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Mensch auf Eisscholle

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/mensch-auf-eisscholle/

Question

Solution

Short

Video

\(\LaTeX\)

Need help? Yes, please!

The following quantities appear in the problem: Länge \(\ell\) / Masse \(m\) / Kraft \(F\) / Volumen \(V\) / Ortsfaktor \(g\) / Höhe \(h\) / Dichte \(\varrho\) / Breite \(b\) /

The following formulas must be used to solve the exercise: \(F = \varrho V g \quad \) \(F = mg \quad \) \(V = abc \quad \)

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No explanation / solution video for this exercise has yet been created.
But there is a video to a similar exercise:

In case your browser prevents YouTube embedding: https://youtu.be/bPb6s-kPkn4

Exercise:
Auf einem nur zum Teil gefrorenen und noch nicht freigegebenen See bewegt sich ein unvorsichtiger Wanderer. Plötzlich löst sich ein .cm dickes quaderförmiges Stück Eis und treibt mitsamt Wanderer in Richtung Seemitte. Wie gross muss es mindestens sein Fläche wenn es den .kg schweren Mann tragen soll? Dichte von Wasser: varrho_W apx kg/m^; Dichte von Eis: varrho_E apx kg/m^

Solution:
Da die Mindestgrösse gesucht ist bedeutet dies dass der Körper vollständig eingetaucht ist aber direkt unter der Oberfläche ist. Damit kann man das gesamte Volumen betrachten. Für das Kräftegleichgewicht gilt: F_A F_g myRarrow varrho_W gV m_M+m_Eg wobei m_M die Masse der Person und m_E die Masse der Eisscholle ist. Mit VAh erhalten wir: varrho_W Ah m_M + varrho_EAh myRarrow Ahvarrho_W - varrho_E m_M. Somit ist die Fläche: A fracm_Mhvarrho_W-varrho_Eapx .m^.

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Contained in these collections:

Floss oder Eisscholle by TeXercises

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Attributes & Decorations

Branches	Hydrostatics
Tags	auftrieb, hydrostatik, mechanik
Content image
Difficulty	(2, default)
Points	0 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	cm
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