If the LHC collider can accellerate protons to near the speed of light is their increase in mass negligible

The increase in mass of particles at relativistic speeds can be quite significant. Relativistic mass is calculated from:


m = \frac {m_0}{\sqrt{1 - \frac {v^2}{c^2}}}


at 95% speed of light mass increases over rest by a factor of 3.

Actually a better way tio state this is that the particle momentum increases at relativistic speeds following:


p = \frac {mv}{\sqrt{1 - \frac {v^2}{c^2}}}