física mecânica QUESTÕES DE VESTIBULARES 2009.1 (1o semestre) 2009.2 (2o semestre)
sumário CINEMÁTICA VESTIBULARES 2009.1 ..................... ............................... ..................... ...................... ..................... ..................... ..................... ..................... ...................... ................ ............. ........ 2 VESTIBULARES 2009.2 ..................... ............................... ..................... ...................... ..................... ..................... ..................... ..................... ...................... ................ ........... ...... 26
LEIS DE NEWTON VESTIBULARES 2009.1 ..................... ............................... ..................... ...................... ..................... ..................... ..................... ..................... ...................... ................ ........... ...... 33 VESTIBULARES 2009.2 ..................... ............................... ..................... ...................... ..................... ..................... ..................... ..................... ...................... ................ ........... ...... 53
ENERGIA VESTIBULARES 2009.1 ..................... ............................... ..................... ...................... ..................... ..................... ..................... ..................... ...................... ................ ........... ...... 61 VESTIBULARES 2009.2 ..................... ............................... ..................... ...................... ..................... ..................... ..................... ..................... ...................... ................ ........... ...... 88
GRAVITAÇÃO VESTIBULARES 2009.1 ..................... ............................... ..................... ...................... ..................... ..................... ..................... ..................... ...................... ................ ........... ...... 96 VESTIBULARES 2009.2 ..................... ............................... ..................... ...................... ..................... ..................... ..................... ..................... ...................... ............... ......... ..... 101
ESTÁTICA VESTIBULARES 2009.1 ..................... ............................... ..................... ...................... ..................... ..................... ..................... ..................... ...................... ............... ......... ..... 104 VESTIBULARES 2009.2 ..................... ............................... ..................... ...................... ..................... ..................... ..................... ..................... ...................... ............... ......... ..... 107
HIDROSTÁTICA VESTIBULARES 2009.1 ..................... ............................... ..................... ...................... ..................... ..................... ..................... ..................... ...................... ............... ......... ..... 108 VESTIBULARES 2009.2 ..................... ............................... ..................... ...................... ..................... ..................... ..................... ..................... ...................... ............... ......... ..... 122
HIDRODINÂMICA VESTIBULARES 2009.1 ..................... ............................... ..................... ...................... ..................... ..................... ..................... ..................... ...................... ............... ......... ..... 127 VESTIBULARES 2009.2 ..................... ............................... ..................... ...................... ..................... ..................... ..................... ..................... ...................... ............... ......... ..... 128
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MECÂNICA: CINEMÁTICA
(UERJ-2009.1) - ALTERNATIVA: C Os gráficos I e II representam as posições S de dois corpos em função do tempo t.
VESTIBULARES 2009.1 VESTIBULARES VESTIBULARES 2009.2 2009.2 PÁG. PÁG. 26 (UERJ-2009.1) - ALTERNATIVA: D Segundo o modelo simplificado de Bohr, o elétron do átomo de hidrogênio executa um movimento circular uniforme, de raio igual a 5,0×10 –11m, em torno do próton, com período igual a 2×10 –15s. Com o mesmo valor da velocidade orbital no átomo, a distância, em quilômetros, que esse elétron percorreria no espaço livre, em linha reta, durante 10 minutos, seria da ordem de: a) 102 b) 103 c) 104 *d) 105 (UERJ-2009.1) - ALTERNATIVA: C Os gráficos 1 e 2 representam a posição S de dois corpos em função do tempo t.
No gráfico I, a função horária é definida pela equação S = a 1.t2 + b1.t e, no gráfico II, por S = a2.t2 + b 2.t. Admita que V1 e V 2 são, respectivamente, os vértices das curvas traçadas nos gráficos I e II II.. Assi Assim, m, a razã razãoo No gráf gráfic icoo 1,a funç funçãão horá orária ria é defin efinid idaa pelaeq pelaequa uaçção
.
Assim, a equação que define o movimento representado pelo gráfico 2 corresponde a:
é igua iguall a:
a) 1 b) 2 *c) 4 d) 8
a) b) *c) d) (UERJ-2009.1) - ALTERNATIVA: A Ao se deslocar do Rio de Janeiro a Porto Alegre, um avião percorre corre essa distâ distância ncia com com vel velocid ocidade ade média média v no prime primeiro iro
do
trajeto e 2v no trecho restante. A velocidade média do avião no percurso total foi igual a: *a) b)
(UNISA-2009.1) - ALTERNATIVA: A Um corpo é lançado verticalmente para cima com velocidade inicial v0. Considerando a orientação da trajetória de baixo para cima, os sinais a serem considerados considerados para a velocidade inicial v 0 e a aceleração da gravidade g serão, respectivamente: *a) positiva e negativa; b) positiva e positiva; c) negativa e positiva; d) negativa e negativa; e) faltam informações para definir os sinais. (UFABC-2009.1) - ALTERNATIVA: C Em certa ocasião, enquanto regava um jardim, um jardineiro percebeu que, colocando a saída de água da mangueira quase na posição vertical e junto ao solo, se ele variasse a inclinação com a qual a água saía, ela atingia posições diferentes, mas nunca ultrapassava ultrapassava a distância horizontal de 9,8 m do ponto de partida. Com essa informação, adotando g = 10 m/s 2, desprezando a resistência do ar e sabendo que a água sai da mangueira com
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(UERJ-2009.1) - ALTERNATIVA: A Um avião sobrevoa, com velocidade constante, uma área devastada, no sentido sul-norte, em relação a um determinado observador. A figura a seguir ilustra como esse observador, em repouso, no solo, vê o avião.
(FGVRJ-2009.1) - ALTERNATIVA: C A figura mostra os gráficos da velocidade em função do tempo de dois rapazes, João e Pedro, durante uma corrida.
