Question

Particle X has a speed of 0.760 c and a momentum of 4.87×10^-19 kgm/s.

1. What is the mass of the particle?

2. What is the rest energy of the particle?
3. What is the kinetic energy of the particle?
4. What is the total energy of the particle?

Answer 1

p = m0 v / sqrt ( 1- (v/c)^2)

here v = speed = 0.76 c, p = 4.87*10^(-19) kgm/s

so, 4.87*10^(-19) = (m0 * 0.76 * (10^8))/ sqrt ( 1- (0.76 c/ c)^2)

m0 = 4.87*10^(-19) * sqrt ( 1- (0.76 c/ c)^2) / (0.76 * (10^8))

m0 = 4.15 * (10^-27) Kg is the rest mass.

rest energy = m0 * c^2 = 4.15 * (10^-27) * (3*10^8)^2 = 3.73 * (10^-10) J

Kinetic Energy = (m - m0)c^2 = (m0/sqrt ( 1- (0.76 c/ c)^2) - m0)c^2

KE = (4.15 * (10^-27) / 0.649 - 4.15 * (10^-27))*(3*10^8)^2 = 2.02*10^-10 J

Total Energy = KE + rest energy =   2.02*10^-10 + 3.73 * (10^-10) = 5.75*10^(-10) J