Aufhängepunkt für Holzstab
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:
Länge \(\ell\) / Kraft \(F\) / Drehmoment \(\vec M\) /
The following formulas must be used to solve the exercise:
\(\vec M = \vec \ell \times \vec F \quad \) \(\sum \stackrel{\curvearrowleft}{M} \stackrel{!}{=} \sum \stackrel{\curvearrowright}{M} \quad \)
No explanation / solution video to this exercise has yet been created.
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Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
Gegeben sei ein lSO langer Holzstab mit mSO Masse. Wo muss er aufgehängt werden damit er sich im Gleichgewicht befindet falls man an das eine Ende maO und an das andere Ende mbO hängt? Es ist eine Skizze anzufertigen aus welcher die Holzstange der Drehpunkt die Kräfte sowie die Hebelarme hervorgehen!
Solution:
newqtylm newqtymhkg newqtymekg newqtymzkg % unknownell_ % DrehmomentSchritte % Die Stange muss am Schwerpunkt des gesamten Systems aufgehängt werden. Dieser liegt näher an der grösseren zweiten Masse. center tikzpicturelatex drawvery thick -- ; draw-thickdarkgreen --++ -. nodebelow sscFH; draw-thickdarkgreen --++ -. nodebelow sscF; draw-thickdarkgreen --++ -. nodebelow sscF; drawdarkredthick . coordinate SP --++ .; drawsnakebrace . --++ SP; drawsnakebrace . -- ++.; drawsnakebrace .. --.; fill circle pt; filldarkred . circle pt; nodebelowdarkred at . SP; nodeabove at .. ell_ ell - ell_; nodeabove at .. sscellH fracell - ell_; nodeabove at .. ell_?; tikzpicture center % PGleichungM_ + sscMH M_ PGleichungF_ell_ + sscFHsscellH F_ell_ PGleichungm_gell-uk + sscmHgqtyfracell-uk m_guk % MGleichungm_gell-m_guk + sscmHgell-sscmHguk m_guk MGleichungm_guk+m_guk+sscmHguk m_gell+sscmHgell MGleichungm_+m_+sscmHguk m_+sscmHgell MGleichunguk fracm_+sscmHm_+m_+sscmHell % PHYSMATH Der Hebel muss also solqtylzfracm_+sscmHm_+m_+sscmHell*men+mhn/*mzn+men+mhn*lnm al ell_ lzf fracme+mhmz+me+mhl lz Teclz- von dem Ende mit der Masse mz entfernt aufgehängt werden.
Gegeben sei ein lSO langer Holzstab mit mSO Masse. Wo muss er aufgehängt werden damit er sich im Gleichgewicht befindet falls man an das eine Ende maO und an das andere Ende mbO hängt? Es ist eine Skizze anzufertigen aus welcher die Holzstange der Drehpunkt die Kräfte sowie die Hebelarme hervorgehen!
Solution:
newqtylm newqtymhkg newqtymekg newqtymzkg % unknownell_ % DrehmomentSchritte % Die Stange muss am Schwerpunkt des gesamten Systems aufgehängt werden. Dieser liegt näher an der grösseren zweiten Masse. center tikzpicturelatex drawvery thick -- ; draw-thickdarkgreen --++ -. nodebelow sscFH; draw-thickdarkgreen --++ -. nodebelow sscF; draw-thickdarkgreen --++ -. nodebelow sscF; drawdarkredthick . coordinate SP --++ .; drawsnakebrace . --++ SP; drawsnakebrace . -- ++.; drawsnakebrace .. --.; fill circle pt; filldarkred . circle pt; nodebelowdarkred at . SP; nodeabove at .. ell_ ell - ell_; nodeabove at .. sscellH fracell - ell_; nodeabove at .. ell_?; tikzpicture center % PGleichungM_ + sscMH M_ PGleichungF_ell_ + sscFHsscellH F_ell_ PGleichungm_gell-uk + sscmHgqtyfracell-uk m_guk % MGleichungm_gell-m_guk + sscmHgell-sscmHguk m_guk MGleichungm_guk+m_guk+sscmHguk m_gell+sscmHgell MGleichungm_+m_+sscmHguk m_+sscmHgell MGleichunguk fracm_+sscmHm_+m_+sscmHell % PHYSMATH Der Hebel muss also solqtylzfracm_+sscmHm_+m_+sscmHell*men+mhn/*mzn+men+mhn*lnm al ell_ lzf fracme+mhmz+me+mhl lz Teclz- von dem Ende mit der Masse mz entfernt aufgehängt werden.
