Question

Part A

A proton (rest mass 1.67×10^−27kg ) is moving at 0.955c. Find the momentum of the proton. Express your answer with the appropriate units. P = Part B
Find the proton's acceleration if a force of 9.00×10^−14 N acts on the proton in the direction of its motion. Express your answer with the appropriate units. Gparallel = Part C
Find the proton's acceleration if a force of 9.00×10^−14 N acts on the proton perpendicular to the direction of its motion. Express your answer with the appropriate units.
Gperpendicular =

Answer 1

To find the momentum of a relativistic proton, calculate the Lorentz factor and use the formula p = γmv. Use Newton's second law to determine acceleration when a force acts on the proton either parallel or perpendicular to its motion, considering the relativistic mass for parallel forces.

Step-by-step explanation:

The momentum p of a particle with rest mass m moving at a relativistic speed v can be calculated using the formula p = γmv, where γ (gamma) is the Lorentz factor given by γ = 1/√(1 - v^2/c^2) and c is the speed of light.

Using the provided data for a proton with rest mass m = 1.67 × 10^-27 kg moving at a velocity v = 0.955c, we first calculate the Lorentz factor γ and then the momentum p.

For parts B and C, when a force F acts on a particle with mass m, the acceleration a can be calculated using Newton's second law, given by F = ma. If the force is parallel to the proton's motion, the mass in this formula is the relativistic mass calculated by m' = γm. If the force is perpendicular to the proton's motion, the Lorentz factor γ does not apply.

Part B would involve the relativistic mass, and Part C would involve the rest mass when calculating the acceleration.