Question

A proton moves at \(0.90 c .\) What is its momentum in \(\mathrm{SI}\) units?

Short answer

Answer: The momentum of the proton moving at 0.90c is approximately \(4.509 \times 10^{-19}\) kg m/s.

Step-by-step solution

Identify the given information and the required constants

We are given the velocity of the proton (\(0.90 c\)) and are asked to find its momentum. We need the mass of a proton and the speed of light (in SI units) as additional information. - Proton mass (m) = \(1.67 \times 10^{-27}\) kg - Speed of light (c) = \(3.00 \times 10^8\) m/s

Calculate the velocity of the proton

The proton is moving at \(0.90 c\), so its velocity (v) can be calculated using the following formula: \(v = 0.90 \times c\) \(v = 0.90 \times 3.00 \times 10^8\) m/s Plug in the value of the speed of light and perform the multiplication to find the velocity of the proton: \(v = 2.70 \times 10^8\) m/s

Calculate the momentum of the proton

Now that we have the mass of a proton (m) and its velocity (v), we can calculate its momentum (p) using the formula: \(p = mv\) Plug in the values for mass and velocity and perform the multiplication: \(p = (1.67 \times 10^{-27} \text{ kg})(2.70 \times 10^8 \text{ m/s})\)

Calculate the momentum in SI units

Multiply the mass and velocity together: \(p = 4.509 \times 10^{-19}\) kg m/s The momentum of the proton moving at \(0.90c\) is approximately \(4.509 \times 10^{-19}\) kg m/s in SI units.