Kraft als Vektor
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 Am rechts abgebildeten Punkt P greifen die Kräfte vec F_ und vec F_ an. abclist abc Konstruiere den Vektor der resultieren Kraft sscvec Fres. abc Zerlege vec F_ vec F_ und sscvec Fres zeichnerisch in geeignete Komponenten. abc Drücke den Betrag der resultieren Kraft sscFres in Abhängigkeit der Beträge F_ und F_ sowie in der Skizze sichtbare Winkel aus ohne es algebraisch zu vereinfachen. abc Zusatzaufgabe: Vereinfache das Ergebnis von c unter Verwung der trigonometrischen Identitäten al sinx + cosx sinxsiny cosx-y - cosx+y cosxcosy cosx-y + cosx+y. abclist Wichtig: Alle eingezeichneten Kraftvektoren müssen sinnvoll beschriftet werden. Ein eingezeichneter Vektor ohne Beschriftung gibt keine Punkte! defgridwidth
Solution:
Wie üblich lassen sich die Komponenten über al F_ix F_i cosalpha_i F_iy F_i sinalpha_i zerlegen. Für die resultiere Kraft folgt dann al sscFres sqrtsscFresx^ + sscFresy^ sqrtqtyF_cosalpha_ + F_ cosalpha_^ + qtyF_ sinalpha_-F_sinalpha_^ sqrtF_^ + F_^ + F_F_cosalpha_cosalpha_-sinalpha_sinalpha_ sqrtF_^ + F_^ + F_F_cosalpha_+alpha_ center tikzpicturelatexscale . fill nodeleftP circle pt; draw- -- nodeabove vec F_; draw- dashed . -- . nodeabove rightvec F_x; draw- dashed . -- nodebelow rightvec F_y; draw- -- . - nodebelow vec F_; draw- dashed -. -- .-. nodebelow rightvec F_x; draw- dashed .-. -- .- nodeabove rightvec F_y; draw- darkred -- . nodeabove sscvec Fres; draw- dashed darkred -- . nodebelow rightvec F_rm resx; draw- dashed darkred . -- . nodebelow rightvec F_rm resy; draw . arc :.:.cm nodeabove right yshift-.cmalpha_; draw . arc :-.:.cm nodeabove right yshift-.cmalpha_; tikzpicture center
minipagec.textwidth Am rechts abgebildeten Punkt P greifen die Kräfte vec F_ und vec F_ an. abclist abc Konstruiere den Vektor der resultieren Kraft sscvec Fres. abc Zerlege vec F_ vec F_ und sscvec Fres zeichnerisch in geeignete Komponenten. abc Drücke den Betrag der resultieren Kraft sscFres in Abhängigkeit der Beträge F_ und F_ sowie in der Skizze sichtbare Winkel aus ohne es algebraisch zu vereinfachen. abc Zusatzaufgabe: Vereinfache das Ergebnis von c unter Verwung der trigonometrischen Identitäten al sinx + cosx sinxsiny cosx-y - cosx+y cosxcosy cosx-y + cosx+y. abclist Wichtig: Alle eingezeichneten Kraftvektoren müssen sinnvoll beschriftet werden. Ein eingezeichneter Vektor ohne Beschriftung gibt keine Punkte! defgridwidth
Solution:
Wie üblich lassen sich die Komponenten über al F_ix F_i cosalpha_i F_iy F_i sinalpha_i zerlegen. Für die resultiere Kraft folgt dann al sscFres sqrtsscFresx^ + sscFresy^ sqrtqtyF_cosalpha_ + F_ cosalpha_^ + qtyF_ sinalpha_-F_sinalpha_^ sqrtF_^ + F_^ + F_F_cosalpha_cosalpha_-sinalpha_sinalpha_ sqrtF_^ + F_^ + F_F_cosalpha_+alpha_ center tikzpicturelatexscale . fill nodeleftP circle pt; draw- -- nodeabove vec F_; draw- dashed . -- . nodeabove rightvec F_x; draw- dashed . -- nodebelow rightvec F_y; draw- -- . - nodebelow vec F_; draw- dashed -. -- .-. nodebelow rightvec F_x; draw- dashed .-. -- .- nodeabove rightvec F_y; draw- darkred -- . nodeabove sscvec Fres; draw- dashed darkred -- . nodebelow rightvec F_rm resx; draw- dashed darkred . -- . nodebelow rightvec F_rm resy; draw . arc :.:.cm nodeabove right yshift-.cmalpha_; draw . arc :-.:.cm nodeabove right yshift-.cmalpha_; tikzpicture center
Meta Information
