[latex]17.\dane:\s_1 = 50 m\m_1 = 60 kg\s_2 = 100 m\m_2 = 30 kg\t_1 = t_2 = t\g = 10 m/s^{2}\szukane:\P_1 = ?\P_2 = ?\\P = frac{W}{t}[/latex] gdzie: W - praca t - czas, w jakim ta praca została wykonana [latex]W = F * s\F = m * g\\P = frac{m * g * s}{t}\\P_1 = frac{m_1 * g * s_1}{t} = frac{60kg * 10N/kg * 50m}{t} = frac{30000J}{t}\\P_2 = frac{m_2 * g * s_2}{t} = frac{30kg * 10N/kg * 100m}{t} = frac{30000J}{t}\\P_1 = P_2[/latex] Odp. a) [latex]18.\dane:\r_1 = 40 cm = 0,4 m\F_1 = 20 N\r_2 = 1 m\szukane:\F_2 = ?[/latex] Warunek równowagi dźwigni dwustronnej: [latex]r_1 * F_1 = r_2 * F_2\\F_2 = frac{r_1 * F_1}{r_2}\\F_2 = frac{0,4m * 20N}{1m}\\F_2 = 8 N[/latex] [latex]19,\dane:\v = 10 m/s\g = 10 m/s^{2}\szukane:\h = ?\\Ep = Ek\\mgh = mv^{2}/2\\gh = v^{2}/2\\2gh = v^{2}[/latex] [latex]h = frac{v^{2}}{2g} = frac{(10m/s)^{2}}{2 * 10m/s^{2}}\\h = 5 m[/latex]
