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Uma viga tem seção reta retangular de dimensões 20 \text{ cm} e 30 \text{ cm}. Uma força de 60 \text{ kN} é aplicada compressivamente tal que forma um ângulo de 60^\text{o} com a vertical. Determine a tensão normal média.

","status","pending_classification","hasRelatedVideo","relatedVideos",[109],{"_110":111,"_129":130,"_51":145,"_180":181,"_198":199},"content",{"_43":112,"_57":113,"_114":-5,"_115":116,"_117":118,"_119":-5,"_45":120,"_123":124,"_125":124,"_126":-5,"_127":128},"468e3e62-35e0-47be-a15f-68dd43bb32bb","Óptica Geométrica - Parte 1","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","fa6aaf42-4cc4-4d76-8915-7a67081f7e9a","user_id",{"_121":122},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_131":132,"_138":139,"_140":141,"_142":143,"_28":144},"provider",{"_43":133,"_134":135,"_136":137},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","d80487a0-0f98-42c8-99bb-551165ba3068","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/d80487a0-0f98-42c8-99bb-551165ba3068/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/d80487a0-0f98-42c8-99bb-551165ba3068/levels.m3u8",[146],{"_43":147,"_57":148,"_59":149,"_150":151,"_152":-5,"_123":153,"_125":153,"_45":154,"_127":149,"_161":162},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","2025-04-29T01:56:45.284172+00:00",{"_155":156,"_157":158,"_159":160},"childrenCount",18,"content_count",0,"question_count",135489,"children",[163],{"_43":164,"_57":165,"_59":166,"_150":151,"_152":147,"_123":167,"_125":167,"_45":168,"_127":171,"_161":172},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_155":169,"_157":158,"_159":170},10,19948,"mecanica-2",[173],{"_43":174,"_57":58,"_59":60,"_150":151,"_152":164,"_123":175,"_125":175,"_45":176,"_127":178,"_161":179},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_155":158,"_157":158,"_159":177},3376,"resistencia-dos-materiais-4",[],"video",{"_43":118,"_13":113,"_114":-5,"_182":183,"_184":185,"_28":-5,"_186":-5,"_131":185,"_187":188,"_142":-5,"_189":-5,"_190":-5,"_191":-5,"_192":-5,"_45":193,"_194":158,"_195":-5,"_104":196,"_123":197,"_125":197},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_121":122},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag",{"_43":147,"_57":148,"_59":149,"_150":151,"_152":-5,"_123":153,"_125":153,"_45":200,"_127":149,"_161":201},{"_155":156,"_157":158,"_159":160},[202],{"_43":164,"_57":165,"_59":166,"_150":151,"_152":147,"_123":167,"_125":167,"_45":203,"_127":171,"_161":204},{"_155":169,"_157":158,"_159":170},[205],{"_43":174,"_57":58,"_59":60,"_150":151,"_152":164,"_123":175,"_125":175,"_45":206,"_127":178,"_161":207},{"_155":158,"_157":158,"_159":177},[],"similarQuestions",[210,240,260],{"_40":211,"_42":41,"_43":212,"_77":213,"_101":228,"_102":229,"_51":230},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[214,217,220,223,226],{"_43":215,"_81":82,"_83":216},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":218,"_81":87,"_83":219},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":221,"_81":91,"_83":222},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":224,"_81":95,"_83":225},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":211,"_81":99,"_83":227},"y'' - 2y' + 6y = 0","Somente em y''−2y'+6y=0 o polinômio característico r²−2r+6=0 tem Δ<0, gerando raízes complexas conjugadas (1±i√5) e, portanto, solução em termos de exponencial modulando seno e cosseno. Nos demais itens (a–d) o discriminante é ≥0, produzindo raízes reais (distintas ou repetidas).","

Resolva as seguintes EDOs determinando a solução geral e, quando houver condições iniciais do PVI, a solução particular.

