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Pertanyaan

Dua buah proton ditahan dalam keadaan diam pada jarak begin mathsize 14px style 5 cross times 10 to the power of negative 12 end exponent space straight m end style. Jika dilepaskan, mereka akan saling menjauh. Berapakah kecepatan tiap proton jika keduanya sudah sangat berjauhan satu sama lain?

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A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

kecepatan masing-masing proton saat terpisah sangat jauh sebesar begin mathsize 14px style 1 comma 70 times space 10 to the power of 5 space straight m divided by straight s end style.

Pembahasan

Diketahui:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell r subscript 1 end cell equals cell 5 times 10 to the power of negative 12 end exponent space straight m end cell row cell v subscript 1 end cell equals 0 end table end style 

Ditanyakan:

begin mathsize 14px style v subscript 2 equals ? end style saat begin mathsize 14px style r subscript 2 rightwards arrow infinity end style 

Jawab:

Ambil begin mathsize 14px style q equals 1 comma 6 times 10 to the power of negative 19 end exponent space straight C end style dan begin mathsize 14px style m subscript p equals 1 comma 6 times 10 to the power of negative 27 end exponent space kg end style.

Ketika undefined, energi potensial listrik bernilai nol (begin mathsize 14px style E p equals k q squared over r end style). Hukum Kekekalan Energi Mekanik berlaku:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell E m subscript 1 end cell equals cell E m subscript 2 end cell row cell E p subscript 1 plus E k subscript 1 end cell equals cell E p subscript 2 plus E k subscript 2 end cell row cell k q squared over r subscript 1 plus up diagonal strike 2 open parentheses 1 half m v subscript 1 squared close parentheses end strike to the power of 0 end cell equals cell up diagonal strike k q squared over r subscript 2 end strike to the power of 0 plus 2 open parentheses 1 half m v subscript 2 squared close parentheses end cell row cell m v subscript 2 squared end cell equals cell k q squared over r subscript 1 end cell row cell v subscript 2 end cell equals cell square root of fraction numerator k q squared over denominator m r subscript 1 end fraction end root equals square root of fraction numerator open parentheses 9 times 10 to the power of 9 close parentheses open parentheses 1 comma 6 times 10 to the power of negative 19 end exponent close parentheses squared over denominator open parentheses 1 comma 6 times 10 to the power of negative 27 end exponent close parentheses open parentheses 5 times 10 to the power of negative 12 end exponent close parentheses end fraction end root end cell row blank equals cell square root of fraction numerator open parentheses 9 close parentheses open parentheses 1 comma 6 close parentheses squared over denominator open parentheses 1 comma 6 close parentheses open parentheses 5 close parentheses end fraction times fraction numerator 10 to the power of 9 times 10 to the power of negative 38 end exponent over denominator 10 to the power of negative 27 end exponent times 10 to the power of negative 12 end exponent end fraction end root end cell row cell v subscript 2 end cell equals cell fraction numerator 6 square root of 2 over denominator 5 end fraction times 10 to the power of 5 almost equal to bold 1 bold comma bold 70 bold times bold 10 to the power of bold 5 bold space bold m bold divided by bold s end cell end table end style 

Dengan demikian, kecepatan masing-masing proton saat terpisah sangat jauh sebesar begin mathsize 14px style 1 comma 70 times space 10 to the power of 5 space straight m divided by straight s end style.

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