Der Winkel hängt!
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:
Ein homogener Draht werde wie in der Abbildung gebogen und zwar so dass ein spitzer Winkel von alpha grad zwischen den Schenkel von l und l entsteht. Bestimmen Sie die Koordinaten kartesisch und polar des Schwerpunktes. center tikzpicturescale. drawstylehelp linesstep.cm grid ..; draw- -.-- noderight x; draw- -.--. nodeleft y; drawline width.pt gray -- ; node at -. l; drawline width.pt grayrotate -- ; node at .. l; drawthick . arc ::.; node at .. alpha; tikzpicture center
Solution:
Die Schwerpunktskoordinate kartesisch in x-Richtung ist: x_s fraclleftl l + tfraclcosalpha lright fracl+cosalpha approx .l wobei wir die Massen in l angeben da der Draht homogen ist.mm Die Schwerpunktskoordinate in y-Richtung ist: y_s fracllefttfraclsinalpha lright fraclsinalpha approx .l. Die Polarkoordinaten erhalten wir durch: r_s sqrtx_s^+y_s^ fraclsqrt+cosalpha approx . und tantheta fracy_sx_s fracsinalpha+cosalpha Rightarrow theta_s approx .grad.
Ein homogener Draht werde wie in der Abbildung gebogen und zwar so dass ein spitzer Winkel von alpha grad zwischen den Schenkel von l und l entsteht. Bestimmen Sie die Koordinaten kartesisch und polar des Schwerpunktes. center tikzpicturescale. drawstylehelp linesstep.cm grid ..; draw- -.-- noderight x; draw- -.--. nodeleft y; drawline width.pt gray -- ; node at -. l; drawline width.pt grayrotate -- ; node at .. l; drawthick . arc ::.; node at .. alpha; tikzpicture center
Solution:
Die Schwerpunktskoordinate kartesisch in x-Richtung ist: x_s fraclleftl l + tfraclcosalpha lright fracl+cosalpha approx .l wobei wir die Massen in l angeben da der Draht homogen ist.mm Die Schwerpunktskoordinate in y-Richtung ist: y_s fracllefttfraclsinalpha lright fraclsinalpha approx .l. Die Polarkoordinaten erhalten wir durch: r_s sqrtx_s^+y_s^ fraclsqrt+cosalpha approx . und tantheta fracy_sx_s fracsinalpha+cosalpha Rightarrow theta_s approx .grad.
Meta Information
Exercise:
Ein homogener Draht werde wie in der Abbildung gebogen und zwar so dass ein spitzer Winkel von alpha grad zwischen den Schenkel von l und l entsteht. Bestimmen Sie die Koordinaten kartesisch und polar des Schwerpunktes. center tikzpicturescale. drawstylehelp linesstep.cm grid ..; draw- -.-- noderight x; draw- -.--. nodeleft y; drawline width.pt gray -- ; node at -. l; drawline width.pt grayrotate -- ; node at .. l; drawthick . arc ::.; node at .. alpha; tikzpicture center
Solution:
Die Schwerpunktskoordinate kartesisch in x-Richtung ist: x_s fraclleftl l + tfraclcosalpha lright fracl+cosalpha approx .l wobei wir die Massen in l angeben da der Draht homogen ist.mm Die Schwerpunktskoordinate in y-Richtung ist: y_s fracllefttfraclsinalpha lright fraclsinalpha approx .l. Die Polarkoordinaten erhalten wir durch: r_s sqrtx_s^+y_s^ fraclsqrt+cosalpha approx . und tantheta fracy_sx_s fracsinalpha+cosalpha Rightarrow theta_s approx .grad.
Ein homogener Draht werde wie in der Abbildung gebogen und zwar so dass ein spitzer Winkel von alpha grad zwischen den Schenkel von l und l entsteht. Bestimmen Sie die Koordinaten kartesisch und polar des Schwerpunktes. center tikzpicturescale. drawstylehelp linesstep.cm grid ..; draw- -.-- noderight x; draw- -.--. nodeleft y; drawline width.pt gray -- ; node at -. l; drawline width.pt grayrotate -- ; node at .. l; drawthick . arc ::.; node at .. alpha; tikzpicture center
Solution:
Die Schwerpunktskoordinate kartesisch in x-Richtung ist: x_s fraclleftl l + tfraclcosalpha lright fracl+cosalpha approx .l wobei wir die Massen in l angeben da der Draht homogen ist.mm Die Schwerpunktskoordinate in y-Richtung ist: y_s fracllefttfraclsinalpha lright fraclsinalpha approx .l. Die Polarkoordinaten erhalten wir durch: r_s sqrtx_s^+y_s^ fraclsqrt+cosalpha approx . und tantheta fracy_sx_s fracsinalpha+cosalpha Rightarrow theta_s approx .grad.
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