Question

A particle's four momentum has the components of (4,1,1,0) kg. Determine:

i) the energy of the particle.

ii) the rest mass of the particle.

iii) the three velocity of the particle

Answer 1

Four momentum vector

p = (E/c, p_x, p_y, p_z ) = (4,1,1,0) kg

momentum units are kg-m/s , it is given as kg

The values is divided by c so that they are expressed in units of c - speed of light

E/c = 4c kg-m/s ; p_x =1c kg-m/s ; p_y =1c kg-m/s ; p_z =0

Total relativistic energy

E² = p²c² + (mc²)²  

p² = 1c² +1c² = 2c²

(mc²)² = 16c² - 2c²

mc² = 3.74c

rest mass m = 3.74/c = 1.25e-8 kg - conventional units

E = mc² - relativistic energy

= 1/(1-v²/c²)^1/2 = E/ mc² = 4/3.74 = 1.069

v²/c² = 0.1258

velocity v= 0.355c

The particle velocity v_x = v_y and v_z =0

v_x = v_y = v*cos(45) = 0.251c