Example: Calculating the momentum of a fast-moving object

An electron is observed to be moving with a velocity of $\langle 2.05\times10^7, 6.02\times10^7, 0\rangle\:\dfrac{m}{s}$. Determine the momentum of this electron.

You need to compute the momentum of this electron using the information provided and any information that you can collect or assume.

• An electron is in motion
• It has a velocity of $\langle 2.05\times10^7, 6.02\times10^7, 0\rangle\:\dfrac{m}{s}$.
• This velocity is near the speed of light ($c = 3.00\times10^8 \dfrac{m}{s}$).

• The mass of the electron is not given, but can be found online ($m_e = 9.11\times10^{-31} kg$).

• The electron does not experience any interactions, so its velocity will remain unchanged.

• The momentum of the electron is given by $\vec{p} = \gamma m \vec{v}$ where $\gamma = \dfrac{1}{\sqrt{1-\left(\dfrac{|\vec{v}|}{c}\right)^2}}$.