Quatro pequenas caixas idênticas de remédios são largadas de um compartimento da base do avião, uma a uma, a pequenos intervalos regulares. Nessas circunstâncias, circunstâncias, os efeitos do ar praticamente não interferem no movimento das caixas. O observador tira uma fotografia, logo após o início da queda da quarta caixa e antes de a primeira atingir o solo. A ilustração mais adequada dessa fotografia é apresentada em:
*a)
b)
c)
d)
(UFABC-2009.1) - ALTERNATIVA: A A instalação de turbinas eólicas é conveniente em locais cuja velocidade média anual dos ventos seja superior a 3,6 m/s. O movimento do ar em um parque eólico foi monitorado observando o deslocamento de partículas suspensas durante intervalos de tempos de duração irregular. DESLOC DESLOCAME AMENT NTOS OS (m) (m) INTERV INTERVALO ALOS S DE TEMPO TEMPO (s) - 175 35 - 90 18 - 135 27 A partir de uma trajetória de origem convenientemente convenientemente definida e supondo que o ar se movimente com aceleração nula, das fun-
Sobre essa corrida foram feitas três afirmações: I. Entre os instantes t = 0 e t = 2s, os dois rapazes têm a mesma aceleração. II. No instante t = 14s, os dois rapazes estão empatados na corrida. III. João venceu a corrida. Com base na análise do gráfico, assinale a alternativa que contém a(s) afirmação(ões) verdadeira(s). a) Apenas I. b) Apenas II. *c) Apenas III. d) II e III. e) I, II e III. (VUNESP/UNISA-2009.1) - ALT (VUNESP/UNISA-2009.1) A LTERNA ERNATIVA: TIVA: E Em um local em que as forças de resistência do ar podem ser desprezadas e a aceleração da gravidade tem intensidade g = 10 m/s2, uma pequena esfera foi abandonada a partir do repouso, de uma altura h em relação ao solo. Sabendo-se que durante o último segundo de seu movimento de queda a esfera percorreu uma distância de 35 m, é possível afirmar que a velocidade, em m/s, com que ela chegou ao solo foi de a) 10. d) 35. b) 20. *e) 40. c) 25. (PUCRIO-2009.1) - ALTERNATIVA: E Um pacote do correio é deixado cair de um avião que voa horizontalmente com velocidade constante. Podemos afirmar que (desprezando a resistência do ar): a) um observador no avião e um observador em repouso no solo vêem apenas o movimento vertical do objeto. b) um observador no avião e um observador em repouso no solo vêem apenas o movimento horizontal do objeto. c) um observador no solo vê apenas um movimento vertical do objeto, enquanto um observador no avião vê o movimento hori-
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(PUCRIO-2009.1) - ALTERNATIVA: D Uma bola é lançada verticalmente para cima. Podemos dizer que no ponto mais alto de sua trajetória: a) a velocidade da bola é máxima, e a aceleração da bola é vertical e para baixo. b) a velocidade da bola é máxima, e a aceleração da bola é vertical e para cima. c) a velocidade da bola é mínima, e a aceleração da bola é nula. *d) a velocidade da bola é mínima, e a aceleração da bola é vertical e para baixo. e) a velocidade da bola é mínima, e a aceleração da bola é vertical e para cima. (PUCRIO-2009.1) - ALTERNATIVA: D Um objeto é lançado verticalmente para cima de uma base com velocidade v = 30 m/s. Considerando a aceleração da gravidade g = 10 m/s 2 e desprezando-se a resistência do ar, determine o tempo que o objeto leva para voltar à base da qual foi lançado. a) 3 s *d) 6 s b) 4 s e) 7 s c) 5 s (PUCRIO-2009.1) - ALTERNATIVA: A Uma família viaja de carro com velocidade constante de 100 km/ h, durante 2 h. Após parar em um posto de gasolina por 30 min, continua sua viagem por mais 1h 30 min com velocidade constante de 80 km/h. A velocidade média do carro durante toda a viagem foi de: *a) 80 km/h. b) 100 km/h. c) 120 km/h. d) 140 km/h. e) 150 km/h. (PUCRIO-2009.1) - ALTERNATIVA: A O ponteiro dos minutos de um relógio tem 1 cm. Supondo que o movimen mov imento to deste deste ponteiro ponteiro é contín contínuo uo e que = 3, a velocida velocidade de de translação na extremidade deste ponteiro é: *a) 0,1 cm/min. b) 0,2 cm/min. c) 0,3 cm/min. d) 0,4 cm/min. e) 0,5 cm/min. (PUCRIO-2009.1) - ALTERNATIVA: C O movimento de um objeto pode ser descrito pelo gráfico velocidade versus tempo, apresentado na figura abaixo.
Podemos afirmar que: a) a aceleração do objeto é 2,0 m/s 2, e a distância percorrida em 5,0 s é 10,0 m. b) a aceleração do objeto é 4,0 m/s 2, e a distância percorrida em 5,0 s é 20,0 m.
(PUCRIO-2009.1) - ALTERNATIVA: D Um objeto é lançado verticalmente para cima, de uma base, com velocidade v = 30 m/s. Indique a distância total percorrida pelo objeto desde sua saída da base até seu retorno, considerando a aceleração da gravidade g = 10 m/s 2 e desprezando a resistência do ar. a) 30 m. *d) 90 m. b) 55 m. e) 100 m. c) 70 m. (PUCRIO-2009.1) - ALTERNATIVA: C Um satélite geoestacionário encontra-se sempre posicionado sobre o mesmo ponto em relação à Terra. Sabendo-se que o raio da órbita deste satélite é de 36 × 10 3 km e consider considerando ando-se -se = 3, podemos dizer que sua velocidade é: a) 0,5 km/s. d) 3,5 km/s. b) 1,5 km/s. e) 4,5 km/s. *c) 2,5 km/s. (UFG/GO-2009.1) (UFG/GO-2009.1) - RESPOSTA: RESPOSTA: a) 4 meses b) 120o Sabe-se que a razão entre o período da Terra (TT) e o de Mercúrio (TM), em torno do Sol, é da ordem de 4. Considere que os planetas Terra e Mercúrio estão em órbitas circulares em torno do Sol, em um mesmo plano. Nessas condições, a) qual é, em meses, o tempo mínimo entre dois alinhamentos consecutivos dos dois planetas com o Sol? b) Qual é, em graus, o ângulo que a Terra terá percorrido nesse intervalo de tempo? (PUCPR-2009.1) - ALTERNATIVA: C O sistema rodoviário ainda é o principal transportador de cargas agrícolas. Na maioria das vezes, é a única alternativa para movimentação desse tipo de produto, devido à escassez de hidrovias e ferrovias que liguem grandes distâncias e, ao mesmo tempo, situem-se perto das fazendas, com ramais e estações de embarque e descarga. O transporte de cargas agrícolas através da navegação costeira (cabotagem) tem-se mostrado eficaz para a movimentação de grandes volumes. No entanto, a utilização da cabotagem como alternativa a outros tipos de transporte enfrenta problemas com a falta de navios e a inexistência de serviços com escalas regulares. Além disso, o Brasil possui 42 mil quilômetros de hidrovia, mas apenas 10 mil quilômetros são efetivamente utilizados. A ineficiência no transporte de produtos agrícolas também está presen presente te nasferrovias nasferrovias que,emboratenhamrecebi que,emboratenhamrecebido do inve investim stimento ento com a privatização, ainda estão longe de suprir a demanda do setor do agronegócio. Além da ampliação da malha, é urgente a modernização do maquinário. Com os trens e bitolas atuais, a velocidade média das composições não ultrapassa lentos 25 km/ h. Analise os itens a seguir e marque a alternativa CORRETA: a) Suponha que um caminhão faça um percurso de 420 km em 6 h então sua velocidade média é 2,5 vezes maior que a velocidade média dos trens. b) Se uma carga de soja percorrer, através de meio rodoviário, uma distância de 3000 km com velocidade média de 60 km/h pode-se dizer que o percurso será feito no máximo em dois dias. *c) Se a velocidade dos trens sofresse aumento de 5 km/h na sua velocidade média, um percurso de 600 km poderia ser realizado em 4 horas a menos. d) De acordo com estudos, a hidrovia é o transporte mais barato e menos utilizado no Brasil. Considerando Considerando que a velocidade das águas de um rio é de 15 km/
