Questões - ITA 2011 | Gabarito e resoluções

[ITA - 1 FASE - 2011] Um prisma regular hexagonal homogneo com peso de 15 N e aresta da base de 2,0 m mantido de p graas ao apoio de um dos seus vrtices da base inferior (ver figura) e ao de uma fora vertical de suspenso de 10 N (no mostrada). Nessas condies, o ponto de aplicao da fora na base superior do prisma encontra-se:

(ITA - 2011- 1 FASE) Assinale a opo em que o autor expressa claramente seu julgamento.

(ITA - 2011- 1 FASE) Our Imaginary, Hotter Selves Avatars might serve therapeutic purposes, helping those with social phobia become more confident. by Sharon Begley Anyone who has ever had a bad hair day, when looking like a latter-day Medusa makes you feel cranky and antisocial and plodding, can sympathize with the Oakland Raiders - and not because the players get helmet hair. The Raiders alternated between mostly black and mostly white uniforms,10depending on whether they were playing at home or away.11Knowing that appearance affects peoples mood and outlook, psychologists wondered whether uniform color influenced the Raiders aggressiveness. 12Using data from the 1970s and 1980s,1they found that the team racked up way more penalty yards 6a measure of aggression when2they wore black than when they wore white, for infractions both minor7(encroachment) and major8(roughing the kicker). The pattern held even when the scientists took into account different conditions and styles of play at home and away.13But while the 1988 finding has become a classic in psychology, the explanation remains controversial. Do referees, because of blacks cultural baggage, see black-clad players as meaner and badder than3those in, say, baby blue? Or does wearing black make players see themselves as tougher and meaner and therefore4cause them to play that way? Jeremy Bailenson and Nick Yee of Stanford University had this and other classic studies in mind14when they started wondering about the effect of being able to alter ones appearance. They werent going to study wardrobe choices, however.5Their quarry is avatars,9digital representations of players in such games as Second Life. Your physical appearance changes how people treat you, says Bailenson. But independent of that, when you perceive yourself in a certain way, you act differently. He and Yee call it the Proteus effect, after theshape-changing Greek god. The effect of appearance on behavior, they find, carries over from the virtual world to the real one, with intriguing consequences. (...) http://www.newsweek.com. Acesso em 5/6/2010. Assinale a opo em que o referente do pronome est INCORRETO.

(ITA 2011- 2 fase -Questo 10) Considere um tringulo equiltero cujo lado mede 2 3 cm. No interior deste tringulo existem 4 crculos de mesmo raio r. O centro de um dos crculos coincide com o baricentro do tringulo. Este crculo tangencia externamente os demais e estes, por sua vez, tangenciam 2 lados do tringulo. a) Determine o valor de r. b) Calcule a rea do tringulo no preenchida pelos crculos. c) Para cada crculo que tangencia o tringulo, determine a distncia do centro ao vrtice mais prximo.

(ITA - 2011) Estima-se que a exposio a 16 mg m3 de vapor de mercrio por um perodo de 10 min seja letal para um ser humano. Um termmetro de mercrio foi quebrado e todo o seu contedo foi espalhado em uma sala fechada de 10 m de largura, 10 m de profundidade e 3 m de altura, mantida a 25 C. Calcule a concentrao de vapor de mercrio na sala aps o estabelecimento do equilbrio Hg(l)⇌Hg(g), sabendo que a presso de vapor do mercrio a 25 C e 3 x 106 atm, e verifique se a concentrao de vapor do mercrio na sala ser letal para um ser humano que permanea em seu interior por 10 min. Dados: massa molar do mercrio = 200,6 g.mol1 constante dos gases ideais: R = 0,082L atm K1 mol1

(ITA - 2011- 1 Fase) Assinale a opo CORRETA que apresenta o potencial de equilbrio do eletrodo Al3+ / Al, em volt, na escala do eletrodo de referncia de cobre-sulfato de cobre, temperatura de 25 C, calculado para uma concentrao do on alumnio de 10-3 mol L-1. Dados: Potenciais de eletrodo padro do cobre-sulfato de cobre (E0CuSO4/Cu)e do alumnio (E0Al3+/Al) , na escala do eletrodo de hidrognio, nas condies-padro: E0CuSO4/Cu= +0,310 V E0Al3+/Al= -1,67 V

[ITA - 1 FASE - 2011] Um relgio tem um pndulo de 35 cm de comprimento. Para regular seu funcionamento, ele possui uma porca de ajuste que encurta o comprimento do pndulo de 1 mm a cada rotao completa direita e alonga este comprimento de 1 mm a cada rotao completa esquerda. Se o relgio atrasa um minuto por dia, indique o nmero aproximado de rotaes da porca e sua direo necessrios para que ele funcione corretamente.

