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 [2023/03/10 11:26] – mexleadmin | electrical_engineering_2:task_1.2.1_with_calc [2024/06/25 23:11] (aktuell) – [Bearbeiten - Panel] mexleadmin | ||
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| Zeile 1: | Zeile 1: | ||
| - | <panel type=" | + | <panel type=" |
| <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: \\ | ||
| - | $F_{01}=-5 ~N$ \\ | + | $F_{01}=-5 ~\rm{N}$ \\ |
| - | $F_{02}=-6 ~N$ \\ | + | $F_{02}=-6 ~\rm{N}$ \\ |
| - | $F_{03}=+3 ~N$ | + | $F_{03}=+3 ~\rm{N}$ |
| Calculate the magnitude of the resulting force. | Calculate the magnitude of the resulting force. | ||
| <button size=" | <button size=" | ||
| - | * How have the forces be prepared, | + | * How have the forces be prepared, to add them correctly? |
| </ | </ | ||
| Zeile 24: | Zeile 24: | ||
| The forces have to be resolved into coordinates. Here, it is recommended to use an orthogonal coordinate system ($x$ and $y$). \\ | The forces have to be resolved into coordinates. Here, it is recommended to use an orthogonal coordinate system ($x$ and $y$). \\ | ||
| - | The coordinate system | + | The coordinate system shall be in such a way, that the origin |
| - | 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: $\alpha_{0n} = \arctan(\frac{\Delta y}{\Delta x})$ \\ |
| - | $\alpha_{01} = atan(\frac{3}{1})= 1.249 = 71.6°$ \\ | + | $\alpha_{01} = \arctan(\frac{3}{1})= 1.249 = 71.6°$ \\ |
| - | $\alpha_{02} = atan(\frac{4}{3})= 0.927 = 53.1°$ \\ | + | $\alpha_{02} = \arctan(\frac{4}{3})= 0.927 = 53.1°$ \\ |
| - | $\alpha_{03} = atan(\frac{0}{3})= 0= 0°$ \\ | + | $\alpha_{03} = \arctan(\frac{0}{3})= 0= 0°$ \\ |
| 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} &= (-5~N) \cdot sin(71.6°) + (-6~N) \cdot sin(53.1°) + (+3~N) \cdot sin(0°) | ||
| - | F_{x,0} &= -2.18 ~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_{x,0} &= F_{x,01} + F_{x,02} + F_{x,03} && | \quad \text{with } F_{x,0n} = F_{0n} \cdot \cos(\alpha_{0n}) |
| - | F_{y,0} &= (-5~N) \cdot cos(71.6°) + (-6~N) \cdot cos(53.1°) + (+3~N) \cdot cos(0°) | + | F_{x,0} &= (-5~\rm{N}) \cdot \cos(71.6°) + (-6~\rm{N}) \cdot \cos(53.1°) + (+3~\rm{N}) \cdot \cos(0°) |
| - | F_{y,0} &= -9.54 ~N \\ \\ | + | F_{x,0} &= -9.54 ~\rm{N} \\ \\ |
| + | |||
| + | F_{y,0} &= F_{y,01} + F_{y,02} + F_{y,03} && | \quad \text{with } F_{y,0n} = F_{0n} \cdot \sin(\alpha_{0n}) | ||
| + | F_{y,0} &= (-5~\rm{N}) \cdot \sin(71.6°) + (-6~\rm{N}) \cdot \sin(53.1°) + (+3~\rm{N}) \cdot \sin(0°) | ||
| + | F_{y,0} &= -2.18 ~\rm{N} | ||
| \end{align*} | \end{align*} | ||
| Zeile 49: | Zeile 50: | ||
| <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{ (-9.54 ~\rm{N})^2 + (-2.18 ~\rm{N})^2} = 9.79 ~\rm{N} \rightarrow 9.8 ~\rm{N} \\ |
| \end{align*} | \end{align*} | ||
| \\ | \\ | ||