An Kugel gehängtes Gewicht
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
\(\LaTeX\)
Need help? Yes, please!
The following quantities appear in the problem:
Winkelbeschleunigung \(\alpha\) / Trägheitsmoment \(J, \Theta, I\) / Energie \(E\) / Radius \(r\) / Ortsfaktor \(g\) / Höhe \(h\) / Geschwindigkeit \(v\) / Winkelgeschwindigkeit / Kreisfrequenz \(\omega\) / Kraft \(F\) / Drehmoment \(\vec M\) / Strecke \(s\) / Masse \(m\) / Beschleunigung \(a\) /
The following formulas must be used to solve the exercise:
\(a = r\alpha \quad \) \(v = r \omega \quad \) \(s = \dfrac{1}{2}at^2+v_0 t \quad \) \(s = \dfrac{v^2-v_0^2}{2a} \quad \) \(M = J\alpha \quad \) \(\sum E_{\scriptscriptstyle\rm tot} \stackrel{!}{=} \sum E_{\scriptscriptstyle\rm tot}' \quad \) \(F = mg \quad \) \(E_{\rm \scriptscriptstyle kin} = \dfrac12 mv^2 \quad \) \(F = ma \quad \) \(E_{\rm \scriptscriptstyle pot} = mgh \quad \) \(E = \frac12 J\omega^2 \quad \) \(J = \frac25 mr^2 \quad \) \(J = \frac12 mr^2 \quad \)
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Exercise:
Eine homogene Kugel Masse m_ Radius R kann frei um eine horizontale Achse rotieren. Um die Kugel ist ein Seil gewickelt an welchem ein Körper der Masse m_ hängt. Bestimme abcliste abc die Beschleunigung des Körpers mit der Masse m_ und abc die Zugkraft im Seil. abcliste center tikzpicture shadeball colorred circle .; filldrawblack circle .; draw .--.-; filldrawblue .-. rectangle ++..; tikzpicture center
Solution:
abcliste abc Der Körper mit der Masse m_ bewirkt an der Kugel ein Drehmoment; die dadurch hervorgerufene Winkelbeschleunigung der Kugel ist alpha fracMI fracm_grfrac m_r^ fracm_gm_r. Weil das Gewicht über ein Seil an der Kugel hängt wird durch diese Winkelbeschleunigung auch die Beschleunigung des Gewichts bestimmt a r alpha fracm_m_ g. abc Die Zugkraft im Seil besteht aus der Differenz der Gewichtskraft und der Bewegung nach unten also Z m_g - m_a m_ leftg-fracm_m_ gright m_g left-fracm_m_right. abcliste
Eine homogene Kugel Masse m_ Radius R kann frei um eine horizontale Achse rotieren. Um die Kugel ist ein Seil gewickelt an welchem ein Körper der Masse m_ hängt. Bestimme abcliste abc die Beschleunigung des Körpers mit der Masse m_ und abc die Zugkraft im Seil. abcliste center tikzpicture shadeball colorred circle .; filldrawblack circle .; draw .--.-; filldrawblue .-. rectangle ++..; tikzpicture center
Solution:
abcliste abc Der Körper mit der Masse m_ bewirkt an der Kugel ein Drehmoment; die dadurch hervorgerufene Winkelbeschleunigung der Kugel ist alpha fracMI fracm_grfrac m_r^ fracm_gm_r. Weil das Gewicht über ein Seil an der Kugel hängt wird durch diese Winkelbeschleunigung auch die Beschleunigung des Gewichts bestimmt a r alpha fracm_m_ g. abc Die Zugkraft im Seil besteht aus der Differenz der Gewichtskraft und der Bewegung nach unten also Z m_g - m_a m_ leftg-fracm_m_ gright m_g left-fracm_m_right. abcliste
Meta Information
Exercise:
Eine homogene Kugel Masse m_ Radius R kann frei um eine horizontale Achse rotieren. Um die Kugel ist ein Seil gewickelt an welchem ein Körper der Masse m_ hängt. Bestimme abcliste abc die Beschleunigung des Körpers mit der Masse m_ und abc die Zugkraft im Seil. abcliste center tikzpicture shadeball colorred circle .; filldrawblack circle .; draw .--.-; filldrawblue .-. rectangle ++..; tikzpicture center
Solution:
abcliste abc Der Körper mit der Masse m_ bewirkt an der Kugel ein Drehmoment; die dadurch hervorgerufene Winkelbeschleunigung der Kugel ist alpha fracMI fracm_grfrac m_r^ fracm_gm_r. Weil das Gewicht über ein Seil an der Kugel hängt wird durch diese Winkelbeschleunigung auch die Beschleunigung des Gewichts bestimmt a r alpha fracm_m_ g. abc Die Zugkraft im Seil besteht aus der Differenz der Gewichtskraft und der Bewegung nach unten also Z m_g - m_a m_ leftg-fracm_m_ gright m_g left-fracm_m_right. abcliste
Eine homogene Kugel Masse m_ Radius R kann frei um eine horizontale Achse rotieren. Um die Kugel ist ein Seil gewickelt an welchem ein Körper der Masse m_ hängt. Bestimme abcliste abc die Beschleunigung des Körpers mit der Masse m_ und abc die Zugkraft im Seil. abcliste center tikzpicture shadeball colorred circle .; filldrawblack circle .; draw .--.-; filldrawblue .-. rectangle ++..; tikzpicture center
Solution:
abcliste abc Der Körper mit der Masse m_ bewirkt an der Kugel ein Drehmoment; die dadurch hervorgerufene Winkelbeschleunigung der Kugel ist alpha fracMI fracm_grfrac m_r^ fracm_gm_r. Weil das Gewicht über ein Seil an der Kugel hängt wird durch diese Winkelbeschleunigung auch die Beschleunigung des Gewichts bestimmt a r alpha fracm_m_ g. abc Die Zugkraft im Seil besteht aus der Differenz der Gewichtskraft und der Bewegung nach unten also Z m_g - m_a m_ leftg-fracm_m_ gright m_g left-fracm_m_right. abcliste
Contained in these collections
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Atwood'sche Fallmaschine by TeXercises
| Title | Matched on |
|---|---|
| Karussell | tags |
| Zentrifuge | tags |
| Salatschleuder | tags |
| Rotationsdynamik | tags |
| Rotationsdynamik | tags |
Similar exercises (7)
| Title | Matched on |
|---|---|
| Karussell | tags |
| Zentrifuge | tags |
| Salatschleuder | tags |
| Rotationsdynamik | tags |
| Rotationsdynamik | tags |
| Reifen | tags |
| Achsenantrieb | tags |