Unknown density of a fluid
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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.
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
\(\LaTeX\)
Ichwarsnur, , 2019, digital photograph, Wikipedia
<Wikipedia> (retrieved on February 26, 2023)
Need help? Yes, please!
The following quantities appear in the problem:
Masse \(m\) / Volumen \(V\) / Dichte \(\varrho\) /
The following formulas must be used to solve the exercise:
\(\varrho = \dfrac{m}{V} \quad \)
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Exercise:
A pycnometer is a small bottle with a precisely known ernal volume that is used to measure densities of liquids. Consider a pycnometer with mPyO mass when empty and mWtO when filled with water. When filled with another fulid its mass is mFlO. What is the density of this other fluid?
Solution:
Geg m_ mPyO mPy m_ mWtO mWt m_ mFlO mFl GesDensityrho_sikilogrampercubicmeter The bottle holds m m_-m_ mWt - mPy mw water i.e. V fracm_rho_ fracm_-m_rho_ fracmwrw V When filled with the other fluid the bottle holds m' m_-m_ mFl - mPy mf of it in its V capacity i.e. the density of this fluid is: rho_ fracm'V fracm_-m_fracm_-m_rho_ fracm_-m_m_-m_rho_ fracmfV rf rho_ fracm_-m_m_-m_rho_ rfS
A pycnometer is a small bottle with a precisely known ernal volume that is used to measure densities of liquids. Consider a pycnometer with mPyO mass when empty and mWtO when filled with water. When filled with another fulid its mass is mFlO. What is the density of this other fluid?
Solution:
Geg m_ mPyO mPy m_ mWtO mWt m_ mFlO mFl GesDensityrho_sikilogrampercubicmeter The bottle holds m m_-m_ mWt - mPy mw water i.e. V fracm_rho_ fracm_-m_rho_ fracmwrw V When filled with the other fluid the bottle holds m' m_-m_ mFl - mPy mf of it in its V capacity i.e. the density of this fluid is: rho_ fracm'V fracm_-m_fracm_-m_rho_ fracm_-m_m_-m_rho_ fracmfV rf rho_ fracm_-m_m_-m_rho_ rfS
Meta Information
Exercise:
A pycnometer is a small bottle with a precisely known ernal volume that is used to measure densities of liquids. Consider a pycnometer with mPyO mass when empty and mWtO when filled with water. When filled with another fulid its mass is mFlO. What is the density of this other fluid?
Solution:
Geg m_ mPyO mPy m_ mWtO mWt m_ mFlO mFl GesDensityrho_sikilogrampercubicmeter The bottle holds m m_-m_ mWt - mPy mw water i.e. V fracm_rho_ fracm_-m_rho_ fracmwrw V When filled with the other fluid the bottle holds m' m_-m_ mFl - mPy mf of it in its V capacity i.e. the density of this fluid is: rho_ fracm'V fracm_-m_fracm_-m_rho_ fracm_-m_m_-m_rho_ fracmfV rf rho_ fracm_-m_m_-m_rho_ rfS
A pycnometer is a small bottle with a precisely known ernal volume that is used to measure densities of liquids. Consider a pycnometer with mPyO mass when empty and mWtO when filled with water. When filled with another fulid its mass is mFlO. What is the density of this other fluid?
Solution:
Geg m_ mPyO mPy m_ mWtO mWt m_ mFlO mFl GesDensityrho_sikilogrampercubicmeter The bottle holds m m_-m_ mWt - mPy mw water i.e. V fracm_rho_ fracm_-m_rho_ fracmwrw V When filled with the other fluid the bottle holds m' m_-m_ mFl - mPy mf of it in its V capacity i.e. the density of this fluid is: rho_ fracm'V fracm_-m_fracm_-m_rho_ fracm_-m_m_-m_rho_ fracmfV rf rho_ fracm_-m_m_-m_rho_ rfS
Contained in these collections:
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Pyknometer by TeXercises
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Dichte 2 by uz
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Dichte I by pw
Physical Quantity
Massendichte
Verhältnis von Masse zu Volumen
\(\varrho = \dfrac{m}{V}\)
Unit
Kilogramm pro Kubikmeter (\(\rm \frac{kg}{m^3}\))
Base?
SI?
Metric?
Coherent?
Imperial?