize 14px style fraction numerator T subscript 3 over denominator sin space 120 degree end fraction equals fraction numerator T subscript 2 over denominator sin space 90 degree end fraction fraction numerator 100 over denominator 0 comma 5 square root of 3 end fraction equals T subscript 2 over 1 T subscript 2 equals fraction numerator 200 square root of 3 over denominator 3 end fraction space straight N end style 

Jadi, besar T1, T2, T3 masing-masing adalah begin mathsize 14px style fraction numerator 100 square root of 3 over denominator 3 end fraction space straight N comma space fraction numerator 200 square root of 3 over denominator 3 end fraction space straight N comma space d a n space 100 space straight N end style.undefined

Roboguru

Perhatikan gambar dibawah. Sistem dalam keadaan seimbang. Jika  = 60°,  = 60°,  = 10 kg, and g = 10 , tentukan  and .

Pembahasan Soal:

Sistem dalam keadaan seimbang begin mathsize 14px style begin inline style sum for f subscript x of end style end style = 0 dan begin mathsize 14px style begin inline style sum for f subscript y of end style end style = 0. O;undefined 

Diket: begin mathsize 14px style alpha equals 60 degree end stylebegin mathsize 14px style beta equals 60 degree end styleundefined = 10 kg; g = 10 undefined.

Ditanya: begin mathsize 14px style m subscript 1 space dan space m subscript 2 end style = ...?

begin mathsize 14px style T subscript 3 equals W subscript 3 T subscript 3 equals m subscript 3 times g T subscript 3 equals 10 times 10 equals 100 space straight N end style 

Mencari m1

begin mathsize 14px style fraction numerator T subscript 1 over denominator sin space left parenthesis 90 degree plus beta right parenthesis end fraction equals fraction numerator T subscript 3 over denominator sin space left parenthesis 90 degree plus alpha right parenthesis end fraction fraction numerator T subscript 1 over denominator cos space beta end fraction equals fraction numerator T subscript 3 over denominator cos space alpha end fraction fraction numerator T subscript 1 over denominator cos space 60 degree end fraction equals fraction numerator T subscript 3 over denominator cos space 60 degree end fraction T subscript 1 equals T subscript 3 T subscript 1 equals 100 space straight N m subscript 1 times left parenthesis 10 right parenthesis equals 100 m subscript 1 equals 10 space kg end style 

Mencari m2

begin mathsize 14px style fraction numerator T subscript 2 over denominator sin space left parenthesis 180 degree minus left parenthesis alpha plus beta right parenthesis right parenthesis end fraction equals fraction numerator T subscript 3 over denominator sin space left parenthesis 90 degree plus alpha right parenthesis end fraction fraction numerator T subscript 2 over denominator sin space left parenthesis alpha plus beta right parenthesis end fraction equals fraction numerator T subscript 3 over denominator cos space alpha end fraction fraction numerator T subscript 2 over denominator sin space 120 degree end fraction equals fraction numerator T subscript 3 over denominator cos space 60 degree end fraction T subscript 2 equals T subscript 3 times square root of 3 T subscript 2 equals 100 square root of 3 space straight N m subscript 2 times left parenthesis 10 right parenthesis equals 100 square root of 3 m subscript 2 equals 10 square root of 3 space kg end style 

Jadi, m1 dan m2 masing-masing adalah begin mathsize 14px style 10 space kg space dan space 10 square root of 3 space kg end style.undefined 

 

Roboguru

Sebuah benda digantung seperti gambar di samping. Hitunglah besar tegangan tali T1 dan T2 jika percepatan gravitasi bumi 9,8 m/s2!

Pembahasan Soal:

Diketahui:

m = 5 kg 

g = 9,8 m/s2

θ1 = 30o

θ2 = 60o

Ditanya: T1 dan T2 = ?

