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Seorang pengamat di S mencatat kejadian pada X = 5 m dan t = 3 × 1 0 − 8 s .Sistem S bergerak dengan kecepatan 0,6 c relatif terhadap sistem S searahsumbu x. Tentukan koordinat yang dicatat oleh sistem pengamat di sistem S! Bandingkan hasil yang diperoleh dengan hasil transformasi Galileo!

Seorang pengamat di S mencatat kejadian pada X = 5 m dan . Sistem S bergerak dengan kecepatan 0,6 c relatif terhadap sistem S searah sumbu x. Tentukan koordinat yang dicatat oleh sistem pengamat di sistem S! Bandingkan hasil yang diperoleh dengan hasil transformasi Galileo!

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Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah .

jawaban yang tepat adalah begin mathsize 14px style negative 0 comma 5 space straight m semicolon space 2 comma 5 cross times 10 to the power of negative 8 end exponent space straight s semicolon space minus 0.4 space straight m semicolon space 3 cross times 10 to the power of negative 8 end exponent space straight s end style.

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Pembahasan

Diketahui: Ditanya: x' dan t' berdasarkan transformasi Lorentz dantransformasi Galileo Jawab: Transformasi Lorentz Transformasi Galileo Jadi, jawaban yang tepat adalah .

Diketahui:

begin mathsize 14px style x equals 5 space straight m t equals 3 cross times 10 to the power of negative 8 end exponent space straight s v equals 0 comma 6 space straight c equals 1 comma 8 space cross times 10 to the power of 8 space bevelled straight m over straight s end style

Ditanya: x' dan t' berdasarkan transformasi Lorentz dan transformasi Galileo

Jawab:

Transformasi Lorentz

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x to the power of apostrophe end cell equals cell fraction numerator x minus v t over denominator square root of 1 minus begin display style v squared over c squared end style end root end fraction end cell row blank equals cell fraction numerator 5 minus 1 comma 8 cross times 10 to the power of 8 times 3 cross times 10 to the power of negative 8 end exponent over denominator square root of 1 minus begin display style open parentheses 0 comma 6 space c close parentheses squared over c squared end style end root end fraction end cell row blank equals cell fraction numerator 5 minus 5 comma 4 over denominator square root of 1 minus begin display style fraction numerator 0 comma 36 space c squared over denominator c squared end fraction end style end root end fraction end cell row blank equals cell fraction numerator negative 0 comma 4 over denominator square root of 1 minus begin display style 0 comma 36 end style end root end fraction end cell row blank equals cell fraction numerator negative 0 comma 4 over denominator square root of 0 comma 64 end root end fraction end cell row blank equals cell fraction numerator negative 0 comma 4 over denominator 0 comma 8 end fraction end cell row blank equals cell negative 0 comma 5 space straight m end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell t to the power of apostrophe end cell equals cell fraction numerator t minus begin display style bevelled fraction numerator v x over denominator c squared end fraction end style over denominator square root of 1 minus begin display style v squared over c squared end style end root end fraction end cell row blank equals cell fraction numerator 3 cross times 10 to the power of negative 8 end exponent minus begin display style fraction numerator open parentheses 1 comma 8 cross times 10 to the power of 8 times 5 close parentheses over denominator open parentheses 3 cross times 10 to the power of 8 close parentheses squared end fraction end style over denominator square root of 1 minus begin display style open parentheses 0 comma 6 space c close parentheses squared over c squared end style end root end fraction end cell row blank equals cell fraction numerator 3 cross times 10 to the power of negative 8 end exponent minus 1 cross times 10 to the power of negative 8 end exponent over denominator square root of 1 minus begin display style fraction numerator 0 comma 36 space c squared over denominator c squared end fraction end style end root end fraction end cell row blank equals cell fraction numerator 2 cross times 10 to the power of negative 8 end exponent over denominator square root of 1 minus begin display style 0 comma 36 end style end root end fraction end cell row blank equals cell fraction numerator 2 cross times 10 to the power of negative 8 end exponent over denominator square root of 0 comma 64 end root end fraction end cell row blank equals cell fraction numerator 2 cross times 10 to the power of negative 8 end exponent over denominator 0 comma 8 end fraction end cell row blank equals cell 2 comma 5 space cross times 10 to the power of negative 8 end exponent space straight s end cell end table end style

Transformasi Galileo

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x apostrophe end cell equals cell x minus v times t end cell row blank equals cell 5 minus open parentheses 1 comma 8 cross times 10 to the power of 8 times 3 cross times 10 to the power of negative 8 end exponent close parentheses end cell row blank equals cell 5 minus 5 comma 4 end cell row blank equals cell negative 0 comma 4 space straight m end cell row blank blank blank row cell t apostrophe end cell equals t row blank equals cell 3 cross times 10 to the power of negative 8 end exponent space straight s end cell end table end style 
 

Jadi, jawaban yang tepat adalah begin mathsize 14px style negative 0 comma 5 space straight m semicolon space 2 comma 5 cross times 10 to the power of negative 8 end exponent space straight s semicolon space minus 0.4 space straight m semicolon space 3 cross times 10 to the power of negative 8 end exponent space straight s end style.

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Tunjukkanlah bahwa transformasi Lorentz merupakan transformasi yang lebih umum daripada transformasi Galileo!

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