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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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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
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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
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special relativity
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kinematic, lorentz factor, relativistic, time dilation
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ENG (English)
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Calculative / Quantity
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