- #1

- 56

- 0

## Homework Statement

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

## Homework Equations

E

_{rest}= mc

^{2}

E

_{k}= mc

^{2}/√(1-v

^{2}/c

^{2})

## 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 !