Arbeit, Leistung, Energie: Wirkungsgrad 10
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:
Eine Firmenchefin möchte einen Elektromotor mit sikW Dauerleistung kaufen. Der erste Motor hat Wirkungsgrad % der zweite teurere hat %. Eine Kilowattstunde Energie koste Rappen. Die Motoren sollen fünf Jahre durchlaufen. In dieser Zeit müssen sich die Mehrkosten des teureren Motors amortisiert haben. Wie viel darf der Aufpreis maximal betragen? % Motorkennzahlen nach aktuelle Technik Sonderbeilage März
Solution:
% . Mai Lie. Variable: Nutzleistung P_ sikW Wirkungsgrad eta Kosten K.siFr/kWh Zeitraum tsia sih Aufpreis A. * &eta fracP_P_ Rightarrow P_ fracP_eta textquad benötigte Energie &W_a fracP_ teta_a rightarrow A_a W_a K fracP_tKeta_a textquad Energiekosten eines Motors &A A_a-A_b fracP_ t Keta_a - fracP_ tKeta_b P_ t Kleft fraceta_a-fraceta_b right &qquad sikW sih .siFr/kWh left frac.-frac.right uuline.sikFr * newpage
Eine Firmenchefin möchte einen Elektromotor mit sikW Dauerleistung kaufen. Der erste Motor hat Wirkungsgrad % der zweite teurere hat %. Eine Kilowattstunde Energie koste Rappen. Die Motoren sollen fünf Jahre durchlaufen. In dieser Zeit müssen sich die Mehrkosten des teureren Motors amortisiert haben. Wie viel darf der Aufpreis maximal betragen? % Motorkennzahlen nach aktuelle Technik Sonderbeilage März
Solution:
% . Mai Lie. Variable: Nutzleistung P_ sikW Wirkungsgrad eta Kosten K.siFr/kWh Zeitraum tsia sih Aufpreis A. * &eta fracP_P_ Rightarrow P_ fracP_eta textquad benötigte Energie &W_a fracP_ teta_a rightarrow A_a W_a K fracP_tKeta_a textquad Energiekosten eines Motors &A A_a-A_b fracP_ t Keta_a - fracP_ tKeta_b P_ t Kleft fraceta_a-fraceta_b right &qquad sikW sih .siFr/kWh left frac.-frac.right uuline.sikFr * newpage
Meta Information
Exercise:
Eine Firmenchefin möchte einen Elektromotor mit sikW Dauerleistung kaufen. Der erste Motor hat Wirkungsgrad % der zweite teurere hat %. Eine Kilowattstunde Energie koste Rappen. Die Motoren sollen fünf Jahre durchlaufen. In dieser Zeit müssen sich die Mehrkosten des teureren Motors amortisiert haben. Wie viel darf der Aufpreis maximal betragen? % Motorkennzahlen nach aktuelle Technik Sonderbeilage März
Solution:
% . Mai Lie. Variable: Nutzleistung P_ sikW Wirkungsgrad eta Kosten K.siFr/kWh Zeitraum tsia sih Aufpreis A. * &eta fracP_P_ Rightarrow P_ fracP_eta textquad benötigte Energie &W_a fracP_ teta_a rightarrow A_a W_a K fracP_tKeta_a textquad Energiekosten eines Motors &A A_a-A_b fracP_ t Keta_a - fracP_ tKeta_b P_ t Kleft fraceta_a-fraceta_b right &qquad sikW sih .siFr/kWh left frac.-frac.right uuline.sikFr * newpage
Eine Firmenchefin möchte einen Elektromotor mit sikW Dauerleistung kaufen. Der erste Motor hat Wirkungsgrad % der zweite teurere hat %. Eine Kilowattstunde Energie koste Rappen. Die Motoren sollen fünf Jahre durchlaufen. In dieser Zeit müssen sich die Mehrkosten des teureren Motors amortisiert haben. Wie viel darf der Aufpreis maximal betragen? % Motorkennzahlen nach aktuelle Technik Sonderbeilage März
Solution:
% . Mai Lie. Variable: Nutzleistung P_ sikW Wirkungsgrad eta Kosten K.siFr/kWh Zeitraum tsia sih Aufpreis A. * &eta fracP_P_ Rightarrow P_ fracP_eta textquad benötigte Energie &W_a fracP_ teta_a rightarrow A_a W_a K fracP_tKeta_a textquad Energiekosten eines Motors &A A_a-A_b fracP_ t Keta_a - fracP_ tKeta_b P_ t Kleft fraceta_a-fraceta_b right &qquad sikW sih .siFr/kWh left frac.-frac.right uuline.sikFr * newpage
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