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(UNICENTRO/PR-2009.1) - ALTERNATIVA: A Um cachorro caminha, durante 200s, com velocidade constante de 3,0m/s no sentido de Sul para Norte, e, depois corre, durante 100s, com velocidade constante de 8,0m/s no sentido de Leste para Oeste. A velo velocida cidade de veto vetorial rial méd média ia do cachorro cachorro nest nestee intervalo intervalo de temp tempoo foi de *a) 3,3m/s b) 33m/s c) 5,5m/s d) 4,7m/s e) 11m/s (UFRJ-2009.1) - RESPOSTA: 32 × 106 voltas No dia 10 de setembro de 2008, foi inaugurado o mais potente acelerador de partículas já construído. O acelerador tem um anel, considerado nesta questão como circular, de 27 km de comprimento, no qual prótons são postos a girar em movimento uniforme. Fig 2 2009 CIN
(VUNESP/UNINOVE-2009.1) (VUNESP/UNINOVE-2009.1) - ALTERNA ALTERNATIVA: TIVA: D Ao se aproximar de uma curva numa estrada, um motorista, que imprimia a seu veículo a velocidade máxima, diminui uniformemente a velocidade até um valor tal que lhe permita percorrê-la com segurança em movimento uniforme. Ao final da curva, ele acelera uniformemente até atingir a velocidade máxima novamente, prosseguindo sua viagem. O gráfico da velocidade, em função do tempo, que melhor representa a seqüência de procedimentos realizados pelo motorista é o da alternativa:
a)
b)
c)
Supondo que um dos prótons se mova em uma circunferência de 27 km de com compri primen mento, to, comvelocida comvelocidade de de mód módulo ulo v = 240 240.000 .000km km// s, calcule o número de voltas que esse próton dá no anel em uma hora. (VUNESP/UNINOVE-2009.1) - ALTERNATIVA: A Atletas participam de um treinamento para uma maratona correndo por alamedas planas e retilíneas de uma cidade, que formam quarteirões retangulares. Um determinado atleta percorre 5 km da primeira alameda no sentido leste, em 30 min. A seguir, converge à esquerda e corre mais 4 km da segunda alameda no sentido norte, em 20 min. Por fim, converge novamente à esquerda e corre mais 3 km da terceira alameda no sentido oeste, em 10 min. O módulo de sua velocidade vetorial média vale, aproximadamente, aproximadamente, *a) 4,5 km/h. b) 5,1 km/h. c) 12 km/h. d) 8,5 m/min. e) 20,0 m/min. (VUNESP/UNINOVE-2009.1) (VUNESP/UNINOVE-2009.1) - ALTER A LTERNAT NATIVA: IVA: C Um garoto, deslizando em seu “skate”, descreve um movimento retilíneo uniformemente variado cujo gráfico horário da posição, em função do tempo, está representado na figura. A correspondente função horária é dada por a) S = 4 – 16.t – 4.t 2. b) S = 4 + 16.t + 8.t 2. *c) S = 20 – 16.t + 4.t 2. d) S = 20 + 16.t – 4.t 2. 2
*d)
e)
(VUNESP/UNIVONE-2009.1) (VUNESP/UNIVONE-2009.1) - ALTERNA ALTERNATIVA: TIVA: C As rodas de um automóvel têm diâmetro de 60 cm. Quando o veículo transita a 36 km/h e suas rodas não derrapam sobre o piso, a freqüência com que elas giram é, em Hz, de, aproximadamente, a) 16,7. b) 10,6. *c) 5,3. d) 2,7. e) 1,4. (VUNESP/UNINOVE-2009.1) - ALTERNATIVA: A Num teste de balística, um projétil foi lançado do solo sob um ângulo ângu lo (sen = 0,6 e cos = 0,8) retornan retornando do ao solo em 6,0 s. Considerando desprezível a resistência do ar e a aceleração da
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(VUNESP/UNICID-2009.1) - ALTERNATIVA: A Dois jogadores de futebol A e B seguem paralelamente com a mesm mesmaa velo veloci cida dade de cons consta tant ntee em rela relaçã çãoo ao camp campoo ( ), em que que a linha reta reta entre entre os jogado jogadores res forma forma o ângulo ângulo com o sentido de movimento. Em dado instante, o jogador A passa a bola para o jogador B, lançada horizontalmente e sem tocar o gramado.
Desprezando os efeitos do ar, é correto afirmar que, para a bola chegar até o jogador B, o ângulo de lançamento da bola, em relação ao sentido de movimento do jogador A, depende apenas *a) do valor valor de . b) do módulo da velocidade da bola. c) do módulo da velocidade dos jogadores. d) do valor valor de de e do mó módulo dulo da da velocida velocidade de da bola. bola. e) do módulo da velocidade da bola e do módulo da velocidade dos jogadores. (VUNESP/UNICID-2009.1) (VUNESP/UNICID-2009.1) - ALTERNA ALTERNATIVA: B Na tentativa de reproduzir uma cena em movimento, com um projetor de slides, um professor de Física uniu o porta-slides do projetor (raio 10 cm e capacidade para 16 slides) com a roldana de um motor elétrico (raio 1cm), por meio de uma correia. Supondo que a correia não derrape, para projetar em 1 segundo os 16 slides, é necessário que o motor tenha a rotação, em r.p.m., de a) 500. *b) 600. c) 700. d) 800. e) 900. (UFPR-2009.1) - ALTERNATIVA: A A figura abaixo mostra um modelo de uma catapulta no instante em que o seu braço trava e o objeto que ele carrega e arremessado, isto é, esse objeto se solta da catapulta (a figura é meramente ilustrativa e não esta desenhada em escala). No instante do lançamento, o objeto está a uma altura de 1,0 m acima do solo e sua velocidade inicial V 0 form formaa um um ângu ângulo lo de 45O em relação a horizontal. Suponha que a resistência do ar e os efeitos do vento sejam desprezíveis. Considere a aceleração da gravidade como sendo de 10 m/s 2. No lancamento, o objeto foi arremessado a uma distância de 19 m, medidos sobre o solo a partir do ponto em que foi solto. Assinale a alternativa que contém a estimativa correta para o módulo da velocidade inicial do objeto.
(UFF/RJ-2009.1) - ALTERNATIVA: E Na prova de lançamento de martelo nas Olimpíadas, o atleta coloca o martelo a girar e o solta quando atinge a maior velocidade que ele lhe consegue imprimir. Para modelar este fenômeno, suponha que o martelo execute uma trajetória circular num plano horizont horizontal.A al.A figu figura ra abai abaixo xo represen representa ta esqu esquema ematica ticamen mente te esta esta tra jetória enquanto o atleta o acelera, e o ponto A é aquele no qual o martelo é solto.
