Trägheitsmoment eines Dreikantholzes
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
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Video
\(\LaTeX\)
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Exercise:
Berechne mittels Integration über die drei Raumdimensionen das Trägheitsmoment des folg abgebildeten Dreikantholzes mit Masse m bezüglich einer Achse entlang einer langen Kante. Die Grundfläche besteht aus einem gleichseitigen Dreieck mit Seitenlänge a die Länge bzw. Höhe des Kantholzes sei h. Alle Rechenschritte müssen klar ersichtlich sein für die volle Punktzahl; die Angabe eines algebraischen Endausdruckes alleine gibt keine Punkte. center tikzpicturescale. %drawcolorred ultra thick ---; filldrawcolorblack fillyellow!!red --..---..--cycle; filldrawcolorblack fillyellow!!red --..---..--cycle; filldrawcolorblack fillyellow!!red ..---..---..--..--cycle; filldrawcolorblack fillyellow!!red ----..--..--cycle; tikzpicture center
Solution:
J r^ dd m r^ rho dd V x^+y^^ rho dd x dd y dd z rho _^h dd z _^fracsqrta dd x _fracxsqrt^fracxsqrt dd y x^+y^ rho _^h dd z _^fracsqrta dd x _^fracxsqrt dd y x^+y^ rho h _^fracsqrta dd x leftx^y+y^right_^fracxsqrt rho h _^fracsqrta dd x leftfracx^sqrt + fracfracx^sqrtright Und dann weiter mit Integration über x: J rho h frac fracsqrt left fracx^right_^fracsqrta rho h frac fracsqrt frac leftfracsqrtaright^ rho h frac fracsqrt frac frac a^ frac rho fracsqrta^ h a^ fracma^
Berechne mittels Integration über die drei Raumdimensionen das Trägheitsmoment des folg abgebildeten Dreikantholzes mit Masse m bezüglich einer Achse entlang einer langen Kante. Die Grundfläche besteht aus einem gleichseitigen Dreieck mit Seitenlänge a die Länge bzw. Höhe des Kantholzes sei h. Alle Rechenschritte müssen klar ersichtlich sein für die volle Punktzahl; die Angabe eines algebraischen Endausdruckes alleine gibt keine Punkte. center tikzpicturescale. %drawcolorred ultra thick ---; filldrawcolorblack fillyellow!!red --..---..--cycle; filldrawcolorblack fillyellow!!red --..---..--cycle; filldrawcolorblack fillyellow!!red ..---..---..--..--cycle; filldrawcolorblack fillyellow!!red ----..--..--cycle; tikzpicture center
Solution:
J r^ dd m r^ rho dd V x^+y^^ rho dd x dd y dd z rho _^h dd z _^fracsqrta dd x _fracxsqrt^fracxsqrt dd y x^+y^ rho _^h dd z _^fracsqrta dd x _^fracxsqrt dd y x^+y^ rho h _^fracsqrta dd x leftx^y+y^right_^fracxsqrt rho h _^fracsqrta dd x leftfracx^sqrt + fracfracx^sqrtright Und dann weiter mit Integration über x: J rho h frac fracsqrt left fracx^right_^fracsqrta rho h frac fracsqrt frac leftfracsqrtaright^ rho h frac fracsqrt frac frac a^ frac rho fracsqrta^ h a^ fracma^
Meta Information
Exercise:
Berechne mittels Integration über die drei Raumdimensionen das Trägheitsmoment des folg abgebildeten Dreikantholzes mit Masse m bezüglich einer Achse entlang einer langen Kante. Die Grundfläche besteht aus einem gleichseitigen Dreieck mit Seitenlänge a die Länge bzw. Höhe des Kantholzes sei h. Alle Rechenschritte müssen klar ersichtlich sein für die volle Punktzahl; die Angabe eines algebraischen Endausdruckes alleine gibt keine Punkte. center tikzpicturescale. %drawcolorred ultra thick ---; filldrawcolorblack fillyellow!!red --..---..--cycle; filldrawcolorblack fillyellow!!red --..---..--cycle; filldrawcolorblack fillyellow!!red ..---..---..--..--cycle; filldrawcolorblack fillyellow!!red ----..--..--cycle; tikzpicture center
Solution:
J r^ dd m r^ rho dd V x^+y^^ rho dd x dd y dd z rho _^h dd z _^fracsqrta dd x _fracxsqrt^fracxsqrt dd y x^+y^ rho _^h dd z _^fracsqrta dd x _^fracxsqrt dd y x^+y^ rho h _^fracsqrta dd x leftx^y+y^right_^fracxsqrt rho h _^fracsqrta dd x leftfracx^sqrt + fracfracx^sqrtright Und dann weiter mit Integration über x: J rho h frac fracsqrt left fracx^right_^fracsqrta rho h frac fracsqrt frac leftfracsqrtaright^ rho h frac fracsqrt frac frac a^ frac rho fracsqrta^ h a^ fracma^
Berechne mittels Integration über die drei Raumdimensionen das Trägheitsmoment des folg abgebildeten Dreikantholzes mit Masse m bezüglich einer Achse entlang einer langen Kante. Die Grundfläche besteht aus einem gleichseitigen Dreieck mit Seitenlänge a die Länge bzw. Höhe des Kantholzes sei h. Alle Rechenschritte müssen klar ersichtlich sein für die volle Punktzahl; die Angabe eines algebraischen Endausdruckes alleine gibt keine Punkte. center tikzpicturescale. %drawcolorred ultra thick ---; filldrawcolorblack fillyellow!!red --..---..--cycle; filldrawcolorblack fillyellow!!red --..---..--cycle; filldrawcolorblack fillyellow!!red ..---..---..--..--cycle; filldrawcolorblack fillyellow!!red ----..--..--cycle; tikzpicture center
Solution:
J r^ dd m r^ rho dd V x^+y^^ rho dd x dd y dd z rho _^h dd z _^fracsqrta dd x _fracxsqrt^fracxsqrt dd y x^+y^ rho _^h dd z _^fracsqrta dd x _^fracxsqrt dd y x^+y^ rho h _^fracsqrta dd x leftx^y+y^right_^fracxsqrt rho h _^fracsqrta dd x leftfracx^sqrt + fracfracx^sqrtright Und dann weiter mit Integration über x: J rho h frac fracsqrt left fracx^right_^fracsqrta rho h frac fracsqrt frac leftfracsqrtaright^ rho h frac fracsqrt frac frac a^ frac rho fracsqrta^ h a^ fracma^
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