Höhe einer Aquariumscheibe
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
\(\LaTeX\)
Need help? Yes, please!
The following quantities appear in the problem:
Länge \(\ell\) / Kraft \(F\) / Druck \(p\) / Fläche \(A\) / Ortsfaktor \(g\) / Höhe \(h\) / Dichte \(\varrho\) / Breite \(b\) /
The following formulas must be used to solve the exercise:
\(p = \dfrac{F}{A} \quad \) \(A = ab \quad \) \(p = \varrho g h \quad \)
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/SfSEwMwjGks
But there is a video to a similar exercise:
Exercise:
Die Scheibe eines grossen Zoo-Aquariums sei BO breit und das Wasser rage dO über den oberen Scheibenrand hinaus. Das Wasser drücke mit FO gegen die Scheibe. Was hat diese für eine Höhe?
Solution:
Der auf die Scheibe ausgeübte mittlere Wasserdruck beträgt: p rho g d+frach und die Scheibe hat A bh Fläche. Die Kraft auf die Scheibe ist somit F pA rho g d+frach bh rho gbhd + rho gb frach^ Das ist eine quadratische Gleichung in h fracrho gb h^ + rho gbd h -F mit den folgen beiden Lösungen: h_ ha h_ hb
Die Scheibe eines grossen Zoo-Aquariums sei BO breit und das Wasser rage dO über den oberen Scheibenrand hinaus. Das Wasser drücke mit FO gegen die Scheibe. Was hat diese für eine Höhe?
Solution:
Der auf die Scheibe ausgeübte mittlere Wasserdruck beträgt: p rho g d+frach und die Scheibe hat A bh Fläche. Die Kraft auf die Scheibe ist somit F pA rho g d+frach bh rho gbhd + rho gb frach^ Das ist eine quadratische Gleichung in h fracrho gb h^ + rho gbd h -F mit den folgen beiden Lösungen: h_ ha h_ hb
Meta Information
Exercise:
Die Scheibe eines grossen Zoo-Aquariums sei BO breit und das Wasser rage dO über den oberen Scheibenrand hinaus. Das Wasser drücke mit FO gegen die Scheibe. Was hat diese für eine Höhe?
Solution:
Der auf die Scheibe ausgeübte mittlere Wasserdruck beträgt: p rho g d+frach und die Scheibe hat A bh Fläche. Die Kraft auf die Scheibe ist somit F pA rho g d+frach bh rho gbhd + rho gb frach^ Das ist eine quadratische Gleichung in h fracrho gb h^ + rho gbd h -F mit den folgen beiden Lösungen: h_ ha h_ hb
Die Scheibe eines grossen Zoo-Aquariums sei BO breit und das Wasser rage dO über den oberen Scheibenrand hinaus. Das Wasser drücke mit FO gegen die Scheibe. Was hat diese für eine Höhe?
Solution:
Der auf die Scheibe ausgeübte mittlere Wasserdruck beträgt: p rho g d+frach und die Scheibe hat A bh Fläche. Die Kraft auf die Scheibe ist somit F pA rho g d+frach bh rho gbhd + rho gb frach^ Das ist eine quadratische Gleichung in h fracrho gb h^ + rho gbd h -F mit den folgen beiden Lösungen: h_ ha h_ hb
Contained in these collections:
-
Aquarium by TeXercises
Asked Quantity:
Höhe \(h\)
in
Meter \(\rm m\)
Physical Quantity
lotrechter Abstand von Referenzfläche
Unit
Der Meter ist dadurch definiert, dass der Lichtgeschwindigkeit im Vakuum \(c\) ein fester Wert zugewiesen wurde und die Sekunde (\(\rm s\)) ebenfalls über eine Naturkonstante, die Schwingungsfrequenz definiert ist.
Base?
SI?
Metric?
Coherent?
Imperial?