Fizyka. Grawitacja. Interesuje mnie rozwiązanie również zadania 5.

[latex]5.\dane:\m_1 = m_2 = m\r = 1 m\F_{g} = 6,67cdot10^{-9} N\G = 6,67cdot10^{-11}frac{Nm^{2}}{kg^{2}}\szukane:\m = ?[/latex] [latex]F_{g} = Gcdotfrac{m_1 m_2}{r^{2}}\\m_1 = m_2 = m\\F_{g} = frac{Gcdot m^{2}}{r^{2}}\\Gcdot m^{2} = F_{g}cdot r^{2} /:G\\m^{2} = frac{F_{g}cdot r^{2}}{G}\\m = sqrt{frac{F_{g}cdot r^{2}}{G}}{}=sqrt{frac{6,67cdot10^{-9}cdot1^{2}}{6,67cdot10^{-11}}} = sqrt{10^{-9-(-11)}}}=sqrt{10^{2}}\\m = 10 kg\\Odp. C.[/latex]

 zad.3. wektory mają taką samą wartośc bo oddziaływanie jest zawsze wzajemne zad.4. [latex]F = frac{Gm3m}{r^2} = frac{3Gm^2}{r^2} [/latex] [latex]F_1 = frac{G2m*4,5 m }{r^2} = frac{9Gm^2}{r^2} [/latex] [latex] frac{F_1}{F_2 } = frac{9Gm^2}{r^2 } * frac{r^2}{3Gm^2} = 3[/latex] zad.5. r = 1 m F = 6,67 *10⁻⁹ N G = 6,67 *10⁻¹¹ N*m²/kg^2 m = ? [latex]F = frac{Gmm}{r^2 } = frac{Gm^2}{r^2} /*r^2[/latex] [latex]F*r^2 = Gm^2 /: G [/latex] [latex]m^2 = frac{F*r^2}{G} [/latex] [latex]m = sqrt{ frac{F*r^2}{G} } [/latex] [latex]m = sqrt{ frac{6,67 *10 ^{-9} N * ( 1m )^2}{6,67 *10 ^{-11} frac{N*m^2}{kg ^2} } } = sqrt{10^2 kg^2} = 10 kg[/latex]