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Anfangsgeschwindigkeit von Billardkugel

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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".
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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/anfangsgeschwindigkeit-von-billardkugel/

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Exercise:
Eine ruhe Billardkugel mit r Radius erhalte durch das Queue einen kurzen Stoss. Dieser Kraftstoss erfolge horizontal und treffe die Kugel einen Fünftel Radius unterhalb ihres Mittelpunktes. Anschliess drehe sich die Kugel mit f. Wie gross ist die anfängliche Geschwindigkeit der Kugel?

Solution:
Der vom Queue auf die Kugel übertragene Impuls erzeugt ein Drehmoment M fracr F Die Kugel erhält also eine Winkelbeschleunigung von alpha fracMJ fracfracr Ffracmr^ fracFmr währ einer bestimmten unbekannten Zeit nach welcher sie eine Winkelgeschwindigkeit von omega alpha t hat. Für die Translation andererseits gilt dass die Kugel währ dieser Zeit mit a fracFm beschleunigt wurde was in einer Geschwindigkeit von v a t fracFm fracomegaalpha fracFm fracomegafracFmr r omega r pi f pi rf pi rC f v

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\(\LaTeX\)-Code

Contained in these collections:

Translation und Rotation 2 by uz

1 | 5
Billardkugel by TeXercises

6 | 8

Attributes & Decorations

Tags	billard, billardkugel, drehmoment, gleiten, physik, rollen, rotation, trägheitsmoment
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Difficulty	(4, default)
Points	4 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	uz
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