Ski-Fahren
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.
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 -
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 -
Question
Solution
Short
Video
\(\LaTeX\)
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Exercise:
Ein Ski-Fahrer fahre reibungsfrei mit der Geschwindigkeit v_A am Punkt A h_A kh_B los. Wie darf der Koeffizient k gewählt werden damit der Ski-Fahrer beim Punkt B h_B nicht abhebt vgl. Abb.. center tikzpicturedomain.: % Boden drawvery thick - -- .-; % Hoehe bei A drawtriangle -triangle .-. -- ..; node hA at .-. h_A kh_B; % Hoehe bei B drawtriangle -triangle .-. -- ..; node hB at .-. h_B; % Kreis bei B drawdashed .-. circle .cm; % Skipiste drawcolorblackvery thick plotsamples xexp-x/*sinx r; tikzpicture center
Solution:
Bei B gilt sofern der Ski-Fahrer nicht abhebt folge Ungleichung: F_G fracmv_B^r. Mit r h_B/ erhalten wir die Beziehung: v_B sqrtgh_B/. Die Energiebilanz lautet: eqnarray* E_pot^A+E_kin^A & E_pot^B+E_kin^Bmm mgh_A + fracmv_A^ & mgh_B + fracmv_B^mm gkh_B + v_A^ & gh_B + gh_B/mm v_A^ & gh_Bleftfrac - kright eqnarray* Damit v_A definiert ist muss die Klammer / - k sein d.h. frac k Rightarrow k ..
Ein Ski-Fahrer fahre reibungsfrei mit der Geschwindigkeit v_A am Punkt A h_A kh_B los. Wie darf der Koeffizient k gewählt werden damit der Ski-Fahrer beim Punkt B h_B nicht abhebt vgl. Abb.. center tikzpicturedomain.: % Boden drawvery thick - -- .-; % Hoehe bei A drawtriangle -triangle .-. -- ..; node hA at .-. h_A kh_B; % Hoehe bei B drawtriangle -triangle .-. -- ..; node hB at .-. h_B; % Kreis bei B drawdashed .-. circle .cm; % Skipiste drawcolorblackvery thick plotsamples xexp-x/*sinx r; tikzpicture center
Solution:
Bei B gilt sofern der Ski-Fahrer nicht abhebt folge Ungleichung: F_G fracmv_B^r. Mit r h_B/ erhalten wir die Beziehung: v_B sqrtgh_B/. Die Energiebilanz lautet: eqnarray* E_pot^A+E_kin^A & E_pot^B+E_kin^Bmm mgh_A + fracmv_A^ & mgh_B + fracmv_B^mm gkh_B + v_A^ & gh_B + gh_B/mm v_A^ & gh_Bleftfrac - kright eqnarray* Damit v_A definiert ist muss die Klammer / - k sein d.h. frac k Rightarrow k ..
Meta Information
Exercise:
Ein Ski-Fahrer fahre reibungsfrei mit der Geschwindigkeit v_A am Punkt A h_A kh_B los. Wie darf der Koeffizient k gewählt werden damit der Ski-Fahrer beim Punkt B h_B nicht abhebt vgl. Abb.. center tikzpicturedomain.: % Boden drawvery thick - -- .-; % Hoehe bei A drawtriangle -triangle .-. -- ..; node hA at .-. h_A kh_B; % Hoehe bei B drawtriangle -triangle .-. -- ..; node hB at .-. h_B; % Kreis bei B drawdashed .-. circle .cm; % Skipiste drawcolorblackvery thick plotsamples xexp-x/*sinx r; tikzpicture center
Solution:
Bei B gilt sofern der Ski-Fahrer nicht abhebt folge Ungleichung: F_G fracmv_B^r. Mit r h_B/ erhalten wir die Beziehung: v_B sqrtgh_B/. Die Energiebilanz lautet: eqnarray* E_pot^A+E_kin^A & E_pot^B+E_kin^Bmm mgh_A + fracmv_A^ & mgh_B + fracmv_B^mm gkh_B + v_A^ & gh_B + gh_B/mm v_A^ & gh_Bleftfrac - kright eqnarray* Damit v_A definiert ist muss die Klammer / - k sein d.h. frac k Rightarrow k ..
Ein Ski-Fahrer fahre reibungsfrei mit der Geschwindigkeit v_A am Punkt A h_A kh_B los. Wie darf der Koeffizient k gewählt werden damit der Ski-Fahrer beim Punkt B h_B nicht abhebt vgl. Abb.. center tikzpicturedomain.: % Boden drawvery thick - -- .-; % Hoehe bei A drawtriangle -triangle .-. -- ..; node hA at .-. h_A kh_B; % Hoehe bei B drawtriangle -triangle .-. -- ..; node hB at .-. h_B; % Kreis bei B drawdashed .-. circle .cm; % Skipiste drawcolorblackvery thick plotsamples xexp-x/*sinx r; tikzpicture center
Solution:
Bei B gilt sofern der Ski-Fahrer nicht abhebt folge Ungleichung: F_G fracmv_B^r. Mit r h_B/ erhalten wir die Beziehung: v_B sqrtgh_B/. Die Energiebilanz lautet: eqnarray* E_pot^A+E_kin^A & E_pot^B+E_kin^Bmm mgh_A + fracmv_A^ & mgh_B + fracmv_B^mm gkh_B + v_A^ & gh_B + gh_B/mm v_A^ & gh_Bleftfrac - kright eqnarray* Damit v_A definiert ist muss die Klammer / - k sein d.h. frac k Rightarrow k ..
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