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authorNao Pross <naopross@thearcway.org>2019-12-24 15:40:53 +0100
committerNao Pross <naopross@thearcway.org>2019-12-24 15:40:53 +0100
commit9aa6305a9fc8002fe438846cc605827a0ff9f965 (patch)
tree456077fdbb56616f1004098cd2e47445105da8f2
parentAdd postulates start energy and deformation (diff)
downloadPh1Mech-master.tar.gz
Ph1Mech-master.zip
Add rocketHEADmaster
-rw-r--r--Ph1Mech-zf.tex22
-rw-r--r--build/Ph1Mech-zf.pdfbin73667 -> 75996 bytes
2 files changed, 17 insertions, 5 deletions
diff --git a/Ph1Mech-zf.tex b/Ph1Mech-zf.tex
index 7dde7cd..62f1c1c 100644
--- a/Ph1Mech-zf.tex
+++ b/Ph1Mech-zf.tex
@@ -81,10 +81,10 @@
Kraft & \v{F} & kg \(\cdot\) m/s\(^2\) \\
\\
Energie & E & J = Ws \\
- & & J = kg m\(^2\)/s\(^2\) \\
+ & & kg m\(^2\)/s\(^2\) \\
& &
\\
- Spannung & \sigma,\tau & Pa = kg/m\(^2\)
+ Spannung & \sigma,\tau & Pa
\end{tabular}\par
\end{minipage}
\begin{minipage}{.5\textwidth}
@@ -337,7 +337,7 @@
\[
\tilde E = K + V + \textcolor{gray}{T + E_M} \qquad \tilde E = k
\]
- Die kinetische Energie ist der Arbeit der Kraft des Impulses.
+ Die kinetische Energie ist der Arbeit des Kraftsto{\ss}.
\begin{align*}
K_\text{tr} &= \int_\gamma \frac{\dd{\v{p}}}{\dd{t}} \cdot \dd{\v{s}} \doteq \frac{m}{2}\v{v}^2 \\
K_\text{rot} &= \int_\phi \frac{\dd{\v{L}}}{\dd{t}} \,\dd{\vs{\varphi}} \doteq \frac{J}{2}\vs{\omega}^2
@@ -348,7 +348,7 @@
V_g &= mg\Delta z \quad \text{wobei} \quad g = \frac{G M_E}{r_E^2} \\
\end{align*}
\[
- V_F = cs^2
+ V_F = -\int_0^d -cs\,\dd{s} = cd^2
\]
\end{multicols}
\end{mdframed}
@@ -371,7 +371,19 @@
\mdfsubtitle{St\"o{\ss}e}
\mdfsubtitle{Nicht konstante Masse}
- Raketenantrieb
+ (Schub) Raketenantrieb
+ \[
+ \overbrace{\dd{m}(\v{v} - \v{u})}^{\v{p}_s}
+ +
+ \overbrace{(m - \dd{m})(\v{v} + \dd{\v{v}})}^{\v{p}_r}
+ = m\v{v}
+ \]
+ \[
+ \v{v} = \v{u}\int\frac{\dd{m}}{m} = \v{u}\ln(m) + \v{v}_0 \quad (m > 0)
+ \]
+ \[
+ \v{F}_s = \frac{\dd{m}}{\dd{t}}\dot{\v{x}}
+ \]
\end{mdframed}
diff --git a/build/Ph1Mech-zf.pdf b/build/Ph1Mech-zf.pdf
index 80f4dc9..cfcad24 100644
--- a/build/Ph1Mech-zf.pdf
+++ b/build/Ph1Mech-zf.pdf
Binary files differ