Questões - IME 2015 | Gabarito e resoluções

[IME-2015 / 2016 - 1 fase] Sejam dois quadrados de lado a situados em planos distintos que so paralelos entre si esituados a uma distncia d, um do outro. A reta que liga os centros dos quadrados perpendicular a esses planos. Cada diagonal de um quadrado paralela a dois lados do outroquadrado. Liga-se cada vrtice de cada quadrado aos dois vrtices mais prximos do outro quadrado. Obtm-se, assim, tringulos que, conjuntamente com os quadrados, formam umslido S. Qual a distncia entre estes planos distintos em funo de a, de modo que os tringulos descritos acima sejam equilteros?

(IME - 2015/2016- 2 FASE) PARA AS QUESTES DE 1 A 10, ESCOLHA A ALTERNATIVA QUE COMPLETA O TEXTO 1 CORRETAMENTE. Text 1 Water: Unclogging the finance How to improve water systems is one challenge; financing them is another. Public authorities in most countries play the main role in implementing and funding water infrastructure, but it is a model that is under increasing pressure, with government budgets 1.________ and banks still prudent about issuing credit. There is no generic funding model that can be applied to every need; the sheer diversity of water infrastructures and sources of financing 2.________ to be identified, scanned and tapped in line with particular investment types and needs. There may be small-scale projects initiated by local entrepreneurs, or large infrastructures that serve multiple 3. ________, such as energy and heavy manufacturing. Some investments may involve green ecosystems to supply, store or filter water. Not only will these infrastructures have different financing needs, but will access funds in different ways, for instance through capital markets, loans, funds, public expenditures, etc. Take large dams and large reservoirs. These are costly, long-term affairs. The Three Gorges Dam project in China, for instance, could cost over US$22 billion, according to government 4.________, including construction, relocation of residents and financing costs. Moreover, cost recovery is not expected to occur for 10 years after full operation starts. Such major projects tend to be financed 5.________ major development banks such as the Asian Development Bank and World Bank, and institutional investors such as pension funds. The sources for long-term financing are expanding, with the emergence of sovereign funds and philanthropists, 6.________ of new groups like the Chinese-led Asian Infrastructure Investment Bank, 7.________ opened in March 2015. But before leaping into major 8._________ such as dams, policymakers must answer several questions. Will the construction lock them in and still be valuable in 25, 50 or 100 years time? After all, there are several cases of investments that have fallen into disuse or underuse, such as a desalination 9. ________ in Sydney that was built during a severe but temporary drought, and dams in Frances Loire Valley that are now being decommissioned at some cost. Had a more forwardprobing value options approach been used in planning them, they 10._________ in the first place. ( . . . ) Disponvel em http://www.oecdobserver.org/news/fullstory.php/aid/4825/Water:_Unclogging_the_finance.html#sthash.kRhyDJ1.dpuf Acesso em 16 Abr 2015. Escolha entre as alternativas abaixo a opo que completa corretamente o espao 1.

[IME-2015 / 2016 - 1 fase] Um corpo de carga positiva, inicialmente em repouso sobre uma rampa plana isolante com atrito, est apoiado em uma mola, comprimindo-a. Aps ser liberado, o corpo entra emmovimento e atravessa uma regio do espao com diferena de potencial V, sendo acelerado. Para que o corpo chegue ao final da rampa com velocidade nula, a distncia d indicada nafigura : Dados: deformao inicial da mola comprimida: x; massa do corpo: m; carga do corpo: + Q; acelerao da gravidade: g; coeficiente de atrito dinmico entre o corpo e a rampa: ; ngulo de inclinao da rampa: ; constante elstica da mola: K. Consideraes: despreze os efeitos de borda; a carga do corpo permanece constante ao longo da trajetria.

