Perhatikan gamber berikut! Tiga buah vektor gaya, masing - masing besarnya , dan tersusun seperti gambar. Resultan ketiga vektor tersebut adalah....

Perhatikan gamber berikut!

Tiga buah vektor gaya, masing - masing besarnya $straight F subscript 1 equals 12 space straight N comma space straight F subscript 2 equals 6 space straight N$ , dan $straight F subscript 3 equals 12 space straight N$ tersusun seperti gambar. Resultan ketiga vektor tersebut adalah....

6 N
8 N
12 N
16 N
20 N

Jawaban:

Tinjau sumbu x

$sum straight F subscript straight x equals straight F subscript 1 space sin space 30 to the power of 0 space plus space straight F subscript 3 space sin space 30 to the power of 0 space minus space straight F subscript 2 sum straight F subscript straight x equals left parenthesis 12 right parenthesis space left parenthesis 1 half right parenthesis plus left parenthesis 12 right parenthesis space left parenthesis 1 half right parenthesis space minus space 6 sum straight F subscript straight x equals 6 plus 6 minus 6 sum straight F subscript straight x equals 6 space straight N$

Tinjau sumbu y

$sum F subscript y equals F subscript 1 space c o s space 30 to the power of 0 minus F subscript 3 space c o s space 30 to the power of 0 sum F subscript y equals left parenthesis 12 right parenthesis left parenthesis 1 half square root of 3 right parenthesis minus left parenthesis 12 right parenthesis left parenthesis 1 half square root of 3 right parenthesis sum F subscript y equals 0$

Maka, besarnya resultan gayanya :

$straight F subscript straight R equals square root of left parenthesis sum straight F subscript straight x right parenthesis squared plus left parenthesis sum straight F subscript straight y right parenthesis squared end root straight F subscript straight R equals square root of left parenthesis 6 right parenthesis squared plus left parenthesis 0 right parenthesis squared end root straight F subscript straight R equals 6 space straight N$

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