Vektor gaya dan terletak pada sebuah diagram kart...

Vektor gaya $undefined$ dan $F subscript 3$ terletak pada sebuah diagram kartesius seperti gambar :

Resultan ketiga vektor adalah ....

$square root of 26 space straight N$
$square root of 76 space straight N$
$square root of 84 space straight N$
$square root of 168 space straight N$
$square root of 204 space straight N$

Jawaban:

Tinjau sumbu x:

$sum for blank of F subscript x equals F subscript 1 cos space 30 degree minus space F subscript 3 space end subscript sin space 60 degree sum for blank of F subscript x equals left parenthesis 12 right parenthesis left parenthesis 1 half square root of 3 right parenthesis minus left parenthesis 8 right parenthesis left parenthesis 1 half square root of 3 right parenthesis sum for blank of F subscript x equals 6 square root of 3 minus 4 square root of 3 sum for blank of F subscript x equals 2 square root of 3 N$

Tinjau sumbu y:

$sum for blank of F subscript y equals F subscript 1 cos space 30 degree minus space F subscript 3 space end subscript sin space 60 degree minus F subscript 2 sum for blank of F subscript y equals left parenthesis 12 right parenthesis left parenthesis 1 half right parenthesis minus left parenthesis 8 right parenthesis left parenthesis 1 half right parenthesis minus 10 sum for blank of F subscript y equals 6 minus 4 minus 10 sum for blank of F subscript y equals negative 8 N$

Maka, besarnya resultan gaya dengan menggunakan vektor adalah :

$straight F subscript straight R equals square root of left parenthesis sum for blank of straight F subscript straight x right parenthesis squared plus left parenthesis sum for blank of straight F subscript straight y right parenthesis squared end root straight F subscript straight R equals square root of left parenthesis 2 square root of 3 right parenthesis squared plus left parenthesis negative 8 right parenthesis squared end root straight F subscript straight R equals square root of 76 space straight N$

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