# Question: the large hadron collider can accelerate particles to energies of...

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The Large Hadron collider can accelerate particles to energies of up to 10 Teraelectron Volts. Suppose we have two protons in the LHC. They are moving exactly in the same direction. If one of them has an energy of 5 TeV, and the other has an energy of 1 TeV, what speed difference measured for the velocity difference by an observer (a) moving with the 1 TeV particle and (b) at rest relative to the accelerator. You may make use of the fact that the proton rest energy is 938 MeV, that E m c and that 0 = 0 2 E = γm c . 0 2 Express the speeds in units of fractions of the speed of light.