183_notes:examples:momentumfast

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183_notes:examples:momentumfast [2014/07/10 14:12] – [Solution] caballero183_notes:examples:momentumfast [2014/07/10 14:21] – [Solution] caballero
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 $$|\vec{v}| = \sqrt{v_x^2+v_y^2+v_z^2} = \sqrt{(-2.05\times10^7 \dfrac{m}{s})^2+(6.02\times10^7 \dfrac{m}{s})^2+(0)^2} = 6.36 \times 10^7 \dfrac{m}{s}$$ $$|\vec{v}| = \sqrt{v_x^2+v_y^2+v_z^2} = \sqrt{(-2.05\times10^7 \dfrac{m}{s})^2+(6.02\times10^7 \dfrac{m}{s})^2+(0)^2} = 6.36 \times 10^7 \dfrac{m}{s}$$
  
 +Next, we compute the gamma factor.
 +
 +$$\gamma = \dfrac{1}{\sqrt{1-\left(\dfrac{|\vec{v}|}{c}\right)^2}} = \dfrac{1}{\sqrt{1-\left(\dfrac{6.36 \times 10^7 \dfrac{m}{s}}{3.00 \times 10^8 \dfrac{m}{s}}\right)^2}} = \dfrac{1}{\sqrt{1-(0.212)^2}}=1.02$$
 +
 +Finally, we compute the momentum vector.
 +
 +$$\vec{p} = \gamma m \vec{v} = (1.02) (9.11\times10^{-31} kg) \langle -2.05\times10^7, 6.02\times10^7, 0\rangle\dfrac{m}{s} = \langle -1.91 \times 10^{-23}, 5.61\times10^{-23},0\rangle\:\dfrac{kg\:m}{s}$$
  
  • 183_notes/examples/momentumfast.txt
  • Last modified: 2024/01/30 14:18
  • by hallstein