- #1

fatcats

- 34

- 1

## Homework Statement

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 the kinetic energy to the energy of a proton at rest.

c) Explain why no particle accelerator will ever be able to accelerate any particle to the speed of light.

## Homework Equations

a) Ek = Etotal - Erest

Ek = mc^2/sqroot 1 - v^2/c^2 - mc^2

b) Ek/Erest

## The Attempt at a Solution

a) I am including the calculations I have done on my word document page to make it more legible than typing it in here. Please see the attached image.

I think my work is right, but I have cross-referenced this answer with others and the math does not seem to be right... it seems to be correct until at least the step where:

Ek = 1.50 * 10^-10 / sqroot(1.9999*10^-4) - 1.50 *10^-10

After that I am not sure, but the answer I keep getting is 9.11 * 10^-10, and other answers, deemed correct have a totally different number multiplied by 10^-8...

I have been reworking this and trying to figure out where/if my calculation is wrong and I'm stuck.

b) For this question, all I do is divide the two numbers for the ratio, correct? This question is worth three marks and it seems like they want something more than just this? Am I missing something?

c) Not sure how to word this. Here's my best attempt. This question is worth one mark.

No particle accelerator will ever be able to accelerate any particle to the speed of light because according to the denominator of the aforementioned equation, sqroot (1-v^2/c^2), the speed of light acts as a limit to velocity. If velocity were to equal the speed of light, then there would be no difference in resting and kinetic energies.

Please help me understand, I am doing this course online and don't really have a teacher who can help me out. Thanks for your time.