Çözüldü Relativistic Mass, Speed and Kinetic Energy - Radical (Irrational) Numbers

Which of the following is the expression for the relativistic kinetic energy of an object of resting mass m₀ that is moving with a velocity that is 1 / √3 times the speed of light c?

A) m₀·c^2 / √3
B) [ (3 - √6) / √6 ]·m₀·c^2
C) (3 / √6)·m₀·c^2
D) √3·m₀·c^2
E) m₀·c^2 / 3

Object's speed: v
Kinetic energy at rest: E₀ = m₀·c^2 while v = 0
Total energy while moving: E = m₀·c^2 / (1 - v^2 / c^2)^0,5
Kinetic energy while moving:
Ek = E - E₀ = m₀·c^2 / (1 - v^2 / c^2)^0,5 - m₀·c^2
Ek = m₀·c^2·[ 1 / (1 - v^2 / c^2)^0,5 - 1 ]
Ek = m₀·c^2·{ 1 / [ 1 - (c / √3)^2 / c^2)^0,5 ] - 1 }
Ek = m₀·c^2·[ 1 / (1 - 1 / 3)^0,5 - 1 ]
Ek = m₀·c^2·(√3 / √2 - 1)
Ek = m₀·c^2·(3 / √6 - 1)
Ek = m₀·c^2·[ (3 - √6) / √6 ].