Atwoodsche Fallmaschine I
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:
Eine Schnur sei entsprech der Abbildung durch eine ideale Umlenkrolle geführt und auf der einen Seite mit der Masse von m_ kilogram verbunden. Am anderen Ende hänge eine Masse von m_ kilogram. center tikzpicturescale. % Decke draw top colorgray!bottom colorgraymiddle colorgray!shadingaxisdrawnone rectangle .; draw -- ; % Halterung shade left colorbrown! right colorbrown shadingaxis drawnone .-. rectangle .-.; % Seile draw grayvery thick .- -- ++ -.; draw grayvery thick .- -- ++ -.; % Rolle draw gray fillgray! .- circle .cm; draw gray fillgray .- circle .cm; shade left colorgray! right colorgray! shadingaxis drawnone .-. rectangle .-.; draw gray fillgray! .- circle .cm; draw fillblack .- circle .cm; % Massen shadedraw shadingball ball coloryellowdrawnone .-.-. node tiny m_ circle .cm; shadedraw shadingball ball coloryellowdrawnone .--.-. node tiny m_ circle .cm; tikzpicture center Bestimmen Sie enumerate item die Beschleunigung der Massen und item die Seilkraft. enumerate
Solution:
Die Kräfte links sind sofern die Aufwärtsrichtung als positiv gesehen wird: F_res F_S -F_g_ m_a. Die Kräfte recht sind dementsprech: F_res F_g_ - F_S m_a enumerate item Nach F_S auflösen und einsetzen ergibt: F_g_ - m_a-F_g_ m_a Rightarrow a fracm_-m_m_+m_g approx .meter/second^. item Die Seilkraft ist: F_S m_a+F_g_ approx newton. enumerate
Eine Schnur sei entsprech der Abbildung durch eine ideale Umlenkrolle geführt und auf der einen Seite mit der Masse von m_ kilogram verbunden. Am anderen Ende hänge eine Masse von m_ kilogram. center tikzpicturescale. % Decke draw top colorgray!bottom colorgraymiddle colorgray!shadingaxisdrawnone rectangle .; draw -- ; % Halterung shade left colorbrown! right colorbrown shadingaxis drawnone .-. rectangle .-.; % Seile draw grayvery thick .- -- ++ -.; draw grayvery thick .- -- ++ -.; % Rolle draw gray fillgray! .- circle .cm; draw gray fillgray .- circle .cm; shade left colorgray! right colorgray! shadingaxis drawnone .-. rectangle .-.; draw gray fillgray! .- circle .cm; draw fillblack .- circle .cm; % Massen shadedraw shadingball ball coloryellowdrawnone .-.-. node tiny m_ circle .cm; shadedraw shadingball ball coloryellowdrawnone .--.-. node tiny m_ circle .cm; tikzpicture center Bestimmen Sie enumerate item die Beschleunigung der Massen und item die Seilkraft. enumerate
Solution:
Die Kräfte links sind sofern die Aufwärtsrichtung als positiv gesehen wird: F_res F_S -F_g_ m_a. Die Kräfte recht sind dementsprech: F_res F_g_ - F_S m_a enumerate item Nach F_S auflösen und einsetzen ergibt: F_g_ - m_a-F_g_ m_a Rightarrow a fracm_-m_m_+m_g approx .meter/second^. item Die Seilkraft ist: F_S m_a+F_g_ approx newton. enumerate
Meta Information
Exercise:
Eine Schnur sei entsprech der Abbildung durch eine ideale Umlenkrolle geführt und auf der einen Seite mit der Masse von m_ kilogram verbunden. Am anderen Ende hänge eine Masse von m_ kilogram. center tikzpicturescale. % Decke draw top colorgray!bottom colorgraymiddle colorgray!shadingaxisdrawnone rectangle .; draw -- ; % Halterung shade left colorbrown! right colorbrown shadingaxis drawnone .-. rectangle .-.; % Seile draw grayvery thick .- -- ++ -.; draw grayvery thick .- -- ++ -.; % Rolle draw gray fillgray! .- circle .cm; draw gray fillgray .- circle .cm; shade left colorgray! right colorgray! shadingaxis drawnone .-. rectangle .-.; draw gray fillgray! .- circle .cm; draw fillblack .- circle .cm; % Massen shadedraw shadingball ball coloryellowdrawnone .-.-. node tiny m_ circle .cm; shadedraw shadingball ball coloryellowdrawnone .--.-. node tiny m_ circle .cm; tikzpicture center Bestimmen Sie enumerate item die Beschleunigung der Massen und item die Seilkraft. enumerate
Solution:
Die Kräfte links sind sofern die Aufwärtsrichtung als positiv gesehen wird: F_res F_S -F_g_ m_a. Die Kräfte recht sind dementsprech: F_res F_g_ - F_S m_a enumerate item Nach F_S auflösen und einsetzen ergibt: F_g_ - m_a-F_g_ m_a Rightarrow a fracm_-m_m_+m_g approx .meter/second^. item Die Seilkraft ist: F_S m_a+F_g_ approx newton. enumerate
Eine Schnur sei entsprech der Abbildung durch eine ideale Umlenkrolle geführt und auf der einen Seite mit der Masse von m_ kilogram verbunden. Am anderen Ende hänge eine Masse von m_ kilogram. center tikzpicturescale. % Decke draw top colorgray!bottom colorgraymiddle colorgray!shadingaxisdrawnone rectangle .; draw -- ; % Halterung shade left colorbrown! right colorbrown shadingaxis drawnone .-. rectangle .-.; % Seile draw grayvery thick .- -- ++ -.; draw grayvery thick .- -- ++ -.; % Rolle draw gray fillgray! .- circle .cm; draw gray fillgray .- circle .cm; shade left colorgray! right colorgray! shadingaxis drawnone .-. rectangle .-.; draw gray fillgray! .- circle .cm; draw fillblack .- circle .cm; % Massen shadedraw shadingball ball coloryellowdrawnone .-.-. node tiny m_ circle .cm; shadedraw shadingball ball coloryellowdrawnone .--.-. node tiny m_ circle .cm; tikzpicture center Bestimmen Sie enumerate item die Beschleunigung der Massen und item die Seilkraft. enumerate
Solution:
Die Kräfte links sind sofern die Aufwärtsrichtung als positiv gesehen wird: F_res F_S -F_g_ m_a. Die Kräfte recht sind dementsprech: F_res F_g_ - F_S m_a enumerate item Nach F_S auflösen und einsetzen ergibt: F_g_ - m_a-F_g_ m_a Rightarrow a fracm_-m_m_+m_g approx .meter/second^. item Die Seilkraft ist: F_S m_a+F_g_ approx newton. enumerate
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Atwood'sche Fallmaschine by TeXercises