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Massless wooden stick as two-sided lever

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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".
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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/massless-wooden-stick-as-two-sided-lever/

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Solution

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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: \(\vec M = \vec \ell \times \vec F \quad \) \(\sum \stackrel{\curvearrowleft}{M} \stackrel{!}{=} \sum \stackrel{\curvearrowright}{M} \quad \)

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Exercise:
A weight of FaO is attached to one and another weight of FbO to the other of a massless wooden stick with lO length. How far from its center does one have to support the stick in order to balance it?

Solution:
newqtylcm newqtymeg newqtymzg % Die beiden hervorgerufenen Drehmomente müssen sich das Gleichgewicht halten d.h. es gilt das glqq Hebelgesetzgrqq: DrehmomentSchritte PGleichung stackrelcurvearrowleftM stackrelcurvearrowrightM PGleichungM_ M_ PGleichungF_ell_ F_ell_ PGleichungm_gell_ m_g ell-ell_ MGleichungm_gell_ m_g ell-m_gell_ MGleichungm_gell_+m_gell_ m_g ell MGleichungm_+m_gell_ m_g ell MGleichungell_ fracm_ ellm_+m_ % PHYSMATH % Der erste Hebelarm ist somit solqtylefracm_ ellm_+m_mzn*ln/men+mzncm al ell_ lef fracmzlme+mz leTT Für den zweiten Hebelarm folgt solqtylzfracm_ellm_+m_ln-lencm al ell_ ell - ell_ lzf l - leTT lzTT. Die Aufgabe kann selbstverständlich auch mit Verhältnissen gelöst werden; der Hebel ist in Teile zu unterteilen da Newton totale Kraft. Die Hebelarme sind dann entsprech dem Verhältnis : den Kräften zuzuordnen.

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Holzstab als Hebel by TeXercises

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Attributes & Decorations

Branches	Lever
Tags	hebel, hebelarm, kraft, maschine, physik, zweiseitig
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Difficulty	(4, default)
Points	3 (default)
Language	(English)
Type	Calculative / Quantity
Creator	uz
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