Asked by Beth
Determine the ratio of the relativistic kinetic energy to the nonrelativistic kinetic energy (1/2mv2) when a particle has a speed of (a) 2.12 x 10-3c. and (b) 0.959c.
Answers
Answered by
Elena
Relativistic kinetic energy is mₒc²{[1/√(1-β²)] – 1},
nonrelativistic kinetic energy is m v²/2 = 0.5mₒv²
(a) β=v/c=2.12•10^-3•c/c=2.12•10^-3
1/√(1-β²) =1.00000224
1/√(1-β²)] – 1 = 0.00000224=2.24 •10^-6
Relativistic kinetic energy is 2.24 •10^-6•mₒc²
The ratio is 2.24 •10^-6•mₒc²/[0.5•mₒ•(2.12•10^-3)² • c² ]=
=2.24 •10^-6/2.2472•10^-6 = 0.996796.
(b) β=v/c=0.959•c/c= 0.959
1/√(1-β²) = 3.5285,
1/√(1-β²)] – 1 =2.5285
Relativistic kinetic energy is 2.5285 •mₒc²
The ratio is 2.5285 •mₒc² /[0.5•mₒ•( 0.959)² • c² ]=5.499
nonrelativistic kinetic energy is m v²/2 = 0.5mₒv²
(a) β=v/c=2.12•10^-3•c/c=2.12•10^-3
1/√(1-β²) =1.00000224
1/√(1-β²)] – 1 = 0.00000224=2.24 •10^-6
Relativistic kinetic energy is 2.24 •10^-6•mₒc²
The ratio is 2.24 •10^-6•mₒc²/[0.5•mₒ•(2.12•10^-3)² • c² ]=
=2.24 •10^-6/2.2472•10^-6 = 0.996796.
(b) β=v/c=0.959•c/c= 0.959
1/√(1-β²) = 3.5285,
1/√(1-β²)] – 1 =2.5285
Relativistic kinetic energy is 2.5285 •mₒc²
The ratio is 2.5285 •mₒc² /[0.5•mₒ•( 0.959)² • c² ]=5.499
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.