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Suppose there is a wind with velocity $v \ll c$, which is blowing on a person who is moving at velocity $u \ll c$ (both in the $x$-direction). In the rest frame of the person, the wind exerts a force $F$ on the person, where $F$ is proportional to $(v-u)^2$.

Now, say there is an observer moving in the $x$-direction at velocity $w$, which is close to the speed of light. Is there a difference in the force that the observer sees, or is it the same as in the rest frame of the person?

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  • $\begingroup$ I've put your math into MathJax (that is essentially LaTeX math-mode) so that I could use a proper $\ll$ comparison operator. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Sep 26, 2017 at 5:15
  • $\begingroup$ $\:F'=F\:$ but $\:F'\ne \text{ proportional } \left(v'-u'\right)^{2}$. $\endgroup$
    – Voulkos
    Commented Sep 26, 2017 at 7:45

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Hint: Value of force in different reference frame does not depend on the 'form' of the force, just on it's value.

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