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Acceleration of Proton (Kinetic Energy & relativity)

  1. Jan 15, 2013 #1
    1. The problem statement, all variables and given/known data
    a)
    Calculate the kinetic energy required to accelerate a single proton from a rest position to 0.9999c. The mass of a proton is 1.67*10^-27 Kg.

    b)
    Find the ratio of kinetic energy to the energy of a proton at rest

    2. Relevant equations
    Ekrest = mc2

    Ek= (mc2)/√(1-(v2/c2))-mc2


    3. The attempt at a solution
    a)
    Ekrest = mc2
    Ekrest = (1.67*10^-27)(c)2
    Ekrest = 1.5*10^-10

    Ek= (1.5*10^-10)/√(1.9999*10^-4)-(1.5*10^-10)
    EK=1.047*10^-8J

    I am not confident in this answer as that does not seem nearly enough energy to accelerate the proton...

    B)
    1.047*10^-8/ 1.5*10^-10
    =69.66%


    I am very confused! Any help is much appreciated.
     
  2. jcsd
  3. Jan 15, 2013 #2

    collinsmark

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    Homework Helper
    Gold Member

    I think you might find it easier for this problem to first define gamma, [itex] \gamma [/itex] as

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

    and then just define the kinetic energy as

    [tex] E_k = \left( \gamma - 1 \right) mc^2. [/tex]

    But of course, it's up to you.

    That looks about right to me! :approve: Very nice.
    Protons are pretty small, don't forget.
    Ignoring a rather minor difference in rounding errors (between your result and mine), why in the world did you throw on a "%" at the end?

    (That "%" is throwing you off by two orders of magnitude. :wink:)
     
  4. Jan 15, 2013 #3
    Thank you very much!! and I honestly have no idea why I put the % haha thank you :)
     
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