1. The problem statement, all variables and given/known data Calculate the kinetic energy required to accelerate a proton from a rest position to 0.9999c. The mass of the proton is 1.67x10-27 Find the ratio of kinetic energy to the energy of a proton at rest 2. Relevant equations Erest = mc2 Ek = mc2/√(1-v2/c2) 3. The attempt at a solution Ok So calculating the rest energy is easy E= (1.67x10-27)(3x108)2 E= 1.503x10-10 Ekinetic= mc2/√(1-v2/c2) =((1.67x10-27)(3x108)2)/√(1-0.9999c2/c2) =1.503x10-10/√(1-0.9998) = 1.503x10-10/ 0.0141418 = 1x10 -8 J This doesn't seem like a lot of energy to accelerate something to almost light speed I feel like I am missing something... even when using Etotal =Erest+EK I get 1x10-8 J can someone point out my mistake? Ratio of kinetic energy to rest energy is 1.503x10-10 / 1x10-8 = 1.503 % of the energy is kinetic energy ? ( really unsure about this) Thanks! Happy monday !