Gravitationsbeschleunigung auf Saturn
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
\(\LaTeX\)
NASA/JPL/Space Science Institute, , 2004, digital photograph, NASA
<Wikipedia> (retrieved on October 20, 2022)
Need help? Yes, please!
The following quantities appear in the problem:
Masse \(m\) / Volumen \(V\) / Ortsfaktor \(g\) / Radius \(r\) / Dichte \(\varrho\) /
The following formulas must be used to solve the exercise:
\(\varrho = \dfrac{m}{V} \quad \) \(g = \dfrac{GM}{r^2} \quad \) \(V = \dfrac{4}{3}\pi r^3 \quad \)
No explanation / solution video to this exercise has yet been created.
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Visit our YouTube-Channel to see solutions to other exercises.
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Exercise:
Der Planet Saturn besitzt mO Gesamtmasse und rO mittlere Dichte. Berechne die Gra-vi-ta-ti-ons- bzw. Fall-bschleu-ni-gung auf seiner Oberfläche aus diesen Daten.
Solution:
Geg M mO m rho rO r GestextGravitations-/FallbeschleunigunggsimeterpersecondsquaredsiNpkg Das Volumen von Saturn beträgt: V fracMrho fracmr V Den Radius von Saturn unter der Annahme dass er kugelförmig ist beträgt: r sqrtfracVpi leftfracVpiright^frac leftfracMpirhoright^frac sqrtfrac V pi R Damit kann die Gravitationsbeschleunigung auf diesem Himmelskörper ausgerechnet werden: g_SaturnIndex fracGMr^ fracGMleftfracMpirhoright^frac GM leftfracpirhoMright^frac GM^frac leftfracpirhoright^frac fracncG mqtyR^ g approx gS gP g_SaturnIndex GM^frac leftfracpirhoright^frac gP
Der Planet Saturn besitzt mO Gesamtmasse und rO mittlere Dichte. Berechne die Gra-vi-ta-ti-ons- bzw. Fall-bschleu-ni-gung auf seiner Oberfläche aus diesen Daten.
Solution:
Geg M mO m rho rO r GestextGravitations-/FallbeschleunigunggsimeterpersecondsquaredsiNpkg Das Volumen von Saturn beträgt: V fracMrho fracmr V Den Radius von Saturn unter der Annahme dass er kugelförmig ist beträgt: r sqrtfracVpi leftfracVpiright^frac leftfracMpirhoright^frac sqrtfrac V pi R Damit kann die Gravitationsbeschleunigung auf diesem Himmelskörper ausgerechnet werden: g_SaturnIndex fracGMr^ fracGMleftfracMpirhoright^frac GM leftfracpirhoMright^frac GM^frac leftfracpirhoright^frac fracncG mqtyR^ g approx gS gP g_SaturnIndex GM^frac leftfracpirhoright^frac gP
Meta Information
Exercise:
Der Planet Saturn besitzt mO Gesamtmasse und rO mittlere Dichte. Berechne die Gra-vi-ta-ti-ons- bzw. Fall-bschleu-ni-gung auf seiner Oberfläche aus diesen Daten.
Solution:
Geg M mO m rho rO r GestextGravitations-/FallbeschleunigunggsimeterpersecondsquaredsiNpkg Das Volumen von Saturn beträgt: V fracMrho fracmr V Den Radius von Saturn unter der Annahme dass er kugelförmig ist beträgt: r sqrtfracVpi leftfracVpiright^frac leftfracMpirhoright^frac sqrtfrac V pi R Damit kann die Gravitationsbeschleunigung auf diesem Himmelskörper ausgerechnet werden: g_SaturnIndex fracGMr^ fracGMleftfracMpirhoright^frac GM leftfracpirhoMright^frac GM^frac leftfracpirhoright^frac fracncG mqtyR^ g approx gS gP g_SaturnIndex GM^frac leftfracpirhoright^frac gP
Der Planet Saturn besitzt mO Gesamtmasse und rO mittlere Dichte. Berechne die Gra-vi-ta-ti-ons- bzw. Fall-bschleu-ni-gung auf seiner Oberfläche aus diesen Daten.
Solution:
Geg M mO m rho rO r GestextGravitations-/FallbeschleunigunggsimeterpersecondsquaredsiNpkg Das Volumen von Saturn beträgt: V fracMrho fracmr V Den Radius von Saturn unter der Annahme dass er kugelförmig ist beträgt: r sqrtfracVpi leftfracVpiright^frac leftfracMpirhoright^frac sqrtfrac V pi R Damit kann die Gravitationsbeschleunigung auf diesem Himmelskörper ausgerechnet werden: g_SaturnIndex fracGMr^ fracGMleftfracMpirhoright^frac GM leftfracpirhoMright^frac GM^frac leftfracpirhoright^frac fracncG mqtyR^ g approx gS gP g_SaturnIndex GM^frac leftfracpirhoright^frac gP
Contained in these collections:
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Planet und Dichte by TeXercises
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Gravitationsgesetz by uz
Asked Quantity:
Ortsfaktor \(g\)
in
Newton pro Kilogramm \(\rm \frac{N}{kg}\)
Physical Quantity
Schwerefeld, Fallbeschleunigung
Gewichtskraft pro Masse
Unit
Newton pro Kilogramm (\(\rm \frac{N}{kg}\))
Base?
SI?
Metric?
Coherent?
Imperial?
\(\rm9.81\,\frac{N}{kg}\): Erde
\(\rm3.69\,\frac{N}{kg}\): Mars
\(\rm1.62\,\frac{N}{kg}\): Mond