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Homework Help: Speed of particle before its KE is doubled

  1. May 3, 2009 #1
    1. The problem statement, all variables and given/known data
    What speed must a particle attain before its kinetic energy is double the value predicted by the nonrelativistic expression KE=0.5mv^2?
    (there is no data given)

    2. Relevant equations
    How should I solve this if I have no numbers to insert...? Should I set this equation equal to the relativist one (e.g. E=KE-rest energy)
    In the end v/c=~0.786151
  2. jcsd
  3. May 3, 2009 #2
    Corrct, but I think you meant to equate the relativistic kenetic energy to twice the classical kinetic energy:

    Kinetic energy is (gamma - 1) m c^2, so we have:

    (gamma - 1) m c^2 = m v^2 -------->

    gamma - 1 = (v/c)^2

    v = c sqrt{[sqrt(5) - 1]/2}
  4. May 4, 2009 #3
    Thank you..But I don't get it how you have this 5 in the 2nd sqrt...v = c sqrt{[sqrt(5) - 1]/2} The result is correct.
  5. May 4, 2009 #4
    You just put gamma = 1/sqrt[1-(v/c)^2], move gamma to one side of the equation, square both sides, and solve the quadratic equation.
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