Alien Spaceship
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:
Zeit \(t\) / Geschwindigkeit \(v\) / Strecke \(s\) /
The following formulas must be used to solve the exercise:
\(s = vt \quad \) \(\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \quad \) \(t = \gamma t_0 \quad \)
No explanation / solution video to this exercise has yet been created.
Visit our YouTube-Channel to see solutions to other exercises.
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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:
An alien spaceship from Sirius laO covers the distance to Earth in taO of its proper time. Calculate the Lorentz factor and the time the journey take as measured from an observer on Earth. vspacemm Interpret the result in both reference frames spaceship and Earth.
Solution:
For an observer at rest with respect to the Earth the distance to Sirius proper length can be expressed as lambda v t beta c gamma tau ctausqrt-fracgamma^gamma ctausqrtgamma^- It follows for the Lorentz factor gamma gaF sqrt+leftfraclactimestaright^ resultgaP The time for an observer in the rest frame of the Earth is t tF gatimesta resulttP In the reference frame of the Earth a trip from Sirius to Earth cannot be shorter than tminP travel time at the speed of light. The result reflects this fact. In the reference frame of the spaceship the distance to sirius is elllambda/gammalP. This is much shorter than laO so the travel time can be less than tminP.
An alien spaceship from Sirius laO covers the distance to Earth in taO of its proper time. Calculate the Lorentz factor and the time the journey take as measured from an observer on Earth. vspacemm Interpret the result in both reference frames spaceship and Earth.
Solution:
For an observer at rest with respect to the Earth the distance to Sirius proper length can be expressed as lambda v t beta c gamma tau ctausqrt-fracgamma^gamma ctausqrtgamma^- It follows for the Lorentz factor gamma gaF sqrt+leftfraclactimestaright^ resultgaP The time for an observer in the rest frame of the Earth is t tF gatimesta resulttP In the reference frame of the Earth a trip from Sirius to Earth cannot be shorter than tminP travel time at the speed of light. The result reflects this fact. In the reference frame of the spaceship the distance to sirius is elllambda/gammalP. This is much shorter than laO so the travel time can be less than tminP.
Meta Information
Exercise:
An alien spaceship from Sirius laO covers the distance to Earth in taO of its proper time. Calculate the Lorentz factor and the time the journey take as measured from an observer on Earth. vspacemm Interpret the result in both reference frames spaceship and Earth.
Solution:
For an observer at rest with respect to the Earth the distance to Sirius proper length can be expressed as lambda v t beta c gamma tau ctausqrt-fracgamma^gamma ctausqrtgamma^- It follows for the Lorentz factor gamma gaF sqrt+leftfraclactimestaright^ resultgaP The time for an observer in the rest frame of the Earth is t tF gatimesta resulttP In the reference frame of the Earth a trip from Sirius to Earth cannot be shorter than tminP travel time at the speed of light. The result reflects this fact. In the reference frame of the spaceship the distance to sirius is elllambda/gammalP. This is much shorter than laO so the travel time can be less than tminP.
An alien spaceship from Sirius laO covers the distance to Earth in taO of its proper time. Calculate the Lorentz factor and the time the journey take as measured from an observer on Earth. vspacemm Interpret the result in both reference frames spaceship and Earth.
Solution:
For an observer at rest with respect to the Earth the distance to Sirius proper length can be expressed as lambda v t beta c gamma tau ctausqrt-fracgamma^gamma ctausqrtgamma^- It follows for the Lorentz factor gamma gaF sqrt+leftfraclactimestaright^ resultgaP The time for an observer in the rest frame of the Earth is t tF gatimesta resulttP In the reference frame of the Earth a trip from Sirius to Earth cannot be shorter than tminP travel time at the speed of light. The result reflects this fact. In the reference frame of the spaceship the distance to sirius is elllambda/gammalP. This is much shorter than laO so the travel time can be less than tminP.
Contained in these collections:
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Zeitdilatation Lorentz-Faktor gleichförmige Bewegung by TeXercises
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Relativistic Kinematics by by
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