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Masse eines fremden Planeten

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/masse-eines-fremden-planeten/

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Exercise:
Welche Masse müsste ein Planet mit km Durchmesser haben damit der cm ausgelenkte Pelkörper eines mathematischen Pels mit dm Länge eine maximale Geschwindigkeit von kilometerperhour erfahren würde?

Solution:
Ein mathematisches Pel schwingt -- unter der Voraussetzung kleiner Auslenkungen -- harmonisch; der Proportionalitätsfaktor zwischen rücktreiber Kraft und Auslenkung ist: K fracmgell Die Winkelfrequenz der Schwingung leitet sich direkt daraus ab: omega_ sqrtfracKm sqrtfracgell Die Elongation Auslenkung kann durch die mathematische Funktion y_t y_ sinomega_ t beschrieben werden; die Geschwindigkeit zu jedem Zeitpunkt ist dann: v_t dot y_t omega_ y_ cosomega_ t Die maximale Geschwindigkeit ist: sscvmax omega_ y_ sqrtfracgell y_ Daraus lässt sich dei Fallbeschleunigung auf diesem Planeten direkt berechnen: g fracsscvmax^y_^ell fracqty.^qty.m^ .m .eq Die Masse des Planeten müsste als M fracgr^G .ekg betragen.

Meta Information

\(\LaTeX\)-Code

Contained in these collections:

Harmonische Schwingung 3 by uz

3 | 9
Mathematisches Pendel by TeXercises

2 | 22

Attributes & Decorations

Branches	Gravitation
Tags	gravitation, gravitationskonstante, harmonisch, harmonische, mathematisches, pendel, physik, planet, schwingung, schwingungen, wellenlehre
Content image
Difficulty	(3, default)
Points	4 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	uz
Decoration
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Link