Potrzebuje na dzis zad 1/ 1.1/1.2 i zad 3 z napisanymi potrzebnymi wzorami itp

[latex]1.1 \ Dane: \ h = 4,8 m \ alpha = 55^o \ I = frac{mr^2}{2} \ r = 0,4 m \ omega = frac{v}{r} \ \ Z zasady zachowania energii: \ \ E_p = E_{k_p} + E_{k_o} \ mgh = frac{mv^2}{2} + frac{Iomega^2}{2} \ mgh = frac{mv^2}{2} + frac{1}{2} frac{mr^2}{2} frac{v^2}{r^2} \ gh = frac{v^2}{2} + frac{v^2}{4} = frac{3}{4}v^2 \ \ v = sqrt{ frac{4gh}{3} } = 8 m/s \ omega = frac{v}{r} = 20 rad/s \ \ frac{h}{s} = sinalpha \ s = frac{h}{sinalpha} [/latex] [latex] a = frac{Delta v}{t} = frac{v_k - v_p}{y} = frac{v_k - 0}{t} = frac{v_k}{t} = frac{v}{t} \ s = frac{at^2}{2} = frac{ frac{v}{t} t^2}{2} = frac{vt}{2} \ t = frac{2s}{v} = frac{2h}{vsinalpha} = 1,47 s [/latex] [latex]1.2 \ Dane: \ r = 0,4 m \ omega_0 = 20 rad/s \ f = 0,45 \ \ v(t) = v_0 - at \ \ v_k = omega_0r - at = omega_0r - frac{T}{m}t = omega_0r - frac{mgf}{m}t = omega_0r - gft \ \ v_k = 0 m/s \ 0 = omega_0r - gft \ gft = omega_0r \ \ t = frac{omega_0r}{gf} \ \ s = v_ot - frac{at^2}{2} = frac{v_0t}{2} = frac{omega_0^2r^2}{2gf} = 7 frac{1}{9} m [/latex] 3. Rozwiązanie w załącznikach