Lorentz Factor
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:
Geschwindigkeit \(v\) /
The following formulas must be used to solve the exercise:
\(\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \quad \)
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Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
abcliste abc Calculate the Lorentz factor for an electron moving at beeO of the speed of light. abc Calculate the Lorentz factor for a velocity of vO typical airplane. abc Calculate the velocity for a Lorentz factor of gaaO and for a Lorentz factor of gabO. abc Calculate the maximum velocity at which the Lorentz factor is within ppmO ppm: part per million of . abcliste
Solution:
abcliste abc gamma gaeF fracsqrt-bee resultgaeP abc gamma gaF fracsqrt-v/ncc^ gaS The Lorentz factor is very close to so it is more useful to calculate the value of gamma-: gamma- resultgamoS For most practical purposes the Lorentz factor can be ased to be equal to i.e. relativistic effects due to the motion of the airplane are irrelevant. abc Solving for the velocity yields beta fracvc beF For gammagaa we find beta sqrt-fracgaa^ fracsqrt approx resultbeP and for gamma beta sqrt-fracgab^ fracsqrtapprox resultbebP abc v c beta vppmF ncctimessqrt-frac+ppm^ vppm resultvppmP abcliste
abcliste abc Calculate the Lorentz factor for an electron moving at beeO of the speed of light. abc Calculate the Lorentz factor for a velocity of vO typical airplane. abc Calculate the velocity for a Lorentz factor of gaaO and for a Lorentz factor of gabO. abc Calculate the maximum velocity at which the Lorentz factor is within ppmO ppm: part per million of . abcliste
Solution:
abcliste abc gamma gaeF fracsqrt-bee resultgaeP abc gamma gaF fracsqrt-v/ncc^ gaS The Lorentz factor is very close to so it is more useful to calculate the value of gamma-: gamma- resultgamoS For most practical purposes the Lorentz factor can be ased to be equal to i.e. relativistic effects due to the motion of the airplane are irrelevant. abc Solving for the velocity yields beta fracvc beF For gammagaa we find beta sqrt-fracgaa^ fracsqrt approx resultbeP and for gamma beta sqrt-fracgab^ fracsqrtapprox resultbebP abc v c beta vppmF ncctimessqrt-frac+ppm^ vppm resultvppmP abcliste
Meta Information
Exercise:
abcliste abc Calculate the Lorentz factor for an electron moving at beeO of the speed of light. abc Calculate the Lorentz factor for a velocity of vO typical airplane. abc Calculate the velocity for a Lorentz factor of gaaO and for a Lorentz factor of gabO. abc Calculate the maximum velocity at which the Lorentz factor is within ppmO ppm: part per million of . abcliste
Solution:
abcliste abc gamma gaeF fracsqrt-bee resultgaeP abc gamma gaF fracsqrt-v/ncc^ gaS The Lorentz factor is very close to so it is more useful to calculate the value of gamma-: gamma- resultgamoS For most practical purposes the Lorentz factor can be ased to be equal to i.e. relativistic effects due to the motion of the airplane are irrelevant. abc Solving for the velocity yields beta fracvc beF For gammagaa we find beta sqrt-fracgaa^ fracsqrt approx resultbeP and for gamma beta sqrt-fracgab^ fracsqrtapprox resultbebP abc v c beta vppmF ncctimessqrt-frac+ppm^ vppm resultvppmP abcliste
abcliste abc Calculate the Lorentz factor for an electron moving at beeO of the speed of light. abc Calculate the Lorentz factor for a velocity of vO typical airplane. abc Calculate the velocity for a Lorentz factor of gaaO and for a Lorentz factor of gabO. abc Calculate the maximum velocity at which the Lorentz factor is within ppmO ppm: part per million of . abcliste
Solution:
abcliste abc gamma gaeF fracsqrt-bee resultgaeP abc gamma gaF fracsqrt-v/ncc^ gaS The Lorentz factor is very close to so it is more useful to calculate the value of gamma-: gamma- resultgamoS For most practical purposes the Lorentz factor can be ased to be equal to i.e. relativistic effects due to the motion of the airplane are irrelevant. abc Solving for the velocity yields beta fracvc beF For gammagaa we find beta sqrt-fracgaa^ fracsqrt approx resultbeP and for gamma beta sqrt-fracgab^ fracsqrtapprox resultbebP abc v c beta vppmF ncctimessqrt-frac+ppm^ vppm resultvppmP abcliste
Contained in these collections:
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Lorentz-Faktor by TeXercises
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Relativistic Kinematics by by
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