Allgemeine Relativitätstheorie: Uhren im Schwerefeld 12
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
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Video
\(\LaTeX\)
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Exercise:
Nehmen Sie an von der Sonne werde Licht mit Wellenlänge nm ausgesandt. In grosser Entfernung ist dieses Licht rotverschoben. Warum rotverschoben und wie gross ist diese Verschiebung in Nanometern?
Solution:
% . August Lie. * &fracf_f_ sqrt- fracvarphi_-varphi_c^ sqrt-frac-GMc^r_ + frac-GMc^r_ sqrt+fracGMc^infty -fracGMc^r_S sqrt-fracGMc^r_S &c lambda f Rightarrow &fraclambda_lambda_ fraclambda_lambda_+Delta lambda sqrt-fracGMc^r_S Rightarrow &Delta lambda fraclambda_sqrt-fracGMc^r_S -lambda_ sinm left left - frac .eeesim^/s^.eeesim/s^ .eeesim right^-/ - right &Delta lambda sinm left .ee right uuline.sinm .sipm * Diese Rotverschiebung konnte gemessen werden. Das Schwerefeld kann lokal durch ein nach oben beschleunigtes Bezugsystem simuliert werden. In der Zeit die das Licht benötigt um den Beobachter zu erreichen erhält dieser in der Simulation eine Geschwindigkeit von der Sonne weg. Der Beobachter empfängt dopplerverschobene Strahlung tieferer Frequenz. newpage
Nehmen Sie an von der Sonne werde Licht mit Wellenlänge nm ausgesandt. In grosser Entfernung ist dieses Licht rotverschoben. Warum rotverschoben und wie gross ist diese Verschiebung in Nanometern?
Solution:
% . August Lie. * &fracf_f_ sqrt- fracvarphi_-varphi_c^ sqrt-frac-GMc^r_ + frac-GMc^r_ sqrt+fracGMc^infty -fracGMc^r_S sqrt-fracGMc^r_S &c lambda f Rightarrow &fraclambda_lambda_ fraclambda_lambda_+Delta lambda sqrt-fracGMc^r_S Rightarrow &Delta lambda fraclambda_sqrt-fracGMc^r_S -lambda_ sinm left left - frac .eeesim^/s^.eeesim/s^ .eeesim right^-/ - right &Delta lambda sinm left .ee right uuline.sinm .sipm * Diese Rotverschiebung konnte gemessen werden. Das Schwerefeld kann lokal durch ein nach oben beschleunigtes Bezugsystem simuliert werden. In der Zeit die das Licht benötigt um den Beobachter zu erreichen erhält dieser in der Simulation eine Geschwindigkeit von der Sonne weg. Der Beobachter empfängt dopplerverschobene Strahlung tieferer Frequenz. newpage
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Exercise:
Nehmen Sie an von der Sonne werde Licht mit Wellenlänge nm ausgesandt. In grosser Entfernung ist dieses Licht rotverschoben. Warum rotverschoben und wie gross ist diese Verschiebung in Nanometern?
Solution:
% . August Lie. * &fracf_f_ sqrt- fracvarphi_-varphi_c^ sqrt-frac-GMc^r_ + frac-GMc^r_ sqrt+fracGMc^infty -fracGMc^r_S sqrt-fracGMc^r_S &c lambda f Rightarrow &fraclambda_lambda_ fraclambda_lambda_+Delta lambda sqrt-fracGMc^r_S Rightarrow &Delta lambda fraclambda_sqrt-fracGMc^r_S -lambda_ sinm left left - frac .eeesim^/s^.eeesim/s^ .eeesim right^-/ - right &Delta lambda sinm left .ee right uuline.sinm .sipm * Diese Rotverschiebung konnte gemessen werden. Das Schwerefeld kann lokal durch ein nach oben beschleunigtes Bezugsystem simuliert werden. In der Zeit die das Licht benötigt um den Beobachter zu erreichen erhält dieser in der Simulation eine Geschwindigkeit von der Sonne weg. Der Beobachter empfängt dopplerverschobene Strahlung tieferer Frequenz. newpage
Nehmen Sie an von der Sonne werde Licht mit Wellenlänge nm ausgesandt. In grosser Entfernung ist dieses Licht rotverschoben. Warum rotverschoben und wie gross ist diese Verschiebung in Nanometern?
Solution:
% . August Lie. * &fracf_f_ sqrt- fracvarphi_-varphi_c^ sqrt-frac-GMc^r_ + frac-GMc^r_ sqrt+fracGMc^infty -fracGMc^r_S sqrt-fracGMc^r_S &c lambda f Rightarrow &fraclambda_lambda_ fraclambda_lambda_+Delta lambda sqrt-fracGMc^r_S Rightarrow &Delta lambda fraclambda_sqrt-fracGMc^r_S -lambda_ sinm left left - frac .eeesim^/s^.eeesim/s^ .eeesim right^-/ - right &Delta lambda sinm left .ee right uuline.sinm .sipm * Diese Rotverschiebung konnte gemessen werden. Das Schwerefeld kann lokal durch ein nach oben beschleunigtes Bezugsystem simuliert werden. In der Zeit die das Licht benötigt um den Beobachter zu erreichen erhält dieser in der Simulation eine Geschwindigkeit von der Sonne weg. Der Beobachter empfängt dopplerverschobene Strahlung tieferer Frequenz. newpage
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