Mechanik - Grundlagen Mechanik
- Schiefe Ebene
- $F_{H} = \frac{F_{G} \cdot h}{ l}$
- $F_{G} = \frac{F_{H} \cdot l}{ h}$
- $h = \frac{F_{H} \cdot l}{ F_{G} }$
- $l = \frac{F_{G} \cdot h}{ F_{H} }$
- $F_{N} = \frac{F_{G} \cdot b}{ l}$
- $F_{G} = \frac{F_{N} \cdot l}{ b}$
- $b = \frac{F_{N} \cdot l}{ F_{G} }$
- $l = \frac{F_{G} \cdot b}{ F_{N} }$
- $F_{H} = F_{G} \cdot sin \alpha$
- $F_{G} = \frac{ F_{H} }{sin \alpha }$
- $sin \alpha = \frac{F_{H} }{F_{G} }$
- $F_{N} = F_{G} \cdot cos \alpha$
- $F_{G} = \frac{ F_{N} }{cos \alpha }$
- $cos \alpha = \frac{F_{N} }{F_{G} }$
- Hebelgesetz
- $F_{1} = \frac{F_{2} \cdot l_{2} }{ l_{1} }$
- $l_{1} = \frac{F_{2} \cdot l_{2} }{ F_{1} }$
- Auftrieb in Flüssigkeiten
- $F_{A} = \rho \cdot g\cdot V$
- $\rho = \frac{F_{A} }{g\cdot V}$
- $V = \frac{F_{A} }{g \rho }$
- Körper in Flüssigkeiten
- $F_{A} = \rho \cdot g\cdot V$
- $\rho = \frac{F_{A} }{g\cdot V}$
- $V = \frac{F_{A} }{g \rho }$
Mechanik - Kinematik
- Beschleunigte Bewegung
- $v = a\cdot t$
- $a = \frac{v}{t}$
- $t = \frac{v}{a}$
- $s = \frac{1}{2}\cdot a\cdot t^{2}$
- $a = \frac{2\cdot s}{t^{2} }$
- $t = \sqrt{\frac{2\cdot s}{a}}$
- Beschleunigte Bewegung mit Anfangsgeschwindigkeit
- $v = v_{0} + a\cdot t$
- $v_{0} = v - a\cdot t$
- $t = \frac{v - v_{0} }{a}$
- $a = \frac{v - v_{0} }{ t}$
- $s = s_{0} + v_{0} \cdot t + \frac{1}{2}\cdot a\cdot t^{2}$
- $a = \frac{2\cdot (s - s_{0} - v_{0} \cdot t)}{ t^{2} }$
- $t = \frac{-v_{0} \pm \sqrt{v_{0} ^{2} -4\cdot 0,5\cdot a\cdot (s_{0} -s)}}{ a}$
- $s_{0} = s - v_{0} \cdot t - \frac{1}{2}\cdot a\cdot t^{2}$
- $v_{0} =\frac{s-s_{0} -0,5\cdot a\cdot t^{2} }{ t}$
- $v =\sqrt{2\cdot a \cdot s+ v_{0}^2}$
- $v_{0} =\sqrt{v^2-2\cdot a \cdot s}$
- Freier Fall
- $h = \frac{1}{2}\cdot g\cdot t^{2}$
- $g = \frac{2\cdot h}{ t^{2} }$
- $t = \sqrt{\frac{2\cdot h}{g}}$
- $v = \sqrt{2\cdot h\cdot g}$
- $h = \frac{ v^{2} }{2\cdot g}$
- Senkrechter Wurf nach oben
- $h = h_{0} + v_{0} \cdot t - \frac{1}{2}\cdot g\cdot t^{2}$
- $g = - \frac{2\cdot (h - h_{0} - v_{0} \cdot t)}{ t^{2} }$
- $t = \frac{-v_{0} \pm \sqrt{v_{0} ^{2} +4\cdot 0,5\cdot g\cdot (h_{0} -h)}}{ -g}$
- $h_{0} = h - v_{0} \cdot t + \frac{1}{2}\cdot g\cdot t^{2}$
