A proton moves with a speed of 0.950c. Calculate (a) it's rest energy, (b) it's total energy, and (c) it's kinetic energy.
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Expert's answer
2015-05-14T04:06:59-0400
A proton moves with a speed of 0.950c. Calculate (a) it's rest energy, (b) it's total energy, and (c) it's kinetic energy.
when a particle moves with very high velocity ( close to the speed of light ) then the moving mass of the particle is given as : M = mp/sqrt(1-(v^2/c^2)) where mp = 1.67*10^(-27) kg
In special relatively the energy of an object of rest mass mp is given by E = mp*c^2/sqrt(1 - (v/c)^2)
Solution a: When v=0 you get E=mp*c^2 This is the rest energy of the object E = mp * c^2 = 1.503*10^(-10) J = 938,26 MeV So rest energy = mp * c^2
Solution b: ET = rest energy/sqrt(1-(v/c)^2)
Solution c: The object kinetic energy is the energy in excess of the rest energy so its given by KE = E - mc^2 When the speed of the object is much smaller than the speed of light, you can neglect the higher-order terms and recover the Newtonian expression for kinetic energy
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