Softball
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:
A softball of mass g that is moving with a speed of .meterpersecond collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of .meterpersecond. Calculate abcliste abc the velocity of the target ball after the collision and abc the mass of the target ball. abcliste
Solution:
newqtymekg newqtyve. newqtyw. % We use energy and momentum conservation during the collision. EnergieSchritte setcounterAnzPGlg PGleichungEtot &mustbe Etot' PGleichungsscEkin sscEkin' + sscEkin' PGleichungfracm_v_^ fracm_v_'^ + fracm_v_'^ PHYS % ImpulsSchritte PGleichungp_ p_' + p_' PGleichungm_v_ m_v_' + m_v_' PHYS % Die Endgleichungen der beiden Boxen bilden ein Gleichungssystem mit den Unbekannten m_ und v_'. Wir sortieren die Gleichungen wie üblich so dass links alle Grössen des ersten und rechts alle Grössen des zweiten Stosspartners stehen. Danach können wir die Energi durch die Impuls-Gleichung dividieren und nach v_' auflösen: % al m_v_^-v_'^ m_v_'^ m_v_ - v_' m_v_' v_+v_' v_'. Einsetzen der Geschwindigkeiten unter Berücksichtigung der Richtung liefert solqtywzv_+v_'ven+wen al v_' wzf ve + qtywe wzTT. Auflösen der Impuls-Gleichung nach m_ und Einsetzen dieses Ergebnisses gibt für den zweiten Ball eine Masse von solqtymzfracm_v_-v_'v_'men*ven-wen/wznkg al m_ mzf fracme qtyve - wewz mzTT.
A softball of mass g that is moving with a speed of .meterpersecond collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of .meterpersecond. Calculate abcliste abc the velocity of the target ball after the collision and abc the mass of the target ball. abcliste
Solution:
newqtymekg newqtyve. newqtyw. % We use energy and momentum conservation during the collision. EnergieSchritte setcounterAnzPGlg PGleichungEtot &mustbe Etot' PGleichungsscEkin sscEkin' + sscEkin' PGleichungfracm_v_^ fracm_v_'^ + fracm_v_'^ PHYS % ImpulsSchritte PGleichungp_ p_' + p_' PGleichungm_v_ m_v_' + m_v_' PHYS % Die Endgleichungen der beiden Boxen bilden ein Gleichungssystem mit den Unbekannten m_ und v_'. Wir sortieren die Gleichungen wie üblich so dass links alle Grössen des ersten und rechts alle Grössen des zweiten Stosspartners stehen. Danach können wir die Energi durch die Impuls-Gleichung dividieren und nach v_' auflösen: % al m_v_^-v_'^ m_v_'^ m_v_ - v_' m_v_' v_+v_' v_'. Einsetzen der Geschwindigkeiten unter Berücksichtigung der Richtung liefert solqtywzv_+v_'ven+wen al v_' wzf ve + qtywe wzTT. Auflösen der Impuls-Gleichung nach m_ und Einsetzen dieses Ergebnisses gibt für den zweiten Ball eine Masse von solqtymzfracm_v_-v_'v_'men*ven-wen/wznkg al m_ mzf fracme qtyve - wewz mzTT.
Meta Information
Exercise:
A softball of mass g that is moving with a speed of .meterpersecond collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of .meterpersecond. Calculate abcliste abc the velocity of the target ball after the collision and abc the mass of the target ball. abcliste
Solution:
newqtymekg newqtyve. newqtyw. % We use energy and momentum conservation during the collision. EnergieSchritte setcounterAnzPGlg PGleichungEtot &mustbe Etot' PGleichungsscEkin sscEkin' + sscEkin' PGleichungfracm_v_^ fracm_v_'^ + fracm_v_'^ PHYS % ImpulsSchritte PGleichungp_ p_' + p_' PGleichungm_v_ m_v_' + m_v_' PHYS % Die Endgleichungen der beiden Boxen bilden ein Gleichungssystem mit den Unbekannten m_ und v_'. Wir sortieren die Gleichungen wie üblich so dass links alle Grössen des ersten und rechts alle Grössen des zweiten Stosspartners stehen. Danach können wir die Energi durch die Impuls-Gleichung dividieren und nach v_' auflösen: % al m_v_^-v_'^ m_v_'^ m_v_ - v_' m_v_' v_+v_' v_'. Einsetzen der Geschwindigkeiten unter Berücksichtigung der Richtung liefert solqtywzv_+v_'ven+wen al v_' wzf ve + qtywe wzTT. Auflösen der Impuls-Gleichung nach m_ und Einsetzen dieses Ergebnisses gibt für den zweiten Ball eine Masse von solqtymzfracm_v_-v_'v_'men*ven-wen/wznkg al m_ mzf fracme qtyve - wewz mzTT.
A softball of mass g that is moving with a speed of .meterpersecond collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of .meterpersecond. Calculate abcliste abc the velocity of the target ball after the collision and abc the mass of the target ball. abcliste
Solution:
newqtymekg newqtyve. newqtyw. % We use energy and momentum conservation during the collision. EnergieSchritte setcounterAnzPGlg PGleichungEtot &mustbe Etot' PGleichungsscEkin sscEkin' + sscEkin' PGleichungfracm_v_^ fracm_v_'^ + fracm_v_'^ PHYS % ImpulsSchritte PGleichungp_ p_' + p_' PGleichungm_v_ m_v_' + m_v_' PHYS % Die Endgleichungen der beiden Boxen bilden ein Gleichungssystem mit den Unbekannten m_ und v_'. Wir sortieren die Gleichungen wie üblich so dass links alle Grössen des ersten und rechts alle Grössen des zweiten Stosspartners stehen. Danach können wir die Energi durch die Impuls-Gleichung dividieren und nach v_' auflösen: % al m_v_^-v_'^ m_v_'^ m_v_ - v_' m_v_' v_+v_' v_'. Einsetzen der Geschwindigkeiten unter Berücksichtigung der Richtung liefert solqtywzv_+v_'ven+wen al v_' wzf ve + qtywe wzTT. Auflösen der Impuls-Gleichung nach m_ und Einsetzen dieses Ergebnisses gibt für den zweiten Ball eine Masse von solqtymzfracm_v_-v_'v_'men*ven-wen/wznkg al m_ mzf fracme qtyve - wewz mzTT.
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Elastischer Stoss by pw
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Elastischer Stoss by uz