Dua bintang yang masing-masing massanya 4M dan 9M terpisah sejauh a. Jika sebuah planet berada diantara kedua bintang tersebut dan planet tidak mengalami gaya gravitasi. Tentukan letak planet tersebut dari massa 4M!

Pertanyaan

Dua bintang yang masing-masing massanya 4M dan 9M terpisah sejauh a. Jika sebuah planet berada diantara kedua bintang tersebut dan planet tidak mengalami gaya gravitasi. Tentukan letak planet tersebut dari massa 4M! $undefined$

Pembahasan Soal:

$begin mathsize 14px style m subscript 1 equals 4 M m subscript 2 equals 9 M r subscript 12 equals a misalkan comma space m subscript p equals m end style$

Ditanyakan: Jarak planet dari massa 4M agar tidak mengalami gaya gravitasi?
Jawab:

Misalkan jarak planet ke massa 1 adalah x

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell F subscript p 1 end subscript end cell equals cell F subscript p 2 end subscript end cell row cell fraction numerator G m subscript p m subscript 1 over denominator r subscript p 1 end subscript squared end fraction end cell equals cell fraction numerator G m subscript p m subscript 2 over denominator r subscript p 2 end subscript squared end fraction end cell row cell fraction numerator 4 M over denominator x squared end fraction end cell equals cell fraction numerator 9 M over denominator open parentheses a minus x close parentheses squared end fraction end cell row cell 2 over x end cell equals cell fraction numerator 3 over denominator a minus x end fraction end cell row cell 3 x end cell equals cell 2 a minus 2 x end cell row cell 5 x end cell equals cell 2 a end cell row x equals cell 2 over 5 a end cell row x equals cell 0 comma 4 a end cell end table end style$

Jadi, letak planet dari massa 4M adalah 0,4a.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

J. Khairina

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 30 Maret 2021

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Gaya gravitasi yang bekerja pada benda uji adalah nol, maka resultan gaya gravitasinya sama dengan nol:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sum F end cell equals 0 row cell F subscript A minus F subscript B end cell equals 0 row cell F subscript A end cell equals cell F subscript B end cell row cell G fraction numerator M subscript A times M over denominator r subscript A squared end fraction end cell equals cell G fraction numerator M subscript B times M over denominator r subscript B squared end fraction end cell row cell fraction numerator 4 M subscript B over denominator r squared end fraction end cell equals cell M subscript B over open parentheses R minus r close parentheses squared end cell row cell 2 over r end cell equals cell fraction numerator 1 over denominator open parentheses R minus r close parentheses end fraction end cell row cell 2 R minus 2 r end cell equals r row cell 2 R end cell equals cell 3 r end cell row r equals cell 2 over 3 R end cell row r equals cell 0 comma 67 R end cell end table end style$

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Tiga buah benda A, B dan C membentuk segitiga siku-siku seperti gambar berikut! Tentukan besar gaya gravitasi pada benda B!

Pembahasan Soal:

Diketahui:

$begin mathsize 14px style m subscript 1 equals m subscript 2 equals m subscript 3 equals 1 space kg R subscript B A end subscript equals 1 space straight m R subscript B C end subscript equals square root of 2 space straight m end style$

Ditanya: F_B

Jawab:

Benda B ditarik A menghasilkan F_BA dan ditarik benda C menghasilkan F_BC dimana sudut yang terbentuk antara F_BA dan F_BC adalah 60^o.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell F subscript B A end subscript end cell equals cell double-struck G fraction numerator m subscript A times m subscript B over denominator R subscript B A end subscript squared end fraction end cell row blank equals cell double-struck G fraction numerator 1 times 1 over denominator 1 squared end fraction end cell row blank equals double-struck G row cell F subscript B C end subscript end cell equals cell double-struck G fraction numerator m subscript C times m subscript B over denominator R subscript B C end subscript squared end fraction end cell row blank equals cell double-struck G fraction numerator 1 times 1 over denominator open parentheses square root of 2 close parentheses squared end fraction end cell row blank equals cell 1 half double-struck G end cell end table end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell F subscript B end cell equals cell square root of F subscript B A end subscript squared plus F subscript B C end subscript squared plus 2 times F subscript B A end subscript times F subscript B c end subscript times cos space theta end root end cell row blank equals cell square root of double-struck G squared plus open parentheses 1 half double-struck G close parentheses squared plus 2 times double-struck G times 1 half double-struck G times cos space 60 end root end cell row blank equals cell square root of double-struck G squared plus 1 fourth double-struck G squared plus 2 times double-struck G times 1 half double-struck G times 1 half end root end cell row blank equals cell square root of double-struck G squared plus 1 fourth double-struck G squared plus 1 half double-struck G squared end root end cell row blank equals cell square root of 7 over 2 double-struck G squared end root end cell row blank equals cell 1 half double-struck G square root of 7 end cell end table end style$

