Unterschiede
Hier werden die Unterschiede zwischen zwei Versionen angezeigt.
Beide Seiten der vorigen Revision Vorhergehende Überarbeitung Nächste Überarbeitung | Vorhergehende Überarbeitung | ||
electrical_engineering_2:task_1.2.1_with_calc [2022/06/27 21:50] tfischer |
electrical_engineering_2:task_1.2.1_with_calc [2023/03/15 13:20] (aktuell) mexleadmin |
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Zeile 2: | Zeile 2: | ||
<WRAP right> | <WRAP right> | ||
- | {{elektrotechnik_1: | + | {{drawio> |
</ | </ | ||
Given is the arrangement of electric charges in the picture on the right. \\ | Given is the arrangement of electric charges in the picture on the right. \\ | ||
The following force effects result: \\ | The following force effects result: \\ | ||
- | $F_{01}=-5 N$ \\ | + | $F_{01}=-5 |
- | $F_{02}=-6 N$ \\ | + | $F_{02}=-6 |
- | $F_{03}=+3 N$ | + | $F_{03}=+3 |
Calculate the magnitude of the resulting force. | Calculate the magnitude of the resulting force. | ||
Zeile 27: | Zeile 27: | ||
For the resolution of the coordinates it is necessary to get the angles $\alpha_{0n}$ of the forces with respect to the x-axis. \\ | For the resolution of the coordinates it is necessary to get the angles $\alpha_{0n}$ of the forces with respect to the x-axis. \\ | ||
In the chosen coordinate system this leads to: $\alpha_{0n} = atan(\frac{\Delta y}{\Delta x})$ \\ | In the chosen coordinate system this leads to: $\alpha_{0n} = atan(\frac{\Delta y}{\Delta x})$ \\ | ||
- | $\alpha_{01} = atan(\frac{3}{1})= 1.249 = 71.6°$ \\ | + | $\alpha_{01} = \rm{atan}(\frac{3}{1})= 1.249 = 71.6°$ \\ |
- | $\alpha_{02} = atan(\frac{4}{3})= 0.927 = 53.1°$ \\ | + | $\alpha_{02} = \rm{atan}(\frac{4}{3})= 0.927 = 53.1°$ \\ |
- | $\alpha_{03} = atan(\frac{0}{3})= 0= 0°$ \\ | + | $\alpha_{03} = \rm{atan}(\frac{0}{3})= 0= 0°$ \\ |
Consequently, | Consequently, | ||
\begin{align*} | \begin{align*} | ||
- | F_{x,0} &= F_{x,01} + F_{x,02} + F_{x,03} && | \quad \text{mit } F_{x,0n} = F_{0n} \cdot sin(\alpha_{0n}) | + | F_{x,0} &= F_{x,01} + F_{x,02} + F_{x,03} && | \quad \text{with } F_{x,0n} = F_{0n} \cdot \rm{sin}(\alpha_{0n}) |
- | F_{x,0} &= (-5N) \cdot sin(71.6°) + (-6N) \cdot sin(53.1°) + (+3N) \cdot sin(0°) | + | F_{x,0} &= (-5~\rm{N}) \cdot \rm{sin}(71.6°) + (-6~\rm{N}) \cdot \rm{sin}(53.1°) + (+3~\rm{N}) \cdot \rm{sin}(0°) \\ |
- | F_{x,0} &= -2.18 N \\ \\ | + | F_{x,0} &= -2.18 ~\rm{N} \\ \\ |
- | F_{y,0} &= F_{x,01} + F_{x,02} + F_{x,03} && | \quad \text{mit } F_{y,0n} = F_{0n} \cdot cos(\alpha_{0n}) | + | F_{y,0} &= F_{x,01} + F_{x,02} + F_{x,03} && | \quad \text{with } F_{y,0n} = F_{0n} \cdot \rm{cos}(\alpha_{0n}) |
- | F_{y,0} &= (-5N) \cdot cos(71.6°) + (-6N) \cdot cos(53.1°) + (+3N) \cdot cos(0°) | + | F_{y,0} &= (-5~\rm{N}) \cdot \rm{cos}(71.6°) + (-6~\rm{N}) \cdot \rm{cos}(53.1°) + (+3~\rm{N}) \cdot cos(0°) |
- | F_{y,0} &= -9.54 N \\ \\ | + | F_{y,0} &= -9.54 ~\rm{N} \\ \\ |
\end{align*} | \end{align*} | ||
Zeile 49: | Zeile 49: | ||
<button size=" | <button size=" | ||
\begin{align*} | \begin{align*} | ||
- | F_0 &= \sqrt{ (-2.18 N)^2 + (-9.54 N)^2 } = 9.79 N \rightarrow 9.8 N \\ | + | F_0 &= \sqrt{ (-2.18 |
\end{align*} | \end{align*} | ||
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