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Sebuah benda bermassa m = 2 kg digantung seperti tampak pada gambar. Sistem dalam keadaan seimbang statik. Berapa besar tegangan tali T 1 ​ , T 2 ​ dan T 3 ​ ?

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

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F. Afrianto

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

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Pembahasan

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Diketahui : m = 2 kg Pembahasan : Mencari sudut A, B, dan C Jadi, tegangan tali pada sistem sebesar

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 

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