Exercícios Dinâmica Cap 2

2.07\nNc\nP\n0.6 m\n0.8 m\n\nNcy - Pc = 0 m c ac\nNo blanco\n\nNay = Ncosθ\nNex = m t a t\nNex = Nsenθ\n\nPara sume\n\nh = 0.6\n d = 0.8\n\nSc = 0.75 St\nAc = 0.75 At 2.13\nm = 1100\n d1 = 1 m\n d2 = 1.4\nh = 0.8\nv = 20 m/s\nu = 0.8\nuc = 0.2\n\nfat = m a\nN t + N d = P\nN d d2 = N t d1\nfat h = 0\nN d = N t - N d, fat h = 0\n\n0.76N d - N t = 0\nN t + N d = 1100\n\nN t = 1000\n0.76N d N t = 1100\nN d = 6250 N\nN t = 4750 N\n\nb)\n+fat = m a\n1.1N d - N t - 0.15N d 0.8 = 0\nN d - N t = 0\nN t + N d = 1100\nN d = 5500 N\n\nfat d = μN d\nfat d = 0.5 5500\nfat d = 2750 N\n\n- 2750 = 1100 a\n a = 2.5 m/s² 2.14\nm = 650 kg\n d1 = 3.0 m\n d2 = 2.2 mm\ns = 0.6 m\nuc = 0.85\nuc = 0.55\n\n7CM\n{fat = m a\nN t + N d = P\n\nN d = N t - N d, N t - d1 = 0\nu e N t h - N d d2 - N t d1 = 0\n0.51N t + 1.2N d - N t = 0\n-0.49N t + 1.2N d = 0\nN t = 2.415N d\n\nN d(2.415 + 1) = 6500\nN d = 1884.06 N\nN t = 4615.94 N\n\nfat = μN t\nfat = 0.88 · 4615.94\nfat = 3923.55 N\n\nfat = m a\n a = 6m/s² 2.14\nC\nfat.h + Nd.d2 - Nt.d1 = 0\nfat = \\mu_c . Nt\n\n2.15\nvm = 530 kg\n\nd1 = 0.7 m\nd2 = 0.8 m\nln = 0.8 m\na) a ? b) \\mu_f ?\n\n-N1.d1 + fat.hn = 0\nfat = m.a\nN = P\n\n-5500.0.7 + fat.0.8 = 0\nfat = 4812.5 N\n\n4812.5 = 550.a\n\n a = 8.75 m/s^2\n\ncomo fat = \\mu.N\n4812.5 = \\mu.550\n\\mu = 0.875 2.16\nF\n\nm = 450 kg\nlh1 = 1.1 m, lh2 = 0.35 m, d2 = 0.35 m\nd1 = 1.2 m\n\nTCm { F - m.a\nN - P = 0\n}\n\nF = (lh1 - lh2) - N.d2 = 0\nF.0.85 - 4500 - 0.35 = 0\n\nF = 15.75\n0.65\nF = 2423.68 N 2100\n\nb) F = 2100 N\n\na) => F = m.a\n2100 = 450.a\n\na = 4.67 m/s^2 2.17\n\nm = 360 kg\nd1 = 0.4 m\nd2 = 0.6 m\nln = 0.5 m\n\nfat = ?\n\nfat = m.a\nN - P = 0\n\nfat.1 - 3600.0.6 = 0\nfat = 2160 N\n\n a) 2160 = m.a\n2160 = 360.a\n a = 6 m/s^2\n\nc)\nfat = \\mu.N\n2160 = \\mu.3600\n\\mu = 0.6 F\nm = 100kg\nH = 0.7 m\nL = 0.5 m\nu = 0.3\nF = 750N\na) a = ?\nhn = ?