Question

Particle X has a speed of 0.850 c and a momentum of 8.61×10^-19kgm/s. What is the mass of the particle?

What is the rest energy of the particle?

What is the kinetic energy of the particle?

What is the total energy of the particle?

Answer 1

Given,
Speed of Particle = 0.850 c
Momentum = 8.61×10-19kgm/s
a)
As speed of Particle is near to speed of light , we will use Relativistic Mechanics to solve for mass and energy -

Momentum = Y*mo*v
where ,
Y = 1/ sqrt(1 - (v/c)²)
Y = 1/sqrt (1 - 0.850^2) = 1.898
mo = Rest mass of Particle
v = Velocity of Particle = 0.850 c

Substituting Values   

Y*mo*v = 8.61×10-19kgm/s
1.898 * 0.850 * 3 *10^8 * mo = 8.61×10^-19kgm/s
mo = 1.778 * 10^-27 Kg

Rest Mass of Particle mo = 1.778 * 10^-27 Kg

b)
Rest Energy of Particle = Rest Mass of particle (mo) * c^2
Rest Energy of Particle = 1.778 * 10^-27 * (3 * 10^8)^2
Rest Energy of Particle = 1.6002 * 10^-10 J

c)
Kinetic Energy = (m-mo)c^2
where m is mass of particle at speed = 0.850 c
m = Y * mo
Therefore ,
Kinetic Energy = (Ymo-mo)c^2
Kinetic Energy = (Y-1) * moc^2
Kinetic Energy = (1.898 - 1) * 1.6002 * 10^-10 J
Kinetic Energy = 1.437 * 10^-10 J

d)
Total Energy = Kinetic Energy + Rest Energy
Total Energy = 1.437 * 10^-10 + 1.6002 * 10^-10
Total Energy = 3.0372 * 10^-10 J