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Speed of particle before its KE is doubled

  • Thread starter Miri
  • Start date
  • #1
36
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Homework Statement


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)

Homework 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
 

Answers and Replies

  • #2
1,838
7
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}
 
  • #3
36
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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.
 
  • #4
1,838
7
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.
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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