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Kreisförmige Platte

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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/kreisformige-platte/

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The following quantities appear in the problem: Länge \(\ell\) / Temperatur \(T\) / Fläche \(A\) / Radius \(r\) / Längenausdehnungskoeffizient \(\alpha\) /

The following formulas must be used to solve the exercise: \(A = \pi r^2 \quad \) \(\ell = \ell_0 \cdot (1+ \alpha \cdot \Delta\vartheta) \quad \) \(A = A_0 \cdot (1+ 2\alpha \cdot \Delta\vartheta) \quad \)

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Exercise:
Eine kreisförmige Nickelplatte hat bei degreeCelsius einen Durchmesser von .mm. Auf welche Temperatur muss die Platte erwärmt werden damit sich ihre Fläche um millimetersquared vergrössert? Nickel hat einen Längen-aus-dehnungs-koeffi-zien-ten von per-modereciprocal.perkelvin.

Solution:
boxGegeben theta_ degreeCelsius d .mm .m Delta A millimetersquared metersquared alpha per-modereciprocal.perkelvin boxGesucht textTemperatur theta_sidegreeCelsius Die Nickelplatte hat einen Radius von rfracd.m. Ihre anfängliche Fläche ist somit: A_ pi r^ pi leftfracdright^ pi fracd^ pi left.mright^ .metersquared Die Platte muss folge Temperaturdifferenz erfahren damit sie sich ihre Fläche wie angegeben vergrössert: Deltatheta fracDelta AA_ alpha fracDelta Api fracd^ alpha frac Delta Api d^ alpha fracmetersquared.metersquared per-modereciprocal.perkelvin .degreeCelsius Die Endtemperatur auf welche die Platte gebracht werden muss beträgt also: theta_ theta_ + Deltatheta theta_ + frac Delta Api d^ alpha degreeCelsius + .degreeCelsius .degreeCelsius boxbox theta_ theta_ + frac Delta Api alpha d^ .degreeCelsius approx degreeCelsius

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Tags	ausdehnung, festkörper, kreis, nickel, physik, wärmelehre
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Difficulty	(3, default)
Points	3 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	uz
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