Exercise
https://texercises.com/exercise/wurfelgebilde-1/
Question
Solution
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\(\LaTeX\)
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The following quantities appear in the problem: Länge \(\ell\) / Kraft \(F\) / Drehmoment \(\vec M\) /
The following formulas must be used to solve the exercise: \(\vec M = \vec \ell \times \vec F \quad \) \(\sum \stackrel{\curvearrowleft}{M} \stackrel{!}{=} \sum \stackrel{\curvearrowright}{M} \quad \)
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Exercise:
Berechne die dreidimensionalen Koordinaten des Schwerpunktes des folg abgebildeten Körpers. Er besteht aus lauter identischen Würfeln der Kantenlänge a. center tikzpicturescale. latex drawthick- colorgreen!!black -.-- noderight x; drawthick- colorgreen!!black -.--. nodeabovept leftpt y; drawthick- colorgreen!!black --- nodebelowpt leftpt z; draw --------cycle; draw ------------cycle; draw ---; draw ---; draw ---; draw ---; pgftransformyshiftcm; draw --------cycle; draw ------------cycle; draw ---; draw ---; draw ---; draw ---; pgftransformyshiftcm; draw --------cycle; draw ------------cycle; draw ---; draw ---; draw ---; draw ---; pgftransformxshiftcm; draw --------cycle; draw ------------cycle; draw ---; draw ---; draw ---; draw ---; draw ------------cycle; draw ------------cycle; draw ----; draw ----; draw ----; draw ----; pgftransformxshiftcm; draw ------------cycle; draw ------------cycle; draw ----; draw ----; draw ----; draw ----; pgftransformyshift-cm; draw ------------cycle; draw ------------cycle; draw ----; draw ----; draw ----; draw ----; pgftransformyshift-cm; pgftransformxshift-cm; draw --------cycle; draw --------cycle; draw --; draw --; draw --; draw --; pgftransformxshift-cm; draw --------cycle; draw --------cycle; draw --; draw --; draw --; draw --; pgftransformxshift-cm; draw --------cycle; draw --------cycle; draw --; draw --; draw --; draw --; pgftransformyshiftcm; draw --------cycle; draw --------cycle; draw --; draw --; draw --; draw --; pgftransformyshiftcm; draw --------cycle; draw --------cycle; draw --; draw --; draw --; draw --; pgftransformxshiftcm; draw --------cycle; draw --------cycle; draw --; draw --; draw --; draw --; tikzpicture center

Solution:
Das Würfelgebilde besteht aus identischen Würfeln; die Schwerpunktskoordinate in einer beliebigen Richtung berechnet man über folge Formel am Beispiel x-Koordinate: x_S fracM _i^ m_ix_i Konkret hat man für die drei Koordinaten die folgen Situationen der rote Punkt auf den Achsen markiert jeweils den Koordinatenursprung: itemize item x-Koordinate: center tikzpicturelatex filldrawcolorred circle .; drawcolorblack!!green- ---; nodecolorblack!!green at . x; drawcolorblack!!green|- -.--.; node at -.. ; drawcolorblack!!green|- -.--.; node at -.. ; drawcolorblack!!green|- .--.; node at .. ; drawcolorblack!!green|- .--.; node at .. ; drawcolorblack!!green|- .--.; node at .. ; tikzpicture center x_S frac left-.a -.a + .a + .a + .a right frac.a .a item y-Koordinate: center tikzpicturelatex filldrawcolorred circle .; drawcolorblack!!green- --; nodecolorblack!!green at . y; drawcolorblack!!green|- .--.; node at .. ; drawcolorblack!!green|- .--.; node at .. ; drawcolorblack!!green|- .--.; node at .. ; tikzpicture center y_S frac left.a + .a + .a right frac.a .a item z-Koordinate: center tikzpicturelatex filldrawcolorred circle .; drawcolorblack!!green- --; nodecolorblack!!green at . z; drawcolorblack!!green|- -.--.; node at -.. ; drawcolorblack!!green|- -.--.; node at -.. ; drawcolorblack!!green|- .--.; node at .. ; tikzpicture center z_S frac left-.a -.a + .a right frac-.a -.a Der Schwerpunkt dieses Würfelgebildes liegt also beim Punkt S.a.a-.a wobei a die Kantenlänge eines Würfels ist. itemize
