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Hitung besar resultan vektor gaya pada gambar berikut.

Pertanyaan

Hitung besar resultan vektor gaya pada gambar berikut. 

 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

didapatkan besar resultan gaya ketiga vektor adalah bold 10 square root of bold 3 bold space bold N.

Pembahasan

Diketahui :

table attributes columnalign right center left columnspacing 0px end attributes row cell F subscript 1 space end cell equals cell space F subscript 2 space equals space 10 space straight N end cell row cell F subscript 3 space end cell equals cell space 20 square root of 3 space straight N end cell end table    

Ditanyakan : Besar resultan gaya ketiga vektor?

Jawab :

Metode analitis disebut juga metode penguraian yaitu cara menjumlahkan vektor dengan memproyeksikan vektor-vektor pada sumbu X dan sumbu Y diagram cartesian.

Berdasarkan gambar soal,

 

Proyeksikan terlebih dahulu vektor pada sumbu X dan sumbu Y, sebagai berikut :

table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow cell space F subscript 1 x end subscript space equals space F subscript 1 space cos space 60 degree end cell row blank equals cell space open parentheses 10 space straight N close parentheses space open parentheses 1 half close parentheses end cell row blank equals cell space 5 space straight N end cell row blank rightwards arrow cell space F subscript 1 y end subscript space equals space F subscript 1 space sin space 60 degree end cell row blank equals cell space open parentheses 10 space straight N close parentheses space open parentheses 1 half square root of 3 close parentheses end cell row blank equals cell space 5 square root of 3 space straight N end cell row blank blank blank row blank rightwards arrow cell space F subscript 2 x end subscript space equals space F subscript 2 space cos space 60 degree end cell row blank equals cell space open parentheses 10 space straight N close parentheses space open parentheses 1 half close parentheses end cell row blank equals cell space 5 space straight N end cell row blank rightwards arrow cell space F subscript 2 y end subscript space equals space F subscript 2 space sin space 60 degree end cell row blank equals cell space open parentheses 10 space straight N close parentheses space open parentheses 1 half square root of 3 close parentheses end cell row blank equals cell space 5 square root of 3 space straight N end cell row blank blank blank row blank rightwards arrow cell space F subscript 3 x end subscript space equals space 0 space straight N end cell row blank rightwards arrow cell space F subscript 3 y end subscript space equals space 20 square root of 3 space straight N end cell end table     

Kemudian, besar resultan ketiga vektor dapat dihitung :

table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow cell space R subscript x space equals space F subscript 1 x end subscript space minus space F subscript 2 x end subscript space plus space F subscript 3 x end subscript end cell row blank equals cell space 5 space straight N space minus space 5 space straight N space plus space 0 space straight N end cell row blank equals cell space bold 0 bold space bold N end cell row blank blank blank row blank rightwards arrow cell space R subscript y space equals space F subscript 1 y end subscript space plus space F subscript 2 y end subscript space minus space F subscript 3 y end subscript end cell row blank equals cell space 5 square root of 3 space straight N space plus space 5 square root of 3 space straight N space minus space 20 square root of 3 space straight N end cell row blank equals cell space bold minus bold 10 square root of bold 3 bold space bold N end cell row blank blank blank row blank rightwards arrow cell space R space equals space square root of R subscript x squared space plus space R subscript y squared end root end cell row blank equals cell space square root of 0 squared space plus space open parentheses negative 10 square root of 3 close parentheses squared end root end cell row blank equals cell bold space bold 10 square root of bold 3 bold space bold N end cell end table   

Dengan demikian, didapatkan besar resultan gaya ketiga vektor adalah bold 10 square root of bold 3 bold space bold N.

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