Speed of particle before its KE is doubled

[Miri]

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

 

[Count Iblis]

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}

 

[Miri]

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.

 

[Count Iblis]

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.