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Vektor gaya dan terletak pada sebuah diagram kartesius seperti gambar : Resultan ketiga vektor adalah ....

Vektor gaya begin mathsize 12px style straight F subscript 1 comma space straight F subscript 2 comma end style dan begin mathsize 12px style straight F subscript 3 end style terletak pada sebuah diagram kartesius seperti gambar :

Resultan ketiga vektor adalah ....

  1. square root of 26 space straight N

  2. square root of 76 space straight N

  3. square root of 84 space straight N

  4. square root of 168 space straight N

  5. square root of 204 space straight N

Jawaban:

Tinjau sumbu x.

ΣF subscript straight X space equals space straight F subscript 1 space cos space 30 degree space minus space straight F subscript 3 space sin space 60 degree  ΣF subscript straight X space equals space 12 open parentheses 1 half square root of 3 close parentheses minus 8 open parentheses 1 half square root of 3 close parentheses  ΣF subscript straight X space equals space 6 square root of 3 space minus space 4 square root of 3  ΣF subscript straight X space equals 2 square root of 3 space straight N

 

Tinjau sumbu y.

ΣF subscript straight y space equals space straight F subscript 1 space sin space 30 degree space minus space straight F subscript 3 space cos space 60 degree space minus space straight F subscript 2  ΣF subscript straight y space equals space 12 open parentheses 1 half close parentheses minus 8 open parentheses 1 half close parentheses minus 10  ΣF subscript straight y space equals space 6 minus space 4 minus 10  ΣF subscript straight y space equals negative 8 space straight N

 

Maka, besarnya resultan gaya dengan menggunakan vektor adalah :

straight F subscript straight R space equals space square root of open parentheses ΣF subscript straight X close parentheses squared space plus space open parentheses ΣF subscript straight y close parentheses squared end root  straight F subscript straight R space equals space square root of open parentheses 2 square root of 3 space close parentheses squared space plus space open parentheses negative 8 close parentheses squared end root  straight F subscript straight R space equals space square root of 76 space straight N

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