Assinale a opção que representa corretamente a trajetória do martelo, vista de cima, após ser solto.
a)
d)
b)
*e)
c)
(FUVEST-2009.1) - ALTERNATIVA: D Marta e Pedro combinaram encontrar-se em um certo ponto de uma auto-estrada plana, para seguirem viagem juntos. Marta, ao passar pelo marco zero da estrada, constatou que, mantendo uma velocidade média de 80 km/h, chegaria na hora certa ao ponto de encontro combinado. No entanto, quando ela já estava no marco do quilômetro 10, ficou sabendo que Pedro tinha se atrasado e, só então, estava passando pelo marco zero, pretendendo continuar sua viagem a uma velocidade média de 100 km/ h. Mantendo essas velocidades, seria previsível que os dois amigos se encontrassem próximos a um marco da estrada com indicação de
Fig 8 2009 CIN a)
b)
c)
*d)
e)
(UFPB-2009.1) - ALTERNATIVA: A Na revista Superinteressante, foi publicado um artigo afirmando que um fio de cabelo de uma pessoa cresce a uma taxa de 0,06 cm ao dia.
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(UFPB-2009.1) - ALTERNATIVA: C Dois homens, com auxílio de duas cordas, puxam um bloco sobre uma superfície horizontal lisa e sem atrito, conforme representação ao lado.
(UFRJ-2009.1) - RESPOSTA NO FINAL Um móvel parte do repouso e descreve uma trajetória retilínea durant durantee um interv intervalode alode tem tempo po de 50s 50s,, com com a acele aceleraç ração ão indica indicada da no gráfico a seguir.
a) Faça um gráfico da velocidade do móvel no intervalo de 0 até 50 s. b) Calcule a distância percorrida pelo móvel nesse intervalo. Considere que os módulos e direções das forças exercidas pelos homens são dados por: F1 = 5N e F2 = 10N cos cos = 0,8 0,8 e cos cos = 0,6 0,6 Nessa situação, é correto afirmar que a equação cartesiana da força resultante no bloco, em newtons, é: a) -5i + 10 j d) -10i - 5 j b) 10i + 10 j e) 5 i + 10 j *c) 10i - 5 j (UFPB-2009.1) - RESPOSTA: afirmativas corretas: I, II e IV Um jogador de tênis de mesa arremessa uma bola horizontalmente, com velocidade v0, de uma mesa com altura h. A uma distância R dessa mesa existe uma chapa metálica fina e rígida com altura h/2, conforme representado abaixo:
Nesse contexto, desprezando-se as perdas de energia da bola por atrito com o ar, ou devido a possível impacto com a chapa, identifique as afirmativas corretas: I. O menor valor que v 0 pode ter, para que a bola passe por cima da parede, é R.
RESPOSTA UFRJ-2009 a)
b) 1150 m (IMT/MAUÁ (IMT/MAUÁ-200 -2009.1) 9.1) - RESPOST RESPOSTA: A: a) 70,7 km b) 100 100 km km Dois exploradores querem encontrar o templo perdido em meio a uma floresta, usando o fragmento de um mapa que indica dois camin caminhosa hosa pa parti rtirr do cen centro tro de um umaa det determ ermina inada da pov povoaç oação. ão. Cada Cada um decide seguir uma rota. O explorador A segue a direção nordeste enquanto o B toma a direção leste, caminhando 50 km e, a partir dai, a direção norte até encontrar-se com o primeiro explorador. Determine o comprimento total do percurso feito: a) pelo explorador A; b) pelo explorador B´ Para facilitar seus cálculos, esboce um diagrama com as rotas seguidas pelos exploradores. exploradores. (UFTM-2009.1) - ALTERNATIVA: B Um corpo em movimento obedecia à função horária s = 20 + 2.t quando teve uma brusca mudança em seu tipo de movimento. Se o movimento fosse estudado a partir desse ponto de mudança, sua função horária seria dada por s = 32 + 2.t + 3.t 2. Admitindo que o corpo não tenha mudado a direção de seu mo-
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(CEFETMG-2009.1) (CEFETMG-2009.1) - ALTERNATIVA ALTERNATIVA OFICIAL: D Michael Phelps, o melhor nadador de todos os tempos, conquistou o maior número de medalhas de ouro na história dos Jogos Olímpicos, em uma só edição. Em agosto de 2008, ele quebrou o recorde mundial nos 200 m, em nado borboleta, com um tempo de 1 minuto e 52 segundos. Nesse contexto, é correto afirmar que a a) força de empuxo atuando no nadador é nula. b) velocidade média do nadador foi cerca de 7,82 m/s. c) força resultante atuando no nadador durante a prova foi nula. *d) velocidade média do nadador foi aproximadamente aproximadamente 1,78 m/s. e) aceleração do nadador durante a prova manteve-se constante. OBS.: Se a piscina não tiver um comprimento de 200 m, o nadador precisou ir e voltar, portanto, sua velocidade média é zero. (CEFETMG-2009.1) - ALTERNATIVA: D Recentemente, o maior acelerador de partículas do mundo, o LHC (Grande (Grande Colisor Colisor de Hád Hádrons rons)) entrou entrou em funcionam funcionamento. ento. Seu túnel possui uma circunferência de raio R = 4,3 km e está localizado na fronteira da França com a Suíça, como representado na figura. Os prótons acelerados poderão atingir uma velocidade de, aproximadamente, 99,9% da velocidade da luz (Adote c = 3 × 10 8 m/s m/s e = 3,14 3,14). ).
(UTFPR-2009.1) - ALTERNATIVA: C Nos problemas que envolvem o movimento de um corpo na atmosfera terrestre, a resolução simplificada despreza os efeitos do atrito, levando a resultados que, em certos casos, podem ser muito diferentes dos realmente observados. Suponha um caso teórico em que um fuzil é disparado junto à superfície terrestre, apontando verticalmente para cima, de forma que o projétil suba e desça sobre a mesma reta, atingindo a altura de +8.000 m. Qual das linhas indicadas no gráfico melhor representa o comportamento da sua aceleração durante o movimento?
a)
b)
Considerando as leis da física clássica, afirma-se: I - A aceleração das partículas é nula. II - A velocidade angular é cerca de 69,7 × 10 3 rad/s. III - Os prótons são partículas que não possuem carga. IV - Os prótons movem-se com freqüência de, aproximadamente, 11,1 kHz. São corretas apenas as afirmativas a) I e II. b) I e IV. c) II e III. *d) II e IV. e) III e IV. (UTFPR-2009.1) - ALTERNATIVA: B
*c)
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(UFG/GO-2009.1) (UFG/GO-2009.1) - RESPOSTA: a) 10 m/s b) 7,11 m O Comitê Olímpico se preocupa com alguns fatores aparentemente “irrelevantes” na realização das provas, como a velocidade do vento, o tempo chuvoso, a altitude, etc., os quais podem influenciar os resultados e recordes mundiais. Por exemplo, na prova de salto em distância, a atleta brasileira Maurren Maggi ganhou a medalha de ouro em Pequim com a marca de 7,04 m, enquanto a medalha de prata foi obtida com a marca de 7,03 m. Tipicamente, o ângulo de projeção para este tipo de prova varia en entre tre 15o e 25o. Consi Consider derand andoo queem Pequimo Pequimo salto salto de Mau Maurre rrenn Maggi foi realizado com um ângulo de 22,5 o. a) Qual o módulo da velocidade da atleta no momento do salto? b) Se este salto fosse realizado em outro local, cuja aceleração da gravidade fosse 1% menor, qual seria a marca atingida por Maurren Maggi? Dados: Cons Consid ider eree 1,40 1,4088 e acel aceler eraç ação ão da gravidade igual a 10 m/s2.