(a) y'' + 2y' - 3y = 0

(b) 6y'' - y' - y = 0

(d) 9y'' + 6y' + y = 0

(e) y'' - 2y' + 6y = 0

(f) 4y'' + 9y = 0

(g) 6y'' - 5y' + y = 0; \\, y(0) = 4; \\, y'(0) = 0

(h) y'' + 4y' + 4y = 0; \\, y(-1) = 2; \\, y'(-1) = 1

(i) y'' + y = 0; \\, y\bigg(\\frac{\\pi}{3}\\bigg) = 2; \\, y'\\bigg(\\frac{\\pi}{3}\\bigg) = -4

(j) y'' - 2y' - 3y = 3e^{2t}

(k) y'' + 9y = t^2 e^{3t} + 6

(l) 2y'' + 3y' + y = t^2 + 3 \\sin(t)

(m) y'' + y' - 2y = 2t; \\, y(0) = 0; \\, y'(0) = 1

(n) y'' - 2y' + y = te^t + 4; \\, y(0) = 1; \\, y'(0) = 1

(o) y'' + 4y = 3 \\sin(2t); \\, y(0) = 2; \\, y'(0) = -1

",[231],{"_43":232,"_57":233,"_59":234,"_150":151,"_152":235,"_123":236,"_125":236,"_45":237,"_127":234},"6516bbbd-f2a3-4710-8382-702240b17836","Mecânica na Engenharia de Petróleo","mecanica-na-engenharia-de-petroleo","b787e438-0ab3-454c-ab43-5d3d14c2720d","2025-04-29T03:44:35.328997+00:00",{"_155":238,"_157":158,"_159":239},4,12302,{"_40":241,"_42":41,"_43":242,"_77":243,"_101":255,"_102":256,"_51":257},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[244,247,250,252],{"_43":245,"_81":82,"_83":246},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":248,"_81":87,"_83":249},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":241,"_81":91,"_83":251},"

Verdadeiro, falso, verdadeiro

",{"_43":253,"_81":95,"_83":254},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","85,5 % decomposto → 14,5 % restante.\nN/N0 = 0,145 ⇒ t = ln(1/0,145)/(ln2/5730) ≈ 1,6×10⁴ anos.\nItens prováveis: (1) resta 14,5 % do C-14 (V); (2) idade ≈ 1,2×10⁴ anos ou 3 meias-vidas (F); (3) t½ do C-14 = 5730 anos (V). Sequência: V-F-V, correspondendo à alternativa c.","

Qual é a idade da madeira na qual 85,5\\% do C-14 se decompos?

