Exercise
https://texercises.com/exercise/stahltrager-1/
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The following quantities appear in the problem: Länge \(\ell\) / Masse \(m\) / Strecke \(s\) / Fläche \(A\) / Drehmoment \(\vec M\) / Radius \(r\) / Breite \(b\) /
The following formulas must be used to solve the exercise: \(\sum \stackrel{\curvearrowleft}{M} \stackrel{!}{=} \sum \stackrel{\curvearrowright}{M} \quad \) \(A = \pi r^2 \quad \) \(A = s^2 \quad \) \(A = ab \quad \) \(\vec r_{\rm S} = \frac{1}{M} \sum_i m_i \vec r_i \quad \)
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Exercise:
Berechne die xy-Koordinaten des Schwerpunktes des nebenan abgebildeten Stahlträgers. center tikzpicturescale. filldrawfillblack!!white ------------------; draw-latex colorgreen!!black -.---. nodebelow cm; draw-latex colorgreen!!black .--. noderight cm; draw-latex colorgreen!!black -.---. nodeleft cm; draw-latex colorgreen!!black .--. nodeabove cm; tikzpicture center

Solution:
Wir wählen folges Koordinatensystem center tikzpicturescale. latex filldrawcolorblack fillblack!!white ------------------; draw- -.---. nodebelow cm; draw- .--. noderight cm; draw- -.---. nodeleft cm; draw- .--. nodeabove cm; draw- colorgreen!!black -.--. nodeleft y; draw- colorgreen!!black -.--. nodebelow x; draw- colorblack --; draw- colorblack --; draw- colorblack --; draw- colorblack --; drawcolorblack fillyellow . circle .cm; tikzpicture center darin habe der Schwerpunkt die Koordinaten x^*y^*. Mit der Schwerpunktformel finden wir NewQtyAesquarecentimeter NewQtyAzsquarecentimeter NewQtyAdsquarecentimeter NewQtyAvsquarecentimeter NewQtyxecm NewQtyxzcm NewQtyxd.cm NewQtyxvcm NewQtyyecm NewQtyyz.cm NewQtyyd.cm NewQtyyvcm SolQtyxfracA_x_ + A_x_ + A_x_ + A_x_A_ + A_ + A_ + A_AeX*xeX+AzX*xzX+AdX*xdX+AvX*xvX/AeX+AzX+AdX+AvXcm SolQtyyfracA_y_ + A_y_ + A_y_ + A_y_A_ + A_ + A_ + A_AeX*yeX+AzX*yzX+AdX*ydX+AvX*yvX/AeX+AzX+AdX+AvXcm al x^* fracm_x_ + m_x_ + m_x_ + m_x_m_ + m_ + m_ + m_ xF fracAexe+Azxz+Adxd+AvxvAe+Az+Ad+Av xP y^* fracm_y_ + m_y_ + m_y_ + m_y_m_ + m_ + m_ + m_ yF fracAeye+Azyz+Adyd+AvyvAe+Az+Ad+Av yP.
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Exercise:
Berechne die xy-Koordinaten des Schwerpunktes des nebenan abgebildeten Stahlträgers. center tikzpicturescale. filldrawfillblack!!white ------------------; draw-latex colorgreen!!black -.---. nodebelow cm; draw-latex colorgreen!!black .--. noderight cm; draw-latex colorgreen!!black -.---. nodeleft cm; draw-latex colorgreen!!black .--. nodeabove cm; tikzpicture center

Solution:
Wir wählen folges Koordinatensystem center tikzpicturescale. latex filldrawcolorblack fillblack!!white ------------------; draw- -.---. nodebelow cm; draw- .--. noderight cm; draw- -.---. nodeleft cm; draw- .--. nodeabove cm; draw- colorgreen!!black -.--. nodeleft y; draw- colorgreen!!black -.--. nodebelow x; draw- colorblack --; draw- colorblack --; draw- colorblack --; draw- colorblack --; drawcolorblack fillyellow . circle .cm; tikzpicture center darin habe der Schwerpunkt die Koordinaten x^*y^*. Mit der Schwerpunktformel finden wir NewQtyAesquarecentimeter NewQtyAzsquarecentimeter NewQtyAdsquarecentimeter NewQtyAvsquarecentimeter NewQtyxecm NewQtyxzcm NewQtyxd.cm NewQtyxvcm NewQtyyecm NewQtyyz.cm NewQtyyd.cm NewQtyyvcm SolQtyxfracA_x_ + A_x_ + A_x_ + A_x_A_ + A_ + A_ + A_AeX*xeX+AzX*xzX+AdX*xdX+AvX*xvX/AeX+AzX+AdX+AvXcm SolQtyyfracA_y_ + A_y_ + A_y_ + A_y_A_ + A_ + A_ + A_AeX*yeX+AzX*yzX+AdX*ydX+AvX*yvX/AeX+AzX+AdX+AvXcm al x^* fracm_x_ + m_x_ + m_x_ + m_x_m_ + m_ + m_ + m_ xF fracAexe+Azxz+Adxd+AvxvAe+Az+Ad+Av xP y^* fracm_y_ + m_y_ + m_y_ + m_y_m_ + m_ + m_ + m_ yF fracAeye+Azyz+Adyd+AvyvAe+Az+Ad+Av yP.
Contained in these collections
  1. 5 | 6
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Attributes & Decorations
Tags
drehmoment, körper, massenmittelpunkt, massenschwerpunkt, mechanik, physik, schwerpunkt, starrer körper
Difficulty
(4, default)
Points
2 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
Decoration
Content image

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