Verbundene Massen mit Feder
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:
minipagec.textwidth Zwei Massen m_ .kg und m_ .kg sind gemäss der Skizze rechts über eine Feder .kilonewtonpermeter und ein Rad miteinander verbunden. abclist abc Berechne die Beschleunigung der Anordnung. abc Berechne die Verlängerung der Feder im Vergleich zu ihrer entspannten Lage. abclist Hinweis: Die als masselos zu betrachte Feder hat keinen Einfluss auf die Beschleunigung. minipage minipagec.textwidth center tikzpicture draw circle .cm; draw circle pt; drawvery thick . arc ::.cm; drawvery thick . -- ++- coordinate m; drawvery thick -. -- -.-; drawdecorationaspect. segment lengthmm amplitudemmcoildecorate -.- -- ++-. coordinate m; fill m -- ++. -- ++-. -- ++-. -- ++. -- cycle; nodebelowyshift-.cm at m m_; fill m -- ++. -- ++-. -- ++-. -- ++. -- cycle; nodebelowyshift-.cm at m m_; draw . -- ++. coordinate C; filldrawpatternnorth east lines C - - ++. - - ++. - - ++ - - - ++ -. - - cycle; tikzpicture center minipage
Solution:
newqtyme.kg newqtymz.kg newqtyD.eNpm abclist abc Auf die Masse m_ wirken die Gewichtskraft sscFG und die Seilkraft sscFS auf die Masse m_ die Gewichtskraft sscFG und die Federkraft sscFF die betragsmässig gleich gross sein muss wie sscFS. Daraus folgt solqtyafracm_-m_m_+m_ gmzn-men/men+mzn*ncgns al m_ a sscFS - m_ g m_ a m_ g- sscFS m_+m_a m_-m_g a af fracmz - meme + mz ncg a approx aII abc Für die Federkraft gilt solqtyFFfracm_m_m_+m_ g*men*mzn/men+mzn*ncgnN al m_m_ a m_sscFF - m_m_ g -m_m_ a m_sscFF -m_m_ g m_+m_ sscFF - m_m_ g sscFF FFf fracmemzme+mzncg FFTTTT. Die Verlängerung ist damit solqtyyfracm_m_m_+m_ fracgDFFn/Dnm al y fracsscFFD fracFFfD yf fracFFD y approx Tecy-. abclist
minipagec.textwidth Zwei Massen m_ .kg und m_ .kg sind gemäss der Skizze rechts über eine Feder .kilonewtonpermeter und ein Rad miteinander verbunden. abclist abc Berechne die Beschleunigung der Anordnung. abc Berechne die Verlängerung der Feder im Vergleich zu ihrer entspannten Lage. abclist Hinweis: Die als masselos zu betrachte Feder hat keinen Einfluss auf die Beschleunigung. minipage minipagec.textwidth center tikzpicture draw circle .cm; draw circle pt; drawvery thick . arc ::.cm; drawvery thick . -- ++- coordinate m; drawvery thick -. -- -.-; drawdecorationaspect. segment lengthmm amplitudemmcoildecorate -.- -- ++-. coordinate m; fill m -- ++. -- ++-. -- ++-. -- ++. -- cycle; nodebelowyshift-.cm at m m_; fill m -- ++. -- ++-. -- ++-. -- ++. -- cycle; nodebelowyshift-.cm at m m_; draw . -- ++. coordinate C; filldrawpatternnorth east lines C - - ++. - - ++. - - ++ - - - ++ -. - - cycle; tikzpicture center minipage
Solution:
newqtyme.kg newqtymz.kg newqtyD.eNpm abclist abc Auf die Masse m_ wirken die Gewichtskraft sscFG und die Seilkraft sscFS auf die Masse m_ die Gewichtskraft sscFG und die Federkraft sscFF die betragsmässig gleich gross sein muss wie sscFS. Daraus folgt solqtyafracm_-m_m_+m_ gmzn-men/men+mzn*ncgns al m_ a sscFS - m_ g m_ a m_ g- sscFS m_+m_a m_-m_g a af fracmz - meme + mz ncg a approx aII abc Für die Federkraft gilt solqtyFFfracm_m_m_+m_ g*men*mzn/men+mzn*ncgnN al m_m_ a m_sscFF - m_m_ g -m_m_ a m_sscFF -m_m_ g m_+m_ sscFF - m_m_ g sscFF FFf fracmemzme+mzncg FFTTTT. Die Verlängerung ist damit solqtyyfracm_m_m_+m_ fracgDFFn/Dnm al y fracsscFFD fracFFfD yf fracFFD y approx Tecy-. abclist
Meta Information
Exercise:
minipagec.textwidth Zwei Massen m_ .kg und m_ .kg sind gemäss der Skizze rechts über eine Feder .kilonewtonpermeter und ein Rad miteinander verbunden. abclist abc Berechne die Beschleunigung der Anordnung. abc Berechne die Verlängerung der Feder im Vergleich zu ihrer entspannten Lage. abclist Hinweis: Die als masselos zu betrachte Feder hat keinen Einfluss auf die Beschleunigung. minipage minipagec.textwidth center tikzpicture draw circle .cm; draw circle pt; drawvery thick . arc ::.cm; drawvery thick . -- ++- coordinate m; drawvery thick -. -- -.-; drawdecorationaspect. segment lengthmm amplitudemmcoildecorate -.- -- ++-. coordinate m; fill m -- ++. -- ++-. -- ++-. -- ++. -- cycle; nodebelowyshift-.cm at m m_; fill m -- ++. -- ++-. -- ++-. -- ++. -- cycle; nodebelowyshift-.cm at m m_; draw . -- ++. coordinate C; filldrawpatternnorth east lines C - - ++. - - ++. - - ++ - - - ++ -. - - cycle; tikzpicture center minipage
Solution:
newqtyme.kg newqtymz.kg newqtyD.eNpm abclist abc Auf die Masse m_ wirken die Gewichtskraft sscFG und die Seilkraft sscFS auf die Masse m_ die Gewichtskraft sscFG und die Federkraft sscFF die betragsmässig gleich gross sein muss wie sscFS. Daraus folgt solqtyafracm_-m_m_+m_ gmzn-men/men+mzn*ncgns al m_ a sscFS - m_ g m_ a m_ g- sscFS m_+m_a m_-m_g a af fracmz - meme + mz ncg a approx aII abc Für die Federkraft gilt solqtyFFfracm_m_m_+m_ g*men*mzn/men+mzn*ncgnN al m_m_ a m_sscFF - m_m_ g -m_m_ a m_sscFF -m_m_ g m_+m_ sscFF - m_m_ g sscFF FFf fracmemzme+mzncg FFTTTT. Die Verlängerung ist damit solqtyyfracm_m_m_+m_ fracgDFFn/Dnm al y fracsscFFD fracFFfD yf fracFFD y approx Tecy-. abclist
minipagec.textwidth Zwei Massen m_ .kg und m_ .kg sind gemäss der Skizze rechts über eine Feder .kilonewtonpermeter und ein Rad miteinander verbunden. abclist abc Berechne die Beschleunigung der Anordnung. abc Berechne die Verlängerung der Feder im Vergleich zu ihrer entspannten Lage. abclist Hinweis: Die als masselos zu betrachte Feder hat keinen Einfluss auf die Beschleunigung. minipage minipagec.textwidth center tikzpicture draw circle .cm; draw circle pt; drawvery thick . arc ::.cm; drawvery thick . -- ++- coordinate m; drawvery thick -. -- -.-; drawdecorationaspect. segment lengthmm amplitudemmcoildecorate -.- -- ++-. coordinate m; fill m -- ++. -- ++-. -- ++-. -- ++. -- cycle; nodebelowyshift-.cm at m m_; fill m -- ++. -- ++-. -- ++-. -- ++. -- cycle; nodebelowyshift-.cm at m m_; draw . -- ++. coordinate C; filldrawpatternnorth east lines C - - ++. - - ++. - - ++ - - - ++ -. - - cycle; tikzpicture center minipage
Solution:
newqtyme.kg newqtymz.kg newqtyD.eNpm abclist abc Auf die Masse m_ wirken die Gewichtskraft sscFG und die Seilkraft sscFS auf die Masse m_ die Gewichtskraft sscFG und die Federkraft sscFF die betragsmässig gleich gross sein muss wie sscFS. Daraus folgt solqtyafracm_-m_m_+m_ gmzn-men/men+mzn*ncgns al m_ a sscFS - m_ g m_ a m_ g- sscFS m_+m_a m_-m_g a af fracmz - meme + mz ncg a approx aII abc Für die Federkraft gilt solqtyFFfracm_m_m_+m_ g*men*mzn/men+mzn*ncgnN al m_m_ a m_sscFF - m_m_ g -m_m_ a m_sscFF -m_m_ g m_+m_ sscFF - m_m_ g sscFF FFf fracmemzme+mzncg FFTTTT. Die Verlängerung ist damit solqtyyfracm_m_m_+m_ fracgDFFn/Dnm al y fracsscFFD fracFFfD yf fracFFD y approx Tecy-. abclist
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