Galilei'sches Hemmungspendel
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:
Senkrecht über dem tiefsten Bahnpunkt eines .m langen ebenen Fadenpels befindet sich in einem Abstand von cm eine senkrecht zur Schwingungsebene stehe Arretierstange. Wie gross ist die volle Schwingungsdauer dieses Pels? center tikzpicture filldrawcolorblack!!white - rectangle .; filldrawcolorblack!!white .-. circle .cm; drawthick colorblue ---. arc ::.--++:. coordinate sph; filldrawcolorblue sph circle .cm; drawdashed colorblue -.---; filldrawcolorblue!!white fillblue!!white- circle .cm; drawdotted - arc ::.; drawdotted - arc ::; drawdashed colorblue --++: coordinate sphl; filldrawcolorblue!!white sphl circle .cm; tikzpicture center
Solution:
newqtyLe.m newqtyLzocm newqtyLzLzon m % Geg ell_ Le ell_ Lzo Lz % GesSchwingungsdauerTsis % Die Schwingungsdauer ist je zur Hälfte von zwei verschieden langen Peln gegeben: solqtyTfracpisqrtgqtysqrtell_+sqrtell_pi/sqrtncgn*sqrtLen + sqrtLzns T fracT_ + fracT_ pi sqrtfracell_g + pi sqrtfracell_g Tf fracpisqrtncgqtysqrtLe+sqrtLz T. % T Tf TII
Senkrecht über dem tiefsten Bahnpunkt eines .m langen ebenen Fadenpels befindet sich in einem Abstand von cm eine senkrecht zur Schwingungsebene stehe Arretierstange. Wie gross ist die volle Schwingungsdauer dieses Pels? center tikzpicture filldrawcolorblack!!white - rectangle .; filldrawcolorblack!!white .-. circle .cm; drawthick colorblue ---. arc ::.--++:. coordinate sph; filldrawcolorblue sph circle .cm; drawdashed colorblue -.---; filldrawcolorblue!!white fillblue!!white- circle .cm; drawdotted - arc ::.; drawdotted - arc ::; drawdashed colorblue --++: coordinate sphl; filldrawcolorblue!!white sphl circle .cm; tikzpicture center
Solution:
newqtyLe.m newqtyLzocm newqtyLzLzon m % Geg ell_ Le ell_ Lzo Lz % GesSchwingungsdauerTsis % Die Schwingungsdauer ist je zur Hälfte von zwei verschieden langen Peln gegeben: solqtyTfracpisqrtgqtysqrtell_+sqrtell_pi/sqrtncgn*sqrtLen + sqrtLzns T fracT_ + fracT_ pi sqrtfracell_g + pi sqrtfracell_g Tf fracpisqrtncgqtysqrtLe+sqrtLz T. % T Tf TII
Meta Information
Exercise:
Senkrecht über dem tiefsten Bahnpunkt eines .m langen ebenen Fadenpels befindet sich in einem Abstand von cm eine senkrecht zur Schwingungsebene stehe Arretierstange. Wie gross ist die volle Schwingungsdauer dieses Pels? center tikzpicture filldrawcolorblack!!white - rectangle .; filldrawcolorblack!!white .-. circle .cm; drawthick colorblue ---. arc ::.--++:. coordinate sph; filldrawcolorblue sph circle .cm; drawdashed colorblue -.---; filldrawcolorblue!!white fillblue!!white- circle .cm; drawdotted - arc ::.; drawdotted - arc ::; drawdashed colorblue --++: coordinate sphl; filldrawcolorblue!!white sphl circle .cm; tikzpicture center
Solution:
newqtyLe.m newqtyLzocm newqtyLzLzon m % Geg ell_ Le ell_ Lzo Lz % GesSchwingungsdauerTsis % Die Schwingungsdauer ist je zur Hälfte von zwei verschieden langen Peln gegeben: solqtyTfracpisqrtgqtysqrtell_+sqrtell_pi/sqrtncgn*sqrtLen + sqrtLzns T fracT_ + fracT_ pi sqrtfracell_g + pi sqrtfracell_g Tf fracpisqrtncgqtysqrtLe+sqrtLz T. % T Tf TII
Senkrecht über dem tiefsten Bahnpunkt eines .m langen ebenen Fadenpels befindet sich in einem Abstand von cm eine senkrecht zur Schwingungsebene stehe Arretierstange. Wie gross ist die volle Schwingungsdauer dieses Pels? center tikzpicture filldrawcolorblack!!white - rectangle .; filldrawcolorblack!!white .-. circle .cm; drawthick colorblue ---. arc ::.--++:. coordinate sph; filldrawcolorblue sph circle .cm; drawdashed colorblue -.---; filldrawcolorblue!!white fillblue!!white- circle .cm; drawdotted - arc ::.; drawdotted - arc ::; drawdashed colorblue --++: coordinate sphl; filldrawcolorblue!!white sphl circle .cm; tikzpicture center
Solution:
newqtyLe.m newqtyLzocm newqtyLzLzon m % Geg ell_ Le ell_ Lzo Lz % GesSchwingungsdauerTsis % Die Schwingungsdauer ist je zur Hälfte von zwei verschieden langen Peln gegeben: solqtyTfracpisqrtgqtysqrtell_+sqrtell_pi/sqrtncgn*sqrtLen + sqrtLzns T fracT_ + fracT_ pi sqrtfracell_g + pi sqrtfracell_g Tf fracpisqrtncgqtysqrtLe+sqrtLz T. % T Tf TII
Contained in these collections:
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Pendel by aej
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Mathematisches Pendel by TeXercises
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Fadenpendel by pw