(FGVSP-2009.1) - ALTERNATIVA: Uma grande grande mani manivela vela,, quat quatro ro engrenag engrenagens ens pequ pequenas enas de 10 dentes e outra de 24 dentes, tudo associado a três cilindros de 8 cm de diâmetro, constituem este pequeno moedor manual de cana. Fig 12 2009 CIN
Fig 13 2009 CIN (FGVSP-2009.1) - ALTERNATIVA: E Comandada com velocidade constante de 0,4 m/s, a procissão iniciada no ponto indicado da praça Santa Madalena segue com o Santo sobre o andor por toda a extensão da Av. Vanderli Diagramatelli. Fig 11 2009 CIN
Ao produzir caldo de cana, uma pessoa gira a manivela fazendoa completar uma volta a cada meio minuto. Supondo que a vara de cana colocada entre os cilindros seja esmagada sem escorregamento, a velocidade escalar com que a maquina puxa a cana para seu interior, em cm/s, e, aproximadamente, Dado: Dado: Se nece necessar ssario io use = 3 a) 0,20. d) 1,25. *b) 0,35. e) 1,50. c) 0,70. (UNEMAT/MT-2009.1) - ALTERNATIVA: C Um automóvel está em movimento uniformemente variado com aceleração escalar igual a –5 m/s 2, e sua velocidade escalar varia no tempo, de acordo com a tabela abaixo: T(s) 0 V(m/s) 10
1 5
2 0
3 –5
4 –10
5 –15
6 –20
Analise as afirmativas abaixo. I. A velocidade escalar inicial do automóvel é 10 m/s. II. No instante de 2s, o automóvel pára e começa a mudar o sentido do seu movimento. III. No intervalo de tempo entre 0 a 2s, o movimento do automóvel é retardado e progressivo. IV. No intervalo de tempo entre 2 e 6s, o movimento do automóvel é acelerado e retrógrado. Assinale a alternativa correta. a) Somente I e III são verdadeiras.
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(UEM/PR-2009.1) - RESPOSTA: SOMA = 20 (04+16) Um corpo de massa 10,0 kg inicia seu movimento a partir do repouso e, após 10,0 s, sua velocidade é 20,0 m/s. Assinale a(s) alternativa(s) correta(s). 01) Se o corpo realiza um movimento retilíneo uniforme, sua velocidade é constante e igual a 20,0 m/s. 02) Se o corpo realiza um movimento retilíneo uniformemente variado, sua aceleração é constante e igual a 1,0 m/s 2. 04) Se o corpo realiza um movimento retilíneo uniformemente variado até o instante t = 10,0 s, ele percorreu 100,0 m. 08) Se o corpo realiza um movimento retilíneo uniformemente variado até o instante t = 5,0 s, sua velocidade atinge 15,0 m/s. 16) Os gráficos abaixo descrevem, qualitativamente, qualitativamente, o movimento do corpo, quando esse realiza um movimento uniformemente variado.
(UFABC-2009.1) - RESPOSTA: d = 0,45 m Na natureza, muitos animais conseguem guiar-se e até mesmo caçar com eficiência, devido à grande sensibilidade que apresentam para a detecção de ondas, tanto eletromagnéticas quanto mecânicas. O escorpião é um desses animais. O movimento de um besouro próximo a ele gera tanto pulsos mecânicos longitudinais quanto transversais na superfície da areia. Com suas oito patas espalhadas em forma de círculo, o escorpião intercepta primeiro os longitudinais, que são mais rápidos, e depois os transversais.
A pata que primeiro detectar detectar os pulsos determina a direção onde está o besouro. A seguir, seguir, o escorpião avalia o intervalo de tempo entre as duas recepções, e determina a distância d entre ele e o besouro. Considere que os pulsos longitudinais se propaguem com velocidade de 150 m/s, e os transversais com velocidade velocidade de 50 m/s. Se o intervalo de tempo entre o recebimento dos primeiros pulsos longitudinais e os primeiros transversais for de 0,006 s, determine a distância d entre o escorpião e o besouro. (UEM/PR-2009.1) (UEM/PR-2009.1) - RESPOSTA: RESPOSTA: SOMA = 06 (02+04) Veja OBS. no final Um projétil é lançado horizontalmente do alto de um rochedo de 490,0 m de altura, com uma velocidade inicial de 30,0 m/s. Considere g = 9,8 m/s 2 e assinale o que for correto. 01) O projétil alcança o solo a uma distância horizontal de 580,0 m de seu ponto de lançamento. 02) No eixo x, o objeto descreve um movimento retilíneo uniforme, com a = 0,0 m/s 2, e, no eixo y, um movimento retilíneo uniformemente variado, com uma aceleração de 9,8 m/s 2, na direção vertical e no sentido de cima para baixo. 04) Em t = 5,0 s, o objeto encontra-se nas coordenadas coordenadas x = 150,0 m e y = 367,5 m.
(FATECSP-2009.1) - ALTERNATIVA: D César Cielo se tornou o maior nadador brasileiro na história dos Jogos Olímpicos ao conquistar a medalha de ouro na prova dos 50 m livres. Primeiro ouro da natação brasileira em Jogos Olímpicos, Cielo quebrou o recorde olímpico com o tempo de 21s30’’, ficando a apenas dois centésimos de segundo do recorde mundialconquista dialconquistado do pelo pelo austral australianoEamon ianoEamon Sulliva Sullivann num tem tempo po igua iguall a a) 19s28’’. b) 19s30’’. c) 21s10’’. *d) 21s28’’. e) 21s32’’.
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(UFPR-2009.1) (UFPR-2009.1) -RESPOSTA: a) 12×104 volta voltass b) 4 × 103 rad/s Em 10 de setembro de 2008, a Organização Européia para Pesquisa Nuclear (sigla internacional CERN) ligou pela primeira vez o acelerador de partículas Grande Colisor de Hádrons (LHC, em inglês), máquina com a qual se espera descobrir partículas elementares que comprovarão comprovarão ou não o modelo atual das partículas nucleares. nucleares. O colisor foi construído em um gigantesco túnel circular de 27 km de comprimento, situado sob a fronteira entre a Suíça e a França e a uma profundidade de 50 a 120 m. Prótons são injetados no tubo circular do LHC e, após algum tempo em movimento, movimento, atingem velocidades próximas à da luz no vácuo (c). Supondo que após algumas voltas os prótons atinjam a velocidade constante de 0,18c, com base nas informações acima e desprezando os efeitos relativísticos, determine: (Adote c = 3×10 5 km/s) a) Quantas voltas os prótons dariam ao longo do túnel no intervalo de um minuto. b) A velocidade angular desses prótons.
