Kaon in an accelerator, Lorentz transformation problem

[Bowenwww]

Homework Statement

Ok so a Kaon (m = 500MeV) is accelerated from rest along the z-axis to a final energy of 5GeV, I need to find two factors of a lorrentz transformation β and γ and write a four vector for this.

Homework Equations

β=p/E γ=E/m

The Attempt at a Solution

I have calculated this using the above equations but I don't know if I've gone about it the right way.

I have β≈1 and γ=10 - can anyone tell me if this is anything like what it should be??

Thanks,

K xoxo

 

[vela]

Your result for $\gamma$ is right, but you could be a bit more precise about what $\beta$ equals.

 

[Bowenwww]

Yeah it's actually 0.995 or something like that, it's just it seems from the nature of the question that it would require more work than that - I also don't understand where these components fit into a 4-vector?

Thanks for this,

K xx

 

[vela]

The energy-momentum four-vector is simply $p^\mu = (E, p_x, p_y, p_z)$, where E is the total energy and the p_i's are the particle's three-momentum.

 

[paranormal]

I would first commend you for using the correct equations to solve this problem. Your values for β and γ seem to be reasonable based on the given information. However, it would be helpful if you could show your work and explain your reasoning for arriving at these values. This will allow for a more thorough evaluation of your solution and any potential errors or areas for improvement. Additionally, it would be beneficial to provide the four vector you calculated to verify your solution. Keep up the good work!