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binomial expansion for γ.

05. november 2015 af Rossa - Niveau: Universitet/Videregående

Hej derude.
Jeg har en opgave, som lyder;

'

Classical mechanics is an extremely well tested model. Hundreds of years worth of experiments, as well as most feats of engineering, have verified its validity. If special relativity gave very different predictions than classical physics in everyday situations, it would be directly contradicted by this mountain of evidence. In this problem, you will see how some of the usual laws of classical mechanics can be obtained from special relativity by simply assuming that the speeds involved are small compared to the speed of light.

Two of the most surprising results of special relativity are time dilation and length contraction, namely, that measured intervals in time and space are not absolute quantities but instead appear differently to different observers. The equations for time dilation and length contraction can be written 
t = γt0 and  l = l/γ, where

\gamma =\frac{1}{\sqrt(1-\frac{v^2}{c^2})}

Jeg håber, at nogen vil foresøger at hjælpe med opgaven, da jeg har ingen clue til den opgave.

På forhånd tak


Brugbart svar (1)

Svar #1
05. november 2015 af peter lind

Du kan evt. bruge en Taylorrækkeudvikling γ(v2/c2) ≈γ(0) + γ'(0)*v2/c2 hvor v2/c2 betragtes som variablen som der altså skal differentieres med hensyn til


Svar #2
05. november 2015 af Rossa

Det virkede, tak for hjælpen


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