There are several threads on this forum regarding the LHS at CERN however I am interested in a non-calc solution. I recently stumbled upon a multiple choice question about it while studying for a physics exam and am wondering if someone has an elegant way of solving it without a calculator. We are given a sheet with information such as proton mass ect.
The question states: According to a page on Wikipedia which describes the LHC particle accelerator (Large Hadron Collider), protons are accelerated to an energy of 7 TeV ≈ 1.12 μJ. It also states that the protons aquire a speed of about 0.999999991c. On CERN's own website, on the other hand, it has been stated that the protons get a speed of 0.9999c. What speed does a proton have with an energy of 7 TeV?
Here's how I would solve it using a calculator:
I cannot wrap my head around solving this with only a pen and paper especially considering the similarity of the answers. Could it be that they regard this as "presumed knowledge"?