(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculate the kinetic energy required to accelerate a proton from a rest position to 0.9999c. The mass of the proton is 1.67x10^{-27}

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

2. Relevant equations

E_{rest}= mc^{2}

E_{k}= mc^{2}/√(1-v^{2}/c^{2})

3. The attempt at a solution

Ok So calculating the rest energy is easy

E= (1.67x10^{-27})(3x10^{8})^{2}

E= 1.503x10^{-10}

E_{kinetic}= mc^{2}/√(1-v^{2}/c^{2})

=((1.67x10^{-27})(3x10^{8})^{2})/√(1-0.9999c^{2}/c^{2})

=1.503x10^{-10}/√(1-0.9998)

= 1.503x10^{-10}/ 0.0141418

= 1x10^{-8}J

This doesn't seem like a lot of energy to accelerate something to almost light speed I feel like I am missing something...

even when using E_{total }=E_{rest}+E_{K}I get 1x10^{-8}J

can someone point out my mistake?

Ratio of kinetic energy to rest energy is

1.503x10^{-10}/ 1x10^{-8}

= 1.503 % of the energy is kinetic energy ?( really unsure about this)

Thanks! Happy monday !

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# Homework Help: Calculate the kinetic energy required to accelerate a proton

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