Exercise:
minipagec.textwidth Am rechts abgebildeten Punkt P greifen die Kräfte vec F_ und vec F_ an. abclist abc Konstruiere den Vektor der resultieren Kraft sscvec Fres. abc Zerlege vec F_ vec F_ und sscvec Fres zeichnerisch in geeignete Komponenten. abc Drücke den Betrag der resultieren Kraft sscFres in Abhängigkeit der Beträge F_ und F_ sowie in der Skizze sichtbare Winkel aus ohne es algebraisch zu vereinfachen. abc Zusatzaufgabe: Vereinfache das Ergebnis von c unter Verwung der trigonometrischen Identitäten al sinx + cosx sinxsiny cosx-y - cosx+y cosxcosy cosx-y + cosx+y. abclist Wichtig: Alle eingezeichneten Kraftvektoren müssen sinnvoll beschriftet werden. Ein eingezeichneter Vektor ohne Beschriftung gibt keine Punkte! defgridwidth
Solution:
Wie üblich lassen sich die Komponenten über al F_ix F_i cosalpha_i F_iy F_i sinalpha_i zerlegen. Für die resultiere Kraft folgt dann al sscFres sqrtsscFresx^ + sscFresy^ sqrtqtyF_cosalpha_ + F_ cosalpha_^ + qtyF_ sinalpha_-F_sinalpha_^ sqrtF_^ + F_^ + F_F_cosalpha_cosalpha_-sinalpha_sinalpha_ sqrtF_^ + F_^ + F_F_cosalpha_+alpha_ center tikzpicturelatexscale . fill nodeleftP circle pt; draw- -- nodeabove vec F_; draw- dashed . -- . nodeabove rightvec F_x; draw- dashed . -- nodebelow rightvec F_y; draw- -- . - nodebelow vec F_; draw- dashed -. -- .-. nodebelow rightvec F_x; draw- dashed .-. -- .- nodeabove rightvec F_y; draw- darkred -- . nodeabove sscvec Fres; draw- dashed darkred -- . nodebelow rightvec F_rm resx; draw- dashed darkred . -- . nodebelow rightvec F_rm resy; draw . arc :.:.cm nodeabove right yshift-.cmalpha_; draw . arc :-.:.cm nodeabove right yshift-.cmalpha_; tikzpicture center
minipagec.textwidth Am rechts abgebildeten Punkt P greifen die Kräfte vec F_ und vec F_ an. abclist abc Konstruiere den Vektor der resultieren Kraft sscvec Fres. abc Zerlege vec F_ vec F_ und sscvec Fres zeichnerisch in geeignete Komponenten. abc Drücke den Betrag der resultieren Kraft sscFres in Abhängigkeit der Beträge F_ und F_ sowie in der Skizze sichtbare Winkel aus ohne es algebraisch zu vereinfachen. abc Zusatzaufgabe: Vereinfache das Ergebnis von c unter Verwung der trigonometrischen Identitäten al sinx + cosx sinxsiny cosx-y - cosx+y cosxcosy cosx-y + cosx+y. abclist Wichtig: Alle eingezeichneten Kraftvektoren müssen sinnvoll beschriftet werden. Ein eingezeichneter Vektor ohne Beschriftung gibt keine Punkte! defgridwidth
Solution:
Wie üblich lassen sich die Komponenten über al F_ix F_i cosalpha_i F_iy F_i sinalpha_i zerlegen. Für die resultiere Kraft folgt dann al sscFres sqrtsscFresx^ + sscFresy^ sqrtqtyF_cosalpha_ + F_ cosalpha_^ + qtyF_ sinalpha_-F_sinalpha_^ sqrtF_^ + F_^ + F_F_cosalpha_cosalpha_-sinalpha_sinalpha_ sqrtF_^ + F_^ + F_F_cosalpha_+alpha_ center tikzpicturelatexscale . fill nodeleftP circle pt; draw- -- nodeabove vec F_; draw- dashed . -- . nodeabove rightvec F_x; draw- dashed . -- nodebelow rightvec F_y; draw- -- . - nodebelow vec F_; draw- dashed -. -- .-. nodebelow rightvec F_x; draw- dashed .-. -- .- nodeabove rightvec F_y; draw- darkred -- . nodeabove sscvec Fres; draw- dashed darkred -- . nodebelow rightvec F_rm resx; draw- dashed darkred . -- . nodebelow rightvec F_rm resy; draw . arc :.:.cm nodeabove right yshift-.cmalpha_; draw . arc :-.:.cm nodeabove right yshift-.cmalpha_; tikzpicture center
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