Answer to Question #52487 in Mechanics | Relativity for Helen

Question

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.

Answer 1

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