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Pertanyaan

Sebuah proton dengan massa diam 1 , 67 × 1 0 − 27 kg bergerak dengan laju 0,98 c . Hitunglah energi kinetik, energi total, massa, dan momentum proton!

Sebuah proton dengan massa diam  bergerak dengan laju 0,98c. Hitunglah energi kinetik, energi total, massa, dan momentum proton!

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I. Fitriatmoko

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

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Pembahasan

Diketahui : Ditanya : Jawab : Mencari energi kinetik : Mencari energi E : Massa relativistik : Momentum relativistik : Jadi, nilai dari energi kinetik, energi total, massa, dan momentum proton :

Diketahui :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell m subscript o end cell equals cell 1 comma 67 cross times 10 to the power of negative 27 end exponent space kg end cell row v equals cell 0 comma 98 c end cell end table end style 

Ditanya :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell E K end cell equals cell.... ? end cell row E equals cell.... ? end cell row m equals cell.... ? end cell row p equals cell.... ? end cell end table end style 

Jawab :

Mencari energi kinetik :

begin mathsize 14px style E K equals E subscript o open parentheses fraction numerator 1 over denominator square root of 1 minus open parentheses begin display style v over c end style close parentheses squared end root end fraction minus 1 close parentheses E K equals m subscript o c squared open parentheses fraction numerator 1 over denominator square root of 1 minus open parentheses begin display style v over c end style close parentheses squared end root end fraction minus 1 close parentheses E K equals open parentheses 1 comma 67 cross times 10 to the power of negative 27 end exponent close parentheses open parentheses 3 cross times 10 to the power of 8 close parentheses squared open parentheses fraction numerator 1 over denominator square root of 1 minus open parentheses begin display style fraction numerator 0 comma 98 c over denominator c end fraction end style close parentheses squared end root end fraction minus 1 close parentheses E K equals 15 comma 03 cross times 10 to the power of negative 11 end exponent open parentheses fraction numerator 1 over denominator square root of 0 comma 0396 end root end fraction minus 1 close parentheses E K equals 15 comma 03 cross times 10 to the power of negative 11 end exponent open parentheses fraction numerator 1 over denominator 0 comma 199 end fraction minus 1 close parentheses E K equals 15 comma 03 cross times 10 to the power of negative 11 end exponent open parentheses 5 comma 025 minus 1 close parentheses E K equals 60 comma 5 cross times 10 to the power of negative 11 end exponent space joule end style 

Mencari energi E :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row E equals cell m c squared end cell row E equals cell fraction numerator m subscript o c squared over denominator square root of 1 minus open parentheses begin display style v over c end style close parentheses squared end root end fraction end cell row E equals cell fraction numerator 1 comma 67 cross times 10 to the power of negative 27 end exponent open parentheses 3 cross times 10 to the power of 8 close parentheses squared over denominator square root of 1 minus open parentheses begin display style fraction numerator 0 comma 98 c over denominator c end fraction end style close parentheses squared end root end fraction end cell row E equals cell 75 comma 52 cross times 10 to the power of negative 11 end exponent space joule end cell end table end style 

Massa relativistik :

begin mathsize 14px style m equals fraction numerator m subscript o over denominator square root of 1 minus open parentheses begin display style v over c end style close parentheses squared end root end fraction m equals fraction numerator 1 comma 67 cross times 10 to the power of negative 27 end exponent over denominator square root of 1 minus open parentheses begin display style fraction numerator 0 comma 98 c over denominator c end fraction end style close parentheses squared end root end fraction m equals 8 comma 4 cross times 10 to the power of negative 27 end exponent space kg end style 

Momentum relativistik :

begin mathsize 14px style p equals m v p equals 8 comma 4 cross times 10 to the power of negative 27 end exponent cross times 0 comma 98 cross times 3 cross times 10 to the power of 8 p equals 24 comma 696 cross times 10 to the power of negative 19 end exponent space kgm divided by straight s end style 

Jadi, nilai dari energi kinetik, energi total, massa, dan momentum proton :

begin mathsize 14px style bold 60 bold comma bold 5 bold cross times bold 10 to the power of bold minus bold 11 end exponent bold space bold J bold semicolon bold space bold 75 bold comma bold 52 bold cross times bold 10 to the power of bold minus bold 11 end exponent bold space bold J bold semicolon bold space bold 8 bold comma bold 4 bold cross times bold 10 to the power of bold minus bold 27 end exponent bold space bold kg bold semicolon bold space bold 24 bold comma bold 696 bold cross times bold 10 to the power of bold minus bold 19 end exponent bold space bold kgm bold divided by bold s bold. end style

2rb+

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