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Perhatikan gambar berikut! Dua buah bola konduktor identik yang memiliki massa sebesar m dan muatan sebesar q digantung pada tali sepanjang L seperti pada gambar di atas. jika pada saat sudut yang terbentuk sebesar θ kedua muatan berada dalam kesetimbangan tentukan nilai x ! (asumsikan bahwa sudut yang terbentuk kecil sehingga berlaku tan θ ≈ sin θ)

Pertanyaan

Perhatikan gambar berikut!

Dua buah bola konduktor identik yang memiliki massa sebesar m dan muatan sebesar q digantung pada tali sepanjang L seperti pada gambar di atas. jika pada saat sudut yang terbentuk sebesar θ kedua muatan berada dalam kesetimbangan tentukan nilai x !
(asumsikan bahwa sudut yang terbentuk kecil sehingga berlaku tan θsin θ)space

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari x adalah bold italic x bold almost equal to begin bold style left parenthesis fraction numerator begin display style 2 L k q squared end style over denominator begin display style m g end style end fraction right parenthesis end style to the power of bold 1 over bold 3 end exponent.

Pembahasan

Diketahui :

(asumsikan bahwa sudut yang terbentuk kecil sehingga berlaku tan θsin θ)

Ditanya :

x = ....?

Jawab :

Kita gambarkan gaya-gaya yang bekerja pada sistem :

 

Syarat kesetimbangan adalah sum from blank to blank of F subscript x equals 0 dan sum from blank to blank of F subscript y equals 0.

Kita tinjau sumbu x

table attributes columnalign right center left columnspacing 0px end attributes row cell sum from blank to blank of F subscript x end cell equals 0 row cell F subscript c minus T space sin space theta end cell equals 0 row cell F subscript c end cell equals cell T space sin space theta end cell row cell sin space theta end cell equals cell F subscript c over T end cell end table 

Kita tinjau sumbu y

sum from blank to blank of F subscript y equals 0 T space cos space theta minus m g equals 0 T space cos space theta equals m g cos space theta equals fraction numerator m g over denominator T end fraction 

Berdasarkan soal kita punya asumsi bahwa :

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space theta end cell almost equal to cell sin space theta end cell row cell tan space theta end cell almost equal to cell fraction numerator s i s i space d e p a n space theta over denominator s i s i space m i r i n g end fraction end cell row cell tan space theta end cell almost equal to cell fraction numerator begin display style 1 half end style x over denominator L end fraction end cell row cell fraction numerator sin space theta over denominator cos space theta end fraction end cell almost equal to cell fraction numerator begin display style 1 half x end style over denominator L end fraction end cell row cell fraction numerator begin display style F subscript c over T end style over denominator begin display style fraction numerator m g over denominator T end fraction end style end fraction end cell almost equal to cell fraction numerator begin display style 1 half x end style over denominator L end fraction end cell row cell fraction numerator begin display style F subscript c end style over denominator begin display style m g end style end fraction end cell almost equal to cell fraction numerator begin display style 1 half x end style over denominator L end fraction end cell row cell F subscript c open parentheses fraction numerator begin display style 1 end style over denominator begin display style m g end style end fraction close parentheses end cell almost equal to cell fraction numerator begin display style 1 half x end style over denominator L end fraction end cell row cell fraction numerator k q subscript 1 q subscript 2 over denominator r squared end fraction open parentheses fraction numerator begin display style 1 end style over denominator begin display style m g end style end fraction close parentheses end cell almost equal to cell fraction numerator begin display style 1 half x end style over denominator L end fraction end cell row cell fraction numerator k q q over denominator x squared end fraction open parentheses fraction numerator begin display style 1 end style over denominator begin display style m g end style end fraction close parentheses end cell almost equal to cell fraction numerator begin display style 1 half x end style over denominator L end fraction end cell row cell fraction numerator k q squared over denominator x squared end fraction open parentheses fraction numerator begin display style 1 end style over denominator begin display style m g end style end fraction close parentheses end cell almost equal to cell fraction numerator begin display style 1 half x end style over denominator L end fraction end cell row cell k q squared open parentheses fraction numerator begin display style 1 end style over denominator begin display style m g end style end fraction close parentheses L end cell almost equal to cell fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction x x squared end cell row cell fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction x x squared end cell almost equal to cell k q squared open parentheses fraction numerator begin display style 1 end style over denominator begin display style m g end style end fraction close parentheses L end cell row cell fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction x cubed end cell almost equal to cell k q squared open parentheses fraction numerator begin display style 1 end style over denominator begin display style m g end style end fraction close parentheses L end cell row cell x cubed end cell almost equal to cell k q squared open parentheses fraction numerator begin display style 1 end style over denominator begin display style m g end style end fraction close parentheses 2 L end cell row cell x cubed end cell almost equal to cell open parentheses fraction numerator begin display style 2 L k q squared end style over denominator begin display style m g end style end fraction close parentheses end cell row x almost equal to cell open parentheses fraction numerator begin display style 2 L k q squared end style over denominator begin display style m g end style end fraction close parentheses to the power of 1 third end exponent end cell end table 

Dengan demikian, nilai dari x adalah bold italic x bold almost equal to begin bold style left parenthesis fraction numerator begin display style 2 L k q squared end style over denominator begin display style m g end style end fraction right parenthesis end style to the power of bold 1 over bold 3 end exponent.

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