(UFPR-20 (UFPR-2009.1) 09.1) - RESPOST RESPOSTA: A: t = Um dos estudos feitos por Galileu trata do movimento de corpos em queda livre. Considere um objeto que cai em queda livre de uma altura inicial de n metros, a partir do repouso, num local onde a aceleração da gravidade é g. Deduz Deduzaa um umaa exp expres ressãoliter sãoliteral al pa para ra o tem tempo po ne neces cessár sário io para para esse esse objeto percorrer o último metro do seu trajeto. Observe que a expressão deve ser dada em termos de n e g somente. (UFMG-2009.1) - ALTERNATIVA: A Numa corrida, Rubens Barrichelo segue atrás de Felipe Massa, em um trecho da pista reto e plano. Inicialmente, os dois carros movem-se com velocidade constante, de mesmos módulo, direção e sentido. No instante t1, Felipe aumenta a velocidade de seu carro com aceleração constante; e, no instante t 2, Barrichelo também aumenta a velocidade do seu carro com a mesma aceleração. Consider Considerando ando essas essas informaçõ informações, es, assinale assinale a alternativ alternativaa cujo gráfico melhor descreve o módulo da velocidade relativa entre os dois veículos, em função do tempo. *a)
b)
(UFU-2009.1) - RESPOSTA: 1V; 2F; 3V; 4V Duas pedras são abandonadas do repouso, ambas de uma altura de 20 m, porém uma na Terra Terra e outra em Marte. Após 1 s, elas são observadas nas posições indicadas abaixo.
Considerando Considerando gterra = 10 m/s2 e gmarte = g terra 3, marque para as alternativas abaixo (V) Verdadeira ou (F) Falsa. 1 ( ) O planeta A corresponde à Terra e o planeta B corresponde a Marte. 2 ( ) O módulo da velocidade da partícula em Marte, 3 s após ser abandonada, é 30 m/s. 3 ( ) A pedra que é abandonada na Terra Terra percorreu uma uma distância de 20 m, após 2 s de queda. 4 ( ) Para que a pedra abandonada em Marte adquira uma mesma velocidade da abandonada na Terra, a pedra em Marte deve percorrer uma distância três vezes maior que a distância percorrida pela pedra na Terra.
(UFU-2009.1) - RESPOSTA: 1V; 2F; 3F; 4V Em 10 de setembro de 2008, foi inaugurado na Europa o maior acelerador de partículas (LHC), que é capaz de acelerar prótons, em um anel de raio 4,5 km, até uma velocidade próxima da luz. Assuma que o movimento do próton seja descrito pela mecânica newtoniana e que possua a velocidade da luz (3 × 10 8 m/s). Considerand siderandoo = 3, marque marque para as as alternativa alternativass abaixo abaixo (V) VerdaVerdadeira ou (F) Falsa. 1 ( ) O próton gastará um tempo menor que 10 –4 s para dar uma volta completa no anel. 2 ( ) A freqüência de rotação do próton no interior do anel será 105 rotações por segundo. 3 ( ) A velocidade angular do próton será 10 5 rad/s. 4 ( ) O período de rotação do próton será 9 × 10 –5 s.
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(UERJ-2009.1) - RESPOSTA: vM = 10,0 m/s A velocidade de um corpo que se desloca ao longo de uma reta, em função do tempo, é representada pelo seguinte gráfico:
(UFJF/MG-2009.1) - ALTERNATIVA: B O gráfico abaixo representa a variação da posição x versus o tempo t de dois automóveis A e B, registrados por sensores que transferiram os dados para um computado computador. r. Interpretando o gráfico, pode-se afirmar com segurança que:
Calcule a velocidade média desse corpo no intervalo entre 0 e 30 segundos. (UFSCar-2009.1) - ALTERNATIVA: B Um navio é responsável por verificar a energia mareomotriz de determinada região da costa. Na coleta de informações, o timoneiro traça uma rota rumo ao continente. Algum tempo depois, na cabine do capitão, um alarme alerta para as leituras feitas automaticamente pelo sonar, que mostram a rápida diminuição da profundidade do leito oceânico. PROFUNDIDADE (m) 17 INSTANTE (s) 0
15 15
13 30
11 45
Supondo que a inclinação do leito oceânico seja constante e sabendo que a quilha da embarcação está 3 m abaixo da linha d’água, se nenhuma atitude for imediatamente tomada, o encalhe irá ocorrer entre os instantes a) 1,0 minuto e 1,5 minutos. *b) 1,5 minutos e 2,0 minutos. c) 2,0 minutos e 2,5 minutos. d) 2,5 minutos e 3,0 minutos.
a) no instante t1, os dois automóveis têm a mesma velocidade. *b) no instante t2, o automóvel B tem velocidade maior que o automóvel A. c) o automóvel A tem velocidade maior que o automóvel B em todo o intervalo entre os instantes t 1 e t 2. d) no instante t 2, o automóvel A ultrapassa o automóvel B. e) no instante t1, o automóvel A está um pouco à frente do automóvel B.
(VUNESP/FAMECA-2009.1) - ALTERNATIVA: B Um veículo arranca do repouso e percorre uma distância d em movimento retilíneo uniformemente variado e horizontal. Se partir do repouso e percorrer a mesma distância d, descrevendo um movimento uniformemente variado com aceleração duas vezes maior, o tempo gasto para percorrê-la será reduzido em, aproximadamente, aproximadamente,
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(UNESP-2009.1) - ALTERNATIVA: B Admita que em um trator semelhante ao da foto a relação entre o raio dos pneus de trás (r T) e o raio dos pneus da frente (r F) é r T = 1,5·r F. Fig 23 2009 CIN
(www.greenhorse.com.br/site/pops/204.html)
Chamando de vT e vF os módulos das velocidades de pontos desses pneus em contato com o solo e de f T e f F as suas respectivas freqüências de rotação, pode-se afirmar que, quando esse trator se movimenta, sem derrapar, são válidas as relações: a) vT = vF e f T = f F. *b) vT = vF e 1,5·f T = f F. c) vT = vF e f T = 1,5·f F. d) vT = 1,5·vF e f T = f F. e) 1,5·vT = vF e f T = f F. (UNESP-2009.1) - RESPOSTA: hMÍN 18 m e hMÁX 22 m O buriti é uma palmeira alta, comum no Brasil central e no sul da planície amazônica. amazônica. Para avaliar a altura de uma dessas palmeiras, um pesquisador provoca provoca a queda de alguns de seus frutos e cronometra o tempo em que ela ocorre, obtendo valores compreendidos entre 1,9 s e 2,1 s. Desprezando a resistência do ar exercida sobre os frutos em queda, determine as alturas máxima
(ITA-2009.1) - ALTERNATIVA: C Considere hipoteticamente duas bolas lançadas de um mesmo lugar ao mesmo tempo: a bola 1, com velocidade para cima de 30 m/s, e a bola 2, com velocidade de 50 m/s formando um ângulo de 30° com a horizontal. Con siderando g = 10 m/s 2, assinale a distância entre as bolas no instante em que a primeira alcança sua máxima altura. a) d) b) e) *c) (ITA-2009) - ALTERNATIVA: B (RESOLUÇÃO NO FINAL) Dentro de um elevador em queda livre num campo gravitacional g, uma bola é jogada para baixo com velocidade v de uma altura h. Assinale o tempo previsto para a bola atingir o piso do elevador. a) t = v/g d) t = ( – v)/g *b) t = h/v e) t = ( – v)/g c) t = (RESOLUÇÃO: ITA-2009.1 ITA-2009.1 Supondo-se que “para baixo” signifique verticalmente para baixo e levando-se em conta que para o elevador em queda livre a gravidade aparente em seu interior é nula, o movimento da bola em relação ao elevador é retilíneo e uniforme. (UNIFESP-2009.1) - ALTERNATIVA: A Um avião a jato, para transporte de passageiros, passageiros, precisa atingir a velocidade de 252 km/h para decolar em uma pista plana e reta. Para uma decolagem segura, o avião, partindo do repouso, deve percorrer uma distância máxima de 1 960 m até atingir aquela velocidade. Para tanto, os propulsores devem imprimir ao avião uma aceleração mínima e constante de *a) 1,25 m/s2.