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Exercise:
Berechne die dreidimensionalen Koordinaten des Schwerpunktes des folg abgebildeten Körpers. Er besteht aus lauter identischen Würfeln der Kantenlänge a. center tikzpicturescale. latex drawthick- colorgreen!!black -.-- noderight x; drawthick- colorgreen!!black -.--. nodeabovept leftpt y; drawthick- colorgreen!!black --- nodebelowpt leftpt z; draw --------cycle; draw ------------cycle; draw ---; draw ---; draw ---; draw ---; pgftransformyshiftcm; draw --------cycle; draw ------------cycle; draw ---; draw ---; draw ---; draw ---; pgftransformyshiftcm; draw --------cycle; draw ------------cycle; draw ---; draw ---; draw ---; draw ---; pgftransformxshiftcm; draw --------cycle; draw ------------cycle; draw ---; draw ---; draw ---; draw ---; draw ------------cycle; draw ------------cycle; draw ----; draw ----; draw ----; draw ----; pgftransformxshiftcm; draw ------------cycle; draw ------------cycle; draw ----; draw ----; draw ----; draw ----; pgftransformyshift-cm; draw ------------cycle; draw ------------cycle; draw ----; draw ----; draw ----; draw ----; pgftransformyshift-cm; pgftransformxshift-cm; draw --------cycle; draw --------cycle; draw --; draw --; draw --; draw --; pgftransformxshift-cm; draw --------cycle; draw --------cycle; draw --; draw --; draw --; draw --; pgftransformxshift-cm; draw --------cycle; draw --------cycle; draw --; draw --; draw --; draw --; pgftransformyshiftcm; draw --------cycle; draw --------cycle; draw --; draw --; draw --; draw --; pgftransformyshiftcm; draw --------cycle; draw --------cycle; draw --; draw --; draw --; draw --; pgftransformxshiftcm; draw --------cycle; draw --------cycle; draw --; draw --; draw --; draw --; tikzpicture center

Solution:
Das Würfelgebilde besteht aus identischen Würfeln; die Schwerpunktskoordinate in einer beliebigen Richtung berechnet man über folge Formel am Beispiel x-Koordinate: x_S fracM _i^ m_ix_i Konkret hat man für die drei Koordinaten die folgen Situationen der rote Punkt auf den Achsen markiert jeweils den Koordinatenursprung: itemize item x-Koordinate: center tikzpicturelatex filldrawcolorred circle .; drawcolorblack!!green- ---; nodecolorblack!!green at . x; drawcolorblack!!green|- -.--.; node at -.. ; drawcolorblack!!green|- -.--.; node at -.. ; drawcolorblack!!green|- .--.; node at .. ; drawcolorblack!!green|- .--.; node at .. ; drawcolorblack!!green|- .--.; node at .. ; tikzpicture center x_S frac left-.a -.a + .a + .a + .a right frac.a .a item y-Koordinate: center tikzpicturelatex filldrawcolorred circle .; drawcolorblack!!green- --; nodecolorblack!!green at . y; drawcolorblack!!green|- .--.; node at .. ; drawcolorblack!!green|- .--.; node at .. ; drawcolorblack!!green|- .--.; node at .. ; tikzpicture center y_S frac left.a + .a + .a right frac.a .a item z-Koordinate: center tikzpicturelatex filldrawcolorred circle .; drawcolorblack!!green- --; nodecolorblack!!green at . z; drawcolorblack!!green|- -.--.; node at -.. ; drawcolorblack!!green|- -.--.; node at -.. ; drawcolorblack!!green|- .--.; node at .. ; tikzpicture center z_S frac left-.a -.a + .a right frac-.a -.a Der Schwerpunkt dieses Würfelgebildes liegt also beim Punkt S.a.a-.a wobei a die Kantenlänge eines Würfels ist. itemize
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Attributes & Decorations
Branches
Lever
Tags
drehmoment, gleichgewicht, gleichung, hebel, hebelgesetz, körper, mechanik, physik, rotation, schwerpunkt, starrer, statik
Content image
Difficulty
(3, default)
Points
3 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
Creator uz
Decoration
File
Link