- $v = v_{0} - g\cdot t$
- $v_{0} = v + g\cdot t$
- $t = \frac{v_{0} -v}{ g}$
- $g = \frac{v_{0} - v}{ t}$
- Waagrechter Wurf
- $y = \frac{1}{2}\cdot g\cdot t^{2}$
- $t = \sqrt{\frac{2\cdot y}{g}}$
- $s = v\cdot t$
- $v = \frac{s}{t}$
- Schiefer Wurf
- $x_{w} = \frac{v_{0} ^{2} \cdot sin(2\cdot \alpha )}{ g}$
- $t =\frac{v_{0} \cdot sin \alpha }{ g}$
- $v_{y} = v\cdot sin\alpha - g\cdot t$
- $v= \frac{ v_{y} +g\cdot t}{ sin\alpha }$
- $v_{x} = v\cdot cos\alpha$
- $v= \frac{ v_{x} }{ cos\alpha }$
- $v= \sqrt{ v_{x} ^{2} + v_{y} ^{2} }$
- $v_{x} = \sqrt{ v^{2} - v_{y} ^{2} }$
- $v_{y} = \sqrt{ v^{2} - v_{x} ^{2} }$
- $v_{y} = tan \alpha \cdot v_{x}$
- $tan \alpha = \frac{v_{y} }{v_{x} }$
- $v_{x} = \frac{v_{y} }{tan \alpha }$
- $y = x\cdot tan \alpha - \frac{ g\cdot x^{2} }{2\cdot v^{2} _{0} \cdot cos ^{2}\alpha }$
- $t =\frac{2\cdot v_{0} \cdot sin \alpha }{ g}$
Mechanik - Kreisbewegung
- Frequenz-Periodendauer
- $f = \frac{1}{T}$
- $T = \frac{1}{f}$
- $f = \frac{n}{t}$
- $t = \frac{n}{f}$
- $n = f\cdot t$
- Winkelgeschwindigkeit
- $\omega = 2\cdot \pi \cdot f$
- $f = \frac{\omega }{2\cdot \pi }$
- $\omega = \frac{2\cdot \pi }{ T}$
- $T = \frac{2\cdot \pi }{ \omega }$
- Zentralbeschleunigung
- $a_{z} = \omega ^{2} \cdot r$
- $\omega = \sqrt{\frac{a_{z} }{r}}$
- $r = \frac{a_{z} }{\omega }$
- Zentralkraft
- $F_{z} = m\cdot \omega ^{2} \cdot r$
- $m = \frac{ F_{z} }{\omega ^{2} \cdot r}$
- $\omega = \sqrt{\frac{ F_{z} }{m\cdot r}}$
- $r = \frac{ F_{z} }{m\cdot \omega ^{2} }$
Mechanik - Dynamik
- Gravitationsgesetz
- $F = G \cdot \frac{m_{1} \cdot m_{2} }{ r^{2} }$
- $r = \sqrt{\frac{G\cdot m_{1} \cdot m_{2} }{ F}}$
- $m_{1} = \frac{F\cdot r^{2} }{G\cdot m_{2} }$
- $m_{2} = \frac{F\cdot r^{2} }{G\cdot m_{1} }$
Mechanik - Energie - Arbeit - Leistung
- Spannarbeit-Spannenergie
- $W =\frac{1}{2}\cdot D\cdot s^{2}$
- $s = \sqrt{\frac{2\cdot W}{ D}}$
- $D =\frac{2\cdot W}{s^{2} }$
- Beschleunigungsarbeit - kinetische Energie
- $W = \frac{1}{2}\cdot m\cdot v^{2}$
- $m = \frac{2\cdot W}{ v^{2} }$
- $v = \sqrt{\frac{2\cdot W}{ m}}$
- Wirkungsgrad
- $\eta = \frac{P_{2} }{P_{1} }$
- $P_{1} = \frac{p_{2} }{\eta }$
- $P_{2} = \eta \cdot P_{1}$
Mechanik - Schwingungen/Wellen