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(FEI/SP-2009.1) - ALTERNAT ALTERNATIVA: IVA: D Uma senhora deixa um vaso cair acidentalmente da janela de seu apartamento. O vaso atinge o solo 3 s após iniciar o movimento. Adote g = 10 m/s2. Qual é a altura da janela em relação ao solo? a) 20 m *d) 45 m b) 35 m e) 50 m c) 40 m (FEI/SP-2009.1) - ALTERNA ALTERNATIVA: TIVA: E Um automóvel inicia uma curva com raio de 75 m com velocidade v = 5 m/s, aumentando a sua velocidade a uma taxa constante. Após 2,5 s sua velocidade é 15 m/s. Qual é a aceleração do automóvel neste momento? a) 2,0 m/s2 d) 4,0 m/s2 b) 2,5 m/s2 *e) 5,0 m/s2 c) 3,0 m/s 2 (FEI/SP-2009.1) - ALTERNATIVA: ALTERNATIVA: C (RESOLUÇÃO NO FINAL) Um arqueiro deverá acender uma pira olímpica com uma flecha, cuja ponta é incandescente. O arqueiro deverá disparar a flecha com velocidade v 0 formando formando ângu ângulo lo com a horizo horizontal ntal,, conforconforme esquema abaixo. Qual deverá ser o valor mínimo de v 0 min para que ele consiga acender a pira? Desprezar a resistência do ar. Dados: d = 80 m D=8m h = 55 m sen sen = 0,91 0,9100 cos cos = 0,41 0,4155 g = 10 m/s2 a) v 0 min = 40,4 m/s b) v 0 min = 35,2 m/s *c) v0 min = 39,3 m/s d) v 0 min = 41,2 m/s e) v 0 min = 38,9 m/s
(UFU/MG-2009.1) - ALTERNATIVA: A As figuras abaixo representam dois pontos A e B sobre a superfície terrestre, em um mesmo meridiano. meridiano. O ponto A está no equador e o ponto B se encontra no hemisfério norte a uma latitude de 60º.
Sabendo Sabendo que que a Terra Terra gira gira com com velocida velocidade de angular angular e supondo supondo que a Terra é de forma esférica com raio R, a alternativa que apresenta a relação entre as velocidades lineares desses dois pontos A e B é *a) vA / v B = 2 b) vA / vB = 2 / 3 c) v A / v B = 1/ 2 d) vA / vB = (UDESC-2009.1) (UDESC-2009.1) - RESPOSTA: RESPOSTA: a) gráfico: parábola da eq. dada (fazer) (fazer) b) v = 0 c) dist. dist. = 34 m e deslo desloc. c. = 30 m O movimento de uma bola sobre uma trajetória retilínea é descrito de acordo com a seguinte equação: x = 5 + 16t - 2t 2, em que x é medido em metros e t em segundos. a) Faça o esboço do gráfico da posição em função do tempo. b) Calcule a velocidade da bola em t = 4,0 s. c) Calcule a distância percorrida pela bola e o seu deslocamento em t = 5,0 s.
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(UFV/MG-2009.1) - ALTERNATIVA: A Uma bo bola la é lançada lançada horizon horizontalm talmente ente com com velocida velocidade de inicial inicial . Ao percorrer horizontalmente 30 m ela cai verticalmente 20 m, conforme mostrado no gráfico ao lado. Considere a aceleração da gravidade igual a 10 m/s2 e despreze a resistência do ar. É CORRETO afirmar que o módulo da velocidade de lançamento vo é: *a) 15 m/s b) 30 m/s c) 7,5 m/s d) 60 m/s
(UNIOESTE/PR-2009.1) (UNIOESTE/PR-2009.1) - ALTERNA ALTERNATIVA: TIVA: D Na figura abaixo estão representados os gráficos das velocidades de dois móveis A e B, os quais partem de um mesmo ponto a partir do repouso, em instantes diferentes. Ambos se movem no mesmo sentido em uma trajetória retilínea.
(UFV/MG-2009.1) - ALTERNATIVA: A Uma pedra está fixa na periferia de uma roda de raio R= 2 m e gira gira com com veloc velocida idade de linea linearr de módu módulo lo cons consta tanteV.Se nteV.Se A é o módu módulo lo da aceleração da pedra, das opções abaixo, aquela que apresenta valores para V e A, em acordo com a cinemática do movimento circular uniforme, é: *a) V = 2 m/s e A = 2 m /s 2. b) V = 1 m/s e A = 4 m /s 2. c) V = 4 m/s e A = 6 m /s 2. d) V = 6 m/s e A = 0 m /s 2.
Assinale a alternativa correta. a) Os móveis possuem a mesma aceleração. b) Os móveis se encontram em t = 4s. c) Desde a partida até t = 4s o móvel A percorre 32 m. *d) No instante em que os móveis se encontram a velocidade de B é 24 m/s. e) Ambos os móveis desenvolvem movimento retilíneo e uniforme.
(UFV/MG-2009.1) - ALTERNATIVA: A Um bloco desliza em um plano inclinado sem atrito com velocidade inicial de módulo v 0, como mostrado na figura ao lado. Se a aceleração da gravidade é g, o módulo da velocidade (v) do bloco, após este percorrer uma distância d ao longo do plano inclinado, é:
(UNIFOR/CE-2009.1) - ALTERNATIVA: C Do alto de uma torre, um corpo cai livremente a partir do repouso. Se o tempo de queda é de 4,0 s, a razão entre as distâncias percorridas na segunda metade do tempo de queda e na primeira metade desse tempo é a) 1 b) 2 *c) 3 d) 4 e) 5
*a) (UNIFOR/CE-2009.1) - ALTERNATIVA: E
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(UFPE-2009.1) - ALTERNATIVA: A Uma partícula executa um movimento uniformemente uniformemente variado ao longo de uma linha reta. A partir da representação representação gráfica da posição x da partícula, em função do tempo, mostrada abaixo, identifique o gráfico que descreveria corretamente a velocidade v da partícula, em função do tempo.
