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Example: Calculating the momentum of a fast-moving object
An electron is observed to be moving with a velocity of $\langle 2.05e7, 6.02e7, 0\rangle\:\dfrac{m}{s}$. Determine the momentum of this electron.
Setup
You need to compute the momentum of this electron using the information provided and any information that you can collect or assume.
Facts
- An electron is in motion
- It has a velocity of $\langle 2.05e7, 6.02e7, 0\rangle\:\dfrac{m}{s}$.
- This velocity is near the speed of light ($c = 3.00e8 \dfrac{m}{s}$).
Lacking
- The mass of the electron is not given, but can be found online ($m_e = 9.11e-31 kg$).
Approximations & Assumptions
- The electron does not experience any interactions, so its velocity will remain unchanged.
Representations
- The momentum of the electron is given by $\vec{p} = \gamma m \vec{v}$ where $\gamma = \dfrac{1}{\sqrt{1-\left(\dfrac{|\vec{v}|}{c}\right)^2}}$.