Meta Information  Exercise contained in  Rate this Exercise  


0 
Escape velocity from the Earth is \SI{40000}{\kilo\meter\per\hour}. What would be the percent decrease in length of a \SI{95.2}{m} long rocket traveling at that speed?
The percentual change in the length is: \begin{align} \frac{\Delta \ell}{\ell_0} &= \frac{\ell_0\ell}{\ell_0}\\ &= \frac{\ell_0\frac{\ell_0}{\gamma}}{\ell_0}\\ &= 1\frac{1}{\gamma}\\ &= 1\sqrt{1\frac{v^2}{c^2}}\\ &\approx \frac12\frac{v^2}{c^2}\\ &= \numprint{6.868e10} \end{align} The last equation is valid because $v\ll c$. (Taylor expansion for the function $f(x)=1\sqrt{1x}$ around $x=0$, where $x$ substitutes $\frac{v^2}{c^2}$.)
20:13, 3. Oct. 2017  diff  Urs Zellweger (urs)  Current Version 
20:12, 3. Oct. 2017  lsg verbessert  Urs Zellweger (urs)  Compare with Current 
00:09, 5. June 2017  lsg  Urs Zellweger (urs)  Compare with Current 
11:20, 4. June 2017  Initial Version.  Urs Zellweger (urs)  Compare with Current 