anonymous
  • anonymous
Determine the ratio of the relativistic to the non relativistic kinetic energy when V=1.5x10^-3 m/s and when V = 0.97 m/s. I have tried it three times and for some reason my answer is always zero
Physics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[KE _{rel}=mc ^{2}(\gamma-1)\] \[KE _{nonrel}=\frac{ 1 }{ 2 }mV ^{2}\]
Astrophysics
  • Astrophysics
Looks like fun, can you show your work please?
Astrophysics
  • Astrophysics
\[\gamma = \frac{ 1 }{ \sqrt{1-\left( \frac{ v }{ c } \right)}^2 }\] just to note the Lorentz factor

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anonymous
  • anonymous
Sure
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Astrophysics
  • Astrophysics
It's probably best if you do the calculations separately
Astrophysics
  • Astrophysics
\[KE_{rel} = mc^2\left( \frac{ 1 }{ \sqrt{1-\left( \frac{ v }{ c } \right)^2} }-1 \right)\]
Astrophysics
  • Astrophysics
You should find what fraction of the speed of light the given velocities are and then you can find the ratio.
Astrophysics
  • Astrophysics
So \[1.5 \times 10^{-3} m/s = \frac{ 1 }{ 450,000 } c \]
Astrophysics
  • Astrophysics
\[\gamma = \frac{ 1 }{ \sqrt{1-\left( \frac{ (1/450,000)c)^2 }{ c^2 } \right)} }\]
Astrophysics
  • Astrophysics
The reason you're getting 0 is, when you subtract by 1 using a calculator it's approximating to 1 as the numbers are so small, we get something insane such as 0.9999999...
Michele_Laino
  • Michele_Laino
for small velocities (v<

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