(ITA - 2011- 1 FASE) O autor se vale da obra de Julio Cortzar para

(ITA - 2011- 1 FASE) Our Imaginary, Hotter Selves Avatars might serve therapeutic purposes, helping those with social phobia become more confident. by Sharon Begley (1) Anyone who has ever had a bad hair day, when looking like a latter-day Medusa makes you feel cranky and antisocial and plodding, can sympathize with the Oakland Raiders - and not because the players get helmet hair. The Raiders alternated between mostly black and mostly white uniforms, depending on whether they were playing at home or away. Knowing that appearance affects peoples mood and outlook, psychologists wondered whether uniform color influenced the Raiders aggressiveness. Using (5) data from the 1970s and 1980s, they found that the team racked up way more penalty yards - a measure of aggression - when they wore black than when they wore white, for infractions both minor (encroachment) and major (roughing the kicker). The pattern held even when the scientists took into account different conditions and styles of play at home and away. But while the 1988 finding has become a classic in psychology, the explanation remains controversial. Do referees, because of blacks cultural baggage, see black-clad players as meaner and badder than those in, say, baby blue? Or does wearing black make players see themselves as (10) tougher and meaner - and therefore cause them to play that way? Jeremy Bailenson and Nick Yee of Stanford University had this and other classic studies in mind when they started wondering about the effect of being able to alter ones appearance. They werent going to study wardrobe choices, however. Their quarry is avatars, digital representations of players in such games as Second Life. Your physical appearance changes how people treat you, says Bailenson. But independent of that, when you perceive yourself in a certain way, you act differently. He and Yee call it (15) the Proteus effect, after the shape-changing Greek god. The effect of appearance on behavior, they find, carries over from the virtual world to the real one, with intriguing consequences. () http://www.newsweek.com. Acesso em 5/6/2010. * os nmeros entre parnteses correspondem s linhas do texto original. a measure of aggression (linha 5), encroachment (linha 6), roughing the kicker (linha 6) e digital representations of players (linha 13) tm, respectivamente, valor semntico de:

(Ita 2011) A expressão   com x e y reais, representa

[ITA - 1 FASE - 2011] Um hemisfrio de vidro macio de raio de 10 cm e ndice de refrao n = 3/2 tem sua face plana apoiada sobre uma parede, como ilustra a figura. Um feixe colimado de luz de 1 cm de dimetro incide sobre a face esfrica, centrado na direo do eixo de simetria do hemisfrio. Valendo-se das aproximaes de ngulos pequenos, sen e tg , o dimetro do crculo de luz que se forma sobre a superfcie da parede de

(ITA - 2011- 1 FASE) So recursos de progresso no texto I. as perguntas. II. as citaes do conto de Cortzar. III. a meno ao filme de Godard. Est(o) correta(s)

(ITA - 2011- 1 Fase) Em um experimento de laboratrio, cloreto de alumnio, cloreto de zinco e carbonato de sdio so dissolvidos, individualmente, em trs recipientes separados contendo gua neutra aerada com pH = 7. Uma placa de ferro metlico imersa em cada um dos recipientes, que so mantidos temperatura de 25 C. Admitindo-se as condies experimentais apresentadas acima, so feitas as seguintes afirmaes em relao influncia da hidrlise dos sais na velocidade de corroso das placas metlicas: I. O ction alumnio hidratado forma solues aquosas que aceleram a corroso do ferro. II. As solues aquosas produzidas pela hidrlise do nion carbonato inibem a corroso do ferro. III. A corroso do ferro inibida pela soluo aquosa formada no processo de hidrlise do ction zinco hidratado. Das afirmaes acima, est(o) CORRETA(S) apenas

(ITA - 2011) Com respeito a equao polinomial : Saiba queA \ B =

(ITA - 2011) Sejam m e n inteiros tais que a equao 36x2 + 36y2 + mx + ny - 23 = 0 representa uma circunferncia de raio r = 1 cm e centro C localizado no segundo quadrante. Se A e B so os pontos onde a circunferncia cruza o eixo Oy, a rea do tringulo ABC, em cm2, igual a: