Strassenampel
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 Strassenampel sei wie im Bild gezeichnet aufgehängt. Die Winkel sind alphaang und betaang und die Zugkraft im linken Seil betrage N. Berechne die Gewichtskraft der Strassenampel. center tikzpicturescale. filldrawcolorblack fillblack!!white ------.----.--cycle; filldrawcolorblack fillblack!!yellow -.-.--.-.--.-.---.-.--cycle; filldrawcolorblack fillred -. circle.cm; filldrawcolorblack fillyellow -. circle.cm; filldrawcolorblack fillgreen -. circle.cm; drawthick -.-.---.; drawthick .-.---.; draw -.-. arc :-:.; node at -.-. alpha; draw .-. arc ::.; node at .-. beta; tikzpicture center
Solution:
Geg alpha .degree beta .degree F_nwarrow N % GesGewichtskraftFG siN % Der Beitrag des linken Seils vertikal nach oben ist al F_nwarrowuparrow F_nwarrow sinalpha N sin.degree .N. Die Zugkraft im rechten Seil können wir aus der Bedingung berechnen dass in horizontale Richtung ebenfalls Kräftegleichgewicht gelten muss: F_leftarrow mustbe F_rightarrow: al F_nearrow fracF_rightarrowcosbeta F_nwarrow fraccosalphacosbeta N fraccos.degreecos.degree .N. Daraus folgt für den Beitrag des rechten Seils vertikal nach oben al F_nearrowuparrow F_nearrow sinbeta F_nwarrow fraccosalphacosbeta sinbeta F_nwarrow cosalphatanbeta .N sin.degree .N. Die Gewichtskraft der Ampel ist dann al FG F_nwarrowuparrow + F_nearrowuparrow F_nwarrow sinalpha + F_nwarrow cosalphatanbeta F_nwarrowsinalpha +cosalphatanbeta .N + .N .N. % FG F_nwarrowsinalpha +cosalphatanbeta N
Eine Strassenampel sei wie im Bild gezeichnet aufgehängt. Die Winkel sind alphaang und betaang und die Zugkraft im linken Seil betrage N. Berechne die Gewichtskraft der Strassenampel. center tikzpicturescale. filldrawcolorblack fillblack!!white ------.----.--cycle; filldrawcolorblack fillblack!!yellow -.-.--.-.--.-.---.-.--cycle; filldrawcolorblack fillred -. circle.cm; filldrawcolorblack fillyellow -. circle.cm; filldrawcolorblack fillgreen -. circle.cm; drawthick -.-.---.; drawthick .-.---.; draw -.-. arc :-:.; node at -.-. alpha; draw .-. arc ::.; node at .-. beta; tikzpicture center
Solution:
Geg alpha .degree beta .degree F_nwarrow N % GesGewichtskraftFG siN % Der Beitrag des linken Seils vertikal nach oben ist al F_nwarrowuparrow F_nwarrow sinalpha N sin.degree .N. Die Zugkraft im rechten Seil können wir aus der Bedingung berechnen dass in horizontale Richtung ebenfalls Kräftegleichgewicht gelten muss: F_leftarrow mustbe F_rightarrow: al F_nearrow fracF_rightarrowcosbeta F_nwarrow fraccosalphacosbeta N fraccos.degreecos.degree .N. Daraus folgt für den Beitrag des rechten Seils vertikal nach oben al F_nearrowuparrow F_nearrow sinbeta F_nwarrow fraccosalphacosbeta sinbeta F_nwarrow cosalphatanbeta .N sin.degree .N. Die Gewichtskraft der Ampel ist dann al FG F_nwarrowuparrow + F_nearrowuparrow F_nwarrow sinalpha + F_nwarrow cosalphatanbeta F_nwarrowsinalpha +cosalphatanbeta .N + .N .N. % FG F_nwarrowsinalpha +cosalphatanbeta N
Meta Information
Exercise:
