How much work must be done on a particle with a mass of mm to accelerate it from rest to a speed of 0.084 cc ? (Express the answer in terms

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How much work must be done on a particle with a mass of mm to accelerate it from rest to a speed of 0.084 cc ? (Express the answer in terms of mc2mc2.)

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  1. Answer:

    Work = 0.68 mc²

    Explanation:

    given data

    speed = 0.084 cc

    solution

    as kinetic energy of mass particle is

    KE = mc²([tex]\gamma[/tex] – 1 )  …………1

    here [tex]\gamma[/tex] is lorentz constant

    [tex]\gamma[/tex] = [tex]\frac{1}{\sqrt{1-(\frac{v}{c})^2 } }[/tex]    

    [tex]\gamma[/tex] = [tex]\frac{1}{\sqrt{1-(\frac{0.084c}{c})^2 } }[/tex]    

    [tex]\gamma[/tex] =  1.68

    as here particle start from rent so initial KE is 0

    and final KE = mc²(1.68 – 1 )

    final KE = 0.68mc²

    so here work done to increase speed of particle

    W = final KE – initial KE

    Work = 0.68 mc²

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