Jadi, jawaban yang tepat adalah $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank double-struck G end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 7 end cell end table end style$ .

Roboguru

Benda A = 16 kg berada pada jarak 9 m dari benda B = 25 kg, sedangkan benda C = 5 kg di antara benda A dan B. Jika gaya gravitasi pada benda C sama dengan nol, maka tentukan jarak antara benda A dan C...

Pembahasan Soal:

Diketahui:

$begin mathsize 14px style m subscript A equals 16 space kg m subscript B equals 25 space kg m subscript C equals 5 space kg r subscript A B end subscript equals 9 space straight m F subscript A C end subscript equals F subscript C B end subscript G fraction numerator m subscript A m subscript C over denominator r subscript A C end subscript squared end fraction equals G fraction numerator m subscript C m subscript B over denominator open parentheses 9 minus r subscript A C end subscript close parentheses squared end fraction fraction numerator 16 cross times 5 over denominator r subscript A C end subscript squared end fraction equals fraction numerator 5 cross times 25 over denominator open parentheses 9 minus r subscript A C end subscript close parentheses squared end fraction fraction numerator 4 square root of 5 over denominator r subscript A C end subscript end fraction equals fraction numerator 5 square root of 5 over denominator 9 minus r subscript A C end subscript end fraction 4 over r subscript A C end subscript equals fraction numerator 5 over denominator 9 minus r subscript A C end subscript end fraction 4 open parentheses 9 minus r subscript A C end subscript close parentheses equals 5 r subscript A C end subscript 36 equals 9 r subscript A C end subscript bold italic r subscript bold A bold C end subscript bold equals bold 4 bold space bold m end style$

Jadi, jawaban yang tepat adalah 4 m $undefined$

Roboguru

Tiga buah benda A, B dan C berada pada satu garis lurus. Jika nilai konstanta gravitasi , hitunglah besar gaya gravitasi yang bekerja pada benda B!

Pembahasan Soal:

Diketahui:

$begin mathsize 14px style m subscript A equals 1 space kg m subscript B equals 2 space kg m subscript C equals 3 space kg r subscript A B end subscript equals 1 space straight m r subscript B C end subscript equals 2 space straight m double-struck G equals 6 comma 67 cross times 10 to the power of negative 11 end exponent space kg to the power of negative 1 end exponent space straight m cubed space straight s to the power of negative 2 end exponent end style$

Ditanya: $begin mathsize 14px style F subscript B end style$

Jawab:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell F subscript A B end subscript end cell equals cell double-struck G fraction numerator m subscript A times m subscript B over denominator r subscript A B end subscript squared end fraction end cell row blank equals cell 6 comma 67 cross times 10 to the power of negative 11 end exponent cross times fraction numerator 1 cross times 2 over denominator open parentheses 1 close parentheses squared end fraction end cell row blank equals cell 6 comma 67 cross times 10 to the power of negative 11 end exponent cross times 2 over 1 end cell row blank equals cell 13 comma 34 cross times 10 to the power of negative 11 end exponent space straight N end cell end table end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell F blank subscript B C end subscript end cell equals cell double-struck G fraction numerator m subscript B times m subscript C over denominator r subscript B C end subscript squared end fraction end cell row blank equals cell 6 comma 67 cross times 10 blank to the power of negative 11 end exponent cross times fraction numerator 2 cross times 3 over denominator open parentheses 2 close parentheses squared end fraction end cell row blank equals cell 6 comma 67 cross times 10 blank to the power of negative 11 end exponent cross times 6 over 4 end cell row blank equals cell 10 comma 005 space cross times 10 blank to the power of negative 11 end exponent space straight N end cell end table end style$

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Jadi, jawaban yang tepat adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 34 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cross times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 10 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank to the power of negative 11 end exponent end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight N end table$ .

