Specialioji reliatyvumo teorija: Skirtumas tarp puslapio versijų

:<math>E_k=mv^2-\int_{0}^{v} mvdv=mv^2-\int_{0}^{v}\frac{m_{0}v}{\sqrt{1-\frac{v^2}{c^2}}}dv=mv^2-\int_{0}^{v}\frac{m_{0}v}{\sqrt{1-\frac{v^2}{c^2}}}{d(1-\frac{v^2}{c^2})\over {-2v\over c^2}}=</math>
:<math>mv^2+\int_0^v\frac{m_0 c^2}{2\sqrt{1-\frac{v^2}{c^2}}}d(1-\frac{v^2}{c^2})=mv^2+\Big(m_{0}c^2\sqrt{1-\frac{v^2}{c^2}}\Big)\Big|_0^v=mv^2+m_{0}c^2\sqrt{1-\frac{v^2}{c^2}}-m_{0}c^2;</math>
:<math>E_k\approx mv^2+m_0 c^2(1-{1\over 2}\frac{v^2}{c^2})-m_{0}c^2=mv^2+m_0 c^2-{m_0 v^2\over 2}-m_{0}c^2=mc{mv^2\over 2}-m_{0}c^2={m_0 v^2\over 2}-m_{0}c^2,</math> kai greitis <math>v=0.</math> nerealitivinis (daug mažesnis nei šviesos greitis).
 
Dydį ''m''<sub>0</sub>''c''<sup>2</sup> pavadinsime [[rimties energija]]. Tada gauname, kad:
1 354

pakeitimai