From 4e749fb81f67023b1d7c40dd8b627be794b7f405 Mon Sep 17 00:00:00 2001 From: Filip Znachor Date: Sun, 25 Jun 2023 17:21:52 +0200 Subject: [PATCH] =?UTF-8?q?=C3=9Aprava=204.=20p=C5=99=C3=ADkladu=20z=20FYI?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- KFY FYI1/Priklad04.md | 13 +++++++------ KFY FYI1/_assets/priklad4.svg | 2 +- 2 files changed, 8 insertions(+), 7 deletions(-) diff --git a/KFY FYI1/Priklad04.md b/KFY FYI1/Priklad04.md index 2da48df..c58b302 100644 --- a/KFY FYI1/Priklad04.md +++ b/KFY FYI1/Priklad04.md @@ -16,14 +16,15 @@ Na základě obecného vzorce pro potenciální energii $W_{pot}(r) = -\kappa\fr ### Výpočet -- $\displaystyle W_{pot}(h) = -\kappa \cdot \frac{m \cdot M_{z}}{R_{z} + h} + \kappa \cdot \frac{m \cdot M_{z}}{R_{z}} = \kappa \cdot m \cdot M_{z} \cdot \left[ \frac{1}{R_{z}} - \frac{1}{R_{z}+h} \right] =$ -- $\displaystyle= \kappa \cdot m \cdot M_{z} \cdot \left[ \frac{\cancel{R_{z}}+h-\cancel{R_{z}}}{R_{z}(R_{z}+h)} \right] = \kappa \cdot m \cdot M_{z} \cdot \frac{h}{R_{z}^2\left( 1+\frac{h}{R_{z}} \right)} =$ -- $\displaystyle = m \cdot \left( \kappa \cdot \frac{M_{z}}{R^2_{z}} \right) \cdot h = m \cdot g \cdot h$ +$\displaystyle W_{pot}(h) = -\kappa \cdot \frac{m \cdot M_{z}}{R_{z} + h} + \kappa \cdot \frac{m \cdot M_{z}}{R_{z}} = \kappa \cdot m \cdot M_{z} \cdot \left[ \frac{1}{R_{z}} - \frac{1}{R_{z}+h} \right] =$ +$\displaystyle= \kappa \cdot m \cdot M_{z} \cdot \left[ \frac{\cancel{R_{z}}+h-\cancel{R_{z}}}{R_{z}(R_{z}+h)} \right] = \kappa \cdot m \cdot M_{z} \cdot \frac{h}{R_{z}^2\left( 1+\frac{h}{R_{z}} \right)} =$ -+ $h \ll R_{z} \implies \text{zanedbáme}$ -+ $\displaystyle\kappa \cdot \frac{M_{z}}{R_{z}^2} \sim g$ -+ pouze blízko povrchu Země +$\displaystyle = m \cdot \left( \kappa \cdot \frac{M_{z}}{R^2_{z}} \right) \cdot h = m \cdot g \cdot h$ + +Pouze blízko povrchu Země +- $h \ll R_{z} \implies \text{zanedbáme}$ +- $\displaystyle\kappa \cdot \frac{M_{z}}{R_{z}^2} \sim g$ ### Výsledek diff --git a/KFY FYI1/_assets/priklad4.svg b/KFY FYI1/_assets/priklad4.svg index 13281e3..8426b85 100644 --- a/KFY FYI1/_assets/priklad4.svg +++ b/KFY FYI1/_assets/priklad4.svg @@ -1,4 +1,4 @@ -
Rz
Rz
Mz
Mz
r1 = Rz
r1 = Rz
r2 = Rz + h
r2 = Rz + h
h
h
koncová poloha
koncová poloha
výchozí poloha
výchozí poloha
R = y
R = yText is not SVG - cannot display \ No newline at end of file +
Rz
Rz
Mz
Mz
r1 = Rz
r1 = Rz
r = Rz + h
r = Rz + h
h
h
koncová poloha
koncová poloha
výchozí poloha
výchozí poloha
R = y
R = yText is not SVG - cannot display \ No newline at end of file