(IME - 2015/2016- 2 FASE) PARA AS QUESTES DE 1 A 10, ESCOLHA A ALTERNATIVA QUE COMPLETA O TEXTO 1 CORRETAMENTE. Text 1 Water: Unclogging the finance How to improve water systems is one challenge; financing them is another. Public authorities in most countries play the main role in implementing and funding water infrastructure, but it is a model that is under increasing pressure, with government budgets 1.________ and banks still prudent about issuing credit. There is no generic funding model that can be applied to every need; the sheer diversity of water infrastructures and sources of financing 2.________ to be identified, scanned and tapped in line with particular investment types and needs. There may be small-scale projects initiated by local entrepreneurs, or large infrastructures that serve multiple 3. ________, such as energy and heavy manufacturing. Some investments may involve green ecosystems to supply, store or filter water. Not only will these infrastructures have different financing needs, but will access funds in different ways, for instance through capital markets, loans, funds, public expenditures, etc. Take large dams and large reservoirs. These are costly, long-term affairs. The Three Gorges Dam project in China, for instance, could cost over US$22 billion, according to government 4.________, including construction, relocation of residents and financing costs. Moreover, cost recovery is not expected to occur for 10 years after full operation starts. Such major projects tend to be financed 5.________ major development banks such as the Asian Development Bank and World Bank, and institutional investors such as pension funds. The sources for long-term financing are expanding, with the emergence of sovereign funds and philanthropists, 6.________ of new groups like the Chinese-led Asian Infrastructure Investment Bank, 7.________ opened in March 2015. But before leaping into major 8._________ such as dams, policymakers must answer several questions. Will the construction lock them in and still be valuable in 25, 50 or 100 years time? After all, there are several cases of investments that have fallen into disuse or underuse, such as a desalination 9. ________ in Sydney that was built during a severe but temporary drought, and dams in Frances Loire Valley that are now being decommissioned at some cost. Had a more forwardprobing value options approach been used in planning them, they 10._________ in the first place. ( . . . ) Disponvel emhttp://www.oecdobserver.org/news/fullstory.php/aid/4825/Water:_Unclogging_the_finance.html#sthash.kRhyDJ1.dpuf Acesso em 16 Abr 2015. Escolha entre as alternativas abaixo a opo que completa corretamente o espao 2

[IME-2015 / 2016 - 1 fase] Uma partcula de massa m e carga + Q encontra-se confinada no plano XY entre duas lminasinfinitas de vidro, movimentando-se sem atrito com vetor velocidade (v,0,0) no instante t = 0, quandoum dispositivo externo passa a gerar um campo magntico dependente do tempo, cujo vetor (f(t),f(t),B), onde B uma constante. Pode-se afirmar que a fora normal exercida sobre as lminas nula quando t Considerao: desconsidere o efeito gravitacional.

[IME-2015 / 2016 - 1 fase] A figura acima, cujas cotas esto em metros, exibe uma estrutura em equilbrio formada por trs barrasrotuladas AB, BC e CD. Nos pontos B e C existem cargas concentradas verticais. A maior fora detrao que ocorre em uma barra, em kN, e a altura h, em metros, da estrutura so Considerao: as barras so rgidas, homogneas, inextensveis e de pesos desprezveis.

(IME - 2015/2016- 2 FASE) PARA AS QUESTES DE 1 A 10, ESCOLHA A ALTERNATIVA QUE COMPLETA O TEXTO 1 CORRETAMENTE. Text 1 Water: Unclogging the finance How to improve water systems is one challenge; financing them is another. Public authorities in most countries play the main role in implementing and funding water infrastructure, but it is a model that is under increasing pressure, with government budgets 1.________ and banks still prudent about issuing credit. There is no generic funding model that can be applied to every need; the sheer diversity of water infrastructures and sources of financing 2.________ to be identified, scanned and tapped in line with particular investment types and needs. There may be small-scale projects initiated by local entrepreneurs, or large infrastructures that serve multiple 3. ________, such as energy and heavy manufacturing. Some investments may involve green ecosystems to supply, store or filter water. Not only will these infrastructures have different financing needs, but will access funds in different ways, for instance through capital markets, loans, funds, public expenditures, etc. Take large dams and large reservoirs. These are costly, long-term affairs. The Three Gorges Dam project in China, for instance, could cost over US$22 billion, according to government 4.________, including construction, relocation of residents and financing costs. Moreover, cost recovery is not expected to occur for 10 years after full operation starts. Such major projects tend to be financed 5.________ major development banks such as the Asian Development Bank and World Bank, and institutional investors such as pension funds. The sources for long-term financing are expanding, with the emergence of sovereign funds and philanthropists, 6.________ of new groups like the Chinese-led Asian Infrastructure Investment Bank, 7.________ opened in March 2015. But before leaping into major 8._________ such as dams, policymakers must answer several questions. Will the construction lock them in and still be valuable in 25, 50 or 100 years time? After all, there are several cases of investments that have fallen into disuse or underuse, such as a desalination 9. ________ in Sydney that was built during a severe but temporary drought, and dams in Frances Loire Valley that are now being decommissioned at some cost. Had a more forwardprobing value options approach been used in planning them, they 10._________ in the first place. ( . . . ) Disponvel emhttp://www.oecdobserver.org/news/fullstory.php/aid/4825/Water:_Unclogging_the_finance.html#sthash.kRhyDJ1.dpuf Acesso em 16 Abr 2015. Escolha entre as alternativas abaixo a opo que completa corretamente o espao 3

