Question

Calculate γ for a proton that has a momentum of 1.00 kg⋅m/s.

(a) 1.00
(b) 0.80
(c) 1.25
(d) 1.50

Answer 1

To calculate the Lorentz factor (gamma) for a proton with a given momentum, one must solve for the velocity using the proton's momentum and mass, then use the Lorentz factor equation, which depends on the velocity and the speed of light.

Step-by-step explanation:

To calculate γ (gamma) for a proton that has a momentum of 1.00 kg·m/s, we use the relativistic relationship between momentum (ℓ) and mass-energy (γmc):

ℓ = γmv

Where ℓ is the momentum, γ is the Lorentz factor, m is the mass of the proton, and v is the velocity. The mass of a proton is approximately 1.67 × 10-27 kg. The Lorentz factor is given by:

γ = 1 / √(1 - v2/c2)

where c is the speed of light in a vacuum (approximately 3.00 × 108 m/s). To find γ, we first need to solve for velocity (v) using the proton's momentum and mass, then calculate γ using the Lorentz factor equation.