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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?
  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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