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author | Nao Pross <naopross@thearcway.org> | 2019-12-24 15:40:53 +0100 |
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committer | Nao Pross <naopross@thearcway.org> | 2019-12-24 15:40:53 +0100 |
commit | 9aa6305a9fc8002fe438846cc605827a0ff9f965 (patch) | |
tree | 456077fdbb56616f1004098cd2e47445105da8f2 | |
parent | Add postulates start energy and deformation (diff) | |
download | Ph1Mech-master.tar.gz Ph1Mech-master.zip |
-rw-r--r-- | Ph1Mech-zf.tex | 22 | ||||
-rw-r--r-- | build/Ph1Mech-zf.pdf | bin | 73667 -> 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 Binary files differindex 80f4dc9..cfcad24 100644 --- a/build/Ph1Mech-zf.pdf +++ b/build/Ph1Mech-zf.pdf |