[IME-2015 / 2016 - 1 fase] Uma fonte sonora est situada no ponto de coordenadas x = 0 m e y = 0 m e outra no ponto decoordenadas x = 0 m e y = 4 m. As ondas produzidas pelas duas fontes tm a mesma frequncia eesto em fase. Um observador situado no ponto de coordenadas x = 3 m e y = 0 m nota que aintensidade do som diminui quando ele se move paralelamente ao eixo y no sentido positivo ou nosentido negativo. Se a velocidade do som no local 340 m/s, a menor frequncia das fontes, em Hz,que pode explicar essa observao

(IME - 2015/2016- 2 FASE) PARA AS QUESTES DE 1 A 10, ESCOLHA A ALTERNATIVA QUE COMPLETA O TEXTO 1 CORRETAMENTE. Text 1 Water: Unclogging the finance How to improve water systems is one challenge; financing them is another. Public authorities in most countries play the main role in implementing and funding water infrastructure, but it is a model that is under increasing pressure, with government budgets 1.________ and banks still prudent about issuing credit. There is no generic funding model that can be applied to every need; the sheer diversity of water infrastructures and sources of financing 2.________ to be identified, scanned and tapped in line with particular investment types and needs. There may be small-scale projects initiated by local entrepreneurs, or large infrastructures that serve multiple 3. ________, such as energy and heavy manufacturing. Some investments may involve green ecosystems to supply, store or filter water. Not only will these infrastructures have different financing needs, but will access funds in different ways, for instance through capital markets, loans, funds, public expenditures, etc. Take large dams and large reservoirs. These are costly, long-term affairs. The Three Gorges Dam project in China, for instance, could cost over US$22 billion, according to government 4.________, including construction, relocation of residents and financing costs. Moreover, cost recovery is not expected to occur for 10 years after full operation starts. Such major projects tend to be financed 5.________ major development banks such as the Asian Development Bank and World Bank, and institutional investors such as pension funds. The sources for long-term financing are expanding, with the emergence of sovereign funds and philanthropists, 6.________ of new groups like the Chinese-led Asian Infrastructure Investment Bank, 7.________ opened in March 2015. But before leaping into major 8._________ such as dams, policymakers must answer several questions. Will the construction lock them in and still be valuable in 25, 50 or 100 years time? After all, there are several cases of investments that have fallen into disuse or underuse, such as a desalination 9. ________ in Sydney that was built during a severe but temporary drought, and dams in Frances Loire Valley that are now being decommissioned at some cost. Had a more forwardprobing value options approach been used in planning them, they 10._________ in the first place. ( . . . ) Disponvel emhttp://www.oecdobserver.org/news/fullstory.php/aid/4825/Water:_Unclogging_the_finance.html#sthash.kRhyDJ1.dpuf Acesso em 16 Abr 2015. Escolha entre as alternativas abaixo a opo que completa corretamente o espao 4.

[IME-2015 / 2016 - 1 fase] Na Figura 1, o corpo A, constitudo de gelo, possui massa m e solto em uma rampa a uma altura h.Enquanto desliza pela rampa, ele derrete e alcana o plano horizontal com metade da energia mecnicae metade da massa iniciais. Aps atingir o plano horizontal, o corpo A se choca, no instante 4T, com ocorpo B, de massa m, que foi retirado do repouso atravs da aplicao da fora f(t), cujo grfico exibido na Figura 2. Para que os corpos parem no momento do choque, F deve ser dado por Dado: acelerao da gravidade: g. Observaes: o choque entre os corpos perfeitamente inelstico; o corpo no perde massa ao longo de seu movimento no plano horizontal.