Meta Information
Exercise:
Gegeben sei ein lSO langer Holzstab mit mSO Masse. Wo muss er aufgehängt werden damit er sich im Gleichgewicht befindet falls man an das eine Ende maO und an das andere Ende mbO hängt? Es ist eine Skizze anzufertigen aus welcher die Holzstange der Drehpunkt die Kräfte sowie die Hebelarme hervorgehen!
Solution:
newqtylm newqtymhkg newqtymekg newqtymzkg % unknownell_ % DrehmomentSchritte % Die Stange muss am Schwerpunkt des gesamten Systems aufgehängt werden. Dieser liegt näher an der grösseren zweiten Masse. center tikzpicturelatex drawvery thick -- ; draw-thickdarkgreen --++ -. nodebelow sscFH; draw-thickdarkgreen --++ -. nodebelow sscF; draw-thickdarkgreen --++ -. nodebelow sscF; drawdarkredthick . coordinate SP --++ .; drawsnakebrace . --++ SP; drawsnakebrace . -- ++.; drawsnakebrace .. --.; fill circle pt; filldarkred . circle pt; nodebelowdarkred at . SP; nodeabove at .. ell_ ell - ell_; nodeabove at .. sscellH fracell - ell_; nodeabove at .. ell_?; tikzpicture center % PGleichungM_ + sscMH M_ PGleichungF_ell_ + sscFHsscellH F_ell_ PGleichungm_gell-uk + sscmHgqtyfracell-uk m_guk % MGleichungm_gell-m_guk + sscmHgell-sscmHguk m_guk MGleichungm_guk+m_guk+sscmHguk m_gell+sscmHgell MGleichungm_+m_+sscmHguk m_+sscmHgell MGleichunguk fracm_+sscmHm_+m_+sscmHell % PHYSMATH Der Hebel muss also solqtylzfracm_+sscmHm_+m_+sscmHell*men+mhn/*mzn+men+mhn*lnm al ell_ lzf fracme+mhmz+me+mhl lz Teclz- von dem Ende mit der Masse mz entfernt aufgehängt werden.
Gegeben sei ein lSO langer Holzstab mit mSO Masse. Wo muss er aufgehängt werden damit er sich im Gleichgewicht befindet falls man an das eine Ende maO und an das andere Ende mbO hängt? Es ist eine Skizze anzufertigen aus welcher die Holzstange der Drehpunkt die Kräfte sowie die Hebelarme hervorgehen!
Solution:
newqtylm newqtymhkg newqtymekg newqtymzkg % unknownell_ % DrehmomentSchritte % Die Stange muss am Schwerpunkt des gesamten Systems aufgehängt werden. Dieser liegt näher an der grösseren zweiten Masse. center tikzpicturelatex drawvery thick -- ; draw-thickdarkgreen --++ -. nodebelow sscFH; draw-thickdarkgreen --++ -. nodebelow sscF; draw-thickdarkgreen --++ -. nodebelow sscF; drawdarkredthick . coordinate SP --++ .; drawsnakebrace . --++ SP; drawsnakebrace . -- ++.; drawsnakebrace .. --.; fill circle pt; filldarkred . circle pt; nodebelowdarkred at . SP; nodeabove at .. ell_ ell - ell_; nodeabove at .. sscellH fracell - ell_; nodeabove at .. ell_?; tikzpicture center % PGleichungM_ + sscMH M_ PGleichungF_ell_ + sscFHsscellH F_ell_ PGleichungm_gell-uk + sscmHgqtyfracell-uk m_guk % MGleichungm_gell-m_guk + sscmHgell-sscmHguk m_guk MGleichungm_guk+m_guk+sscmHguk m_gell+sscmHgell MGleichungm_+m_+sscmHguk m_+sscmHgell MGleichunguk fracm_+sscmHm_+m_+sscmHell % PHYSMATH Der Hebel muss also solqtylzfracm_+sscmHm_+m_+sscmHell*men+mhn/*mzn+men+mhn*lnm al ell_ lzf fracme+mhmz+me+mhl lz Teclz- von dem Ende mit der Masse mz entfernt aufgehängt werden.
Contained in these collections:
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Hebel I by pw
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Holzstab als Hebel by TeXercises
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Hebel 1 by uz