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2014-10-20T22:03:11+03:00
F=ma

Prin derivare succesiva (sau prin formule daca le stii), se obtine viteza si apoi  acceleratia:

v=50\sqrt{3}\left(\cos 10t+\frac{1}{\sqrt{3}}\sin 10t\right)\\ \\ \\ a=500\sqrt{3}\left(-\sin 10t+\frac{1}{\sqrt{3}}\cos 10t\right)

Acum, forta va fi maxima atunci cand acceleratia e maxima. Iat maximul unei functii il aflam prin derivare, ca la matematica:

a'=5000\sqrt{3}\left(-\cos 10t-\frac{1}{\sqrt{3}}\sin 10t\right)\\ \\ \Rightarrow \cos 10t=-\frac{1}{\sqrt{3}}\sin 10t\\ \\ \tan 10t=-\sqrt{3}\\ \\10t=-\frac{\pi}{3}.

Revenind gasim acceleratia maxima inlocuind 10t cu valoarea gasita si calculand:

a_{max}=500\sqrt{3}\left[-\left(-\frac{\sqrt{3}}{2}\right)+\frac{1}{\sqrt{3}}\frac{1}{2}\right]=\\ \\ \\ =250\cdot 3+250=1000.

Iar apoi forta maxima e:

F_{max}=ma_{max}=0,020\cdot 1000=20.

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