Ballistisches Pendel I
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:
Energie \(E\) / Impuls \(p\) / Winkel \(\theta\) / Ortsfaktor \(g\) / Masse \(m\) / Höhe \(h\) / Geschwindigkeit \(v\) /
The following formulas must be used to solve the exercise:
\(\cos\alpha = \dfrac{b}{c} \quad \) \(\sum E_{\scriptscriptstyle\rm tot} \stackrel{!}{=} \sum E_{\scriptscriptstyle\rm tot}' \quad \) \(p = mv \quad \) \(\sum p_{\scriptscriptstyle\rm tot} \stackrel{!}{=} \sum p_{\scriptscriptstyle\rm tot}' \quad \) \(E_{\rm \scriptscriptstyle kin} = \dfrac12 mv^2 \quad \) \(E_{\rm \scriptscriptstyle pot} = mgh \quad \) \(v' = \frac{m_1v_1+m_2v_2}{m_1+m_2} \quad \)
No explanation / solution video for this exercise has yet been created.
But there is a video to a similar exercise:
In case your browser prevents YouTube embedding: https://youtu.be/gfZO6vx39Lc
But there is a video to a similar exercise:
Exercise:
Eine mgram-Kugel werde in das M.kg Gewichtsstück eines ballistischen Pels geschossen. Bei maximaler Auslenkung bilden die Halteschnüre einen Winkel von alpha^circ mit der Vertikalen. Die Pellänge betrage l.m. Bestimmen Sie die Geschwindigkeit der Kugel.
Solution:
Kugel und Gewichtsstück werden am Pel ausgelenkt. Sie erreichen dabei eine Höhe von eqnarray* h & l - l cosalpha & l-cosalpha eqnarray* Gegenüber der Anfangshöhe Flughöhe der Kugel bedeutet das einen Gewinn an potentieller Energie von eqnarray* E_pot & m+Mgh eqnarray* Diese ganze Energie muss von der anfänglichen kinetischen Energie vor der Auslenkung kommen. Damit können wir deren Anfangsgeschwindigkeit v_ berechnen. eqnarray* E_kin & E_pot fracm+Mv_^ & m+Mgh v_ & sqrtgh eqnarray* Daraus lässt sich über den Impulssatz die Anfangsgeschwindigkeit der Kugel bestimmen: eqnarray* p_vor & p_nach mv & m+Mv_ v & fracm+Mmv_ &approx& m/s. eqnarray*
Eine mgram-Kugel werde in das M.kg Gewichtsstück eines ballistischen Pels geschossen. Bei maximaler Auslenkung bilden die Halteschnüre einen Winkel von alpha^circ mit der Vertikalen. Die Pellänge betrage l.m. Bestimmen Sie die Geschwindigkeit der Kugel.
Solution:
Kugel und Gewichtsstück werden am Pel ausgelenkt. Sie erreichen dabei eine Höhe von eqnarray* h & l - l cosalpha & l-cosalpha eqnarray* Gegenüber der Anfangshöhe Flughöhe der Kugel bedeutet das einen Gewinn an potentieller Energie von eqnarray* E_pot & m+Mgh eqnarray* Diese ganze Energie muss von der anfänglichen kinetischen Energie vor der Auslenkung kommen. Damit können wir deren Anfangsgeschwindigkeit v_ berechnen. eqnarray* E_kin & E_pot fracm+Mv_^ & m+Mgh v_ & sqrtgh eqnarray* Daraus lässt sich über den Impulssatz die Anfangsgeschwindigkeit der Kugel bestimmen: eqnarray* p_vor & p_nach mv & m+Mv_ v & fracm+Mmv_ &approx& m/s. eqnarray*
Meta Information
Exercise:
Eine mgram-Kugel werde in das M.kg Gewichtsstück eines ballistischen Pels geschossen. Bei maximaler Auslenkung bilden die Halteschnüre einen Winkel von alpha^circ mit der Vertikalen. Die Pellänge betrage l.m. Bestimmen Sie die Geschwindigkeit der Kugel.
Solution:
Kugel und Gewichtsstück werden am Pel ausgelenkt. Sie erreichen dabei eine Höhe von eqnarray* h & l - l cosalpha & l-cosalpha eqnarray* Gegenüber der Anfangshöhe Flughöhe der Kugel bedeutet das einen Gewinn an potentieller Energie von eqnarray* E_pot & m+Mgh eqnarray* Diese ganze Energie muss von der anfänglichen kinetischen Energie vor der Auslenkung kommen. Damit können wir deren Anfangsgeschwindigkeit v_ berechnen. eqnarray* E_kin & E_pot fracm+Mv_^ & m+Mgh v_ & sqrtgh eqnarray* Daraus lässt sich über den Impulssatz die Anfangsgeschwindigkeit der Kugel bestimmen: eqnarray* p_vor & p_nach mv & m+Mv_ v & fracm+Mmv_ &approx& m/s. eqnarray*
Eine mgram-Kugel werde in das M.kg Gewichtsstück eines ballistischen Pels geschossen. Bei maximaler Auslenkung bilden die Halteschnüre einen Winkel von alpha^circ mit der Vertikalen. Die Pellänge betrage l.m. Bestimmen Sie die Geschwindigkeit der Kugel.
Solution:
Kugel und Gewichtsstück werden am Pel ausgelenkt. Sie erreichen dabei eine Höhe von eqnarray* h & l - l cosalpha & l-cosalpha eqnarray* Gegenüber der Anfangshöhe Flughöhe der Kugel bedeutet das einen Gewinn an potentieller Energie von eqnarray* E_pot & m+Mgh eqnarray* Diese ganze Energie muss von der anfänglichen kinetischen Energie vor der Auslenkung kommen. Damit können wir deren Anfangsgeschwindigkeit v_ berechnen. eqnarray* E_kin & E_pot fracm+Mv_^ & m+Mgh v_ & sqrtgh eqnarray* Daraus lässt sich über den Impulssatz die Anfangsgeschwindigkeit der Kugel bestimmen: eqnarray* p_vor & p_nach mv & m+Mv_ v & fracm+Mmv_ &approx& m/s. eqnarray*
Contained in these collections
-
Ballistisches Pendel by TeXercises
| Title | Matched on |
|---|---|
| Unelastisches Pendel | tags |
| Vereinfachter Neutronenzerfall | tags |
| Kugel um Kugel | tags |
| Gerissenes Pendel | tags |
| Schmerzhafte Schlittenfahrt | tags |