Starrer Körper: Schwerpunkt 8
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
Short
Video
\(\LaTeX\)
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Exercise:
Eine Fabrik möchte mit einem schwachen Motor eine Wanduhr antreiben. Damit der Motor nicht überlastet wird müssen die Zeiger ausbalanciert sein d.h. das Gewicht darf kein Drehmoment erzeugen. Der Zeiger kann als gleichschenkliges Trapez modelliert werden Details siehe Abbildung reffig:ZeigerSP. Berechnen Sie formal wo die Drehachse platziert werden muss.
Solution:
% . Dezember Lie. Die Drehachse muss durch den Schwerpunkt Gravizentrum laufen. Die Dicke und die Masse fallen aus der Rechnung heraus weil die Massenelemente proportional zu den Flächenelementen sind. * &x_S _^ell dm _^ell x dm qquad qquad dm sim dA yx dx &x_S _^ell ydx _^ell x ydx &x_S _^ell leftb- fracb-sell x rightdx _^ell x leftb- fracb-sell x rightdx qquad textBasis b am Nullpunkt der x-Achse &x_S b _^ell dx - x_S fracb-sell_^ell xdx b _^ell xdx - fracb-sell_^ell x^dx &x_S bell - x_S fracb-sell fracell^ b fracell^- fracb-sell fracell^ &x_S fracb+sell fracb+sell^ qquad textBemerkung: Der Faktor nach x_S ist die Trapezfläche! &x_S fracb+sb+s ell &hspace*mm text. Test: Dreieck s Rightarrow x_S tfracell quad checkmark &hspace*mm text. Test: Rechteck b s Rightarrow x_S tfracell quad checkmark * newpage
Eine Fabrik möchte mit einem schwachen Motor eine Wanduhr antreiben. Damit der Motor nicht überlastet wird müssen die Zeiger ausbalanciert sein d.h. das Gewicht darf kein Drehmoment erzeugen. Der Zeiger kann als gleichschenkliges Trapez modelliert werden Details siehe Abbildung reffig:ZeigerSP. Berechnen Sie formal wo die Drehachse platziert werden muss.
Solution:
% . Dezember Lie. Die Drehachse muss durch den Schwerpunkt Gravizentrum laufen. Die Dicke und die Masse fallen aus der Rechnung heraus weil die Massenelemente proportional zu den Flächenelementen sind. * &x_S _^ell dm _^ell x dm qquad qquad dm sim dA yx dx &x_S _^ell ydx _^ell x ydx &x_S _^ell leftb- fracb-sell x rightdx _^ell x leftb- fracb-sell x rightdx qquad textBasis b am Nullpunkt der x-Achse &x_S b _^ell dx - x_S fracb-sell_^ell xdx b _^ell xdx - fracb-sell_^ell x^dx &x_S bell - x_S fracb-sell fracell^ b fracell^- fracb-sell fracell^ &x_S fracb+sell fracb+sell^ qquad textBemerkung: Der Faktor nach x_S ist die Trapezfläche! &x_S fracb+sb+s ell &hspace*mm text. Test: Dreieck s Rightarrow x_S tfracell quad checkmark &hspace*mm text. Test: Rechteck b s Rightarrow x_S tfracell quad checkmark * newpage
Meta Information
Exercise:
Eine Fabrik möchte mit einem schwachen Motor eine Wanduhr antreiben. Damit der Motor nicht überlastet wird müssen die Zeiger ausbalanciert sein d.h. das Gewicht darf kein Drehmoment erzeugen. Der Zeiger kann als gleichschenkliges Trapez modelliert werden Details siehe Abbildung reffig:ZeigerSP. Berechnen Sie formal wo die Drehachse platziert werden muss.
Solution:
% . Dezember Lie. Die Drehachse muss durch den Schwerpunkt Gravizentrum laufen. Die Dicke und die Masse fallen aus der Rechnung heraus weil die Massenelemente proportional zu den Flächenelementen sind. * &x_S _^ell dm _^ell x dm qquad qquad dm sim dA yx dx &x_S _^ell ydx _^ell x ydx &x_S _^ell leftb- fracb-sell x rightdx _^ell x leftb- fracb-sell x rightdx qquad textBasis b am Nullpunkt der x-Achse &x_S b _^ell dx - x_S fracb-sell_^ell xdx b _^ell xdx - fracb-sell_^ell x^dx &x_S bell - x_S fracb-sell fracell^ b fracell^- fracb-sell fracell^ &x_S fracb+sell fracb+sell^ qquad textBemerkung: Der Faktor nach x_S ist die Trapezfläche! &x_S fracb+sb+s ell &hspace*mm text. Test: Dreieck s Rightarrow x_S tfracell quad checkmark &hspace*mm text. Test: Rechteck b s Rightarrow x_S tfracell quad checkmark * newpage
Eine Fabrik möchte mit einem schwachen Motor eine Wanduhr antreiben. Damit der Motor nicht überlastet wird müssen die Zeiger ausbalanciert sein d.h. das Gewicht darf kein Drehmoment erzeugen. Der Zeiger kann als gleichschenkliges Trapez modelliert werden Details siehe Abbildung reffig:ZeigerSP. Berechnen Sie formal wo die Drehachse platziert werden muss.
Solution:
% . Dezember Lie. Die Drehachse muss durch den Schwerpunkt Gravizentrum laufen. Die Dicke und die Masse fallen aus der Rechnung heraus weil die Massenelemente proportional zu den Flächenelementen sind. * &x_S _^ell dm _^ell x dm qquad qquad dm sim dA yx dx &x_S _^ell ydx _^ell x ydx &x_S _^ell leftb- fracb-sell x rightdx _^ell x leftb- fracb-sell x rightdx qquad textBasis b am Nullpunkt der x-Achse &x_S b _^ell dx - x_S fracb-sell_^ell xdx b _^ell xdx - fracb-sell_^ell x^dx &x_S bell - x_S fracb-sell fracell^ b fracell^- fracb-sell fracell^ &x_S fracb+sell fracb+sell^ qquad textBemerkung: Der Faktor nach x_S ist die Trapezfläche! &x_S fracb+sb+s ell &hspace*mm text. Test: Dreieck s Rightarrow x_S tfracell quad checkmark &hspace*mm text. Test: Rechteck b s Rightarrow x_S tfracell quad checkmark * newpage
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Starrer Körper: Schwerpunkt by Lie