Eine Strassenampel sei wie im Bild gezeichnet aufgehängt. Die Winkel sind alphaang und betaang und die Zugkraft im linken Seil betrage N. Berechne die Gewichtskraft der Strassenampel. center tikzpicturescale. filldrawcolorblack fillblack!!white ------.----.--cycle; filldrawcolorblack fillblack!!yellow -.-.--.-.--.-.---.-.--cycle; filldrawcolorblack fillred -. circle.cm; filldrawcolorblack fillyellow -. circle.cm; filldrawcolorblack fillgreen -. circle.cm; drawthick -.-.---.; drawthick .-.---.; draw -.-. arc :-:.; node at -.-. alpha; draw .-. arc ::.; node at .-. beta; tikzpicture center
Solution:
Geg alpha .degree beta .degree F_nwarrow N % GesGewichtskraftFG siN % Der Beitrag des linken Seils vertikal nach oben ist al F_nwarrowuparrow F_nwarrow sinalpha N sin.degree .N. Die Zugkraft im rechten Seil können wir aus der Bedingung berechnen dass in horizontale Richtung ebenfalls Kräftegleichgewicht gelten muss: F_leftarrow mustbe F_rightarrow: al F_nearrow fracF_rightarrowcosbeta F_nwarrow fraccosalphacosbeta N fraccos.degreecos.degree .N. Daraus folgt für den Beitrag des rechten Seils vertikal nach oben al F_nearrowuparrow F_nearrow sinbeta F_nwarrow fraccosalphacosbeta sinbeta F_nwarrow cosalphatanbeta .N sin.degree .N. Die Gewichtskraft der Ampel ist dann al FG F_nwarrowuparrow + F_nearrowuparrow F_nwarrow sinalpha + F_nwarrow cosalphatanbeta F_nwarrowsinalpha +cosalphatanbeta .N + .N .N. % FG F_nwarrowsinalpha +cosalphatanbeta N
Eine Strassenampel sei wie im Bild gezeichnet aufgehängt. Die Winkel sind alphaang und betaang und die Zugkraft im linken Seil betrage N. Berechne die Gewichtskraft der Strassenampel. center tikzpicturescale. filldrawcolorblack fillblack!!white ------.----.--cycle; filldrawcolorblack fillblack!!yellow -.-.--.-.--.-.---.-.--cycle; filldrawcolorblack fillred -. circle.cm; filldrawcolorblack fillyellow -. circle.cm; filldrawcolorblack fillgreen -. circle.cm; drawthick -.-.---.; drawthick .-.---.; draw -.-. arc :-:.; node at -.-. alpha; draw .-. arc ::.; node at .-. beta; tikzpicture center
Solution:
Geg alpha .degree beta .degree F_nwarrow N % GesGewichtskraftFG siN % Der Beitrag des linken Seils vertikal nach oben ist al F_nwarrowuparrow F_nwarrow sinalpha N sin.degree .N. Die Zugkraft im rechten Seil können wir aus der Bedingung berechnen dass in horizontale Richtung ebenfalls Kräftegleichgewicht gelten muss: F_leftarrow mustbe F_rightarrow: al F_nearrow fracF_rightarrowcosbeta F_nwarrow fraccosalphacosbeta N fraccos.degreecos.degree .N. Daraus folgt für den Beitrag des rechten Seils vertikal nach oben al F_nearrowuparrow F_nearrow sinbeta F_nwarrow fraccosalphacosbeta sinbeta F_nwarrow cosalphatanbeta .N sin.degree .N. Die Gewichtskraft der Ampel ist dann al FG F_nwarrowuparrow + F_nearrowuparrow F_nwarrow sinalpha + F_nwarrow cosalphatanbeta F_nwarrowsinalpha +cosalphatanbeta .N + .N .N. % FG F_nwarrowsinalpha +cosalphatanbeta N
Contained in these collections:
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Trigonometrie und Zugkraft by aej
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Strassenampel by TeXercises
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Kraft als Vektor 2 by uz
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Kraft als Vektor II by pw
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Kraft als Vektor by aej