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Berapakah besar gaya gravitasi total yang dialami bulan pada saat terjadi gerhana matahari? Diketahui jarak bumi ke matahari 150 juta km, jarak bumi ke bulan 383.000 km, massa bulan , massa matahari ,...

Pembahasan Soal:

$begin mathsize 14px style r subscript b m end subscript equals 150 space juta space km equals 15 cross times 10 to the power of 10 space straight m r subscript b b end subscript equals 383 cross times 10 cubed space km equals 383 cross times 10 to the power of 6 space straight m m subscript b u l a n end subscript equals 1 over 81 m subscript b u m i end subscript m subscript m a t a h a r i end subscript equals 1 comma 99 cross times 10 to the power of 30 space kg m subscript b u m i end subscript equals 5 comma 98 cross times 10 to the power of 24 space kg end style$

Ditanyakan: Gaya gravitasi total yang dialami bulan?
Jawab:

Saat terjadi gerhana matahari, bulan berada diantara matahari dan bumi, sehingga bulan mengalami gaya gravitasi dari matahari dan dari bumi yang arahnya berlawanan.

Gaya gravitasi bulan oleh matahari
$begin mathsize 14px style F subscript b m end subscript equals fraction numerator G m subscript m a t a h a r i end subscript m subscript b u l a n end subscript over denominator R squared end fraction F subscript b m end subscript equals fraction numerator G m subscript m a t a h a r i end subscript m subscript b u l a n end subscript over denominator left parenthesis r subscript b m end subscript minus r subscript b b end subscript right parenthesis squared end fraction F subscript b m end subscript equals fraction numerator left parenthesis 6 comma 67 cross times 10 to the power of negative 11 end exponent right parenthesis left parenthesis 1 comma 99 cross times 10 to the power of 30 right parenthesis begin display style left parenthesis 1 over 81 cross times 5 comma 98 cross times 10 to the power of 24 right parenthesis end style over denominator left parenthesis 15 cross times 10 to the power of 10 minus 383 cross times 10 to the power of 6 right parenthesis squared end fraction F subscript b m end subscript equals fraction numerator 0 comma 98 cross times 10 to the power of 43 over denominator 2 comma 24 cross times 10 to the power of 22 end fraction F subscript b m end subscript equals 4 comma 375 cross times 10 to the power of 17 space straight N end style$

Gaya garvitasi bulan oleh bumi
$begin mathsize 14px style F subscript b b end subscript equals fraction numerator G m subscript b u m i end subscript m subscript b u l a n end subscript over denominator R squared end fraction F subscript b b end subscript equals fraction numerator G m subscript b u m i end subscript m subscript b u l a n end subscript over denominator left parenthesis r subscript b b end subscript right parenthesis squared end fraction F subscript b b end subscript equals fraction numerator left parenthesis 6 comma 67 cross times 10 to the power of negative 11 end exponent right parenthesis left parenthesis 5 comma 98 cross times 10 to the power of 24 right parenthesis begin display style left parenthesis 1 over 81 cross times 5 comma 98 cross times 10 to the power of 24 right parenthesis end style over denominator left parenthesis 383 cross times 10 to the power of 6 right parenthesis squared end fraction F subscript b b end subscript equals fraction numerator 2 comma 94 cross times 10 to the power of 37 over denominator 146689 cross times 10 to the power of 12 end fraction F subscript b b end subscript equals 2 cross times 10 to the power of 20 space straight N end style$

Maka gaya total yang dialami bulan
$begin mathsize 14px style F subscript b u l a n end subscript equals F subscript b b end subscript minus F subscript b m end subscript F subscript b u l a n end subscript equals left parenthesis 2 cross times 10 to the power of 20 right parenthesis minus left parenthesis 4 comma 375 cross times 10 to the power of 17 right parenthesis F subscript b u l a n end subscript equals 1 comma 99 cross times 10 to the power of 17 space straight N end style$

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