TeXercises.com

Ursache und Wirkung

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/ursache-und-wirkung/

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Solution

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Exercise:
In einem Bezugssystem mathcalS sind zwei Ereignisse voneinander um die Distanz Delta xx_-x_ sowie die Zeit Delta tt_-t_ getrennt. abcliste abc Zeige mittels Lorentz-Transformation dass in einem sich relativ zu mathcalS bewegen Bezugssystem mathcalS' Folges gilt: t_'-t_' gamma leftDelta t -fracv Delta xc^right ist. abc Zeige dass die Ereignisse in mathcalS' nur dann gleichzeitig stattfinden können wenn Delta x cDelta t ist. abc Falls ein Ereignis die Ursache für ein anderes Ereignis ist muss Delta x cDelta t sein weil fracDelta xc die Zeit ist welche ein Signal mindestens braucht um von x_ nach x_ zu gelangen. Zeige das für den Fall dass Delta x cDelta t in allen Bezugssystemen t_'t_' gilt. Das beweist dass in allen Bezugssystemen die Ursache vor der Wirkung stattfindet. abc Nimm an dass ein Signal sich schneller als das Licht also mit c'c ausbreiten kann so dass in mathcalS die Ursache der Wirkung um Delta t fracDelta xc' vorausgeht. Zeige dass in diesem Fall ein Bezugssystem existiert dessen Geschwindigkeit kleiner als die Lichtgeschwindigkeit ist und in welchem die Wirkung der Ursache vorausgeht. abcliste

Solution:

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Tags	einstein, gleichzeitig, physik, relativ, relativitätstheorie, srt, synchron, uhrensynchronität
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Difficulty	(4, default)
Points	8 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	uz
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