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Relativistic Mass Question

  1. Oct 5, 2009 #1
    1. The problem statement, all variables and given/known data
    An electron has a rest mass of 9.11 x 10^-31 kg. The speed of the electron in the cathode ray tube of your computer monitor is 4.00 x 10^7 m/s. However, the speed of the electron is 0.98 c in a particle accelerator used in cancer therapy. How many times heavier is the electron in the particle accelerator than in the computer monitor?


    2. Relevant equations
    m = mo/ sqrt(1 - v^2/c^2)


    3. The attempt at a solution
    mo1 = m sqrt(1 - v^2/c^2)
    = (9.11 x 10^-31 kg) sqrt{ 1 - (4.00 x 10^7 m/s)^2/(3.00 x 10^8 m/s)^2}
    = (9.11 x 10^-31 kg) sqrt(0.017777777)
    = (9.11 x 10-31 kg)(0.13333333)
    = 1.21 x 10^-31 kg

    mo2 = (9.11 x 10-31 kg) sqrt{1 - (0.98 c)2/c^2}
    = (9.11 x 10-31 kg)(0.198997)
    = 1.81 x 10^-31 kg

    (1.81 x 10^-31 kg)/(1.21 x 10^-31 kg)
    = 1.496 times

    Therefore the electron is approx. 1.5 times heavier in the particle accelerator than it is in the computer monitor.


    Is this correct?
    Thanks
     
  2. jcsd
  3. Oct 5, 2009 #2
    Your equations are correct but I am getting different values for mo1 and mo2 than you. For your value of mo1, you forgot to do 1 minus (4.00 x 10^7 m/s)^2/(3.00 x 10^8 m/s)^2. Instead you just took the second quantity and took the square root. For mo2, it looks correct, but when I calculate it I get a different answer. Maybe retype all the numbers into your calculator again and see if it was a typing error.
     
  4. Oct 5, 2009 #3
    did you get (9.03 x 10^-31 kg) for m1? and (1.81 x 10^-31 kg) for m2?
     
  5. Oct 5, 2009 #4
    but now it doesn't make sense, cause those answers are suggesting that the electron is heavier in the computer monitor than the particle accelerator
     
  6. Oct 5, 2009 #5
    i just realized why this whole thing is completely wrong. i need to find m, not mo so the equation is completely wrong.

    the equation is m = mo/ sqrt(1 - v^2/c^2)

    so when i put all the numbers in for both sides

    m1 = 9.19 x 10^-31 kg
    m2 = 4.58 x 10^-31 kg

    but still m2 should be heavier cause its in a particle accelerator, and the speed is much more significant..
     
  7. Oct 5, 2009 #6
    Your m2 should be 4.58 x 10^-30 kg. Your off by an order of magnitude.
     
  8. Oct 5, 2009 #7
    i see that now, sorry, thanks for helping me, honestly.
     
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