1.
[tex]dane:\\m = 0,5 \ t = 500 \ kg\\v = 15\frac{m}{s}\\szukane:\\E_{k} = ?\\\\Rozwiazanie\\\\E_{k} = \frac{mv^{2}}{2}\\\\E_{k} = \frac{500 \ kg\cdot(15\frac{m}{s})^{2}}{2}\\\\\underline{E_{k} = 56 \ 250 \ J = 56,25 \ kJ}\\\\(1 \ kJ = 1000 \ J)[/tex]
2.
[tex]dane:\\P = 36 \ kW = 36 \ 000 \ W\\m = 14 \ 400 \ kg\\h = 200 \ m\\g = 10\frac{N}{kg}\\szukane:\\t = ?\\\\Rozwiazanie\\\\W = E_{p} = mgh\\\\W = 14400 \ kg\cdot10\frac{N}{kg} \cdot200 \ m = 28 \ 800 \ 000 \ J\\\\\\P = \frac{W}{t} \ \ \rightarrow \ \ t = \frac{W}{P}\\\\t = \frac{28800000 \ J}{36000 \ W}\\\\\underline{t = 800 \ s = 13 \ min \ i \ 20 \ s}[/tex]
3.
[tex]v_{o} = 0\\h = 30 \ m\\m = 10 \ kg\\g = 10\frac{N}{kg}\\szukane:\\v = ?\\\\Rozwiazanie\\\\Z \ zasady \ zachowania \ energii\\\\E_{k} = E_{p} = mgh\\\\E_{k} = mgh\\\\E_{k} = 10 \ kg\cdot10\frac{N}{kg}\cdot30 \ m\\\\\underline{E_{k} = 3 \ 000 \ J = 3 \ kJ}[/tex]
4.
[tex]dane:\\m = 3 \ kg\\T_1 = 30^{o}C\\T_2 = 90^{o}C\\\Delta T = T_2 - T_1 = 90^{o}C - 30^{o}C = 60^{o}C\\Q = 3,6 \ kJ = 3,6\cdot1000 \ J = 3 \ 600 \ J\\szukane:\\c_{w} = ?\\\\Rozwiazanie\\\\c_{w} = \frac{Q}{m\cdot \Delta T}\\\\c_{w} = \frac{3600 \ J}{3 \ kg\cdot60^{o}C}\\\\\underline{c_{w} = 20\frac{J}{kg\cdot^{o}C}}[/tex]
