Momentum: A particle is moving at 0.75c relative to a lab on Earth. By what percentage is the Newtonian expression for its momentum in error? (The percentage error is the difference between the erroneous and correct values, divided by the correct one).
A) 34%
B) 28%
C) 38%
D) 43%

Question

Quizplus · Accepted Answer

The Newtonian expression for momentum is p = mv, but at relativistic speeds, the correct expression is p = γmv, where γ is the Lorentz factor. At 0.75c, γ ≈ 1.511. The percentage error is (γ - 1)/γ = (1.511 - 1)/1.511 ≈ 0.338, or 33.8%, which rounds to 34%.

Momentum: a Particle Is Moving at 0