(IME - 2015/2016- 2 FASE) Text 1 Water: Unclogging the finance How to improve water systems is one challenge; financing them is another. Public authorities in most countries play the main role in implementing and funding water infrastructure, but it is a model that is under increasing pressure, with government budgets 1.________ and banks still prudent about issuing credit. There is no generic funding model that can be applied to every need; the sheer diversity of water infrastructures and sources of financing 2.________ to be identified, scanned and tapped in line with particular investment types and needs. There may be small-scale projects initiated by local entrepreneurs, or large infrastructures that serve multiple 3. ________, such as energy and heavy manufacturing. Some investments may involve green ecosystems to supply, store or filter water. Not only will these infrastructures have different financing needs, but will access funds in different ways, for instance through capital markets, loans, funds, public expenditures, etc. Take large dams and large reservoirs. These are costly, long-term affairs. The Three Gorges Dam project in China, for instance, could cost over US$22 billion, according to government 4.________, including construction, relocation of residents and financing costs. Moreover, cost recovery is not expected to occur for 10 years after full operation starts. Such major projects tend to be financed 5.________ major development banks such as the Asian Development Bank and World Bank, and institutional investors such as pension funds. The sources for long-term financing are expanding, with the emergence of sovereign funds and philanthropists, 6.________ of new groups like the Chinese-led Asian Infrastructure Investment Bank, 7.________ opened in March 2015. But before leaping into major 8._________ such as dams, policymakers must answer several questions. Will the construction lock them in and still be valuable in 25, 50 or 100 years time? After all, there are several cases of investments that have fallen into disuse or underuse, such as a desalination 9. ________ in Sydney that was built during a severe but temporary drought, and dams in Frances Loire Valley that are now being decommissioned at some cost. Had a more forward-probing value options approach been used in planning them, they 10._________ in the first place. ( . . . ) Disponvel emhttp://www.oecdobserver.org/news/fullstory.php/aid/4825/Water:_Unclogging_the_finance.html#sthash.kRhyDJ1.dpufAcesso em 16 Abr 2015. Escolha entre as alternativas abaixo a opo que completa corretamente o espao 5

[IME-2015 / 2016 - 1 fase] Considerando o esquema acima, um pesquisador faz trs afirmaes que se encontram listadas aseguir: Afirmao I. Se a diferena de presso entre os dois reservatrios (PA - PB) for equivalente a 20 mm decoluna de gua, a variao de massa especfica entre os dois fluidos (r1 - r2) igual a 0,2 kg/L. Afirmao II. Se o Fluido 1 for gua e se a diferena de presso (PA - PB) for de 0,3 kPa, a massaespecfica do Fluido 2 igual a 0,7 kg/L. Afirmao III. Caso o Fluido 1 tenha massa especfica igual metade da massa especfica da gua, oFluido 3 (que substitui o Fluido 2 da configurao original) deve ser mais denso do que a gua para quea diferena de presso entre os reservatrios seja a mesma da afirmao I. Est(o) correta(s) a(s) afirmao(es) Dados: massa especfica da gua: 1 kg/L; acelerao da gravidade: 10 m/s2; Para as afirmaes I e II: L1 = 0,30 m e L2 = 0,40 m; Para a afirmao III apenas: L1 = 0,60 m e L2 = 0,80 m. Considerao: os fluidos so imiscveis.

