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Which energy equations?

  1. Nov 29, 2015 #1
    1. The problem statement, all variables and given/known data

    To calculate kinetic energy I can either use E=mv^2/2 or for higher velocities I can use E=gamma factormc^2 - mc^2.

    So my question is at which velocity can I use E=gamma factormc^2 - mc^2? Is 1000000m/s a high enough velocity?

    2. Relevant equations


    3. The attempt at a solution
     
  2. jcsd
  3. Nov 29, 2015 #2

    BvU

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    Once ##\gamma## starts to deviate from 1 you will need the relativistic expression. Simple, isn't it ?
     
  4. Nov 29, 2015 #3
    yes thanx alot!
     
  5. Nov 29, 2015 #4

    BvU

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    Just to get an idea: how much does ##\gamma## differ from 1 at the speed you mentioned ?
     
  6. Nov 29, 2015 #5
    I checked it and it doesn't differ :P
     
  7. Nov 29, 2015 #6

    BvU

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    But it does differ! perhaps not on a cheap calculator, but ##\gamma = 1.0000055556... \ne 1 ## :smile:
    What you mean is that it doesn't differ significantly...
     
  8. Nov 29, 2015 #7
    yes well my graph calculator show that the gamma factor is equal to one :) But I get the idea
     
  9. Nov 29, 2015 #8

    BvU

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    Sometimes helping the calculator a little by hand is more accurate: $$
    \gamma = {1\over \sqrt {1-\beta^2}} \approx 1+{1\over 2} \beta^2 \, , $$ in your case ##1+ {1\over 2}{1\over 300^2} = 1+ 1/180000 \ne 1 ##
     
    Last edited: Nov 29, 2015
  10. Nov 29, 2015 #9

    Ray Vickson

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    Actually, the issue is whether ##\gamma## differs significantly from ##1 + \frac{1}{c^2} \frac{1}{2} v^2##, or whether ##c^2 (\gamma - 1)## differs significantly from ##v^2/2##. For lab-scale speeds, ##\gamma## will hardly ever differ "significantly" from 1.
     
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