Úprava 4. příkladu z FYI
This commit is contained in:
parent
3e39b15198
commit
93d6f99b7e
2 changed files with 10 additions and 5 deletions
|
@ -16,9 +16,14 @@ Na základě obecného vzorce pro potenciální energii $W_{pot}(r) = -\kappa\fr
|
|||
|
||||
### Výpočet
|
||||
|
||||
$\displaystyle W_{pot}(h) = -\kappa \cdot \frac{m \cdot M}{R_{z} + h} + \kappa \cdot \frac{m \cdot M}{R_{z}} = \kappa \cdot m \cdot M_{z} \cdot \left[ \frac{1}{R_{z}} - \frac{1}{R_{z}+h} \right] = \dots = m \cdot \left( \kappa \cdot \frac{M_{z}}{R_{z}} \right) \cdot h = m \cdot g \cdot h \cdot \frac{1}{1+\frac{h}{R_{z}}}$
|
||||
- $h \ll R_{z} \implies \text{zanedbáme}$
|
||||
- pouze blízko povrchu Země
|
||||
- $\displaystyle W_{pot}(h) = -\kappa \cdot \frac{m \cdot M_{z}}{R_{z} + h} + \kappa \cdot \frac{m \cdot M_{z}}{R_{z}} = \kappa \cdot m \cdot M_{z} \cdot \left[ \frac{1}{R_{z}} - \frac{1}{R_{z}+h} \right] =$
|
||||
- $\displaystyle= \kappa \cdot m \cdot M_{z} \cdot \left[ \frac{\cancel{R_{z}}+h-\cancel{R_{z}}}{R_{z}(R_{z}+h)} \right] = \kappa \cdot m \cdot M_{z} \cdot \frac{h}{R_{z}^2\left( 1+\frac{h}{R_{z}} \right)} =$
|
||||
- $\displaystyle = m \cdot \left( \kappa \cdot \frac{M_{z}}{R^2_{z}} \right) \cdot h = m \cdot g \cdot h$
|
||||
|
||||
|
||||
+ $h \ll R_{z} \implies \text{zanedbáme}$
|
||||
+ $\displaystyle\kappa \cdot \frac{M_{z}}{R_{z}^2} \sim g$
|
||||
+ pouze blízko povrchu Země
|
||||
|
||||
### Výsledek
|
||||
|
||||
|
|
File diff suppressed because one or more lines are too long
Before Width: | Height: | Size: 14 KiB After Width: | Height: | Size: 26 KiB |
Loading…
Reference in a new issue