(IME - 2015/2016- 2 FASE) PARA AS QUESTES DE 1 A 10, ESCOLHA A ALTERNATIVA QUE COMPLETA O TEXTO 1 CORRETAMENTE. Text 1 Water: Unclogging the finance How to improve water systems is one challenge; financing them is another. Public authorities in most countries play the main role in implementing and funding water infrastructure, but it is a model that is under increasing pressure, with government budgets 1.________ and banks still prudent about issuing credit. There is no generic funding model that can be applied to every need; the sheer diversity of water infrastructures and sources of financing 2.________ to be identified, scanned and tapped in line with particular investment types and needs. There may be small-scale projects initiated by local entrepreneurs, or large infrastructures that serve multiple 3. ________, such as energy and heavy manufacturing. Some investments may involve green ecosystems to supply, store or filter water. Not only will these infrastructures have different financing needs, but will access funds in different ways, for instance through capital markets, loans, funds, public expenditures, etc. Take large dams and large reservoirs. These are costly, long-term affairs. The Three Gorges Dam project in China, for instance, could cost over US$22 billion, according to government 4.________, including construction, relocation of residents and financing costs. Moreover, cost recovery is not expected to occur for 10 years after full operation starts. Such major projects tend to be financed 5.________ major development banks such as the Asian Development Bank and World Bank, and institutional investors such as pension funds. The sources for long-term financing are expanding, with the emergence of sovereign funds and philanthropists, 6.________ of new groups like the Chinese-led Asian Infrastructure Investment Bank, 7.________ opened in March 2015. But before leaping into major 8._________ such as dams, policymakers must answer several questions. Will the construction lock them in and still be valuable in 25, 50 or 100 years time? After all, there are several cases of investments that have fallen into disuse or underuse, such as a desalination 9. ________ in Sydney that was built during a severe but temporary drought, and dams in Frances Loire Valley that are now being decommissioned at some cost. Had a more forwardprobing value options approach been used in planning them, they 10._________ in the first place. ( . . . ) Disponvel emhttp://www.oecdobserver.org/news/fullstory.php/aid/4825/Water:_Unclogging_the_finance.html#sthash.kRhyDJ1.dpuf Acesso em 16 Abr 2015. Escolha entre as alternativas abaixo a opo que completa corretamente o espao 6

(IME - 2015/2016- 2 FASE) PARA AS QUESTES DE 1 A 10, ESCOLHA A ALTERNATIVA QUE COMPLETA O TEXTO 1 CORRETAMENTE. Text 1 Water: Unclogging the finance How to improve water systems is one challenge; financing them is another. Public authorities in most countries play the main role in implementing and funding water infrastructure, but it is a model that is under increasing pressure, with government budgets 1.________ and banks still prudent about issuing credit. There is no generic funding model that can be applied to every need; the sheer diversity of water infrastructures and sources of financing 2.________ to be identified, scanned and tapped in line with particular investment types and needs. There may be small-scale projects initiated by local entrepreneurs, or large infrastructures that serve multiple 3. ________, such as energy and heavy manufacturing. Some investments may involve green ecosystems to supply, store or filter water. Not only will these infrastructures have different financing needs, but will access funds in different ways, for instance through capital markets, loans, funds, public expenditures, etc. Take large dams and large reservoirs. These are costly, long-term affairs. The Three Gorges Dam project in China, for instance, could cost over US$22 billion, according to government 4.________, including construction, relocation of residents and financing costs. Moreover, cost recovery is not expected to occur for 10 years after full operation starts. Such major projects tend to be financed 5.________ major development banks such as the Asian Development Bank and World Bank, and institutional investors such as pension funds. The sources for long-term financing are expanding, with the emergence of sovereign funds and philanthropists, 6.________ of new groups like the Chinese-led Asian Infrastructure Investment Bank, 7.________ opened in March 2015. But before leaping into major 8._________ such as dams, policymakers must answer several questions. Will the construction lock them in and still be valuable in 25, 50 or 100 years time? After all, there are several cases of investments that have fallen into disuse or underuse, such as a desalination 9. ________ in Sydney that was built during a severe but temporary drought, and dams in Frances Loire Valley that are now being decommissioned at some cost. Had a more forwardprobing value options approach been used in planning them, they 10._________ in the first place. ( . . . ) Disponvel emhttp://www.oecdobserver.org/news/fullstory.php/aid/4825/Water:_Unclogging_the_finance.html#sthash.kRhyDJ1.dpuf Acesso em 16 Abr 2015. Escolha entre as alternativas abaixo a opo que completa corretamente o espao 7

[IME-2015 / 2016 - 1 fase] Um corpo rgido e homogneo apresenta seo reta com dimenses representadas na figura acima. Considere que uma fora horizontal F, paralela ao eixo x, aplicada sobre o corpo a uma distncia de1,5 u.c. do solo e que o corpo desliza sem atrito pelo solo plano horizontal. Para que as duas reaesdo solo sobre a base do corpo sejam iguais, a distncia y, em u.c., dever ser Considerao: u.c. unidade de comprimento.