Pembahasan:

Untuk menyelesaikan soal ini dapat digunakan aturan sinus. Adapun gaya-gaya yang bekerja adalah sebagai berikut:

  

Sehingga untuk menentukan T1 dapat digunakan persamaan:

fraction numerator w over denominator sin 90 degree end fraction equals fraction numerator T subscript 1 over denominator sin left parenthesis 90 degree plus theta subscript 1 right parenthesis end fraction fraction numerator m g over denominator sin 90 degree end fraction equals fraction numerator T subscript 1 over denominator sin 120 degree end fraction fraction numerator 5 times 9 comma 8 over denominator 1 end fraction equals fraction numerator T subscript 1 over denominator begin display style bevelled 1 half end style square root of 3 end fraction 49 over 1 equals fraction numerator T subscript 1 over denominator begin display style bevelled 1 half square root of 3 end style end fraction T subscript 1 equals 24 comma 5 square root of 3 space straight N 

Sementara itu untuk menghitung T2 dapat digunakan persamaan:

fraction numerator w over denominator sin 90 degree end fraction equals fraction numerator T subscript 2 over denominator sin left parenthesis 90 degree plus theta subscript 2 right parenthesis end fraction fraction numerator m g over denominator sin 90 degree end fraction equals fraction numerator T subscript 2 over denominator sin 150 degree end fraction fraction numerator 5 times 9 comma 8 over denominator 1 end fraction equals fraction numerator T subscript 2 over denominator begin display style bevelled 1 half end style end fraction 49 over 1 equals fraction numerator T subscript 2 over denominator begin display style bevelled 1 half end style end fraction T subscript 2 equals 24 comma 5 space straight N 

Jadi, gaya tegangan tali pada T1 adalah 24,5√3 N dan gaya tegangan tali pada T2 adalah 24,5 N.

Roboguru

Perhatikan gambar berikut! Tentukan tegangan tali untuk tiap kasus pada gambar di atas. Sistem berada dalam keadaan setimbang.

Pembahasan Soal:

Untuk mengerjakan soal ini, kita bisa menggunakan aturan sinus dari keseimbangan partikel. Aturan ini menyatakan bahwa perbandingan antara gaya dengan nilai sinus sudut di hadapannya selalu tetap.

K i t a space m i s a l k a n space T subscript 1 space t a l i space y a n g space m e n g a r a h space k i r i comma space d a n space T subscript 2 space t a l i space y a n g space m e n g a r a h space k a n a n space a t a s fraction numerator T subscript 1 over denominator s i n open parentheses 150 degree close parentheses end fraction equals fraction numerator T subscript 2 over denominator s i n open parentheses 90 degree close parentheses end fraction equals fraction numerator W over denominator s i n open parentheses 120 degree close parentheses end fraction  Untuk space menghitung space tegangan space 1 fraction numerator T subscript 1 over denominator s i n open parentheses 150 degree close parentheses end fraction equals fraction numerator W over denominator s i n open parentheses 120 degree close parentheses end fraction fraction numerator T subscript 1 over denominator s i n open parentheses 150 degree close parentheses end fraction equals fraction numerator 6 over denominator s i n open parentheses 120 degree close parentheses end fraction fraction numerator T subscript 1 over denominator begin display style 1 half end style end fraction equals fraction numerator 6 over denominator begin display style 1 half end style square root of 3 end fraction T subscript 1 equals fraction numerator 6 over denominator square root of 3 end fraction equals bold 2 square root of bold 3 bold space bold N  Untuk space menghitung space tegangan space 2 fraction numerator T subscript 2 over denominator s i n open parentheses 90 degree close parentheses end fraction equals fraction numerator W over denominator s i n open parentheses 120 degree close parentheses end fraction T subscript 2 over 1 equals fraction numerator 6 over denominator begin display style 1 half end style square root of 3 end fraction T subscript 2 equals fraction numerator 12 over denominator square root of 3 end fraction equals bold 4 square root of bold 3 bold space bold N

Jadi, besar tegangan 1 adalah bold 2 square root of bold 3 bold space bold N dan besar tegangan 2 adalah bold 4 square root of bold 3 bold space bold N

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