Identical massive spheres
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:
Masse \(m\) / Kraft \(F\) / Volumen \(V\) / Radius \(r\) / Dichte \(\varrho\) /
The following formulas must be used to solve the exercise:
\(\varrho = \dfrac{m}{V} \quad \) \(F = G \dfrac{m_1m_2}{r^2} \quad \) \(V = \dfrac{4}{3}\pi r^3 \quad \)
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Exercise:
Two identical massive spheres each with rO radius touch each other. What density would the material of the homogeneous spheres have to have so that they attract each other with FO due to gravity? One inch is .cm one pound-foce is .N.
Solution:
center tikzpicture shadeball color gray! opacity. - circle ; draw - circle ; draw - arc :: and .; drawdashed arc :: and .; shadeball color gray! opacity. circle ; draw circle ; draw arc :: and .; drawdashed arc :: and .; drawthick red - --- nodemidway above Rr; tikzpicture center Geg r rO r F FO F % GesDensityvarrho sikgpcm % The two center pos of the two spheres are separated by SolQtyR*rXm al R r r R. In order to attract each other with the given force the spheres have to have SolQtym*rX*sqrtFX/ncGnkg al m RsqrtfracFG rsqrtfracFG R sqrtfracFG m. mass. Because the volume of a sphere is SolQtyV/*pi*rX^cubicmeter al V frac pi r^ fracpi qtyr^ V their density has to be: SolQtypmX/VXkgpmk al varrho fracmV fracsqrtfracr^ FGfrac pi r^ fracmV p varrho p Ausrufbox The element with the highest density Osmium no. has a density of .ekgpmk standard temperature and pressure. Ausrufbox
Two identical massive spheres each with rO radius touch each other. What density would the material of the homogeneous spheres have to have so that they attract each other with FO due to gravity? One inch is .cm one pound-foce is .N.
Solution:
center tikzpicture shadeball color gray! opacity. - circle ; draw - circle ; draw - arc :: and .; drawdashed arc :: and .; shadeball color gray! opacity. circle ; draw circle ; draw arc :: and .; drawdashed arc :: and .; drawthick red - --- nodemidway above Rr; tikzpicture center Geg r rO r F FO F % GesDensityvarrho sikgpcm % The two center pos of the two spheres are separated by SolQtyR*rXm al R r r R. In order to attract each other with the given force the spheres have to have SolQtym*rX*sqrtFX/ncGnkg al m RsqrtfracFG rsqrtfracFG R sqrtfracFG m. mass. Because the volume of a sphere is SolQtyV/*pi*rX^cubicmeter al V frac pi r^ fracpi qtyr^ V their density has to be: SolQtypmX/VXkgpmk al varrho fracmV fracsqrtfracr^ FGfrac pi r^ fracmV p varrho p Ausrufbox The element with the highest density Osmium no. has a density of .ekgpmk standard temperature and pressure. Ausrufbox
Meta Information
Exercise:
Two identical massive spheres each with rO radius touch each other. What density would the material of the homogeneous spheres have to have so that they attract each other with FO due to gravity? One inch is .cm one pound-foce is .N.
Solution:
center tikzpicture shadeball color gray! opacity. - circle ; draw - circle ; draw - arc :: and .; drawdashed arc :: and .; shadeball color gray! opacity. circle ; draw circle ; draw arc :: and .; drawdashed arc :: and .; drawthick red - --- nodemidway above Rr; tikzpicture center Geg r rO r F FO F % GesDensityvarrho sikgpcm % The two center pos of the two spheres are separated by SolQtyR*rXm al R r r R. In order to attract each other with the given force the spheres have to have SolQtym*rX*sqrtFX/ncGnkg al m RsqrtfracFG rsqrtfracFG R sqrtfracFG m. mass. Because the volume of a sphere is SolQtyV/*pi*rX^cubicmeter al V frac pi r^ fracpi qtyr^ V their density has to be: SolQtypmX/VXkgpmk al varrho fracmV fracsqrtfracr^ FGfrac pi r^ fracmV p varrho p Ausrufbox The element with the highest density Osmium no. has a density of .ekgpmk standard temperature and pressure. Ausrufbox
Two identical massive spheres each with rO radius touch each other. What density would the material of the homogeneous spheres have to have so that they attract each other with FO due to gravity? One inch is .cm one pound-foce is .N.
Solution:
center tikzpicture shadeball color gray! opacity. - circle ; draw - circle ; draw - arc :: and .; drawdashed arc :: and .; shadeball color gray! opacity. circle ; draw circle ; draw arc :: and .; drawdashed arc :: and .; drawthick red - --- nodemidway above Rr; tikzpicture center Geg r rO r F FO F % GesDensityvarrho sikgpcm % The two center pos of the two spheres are separated by SolQtyR*rXm al R r r R. In order to attract each other with the given force the spheres have to have SolQtym*rX*sqrtFX/ncGnkg al m RsqrtfracFG rsqrtfracFG R sqrtfracFG m. mass. Because the volume of a sphere is SolQtyV/*pi*rX^cubicmeter al V frac pi r^ fracpi qtyr^ V their density has to be: SolQtypmX/VXkgpmk al varrho fracmV fracsqrtfracr^ FGfrac pi r^ fracmV p varrho p Ausrufbox The element with the highest density Osmium no. has a density of .ekgpmk standard temperature and pressure. Ausrufbox
Contained in these collections:
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Zwei Kugeln by TeXercises
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Gravitationsgesetz by uz
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?