Steel cable around the earth
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 \(\ell\) / Temperatur \(T\) / Radius \(r\) / Umfang \(u\) / Längenausdehnungskoeffizient \(\alpha\) /
The following formulas must be used to solve the exercise:
\(u = 2\pi r \quad \) \(\ell = \ell_0 \cdot (1+ \alpha \cdot \Delta\vartheta) \quad \) \(\Delta \ell = \ell_0 \cdot \alpha \cdot \Delta\theta \quad \)
No explanation / solution video to this exercise has yet been created.
Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
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:
A steel cable aO is stretched around the Earth's equator at TaO. What is the distance to the Earth's surface at TbO?
Solution:
pmrec NewQtyDTcelsius NewQtyrE.em NewQtyab.perkelvin % Geg Deltatheta DT sscrE rE alpha ab % GesAbstandDelta r sim % Das Stahlband hat bei celsius einen Umfang von SolQtyuEpi ssc rE*pi*rEXm al ssc uE uEF pi rE uES. Bei DT dehnt sich dieser auf SolQtyupi ssc rE + alpha DeltathetauEX*+abX*DTXm al u ssc uE +alpha Deltatheta uF uES qty+ab DT uS aus. Somit ist der neue Radius des Stahlseils SolQtyrssc rE qty+ alpha DeltathetauX/*pim al r fracupi rF fracuSpi rS. Der Abstand zur Erdoberfläche ist folglich SolQtyDrsscrEalphaDeltathetarEX*abX*DTXm al Delta r r - sscrE DrF rS - rE DrS % Delta r DrF DrP pmfrac Hinweis: Man kann auch argumentieren dass sich der Radius und die Radiusveränderung stets proportional zum Umfang verhält d.h. r sim u und deshalb einfach die Radiusveränderung mit der Längenausdehnungsformel berechnet werden kann.
A steel cable aO is stretched around the Earth's equator at TaO. What is the distance to the Earth's surface at TbO?
Solution:
pmrec NewQtyDTcelsius NewQtyrE.em NewQtyab.perkelvin % Geg Deltatheta DT sscrE rE alpha ab % GesAbstandDelta r sim % Das Stahlband hat bei celsius einen Umfang von SolQtyuEpi ssc rE*pi*rEXm al ssc uE uEF pi rE uES. Bei DT dehnt sich dieser auf SolQtyupi ssc rE + alpha DeltathetauEX*+abX*DTXm al u ssc uE +alpha Deltatheta uF uES qty+ab DT uS aus. Somit ist der neue Radius des Stahlseils SolQtyrssc rE qty+ alpha DeltathetauX/*pim al r fracupi rF fracuSpi rS. Der Abstand zur Erdoberfläche ist folglich SolQtyDrsscrEalphaDeltathetarEX*abX*DTXm al Delta r r - sscrE DrF rS - rE DrS % Delta r DrF DrP pmfrac Hinweis: Man kann auch argumentieren dass sich der Radius und die Radiusveränderung stets proportional zum Umfang verhält d.h. r sim u und deshalb einfach die Radiusveränderung mit der Längenausdehnungsformel berechnet werden kann.
Meta Information
Exercise:
A steel cable aO is stretched around the Earth's equator at TaO. What is the distance to the Earth's surface at TbO?
Solution:
pmrec NewQtyDTcelsius NewQtyrE.em NewQtyab.perkelvin % Geg Deltatheta DT sscrE rE alpha ab % GesAbstandDelta r sim % Das Stahlband hat bei celsius einen Umfang von SolQtyuEpi ssc rE*pi*rEXm al ssc uE uEF pi rE uES. Bei DT dehnt sich dieser auf SolQtyupi ssc rE + alpha DeltathetauEX*+abX*DTXm al u ssc uE +alpha Deltatheta uF uES qty+ab DT uS aus. Somit ist der neue Radius des Stahlseils SolQtyrssc rE qty+ alpha DeltathetauX/*pim al r fracupi rF fracuSpi rS. Der Abstand zur Erdoberfläche ist folglich SolQtyDrsscrEalphaDeltathetarEX*abX*DTXm al Delta r r - sscrE DrF rS - rE DrS % Delta r DrF DrP pmfrac Hinweis: Man kann auch argumentieren dass sich der Radius und die Radiusveränderung stets proportional zum Umfang verhält d.h. r sim u und deshalb einfach die Radiusveränderung mit der Längenausdehnungsformel berechnet werden kann.
A steel cable aO is stretched around the Earth's equator at TaO. What is the distance to the Earth's surface at TbO?
Solution:
pmrec NewQtyDTcelsius NewQtyrE.em NewQtyab.perkelvin % Geg Deltatheta DT sscrE rE alpha ab % GesAbstandDelta r sim % Das Stahlband hat bei celsius einen Umfang von SolQtyuEpi ssc rE*pi*rEXm al ssc uE uEF pi rE uES. Bei DT dehnt sich dieser auf SolQtyupi ssc rE + alpha DeltathetauEX*+abX*DTXm al u ssc uE +alpha Deltatheta uF uES qty+ab DT uS aus. Somit ist der neue Radius des Stahlseils SolQtyrssc rE qty+ alpha DeltathetauX/*pim al r fracupi rF fracuSpi rS. Der Abstand zur Erdoberfläche ist folglich SolQtyDrsscrEalphaDeltathetarEX*abX*DTXm al Delta r r - sscrE DrF rS - rE DrS % Delta r DrF DrP pmfrac Hinweis: Man kann auch argumentieren dass sich der Radius und die Radiusveränderung stets proportional zum Umfang verhält d.h. r sim u und deshalb einfach die Radiusveränderung mit der Längenausdehnungsformel berechnet werden kann.
Contained in these collections
-
-
Stahlseil um die Erde by TeXercises
| Title | Matched on |
|---|---|
| Stahlseil um die Erde | tagsformula |
| Zinkblech | tagsformula |
| Anfangsfüllung in Aluminiumkanister | formula |
| Volumenzunahme von heissem Dampfkessel | tagsformula |
| Prozentuale Verlängerung Eisenbahnoberleitung | formula |
Similar exercises (33)
| Title | Matched on |
|---|---|
| Stahlseil um die Erde | tagsformula |
| Zinkblech | tagsformula |
| Anfangsfüllung in Aluminiumkanister | formula |
| Volumenzunahme von heissem Dampfkessel | tagsformula |
| Prozentuale Verlängerung Eisenbahnoberleitung | formula |
| Stahlbrücke | tags |
| Eisenbahnschiene | tags |
| Holzspeichenrad | tags |
| Eisenbahnschiene | tags |
| Glassorte | tags |
| Stossfuge bei der Eisenbahn | tags |
| Mit Benzol randvoller Stahlkanister | tags |
| Metallrohr | tags |
| Vermessung des Bauplatzes | tags |
| Dampfrohrleitung | tags |
| Autobahnbrücke | tags |
| Plexiglasstab abkühlen | tags |
| Bleirohr | tags |
| Stange und Ring | tags |
| Betonwand | tags |
| Mit Heizöl randvoller Stahltank | tags |
| Aluminiumstab | tags |
| Glasstab | tags |
| Volumenzunahme von Quarzglas-Körper | tags |
| Rechteckiges Kupferblech | tags |
| Aluminiumwürfel | tags |
| Eisenkugel | tags |
| Dichte von Stahlguss | tags |
| Kreisförmige Platte | tags |
| Metallstab | tags |
| Massstab aus Messing | tags |
| Nickelplatte | tags |
| Ausdehnungskoeffizient von Grauguss | tags |