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Relativistic Mechanics

Problem 1.374

At what values of the ratio of the kinetic energy to rest energy can the velocity of a particle be calculated from the classical formula with the relative error less than ε=0.010?\varepsilon=0.010 ?

Reveal Answer
 For ε≪1 the ratio is T/m0c2⩽4/3ε≈0.013 . \text { For } \varepsilon \ll 1 \text { the ratio is } T / m_{0} c^{2} \leqslant 4 / 3 \varepsilon \approx 0.013 \text { . }
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