1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook