Exercise
https://texercises.com/exercise/drahtgebilde/
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The following quantities appear in the problem: Drehmoment \(\vec M\) /
The following formulas must be used to solve the exercise: \(\sum \stackrel{\curvearrowleft}{M} \stackrel{!}{=} \sum \stackrel{\curvearrowright}{M} \quad \)
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Exercise:
Berechne die xy-Koordinaten des Schwerpunktes wie folgt geformten homogenen Drahtgebildes: center tikzpicturelatex drawcolorgreen!!black- -.-- noderight x; drawcolorgreen!!black- -.-- nodeabove y; drawcolorgreen!!black .---. nodebelow ; drawcolorgreen!!black .---. nodebelow ; drawcolorgreen!!black .---. nodeleft ; drawcolorgreen!!black .---. nodeleft ; drawthick -------------cycle; tikzpicture center

Solution:
Die Massen der Teilabschnitte des Drahtes sind proportional zu ihrer Länge; daher kann man für die Massen einfach die Längen einsetzen. itemize item x-Koordinate: sscxS fracM _i^ m_i x_i fracsqrt + + + +sqrt +sqrt sqrt++++sqrt+sqrt . item y-Koordinate: sscyS fracM _i^ m_i y_i fracsqrt + + + .+sqrt +sqrt .sqrt++++sqrt+sqrt . itemize center tikzpicturelatex drawcolorgreen!!black- -.-- noderight x; drawcolorgreen!!black- -.-- nodeabove y; drawcolorgreen!!black .---. nodebelow ; drawcolorgreen!!black .---. nodebelow ; drawcolorgreen!!black .---. nodeleft ; drawcolorgreen!!black .---. nodeleft ; drawthick -------------cycle; filldrawcolorred . . circle .cm; tikzpicture center
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\(\LaTeX\)-Code
Exercise:
Berechne die xy-Koordinaten des Schwerpunktes wie folgt geformten homogenen Drahtgebildes: center tikzpicturelatex drawcolorgreen!!black- -.-- noderight x; drawcolorgreen!!black- -.-- nodeabove y; drawcolorgreen!!black .---. nodebelow ; drawcolorgreen!!black .---. nodebelow ; drawcolorgreen!!black .---. nodeleft ; drawcolorgreen!!black .---. nodeleft ; drawthick -------------cycle; tikzpicture center

Solution:
Die Massen der Teilabschnitte des Drahtes sind proportional zu ihrer Länge; daher kann man für die Massen einfach die Längen einsetzen. itemize item x-Koordinate: sscxS fracM _i^ m_i x_i fracsqrt + + + +sqrt +sqrt sqrt++++sqrt+sqrt . item y-Koordinate: sscyS fracM _i^ m_i y_i fracsqrt + + + .+sqrt +sqrt .sqrt++++sqrt+sqrt . itemize center tikzpicturelatex drawcolorgreen!!black- -.-- noderight x; drawcolorgreen!!black- -.-- nodeabove y; drawcolorgreen!!black .---. nodebelow ; drawcolorgreen!!black .---. nodebelow ; drawcolorgreen!!black .---. nodeleft ; drawcolorgreen!!black .---. nodeleft ; drawthick -------------cycle; filldrawcolorred . . circle .cm; tikzpicture center
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Tags
drahgebilde, draht, drehmoment, physik, schwerpunkt, stahldraht
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Difficulty
(3, default)
Points
4 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
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Decoration
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Link