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a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[281],{"_43":232,"_57":233,"_59":234,"_150":151,"_152":235,"_123":236,"_125":236,"_45":282,"_127":234},{"_155":238,"_157":158,"_159":239},[284,286,295,301,305,307,309,317,322,330,332,337,343],{"_43":232,"_57":233,"_59":234,"_150":151,"_152":235,"_123":236,"_125":236,"_45":285,"_127":234},{"_155":238,"_157":158,"_159":239},{"_43":287,"_57":288,"_59":289,"_150":151,"_152":290,"_123":167,"_125":167,"_45":291,"_127":294},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_155":292,"_157":158,"_159":293},5,30614,"engenharia-mecatronica-1",{"_43":296,"_57":58,"_59":60,"_150":151,"_152":297,"_123":298,"_125":298,"_45":299,"_127":300},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_155":158,"_157":158,"_159":177},"resistencia-dos-materiais-6",{"_43":297,"_57":165,"_59":166,"_150":151,"_152":287,"_123":236,"_125":236,"_45":302,"_127":304},{"_155":292,"_157":158,"_159":303},25741,"mecanica-3",{"_43":147,"_57":148,"_59":149,"_150":151,"_152":-5,"_123":153,"_125":153,"_45":306,"_127":149},{"_155":156,"_157":158,"_159":160},{"_43":174,"_57":58,"_59":60,"_150":151,"_152":164,"_123":175,"_125":175,"_45":308,"_127":178},{"_155":158,"_157":158,"_159":177},{"_43":310,"_57":311,"_59":312,"_150":151,"_152":290,"_123":167,"_125":167,"_45":313,"_127":316},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_155":314,"_157":158,"_159":315},21,45865,"engenharia-civil-3",{"_43":235,"_57":318,"_59":319,"_150":151,"_152":290,"_123":167,"_125":167,"_45":320,"_127":321},"Engenharia de Petróleo","engenharia-de-petroleo",{"_155":292,"_157":158,"_159":239},"engenharia-de-petroleo-1",{"_43":323,"_57":324,"_59":325,"_150":151,"_152":310,"_123":326,"_125":326,"_45":327,"_127":329},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_155":292,"_157":158,"_159":328},8852,"estruturas-1",{"_43":164,"_57":165,"_59":166,"_150":151,"_152":147,"_123":167,"_125":167,"_45":331,"_127":171},{"_155":169,"_157":158,"_159":170},{"_43":333,"_57":58,"_59":60,"_150":151,"_152":232,"_123":334,"_125":334,"_45":335,"_127":336},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_155":158,"_157":158,"_159":177},"resistencia-dos-materiais-7",{"_43":338,"_57":339,"_59":60,"_150":151,"_152":323,"_123":340,"_125":340,"_45":341,"_127":342},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_155":158,"_157":158,"_159":177},"resistencia-dos-materiais-5",{"_43":290,"_57":344,"_59":345,"_150":151,"_152":-5,"_123":346,"_125":346,"_45":347,"_127":345},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_155":348,"_157":158,"_159":349},29,351586,"tagsTree",[352,361],{"_43":147,"_57":148,"_59":149,"_150":151,"_152":-5,"_123":153,"_125":153,"_45":353,"_127":149,"_161":354},{"_155":156,"_157":158,"_159":160},[355],{"_43":164,"_57":165,"_59":166,"_150":151,"_152":147,"_123":167,"_125":167,"_45":356,"_127":171,"_161":357},{"_155":169,"_157":158,"_159":170},[358],{"_43":174,"_57":58,"_59":60,"_150":151,"_152":164,"_123":175,"_125":175,"_45":359,"_127":178,"_161":360},{"_155":158,"_157":158,"_159":177},[],{"_43":290,"_57":344,"_59":345,"_150":151,"_152":-5,"_123":346,"_125":346,"_45":362,"_127":345,"_161":363},{"_155":348,"_157":158,"_159":349},[364,373,382],{"_43":287,"_57":288,"_59":289,"_150":151,"_152":290,"_123":167,"_125":167,"_45":365,"_127":294,"_161":366},{"_155":292,"_157":158,"_159":293},[367],{"_43":297,"_57":165,"_59":166,"_150":151,"_152":287,"_123":236,"_125":236,"_45":368,"_127":304,"_161":369},{"_155":292,"_157":158,"_159":303},[370],{"_43":296,"_57":58,"_59":60,"_150":151,"_152":297,"_123":298,"_125":298,"_45":371,"_127":300,"_161":372},{"_155":158,"_157":158,"_159":177},[],{"_43":310,"_57":311,"_59":312,"_150":151,"_152":290,"_123":167,"_125":167,"_45":374,"_127":316,"_161":375},{"_155":314,"_157":158,"_159":315},[376],{"_43":323,"_57":324,"_59":325,"_150":151,"_152":310,"_123":326,"_125":326,"_45":377,"_127":329,"_161":378},{"_155":292,"_157":158,"_159":328},[379],{"_43":338,"_57":339,"_59":60,"_150":151,"_152":323,"_123":340,"_125":340,"_45":380,"_127":342,"_161":381},{"_155":158,"_157":158,"_159":177},[],{"_43":235,"_57":318,"_59":319,"_150":151,"_152":290,"_123":167,"_125":167,"_45":383,"_127":321,"_161":384},{"_155":292,"_157":158,"_159":239},[385],{"_43":232,"_57":233,"_59":234,"_150":151,"_152":235,"_123":236,"_125":236,"_45":386,"_127":234,"_161":387},{"_155":238,"_157":158,"_159":239},[388],{"_43":333,"_57":58,"_59":60,"_150":151,"_152":232,"_123":334,"_125":334,"_45":389,"_127":336,"_161":390},{"_155":158,"_157":158,"_159":177},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários