A proton with mass 1.67 × 10−²⁷ kg moves with a speed of 0.800c in an accelerator.What is its relativistic momentum? (c = 3.00 × 10⁸ m/s) A) 2.40 × 10−¹⁹ kg⋅m/s B) 6.68 × 10−¹⁹ kg⋅m/s C) 0.530 × 10−¹⁹ kg⋅m/s D) 3.76 × 10−¹⁹ kg⋅m/s

Question

Quizplus · Accepted Answer

The relativistic momentum of the proton is given by:
p = γmv
where γ is the Lorentz factor:
γ = 1/√(1 - (v/c)^2)
= 1/√(1 - (0.800c/c)^2) = 1/√(1 - 0.64) = 1/0.7682 = 1.302
and m is the mass of the proton:
m = 1.67 × 10^-27 kg
Therefore, we have:
p = γmv = 1.302(1.67 × 10^-27 kg)(0.800c) = 6.68 × 10^-19 kg⋅m/s
Thus, the best choice is B.

A Proton with Mass 1