Special Relativity, energy and momentum

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Homework Statement



In reference frame S', two protons, each moving at .5c, approach each other head on. A) Calculate the total kinetic energy of the two protons in frame S'. B) Calculate the total kinetic energy of the protons as seen en reference frame S, which is moving with one of the protons.

Homework Equations



K=(mc^2/sqrt(1-(v/c)^2))-mc^2

The Attempt at a Solution


I have no attempt. I have no idea where to start.
 
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Well I will assume you know the answer to A, since you wrote out the equation. And in B, you know the velocity of one of the protons is 0. To get the velocity of the other proton, instead of summing the velocities classically which would get you the 2nd proton moving at the speed of light, c (which is impossible). You would add the velocities relativistically:

http://en.wikipedia.org/wiki/Velocity-addition_formula
 
You could also calculate the energy and momentum of the protons in the S' frame and then use a Lorentz transformation to find their values in the S frame.
 
Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
The value of H equals ## 10^{3}## in natural units, According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##, ## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units. So is this conversion correct? Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?

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