Spezielle Relativitätstheorie: Gesamtenergie 3
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:
Der LHC-Beschleunigerring des CERN hat sim Umfang. Darin laufen Protonen mit .siTeV Gesamtenergie April . a Berechnen Sie - v/c für diese Protonen m_P .siMeV/c^. b Welchen Umfang hat der Beschleunigerring für die Protonen? c Wie viele Proton-Antiproton-Paare können bei einer Frontalkollision zweier solcher Protonen maximal entstehen? d Wie gross ist der Impuls eines solchen Protons in -Einheiten? e Eine Stechmücke habe Masse .simg und Schnelligkeit .sikm/h. Berechnen Sie zum Vergleich den Impuls und die kinetische Energie der Mücke.
Solution:
%. Mai Lie. * &texta Egamma mc^ Rightarrow gammafracEmc^left -fracv^c^right^-/ Rightarrow fracvc sqrt-leftfracmc^Eright^ -frac leftfracmc^Eright^ +dots Rightarrow &qquad -fracvc approx frac leftfracmc^Eright^ frac leftfrac.siMeV.eeesiMeVright^ uulineee &textb l_fracl_gamma Rightarrow l_ ell_ gamma l_fracEmc^ simfrac.eeesiMeV.siMeV uuline.eeesim &textc E mc^+N mc^ Rightarrow N fracEmc^-frac.eeesiMeV.siMeV-uuline.eee &textd pgamma m v approx fracEmc^ mc frac.eeesiMeV.siMeV .eesikg .eeesim/s .eesiNs &texte p_M m_Mv_M .eesikg frac.sim.sis .eesiNs textquad p_M p &quad E_Mtfracm_Mv^tfrac .eesikg leftfrac.sim.sisright^ .eesiJ.eeesieV textquad E_M E * newpage
Der LHC-Beschleunigerring des CERN hat sim Umfang. Darin laufen Protonen mit .siTeV Gesamtenergie April . a Berechnen Sie - v/c für diese Protonen m_P .siMeV/c^. b Welchen Umfang hat der Beschleunigerring für die Protonen? c Wie viele Proton-Antiproton-Paare können bei einer Frontalkollision zweier solcher Protonen maximal entstehen? d Wie gross ist der Impuls eines solchen Protons in -Einheiten? e Eine Stechmücke habe Masse .simg und Schnelligkeit .sikm/h. Berechnen Sie zum Vergleich den Impuls und die kinetische Energie der Mücke.
Solution:
%. Mai Lie. * &texta Egamma mc^ Rightarrow gammafracEmc^left -fracv^c^right^-/ Rightarrow fracvc sqrt-leftfracmc^Eright^ -frac leftfracmc^Eright^ +dots Rightarrow &qquad -fracvc approx frac leftfracmc^Eright^ frac leftfrac.siMeV.eeesiMeVright^ uulineee &textb l_fracl_gamma Rightarrow l_ ell_ gamma l_fracEmc^ simfrac.eeesiMeV.siMeV uuline.eeesim &textc E mc^+N mc^ Rightarrow N fracEmc^-frac.eeesiMeV.siMeV-uuline.eee &textd pgamma m v approx fracEmc^ mc frac.eeesiMeV.siMeV .eesikg .eeesim/s .eesiNs &texte p_M m_Mv_M .eesikg frac.sim.sis .eesiNs textquad p_M p &quad E_Mtfracm_Mv^tfrac .eesikg leftfrac.sim.sisright^ .eesiJ.eeesieV textquad E_M E * newpage
Meta Information
Exercise:
Der LHC-Beschleunigerring des CERN hat sim Umfang. Darin laufen Protonen mit .siTeV Gesamtenergie April . a Berechnen Sie - v/c für diese Protonen m_P .siMeV/c^. b Welchen Umfang hat der Beschleunigerring für die Protonen? c Wie viele Proton-Antiproton-Paare können bei einer Frontalkollision zweier solcher Protonen maximal entstehen? d Wie gross ist der Impuls eines solchen Protons in -Einheiten? e Eine Stechmücke habe Masse .simg und Schnelligkeit .sikm/h. Berechnen Sie zum Vergleich den Impuls und die kinetische Energie der Mücke.
Solution:
%. Mai Lie. * &texta Egamma mc^ Rightarrow gammafracEmc^left -fracv^c^right^-/ Rightarrow fracvc sqrt-leftfracmc^Eright^ -frac leftfracmc^Eright^ +dots Rightarrow &qquad -fracvc approx frac leftfracmc^Eright^ frac leftfrac.siMeV.eeesiMeVright^ uulineee &textb l_fracl_gamma Rightarrow l_ ell_ gamma l_fracEmc^ simfrac.eeesiMeV.siMeV uuline.eeesim &textc E mc^+N mc^ Rightarrow N fracEmc^-frac.eeesiMeV.siMeV-uuline.eee &textd pgamma m v approx fracEmc^ mc frac.eeesiMeV.siMeV .eesikg .eeesim/s .eesiNs &texte p_M m_Mv_M .eesikg frac.sim.sis .eesiNs textquad p_M p &quad E_Mtfracm_Mv^tfrac .eesikg leftfrac.sim.sisright^ .eesiJ.eeesieV textquad E_M E * newpage
Der LHC-Beschleunigerring des CERN hat sim Umfang. Darin laufen Protonen mit .siTeV Gesamtenergie April . a Berechnen Sie - v/c für diese Protonen m_P .siMeV/c^. b Welchen Umfang hat der Beschleunigerring für die Protonen? c Wie viele Proton-Antiproton-Paare können bei einer Frontalkollision zweier solcher Protonen maximal entstehen? d Wie gross ist der Impuls eines solchen Protons in -Einheiten? e Eine Stechmücke habe Masse .simg und Schnelligkeit .sikm/h. Berechnen Sie zum Vergleich den Impuls und die kinetische Energie der Mücke.
Solution:
%. Mai Lie. * &texta Egamma mc^ Rightarrow gammafracEmc^left -fracv^c^right^-/ Rightarrow fracvc sqrt-leftfracmc^Eright^ -frac leftfracmc^Eright^ +dots Rightarrow &qquad -fracvc approx frac leftfracmc^Eright^ frac leftfrac.siMeV.eeesiMeVright^ uulineee &textb l_fracl_gamma Rightarrow l_ ell_ gamma l_fracEmc^ simfrac.eeesiMeV.siMeV uuline.eeesim &textc E mc^+N mc^ Rightarrow N fracEmc^-frac.eeesiMeV.siMeV-uuline.eee &textd pgamma m v approx fracEmc^ mc frac.eeesiMeV.siMeV .eesikg .eeesim/s .eesiNs &texte p_M m_Mv_M .eesikg frac.sim.sis .eesiNs textquad p_M p &quad E_Mtfracm_Mv^tfrac .eesikg leftfrac.sim.sisright^ .eesiJ.eeesieV textquad E_M E * newpage
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