Úprava 4. příkladu z FYI
This commit is contained in:
parent
2b73d2d491
commit
4e749fb81f
2 changed files with 8 additions and 7 deletions
|
@ -16,14 +16,15 @@ Na základě obecného vzorce pro potenciální energii $W_{pot}(r) = -\kappa\fr
|
||||||
|
|
||||||
### Výpočet
|
### Výpočet
|
||||||
|
|
||||||
- $\displaystyle W_{pot}(h) = -\kappa \cdot \frac{m \cdot M_{z}}{R_{z} + h} + \kappa \cdot \frac{m \cdot M_{z}}{R_{z}} = \kappa \cdot m \cdot M_{z} \cdot \left[ \frac{1}{R_{z}} - \frac{1}{R_{z}+h} \right] =$
|
$\displaystyle W_{pot}(h) = -\kappa \cdot \frac{m \cdot M_{z}}{R_{z} + h} + \kappa \cdot \frac{m \cdot M_{z}}{R_{z}} = \kappa \cdot m \cdot M_{z} \cdot \left[ \frac{1}{R_{z}} - \frac{1}{R_{z}+h} \right] =$
|
||||||
- $\displaystyle= \kappa \cdot m \cdot M_{z} \cdot \left[ \frac{\cancel{R_{z}}+h-\cancel{R_{z}}}{R_{z}(R_{z}+h)} \right] = \kappa \cdot m \cdot M_{z} \cdot \frac{h}{R_{z}^2\left( 1+\frac{h}{R_{z}} \right)} =$
|
|
||||||
- $\displaystyle = m \cdot \left( \kappa \cdot \frac{M_{z}}{R^2_{z}} \right) \cdot h = m \cdot g \cdot h$
|
|
||||||
|
|
||||||
|
$\displaystyle= \kappa \cdot m \cdot M_{z} \cdot \left[ \frac{\cancel{R_{z}}+h-\cancel{R_{z}}}{R_{z}(R_{z}+h)} \right] = \kappa \cdot m \cdot M_{z} \cdot \frac{h}{R_{z}^2\left( 1+\frac{h}{R_{z}} \right)} =$
|
||||||
|
|
||||||
+ $h \ll R_{z} \implies \text{zanedbáme}$
|
$\displaystyle = m \cdot \left( \kappa \cdot \frac{M_{z}}{R^2_{z}} \right) \cdot h = m \cdot g \cdot h$
|
||||||
+ $\displaystyle\kappa \cdot \frac{M_{z}}{R_{z}^2} \sim g$
|
|
||||||
+ pouze blízko povrchu Země
|
Pouze blízko povrchu Země
|
||||||
|
- $h \ll R_{z} \implies \text{zanedbáme}$
|
||||||
|
- $\displaystyle\kappa \cdot \frac{M_{z}}{R_{z}^2} \sim g$
|
||||||
|
|
||||||
### Výsledek
|
### Výsledek
|
||||||
|
|
||||||
|
|
File diff suppressed because one or more lines are too long
Before Width: | Height: | Size: 26 KiB After Width: | Height: | Size: 26 KiB |
Loading…
Reference in a new issue