TeXercises.com

Sich logarithmisch füllender Behälter

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.

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 -

Exercise

https://texercises.com/exercise/sich-logarithmisch-fullender-behalter/

Question

Solution

Short

Video

\(\LaTeX\)

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!

Exercise:
Ein zylinderförmiger Behälter mit centimetersquared Grundfläche und g Masse sei mit einem langen Schlauch verbunden. Der Behälter werde nun am Schlauch aus einem m tiefen Schacht hochgezogen währ durch den Schlauch ständig Wasser in den anfänglich leeren Behälter laufe diesen aber nicht mit konstanter Geschwindigkeit fülle. Die Füllhöhe variiere mit der Zeit wie folgt: hteta lnmu t wobei etacm ist und muper-modereciprocalpersecond. Welche Hubarbeit würde verrichtet falls man den Schlauch mit centimeterpersecond einzöge? Die Masse des Schlauches könne vernachlässigt werden.

Solution:
Die Gewichtskraft des Behälters in Abhängigkeit von der Zeit beträgt: F F_B + F_W mg + tilde m g mg + rho V g mg + rho Aht g mg + rho A eta lnmu t g g leftm+ rho A eta lnmu tright In Abhängigkeit von der Höhe die der Behälter schon aus dem Schacht gezogen wurde beträgt die Gewichtskraft des Behälters: F g m+ rho A eta lnmu frachv Das gilt weil hvt. Nun beträgt die totale Hubarbeit: W Fh textdh _^m g leftm+ rho A eta lnmu frachvright textdh g leftmh + rho A eta h leftlnmu frachv -rightright_^m .eJ

Meta Information

\(\LaTeX\)-Code

Contained in these collections:

Attributes & Decorations

Branches	Work, Energy, Power
Tags	arbeit, arbeitsintegral, behälter, hubarbeit, integral, mechanik, physik
Content image
Difficulty	(5, default)
Points	5 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	uz
Decoration
File
Link