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Finding relativistic mass and energy of an electron

  1. Jun 24, 2016 #1
    1. The problem statement, all variables and given/known data

    A resting electron was sped up to 0.5 of the speed of light. Find:
    A. relativistic mass of the electron,
    B. total energy of the electron,
    C. kinetic energy of the electron.

    2. Relevant equations
    K = mv^2/2
    E=mc^2

    3. The attempt at a solution
    Let’s first find the kinetic energy:
    K = m*v^2/2
    K = (9.1*10^-31*0.25*9*10^16)/2 = 1.02375*10^-14 J

    Now we should find relativistic mass using E=mc^2.
    m(rel) = E/c^2 = (1.02375*10^-14)/(9*10^16) = 1.1375*10^-31 kg

    Total energy must be = m(rest)*c^2
    Then E(total) = 9.1*10^-31*9*10^16 = 8.19*10^-14 J

    Is this solution correct?
    And I suppose potential energy = 8.19*10^-14 - 1.02375*10^-14 = 7.16625*10^-14 ? :)
     
    Last edited: Jun 24, 2016
  2. jcsd
  3. Jun 24, 2016 #2
    No, that is not correct. Do you have an equation with rest mass and Gamma (which is a relationship that crops up a lot in relativistic formula)?
     
  4. Jun 24, 2016 #3
    I'm not sure what equation you mean. I found p = mv*gamma, but I don't understand what gamma means there.
     
  5. Jun 24, 2016 #4
    This is gamma

    ##\gamma =\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}##
     
  6. Jun 24, 2016 #5
    You were never taught this?
     
  7. Jun 24, 2016 #6
  8. Jun 24, 2016 #7
    I have a ton of stuff to figure out by myself in a short period of time, so sorry for stupid questions :( I don't remember anything about relativistic mass from school.
    So gamma is also relativistic mass/rest mass?
     
  9. Jun 24, 2016 #8
    Its not a stupid question, I am just wondering what you know about mass at relativistic speeds. Check out the article I sent, there is a ratio embedded in there that you will find useful. :)
     
  10. Jun 24, 2016 #9
    Ok, then m(rel) = gamma*m(rest)
    gamma = sqrt(1-0.25) = sqrt(0.75)
    m(rel) = sqrt(0.75)*9.1*10^-31 = 7.88*10^-31

    Is it correct now?
     
  11. Jun 24, 2016 #10
    Gamma is almost like a way of translating mass/lengths/time from the ordinary or Newtonian way of thinking of life to the relativistic way... It's usually a multiplier of some kind.
     
  12. Jun 24, 2016 #11
    You are close. It should be m_electron/sqrt(0.75)
     
  13. Jun 24, 2016 #12
    Hm, but why? On wikipedia the equation is m(rel)/m(rest) = gamma, so gamma*m(rest) = m(rel)
     
  14. Jun 24, 2016 #13
    Mass increases as speed increases
     
  15. Jun 24, 2016 #14
    Right, got it. So then I should plug in relativistic mass as m into K = mv^2/2 and E=mc^2 and get the kinetic and total energies?
    Then m = 9.1*10^-31/sqrt(75) = 1.05 * 10^-30
    Total energy E = 1.05*10^-30*9*10^16 = 9.45*10^-14
    Kinetic energy K = (1.05*10^-30*0.25*9*10^8)/2 = 1.18*10^-22

    Or am I wrong again?
     
  16. Jun 24, 2016 #15
    Oh, looked it up. KE = mc^2 - m0c^2 = 1.05*10^-30*9*10^16 - 9.1*10^-31*9*10^16 = 1.26*10^-14 J
    Now I have to figure what "total energy" means.
    KE = Total energy - Potential energy, so I suppose m(rel)*c^2 = 9.45*10^-14 is total energy like I wrote in the previous message? I hope it's correct now? :)
     
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