Question

If the formula for kinetic energy is KE=1/2mv^2 then why is Einstein’s equation for the total energy in a given mass E=mc^2? Shouldn’t it be E=1/2mc^2? They are kind of the same equation and in my mind Einstein was basically declaring that the energy a given mass would be limited by the maximum velocity observed in the universe.

Answer 1

E=mc^2 is relativistic mechanical energy. here the energy E will be available only if all the mass gets converted into energy. that mass will no longer have property of mass i.e. physical appereance or say its volume.its like mass disappeared into something known as energy. this enrgy travels with the speed of light , which are known as rays.

where as KE=0.5mv^2 is the energy possesed by a moving mass which is again dependent on different frame of references. in a particluar reference frame, KE may be 0 while at the same time it may be non zero in other Reference frame.