Astronomie: Gravitationskraft 20
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 kleiner fester Mond mit Radius r_M umkreise einen Planeten mit Radius r_P Abb.reffig:RocheL. Der Mond sei mit einer Schicht Kies bedeckt. In welchem Abstand R vom Planeten löst sich der Kies vom Mond und umkreist den Planeten auf einer eigenen Bahn? RochGrenze. Tipp: Starten Sie bei der Rechnung wie bei der Bestimmung des Lagrangepunktes L_. Verwen Sie für die Näherungsformeln die Information R gg r_M und rho_P approx rho_M. quad figureH includegraphicswidthtextwidth#image_path:RocheL# caption labelfig:RocheL figure
Solution:
% . Jan. Lie. * &F_textres m_ a_z rightarrow fracGm_Pm_left R-r_M right^ - fracGm_Mm_r_M^ m_ left R-r_M right omega^ m_ left R-r_M right fracGm_PR^ &fracGm_Pleft R-r_M right^ - fracGm_Mr_M^ left R-r_M right fracGm_PR^ Rightarrow fracleft R-r_M right^ - fracm_M/m_Pr_M^ left R-r_M right fracR^ Rightarrow &fracR^left -r_M/R right^ - fracm_M/m_Pr_M^ Rleft -r_M/R right fracR^ rightarrow fracR^left +r_M/R right - fracm_M/m_Pr_M^ left -r_M/R right fracR^ &fracr_MR^ fracm_Mm_P r_M^ Rightarrow R^ r_M^fracm_Pm_M r_M^fracrho_P r_P^rho_M r_M^ rightarrow R^ approx r_P^ Rightarrow R sqrt r_P . r_P * newpage
Ein kleiner fester Mond mit Radius r_M umkreise einen Planeten mit Radius r_P Abb.reffig:RocheL. Der Mond sei mit einer Schicht Kies bedeckt. In welchem Abstand R vom Planeten löst sich der Kies vom Mond und umkreist den Planeten auf einer eigenen Bahn? RochGrenze. Tipp: Starten Sie bei der Rechnung wie bei der Bestimmung des Lagrangepunktes L_. Verwen Sie für die Näherungsformeln die Information R gg r_M und rho_P approx rho_M. quad figureH includegraphicswidthtextwidth#image_path:RocheL# caption labelfig:RocheL figure
Solution:
% . Jan. Lie. * &F_textres m_ a_z rightarrow fracGm_Pm_left R-r_M right^ - fracGm_Mm_r_M^ m_ left R-r_M right omega^ m_ left R-r_M right fracGm_PR^ &fracGm_Pleft R-r_M right^ - fracGm_Mr_M^ left R-r_M right fracGm_PR^ Rightarrow fracleft R-r_M right^ - fracm_M/m_Pr_M^ left R-r_M right fracR^ Rightarrow &fracR^left -r_M/R right^ - fracm_M/m_Pr_M^ Rleft -r_M/R right fracR^ rightarrow fracR^left +r_M/R right - fracm_M/m_Pr_M^ left -r_M/R right fracR^ &fracr_MR^ fracm_Mm_P r_M^ Rightarrow R^ r_M^fracm_Pm_M r_M^fracrho_P r_P^rho_M r_M^ rightarrow R^ approx r_P^ Rightarrow R sqrt r_P . r_P * newpage
Meta Information
Exercise:
Ein kleiner fester Mond mit Radius r_M umkreise einen Planeten mit Radius r_P Abb.reffig:RocheL. Der Mond sei mit einer Schicht Kies bedeckt. In welchem Abstand R vom Planeten löst sich der Kies vom Mond und umkreist den Planeten auf einer eigenen Bahn? RochGrenze. Tipp: Starten Sie bei der Rechnung wie bei der Bestimmung des Lagrangepunktes L_. Verwen Sie für die Näherungsformeln die Information R gg r_M und rho_P approx rho_M. quad figureH includegraphicswidthtextwidth#image_path:RocheL# caption labelfig:RocheL figure
Solution:
% . Jan. Lie. * &F_textres m_ a_z rightarrow fracGm_Pm_left R-r_M right^ - fracGm_Mm_r_M^ m_ left R-r_M right omega^ m_ left R-r_M right fracGm_PR^ &fracGm_Pleft R-r_M right^ - fracGm_Mr_M^ left R-r_M right fracGm_PR^ Rightarrow fracleft R-r_M right^ - fracm_M/m_Pr_M^ left R-r_M right fracR^ Rightarrow &fracR^left -r_M/R right^ - fracm_M/m_Pr_M^ Rleft -r_M/R right fracR^ rightarrow fracR^left +r_M/R right - fracm_M/m_Pr_M^ left -r_M/R right fracR^ &fracr_MR^ fracm_Mm_P r_M^ Rightarrow R^ r_M^fracm_Pm_M r_M^fracrho_P r_P^rho_M r_M^ rightarrow R^ approx r_P^ Rightarrow R sqrt r_P . r_P * newpage
Ein kleiner fester Mond mit Radius r_M umkreise einen Planeten mit Radius r_P Abb.reffig:RocheL. Der Mond sei mit einer Schicht Kies bedeckt. In welchem Abstand R vom Planeten löst sich der Kies vom Mond und umkreist den Planeten auf einer eigenen Bahn? RochGrenze. Tipp: Starten Sie bei der Rechnung wie bei der Bestimmung des Lagrangepunktes L_. Verwen Sie für die Näherungsformeln die Information R gg r_M und rho_P approx rho_M. quad figureH includegraphicswidthtextwidth#image_path:RocheL# caption labelfig:RocheL figure
Solution:
% . Jan. Lie. * &F_textres m_ a_z rightarrow fracGm_Pm_left R-r_M right^ - fracGm_Mm_r_M^ m_ left R-r_M right omega^ m_ left R-r_M right fracGm_PR^ &fracGm_Pleft R-r_M right^ - fracGm_Mr_M^ left R-r_M right fracGm_PR^ Rightarrow fracleft R-r_M right^ - fracm_M/m_Pr_M^ left R-r_M right fracR^ Rightarrow &fracR^left -r_M/R right^ - fracm_M/m_Pr_M^ Rleft -r_M/R right fracR^ rightarrow fracR^left +r_M/R right - fracm_M/m_Pr_M^ left -r_M/R right fracR^ &fracr_MR^ fracm_Mm_P r_M^ Rightarrow R^ r_M^fracm_Pm_M r_M^fracrho_P r_P^rho_M r_M^ rightarrow R^ approx r_P^ Rightarrow R sqrt r_P . r_P * newpage
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