The LHC accelerates protons to a speed of 0.999999991c around a 27km ring. Due to relativistic effects, their mass increases. Given that the magnetic fields used are 8T, calculate this mass. What is the total energy of an LHC beam containing 3e14 protons?
Balancing the centripetal force mv^2/r with the force experienced due to motion in a magnetic field qvB: m = qBr/v = qBC/2piv (C circumference). Putting in numbers: m = 1.83e-23 kg (~11,000 mass of proton at rest!). Energy of beam = Np * 1/2 m v^2 (Np number of protons). Again, using the numbers, we get energy = 2.4e8 J. This is equivalent to the energy a standard car (mass 1.5t) has when traveling at around 1300 mph! (I originally asked this in the question but I went over the character count!).
TD
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