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Kugelförmige Schale

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.

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 -

Exercise

https://texercises.com/exercise/kugelformige-schale/

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Exercise:
Ein kleines Teilchen mit Masse m gleite reibungsfrei in einer kugelförmigen Schale mit Radius r. abcliste abc Zeige dass die Bewegung die gleiche wäre falls das Teilchen an einem Faden der Länge r aufgehängt wäre. abc Ein kleines Teilchen der Masse m_ sei um die Bogenlänge s_ zur einen Seite der Schale ausgelenkt. Ein zweites Teilchen sei auf die andere Seite um s_s_ ausgelenkt. Wo treffen sich die Teilchen wenn sie gleichzeitig losgelassen werden? Warum? abcliste

Solution:
abcliste abc Wie beim mathematischen Pel ist die rücktreibe Kraft mgsinphi. Für kleine Winkel phi ang gilt sinphi approxphi wie schon beim Pel gesehen. In solchen Fällen schwingt also die Kugel in der Schale harmonisch. abc Beide Teilchen treffen sich unten in der Mitte; die Schwingungsdauer und damit auch ein Viertel der Schwingungsdauer ist unabhängig von der Masse bzw. der Elongation. Sie hängt nur vom Radius der Schale sowie der Erdbeschleunigung ab. abcliste

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Tags	mathematisches, pendel, physik, schwingung, wellenlehre
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Difficulty	(2, default)
Points	4 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	uz
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