Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision Next revisionBoth sides next revision | ||
183_notes:examples:momentumfast [2014/07/10 14:04] – caballero | 183_notes:examples:momentumfast [2014/07/10 14:18] – [Solution] caballero | ||
---|---|---|---|
Line 2: | Line 2: | ||
====== Example: Calculating the momentum of a fast-moving object ====== | ====== 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, | + | An electron is observed to be moving with a velocity of $\langle |
==== Setup ==== | ==== Setup ==== | ||
Line 11: | Line 11: | ||
* An electron is in motion | * An electron is in motion | ||
- | * It has a velocity of $\langle 2.05\times10^7, | + | * It has a velocity of $\langle |
* This velocity is near the speed of light ($c = 3.00\times10^8 \dfrac{m}{s}$). | * This velocity is near the speed of light ($c = 3.00\times10^8 \dfrac{m}{s}$). | ||
Line 27: | Line 27: | ||
==== Solution ==== | ==== Solution ==== | ||
+ | |||
+ | First, we compute the speed of the electron. | ||
+ | |||
+ | $$|\vec{v}| = \sqrt{v_x^2+v_y^2+v_z^2} = \sqrt{(-2.05\times10^7 \dfrac{m}{s})^2+(6.02\times10^7 \dfrac{m}{s})^2+(0)^2} = 6.36 \times 10^7 \dfrac{m}{s}$$ | ||
+ | |||
+ | 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. | ||
+ | |||
+ |