183_notes:examples:momentumfast

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Example: Calculating the momentum of a fast-moving object

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

Facts

  • 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 ($c = 3.00\times10^8 \dfrac{m}{s}$).

Lacking

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

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 $\gamma = \dfrac{1}{\sqrt{1-\left(\dfrac{|\vec{v}|}{c}\right)^2}}$.

First, we compute the speed of the electron.

$$|\vec{v}| = \sqrt{v_x^2+v_y^2+v_z^2} = \sqrt{(-2.05\times10^7 \dfrac{m}{s})^2+(6.02\times10^7 \dfrac{m}{s})^2+(0)^2} = 6.36 \times 10^7 \dfrac{m}{s}$$

  • 183_notes/examples/momentumfast.1405001517.txt.gz
  • Last modified: 2014/07/10 14:11
  • by caballero