\nF - fat = m.a\nNT = Na + Nl\nTCM[F - fat = m.a]\nNT - P = 0\nfat = u.NT\nfat -> Máximo pois o corpo escorrega\nfat = 0.3.1000 = 300N\n\nF - fat = m.a\n750 - 300 = 100.a\n450 = 100.a\na = 4.5 m/s²\n\nb) NT -> logo fat = 0\nM0R {Nd. l - fat.d. H/2 - ln - H/2 = 0\n1000.0.25 - 300.0.7 - 750.ln - 0.7/2 = 0\n250 - 105 - 262.5 ln = 0\nln = 0.55 m N0.2 - F.0.2 - Nb.0.7 = 0\nN0.2NA - 0.07Nb - 2 = 0\nNa + Nb = 50 logo 0.2NA - 0.07(NA + 50) - 2 = 0\n0.2Na + 0.07Nb - 3 - 2 = 0\nNa = 0.5\nNa ≈ 18N\nNb ≈ 32N\nF = ma\n10 = 5.a\na = 2 m/s² F\nm = 180 kg\nH = 0.2 m\nL = 0.5 m\nu = 0.3\nF = 750N\nsh = 0.45 m\n\na) a = ?\nb) x = ?\nTCM { F - fat = m.a\nN - P = 0\nfat = max\nfat = u.N\nfat = 0.3.1800\nfat = 540N\n750 - 540 = m.a\n210 = 180.a\na = 1.17 m/s²\n\nb) M0R { N.x - fat.d. H/2 - F. (ln - H/2) = 0\n1800.x - 540 - 750.(0.45 - 0.7/x) = 0\n1800.x - 189 - 75 = 0\nx = 0.15 m 291\nm = 220kg\nH = 1.2m\nL = 0.42m 0.12m\nu = 0.12\nF = 250N\nf_tot = m.a\nN - P = 0\n750 - 264 = 200.a\n486 = 200.a\na = 2.21 m/s²\n\nb)\npara tombamento x = l/2\nF.(l/2 - h_n) - N.l/2 - f_at.H/2 = 0\n750.(l/2 - h_n) - 2200.0.2 - 264.1.2 = 0\n450 - 78.6 - 220 - 158.4 = 0\n\ntotal = 716\nl_n = 0.085\nl_n = 0.045m 222\nm = 15t = 15000kg\na = 6m\nb = 4m\nc = 2.5m\nd = 1.5m\nF = 2.1F = 10000N\n\t\nTCM = F = m.a\n10 000 = 15 000.a\na = 0.67m/s²\n\nM_p12\n-F.d - N_d.a + N_t.b = 0\n-10 000.1.5 - 6N_d + 4N_t = 0\n4N_t - 6N_d = 15 000\nN_d + N_t = 150 000\n(450 000 - N_d) - 6N_d = 15 000\n600 000 - 4N_d - 6N_d = 15 000\nN_d = 58500N\nlogo N_t = 91500N 223\nb = 1m\nc = 2m\nx = ?\n\n\t\nx = ?\na_cm = 4.24m/s²\nu = ?\nx = ?\n\nP_x = P_sinθ = mg.lnθ\nP_y = P_cosθ = mg.cosθ\nTCM = { f_x - f_at = m.a\nN - P_y = 0\n}\nmg.sinθ - u.N = m.a\nmg.sinθ - u.m.g.cosθ = 0\n-g.u.cosθ = a.g.sinθ\nu = g.sinθ - a\ng.cosθ\na = 10.0,7 - 4.24\n\n1) u = 0.4\n\nb) N.x - f_at - c = 0\nx/g.cosθ.e.x - u.m.g.cosθ - c = 0\nx = u.C\nx = 0.8m 2.25\nm = 25kg\nTCh\n(NAy + NBy - P = m.a_y)\n(NAx + NBx = m.a_x)\nN_{A} = N_{A}cos\\theta \nN_{A}y = N_{A}sin\\theta\nNBx = N_{B}cos\\theta , NBy = N_{B}sin\\theta\n\ndm (1 & 2)\nN_{A}sy + N_{B}sy - mg = -m.a_y\nN_{A}cos\\theta + N_{B}cos\\theta = m.a_x\n\ntão N_{B} = N_{A}\nN_{A}sin\\theta +(N_{B}sin\\theta - mg = -m a sin\\theta\nN_{A}cos\\theta + N_{B}cos\\theta = m.a cosine\n\n2N_{A}sin\\theta - mg = -ma sin\\theta\n2N_{A}cos\\theta = m.a cos\\theta -> 2N_{A} = m a\nlogo em(3)\nma sin\\theta - mg = -ma sin\\theta\n2ma sin\\theta = -mg\na = g/2 sin\\theta\n{ ax = 6.4 m/s^2\n{ ay = 4.8 m/s^2