*a)
c)
e)
b)
(UNIFAL/MG-2009.1) (UNIFAL/MG-2009.1) - RESPOSTA RESPOSTA NO FINAL Considere que um projétil é lançado verticalmente para cima por um lança-projétil (uma espécie de mini-canhão) colocado sobre um trenzinho de brinquedo, como mostra a figura a seguir.
Considerando o exposto, execute o que se pede. a) Desenhe a trajetória do projétil considerando que o trenzinho realiz realizaa um Mov Movim iment entoo Retilí Retilíneoe neoe Unifor Uniforme me,, a pa parti rtirr do refere referenc ncial ial de quem está em repouso sobre o trenzinho. b) Desenhe a trajetória do projétil considerando que o trenzinho realiza um Movimento Retilíneo e Uniforme, a partir de um observador externo em repouso em relação ao trem. RESPOSTA: UNIFAL-2009 a trajetória a) b) é parabólica
d)
b)
(CEFETSP-2009.1) - ALTERNATIVA: A O crescente aumento do número de veículos automotores e o conseqüente aumento de engarrafamentos têm levado a Prefeitura do Município de São Paulo a um monitoramento intensivo das condições de circulação nas vias da cidade. Em uma sondagem, um funcionário da companhia de trânsito deslocou seu veículo, constatando que – permaneceu parado, durante 30 minutos;
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(VUNESP/FMJ-2009.1) (VUNESP/FMJ-2009.1) - AL A LTERNATIVA: TERNATIVA: C Numa viagem, um motorista passa pela placa mostrada na Figura 1, quando sua velocidade é 30 m/s. Aciona os freios nesse instante e, mantendo uma desaceleração constante até chegar à lombada, passa pela placa mostrada na Figura 2 quando sua velocidade é 20 m/s.
Pode-se afirmar que, para chegar da primeira placa à lombada, ele demorou um intervalo de tempo, em segundos, de a) 10. b) 15. *c) 20. d) 25. e) 30. (FUVEST-2009.1) - RESPOSTA: a) t1 = 0,50 0,50 s b) vH = 6,0 m/s c) t 2 0,67 s O salto que conferiu a medalha de ouro a uma atleta brasileira,
(UEPG/PR-2009.1) - RESPOSTA: SOMA = 19 (01+02+16) Com base no gráfico abaixo, que representa os movimentos de duas partículas A e B, assinale o que for correto.
01) As partículas partem de pontos diferentes no mesmo instante. 02) As partículas descrevem movimentos uniformes com velocidades iguais. 04) No instante t = 5 s, as posições das partículas A e B serão dadas respectivamente por: S A = 5.v e SB = 20+ 5.v 08) As partículas partem do mesmo ponto em instantes diferentes. 16) Durante o movimento, a partícula B mantém-se distante 20 m da partícula A.
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(UFC/CE-2009.1) - ALTERNATIVA: D Um relógio analógico possui um ponteiroA, ponteiro A, que marca as horas, e um ponteiro B, que marca os minutos. Assinale a alternativa que contém o tempo em que os ponteiros A e B se encontram pela primeira vez após as três horas. a) 15mi 15minn 16 81 s. 90 b) 15mi 15minn 21 81 s. 99 c) 16mi 16minn 16 81 s. 99 *d) *d) 16mi 16minn 21 81 s. 99 81 e) 16mi 16minn 21 s. 90 (UNICAMP-2009.1) (UNICAMP-2009.1) - RESPOSTA: RESPOSTA: a) a) 32 km/h km/h b) 4×102 s Os avanços tecnológicos nos meios de transporte reduziram de forma significativa o tempo de viagem ao redor do mundo. Em 2008 foram comemorados os 100 anos da chegada em Santos do navio Kasato Maru , que, partindo de Tóquio, trouxe ao Brasil os primeiros imigrantes japoneses. A viagem durou cerca de 50 dias.
(FURG/RS-2009.1) - ALTERNATIVA: C Numa tempestade, ouve-se o trovão 7,0 segundos após a visualização visualização do relâmpago. Sabendo que a velocidade da luz é de 3,0x108 m/s e que a velocidade do som é de 3,4x102 m/s, é possível afirmar que a distância entre o local onde ocorreu o relâmpago e onde ele foi visto é de a) 6,2x106 metros. b) 4,8x101 metros. *c) 2,4x103 metros. d) 2,1x109 metros. e) 4,3x106 metros. (VUNESP/UNICISAL-2009.1) - ALTERNATIVA:A A distância aproximada entre Maceió e Recife é melhor expressa, em notação científica, por *a) 3,0 × 108 mm. b) 3,0 × 107 dm. c) 0,3 × 105 km. d) 3 000 000 m. e) 3,0 × 106 m.
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(VUNESP/UNICISAL-2009.1) (VUNESP/UNICISAL-2009.1) - ALTERNATIV ALTERNATIVA: A: D Um veículo trafega por uma estrada retilínea e, em determinado instante, seu motorista avista uma praça de pedágio. Ele passa, então, a desacelerar uniformemente até parar em frente à cabine de arrecadação, onde efetua o pagamento da tarifa para, em seguida, acelerar uniformemente no mesmo sentido de viagem. O gráfico da posição, em função do tempo, que melhor representa o procedimento relatado é o da alternativa
a)
b)
c)
(CEFETCE-2009.1) (CEFETCE-2009.1) - RESPOSTA: RESPOSTA: 113,4 113,4 segundos Um garoto, em pé, às margens de um lago de águas tranqüilas, joga uma pedra na água, para produzir ondas.
*d)
e)
Supondo-se que o lançamento é feito obliquamente com velocidade Vo = 10 m/s, a 1,4 metros da superfície da água, determine após quanto tempo, a partir do lançamento da pedra, a onda formada atingirá a margem no ponto de lançamento. Considere a profundidade do lago igual em todos os pontos e a velocidade das ondas na água igual a 10 cm/s. Despreze a resistência do ar. (CEFETPI-2009.1) - ALTERNATIVA: B
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(UFRGS-2009.1) (UFRGS-2009.1) - ALTERNA ALTERNATIVA: C (RESOLUÇÃO NO FINAL) A seqüência de pontos na figura abaixo marca as posições, em intervalos de 1 segundo, de um corredor de 100 m rasos, desde sua largada até a chegada. Fig 47 2009 CIN
(UFLA/MG-2009.1) - ALTERNATIVA: D Três corpos 1, 2 e 3 movem-se movem-se segundo um movimento retilíneo e suas respectivas acelerações a1, a2 e a3 são mostradas no gráfico abaixo.
Assinale Assinale o gráfico gráfico que melhor melhor represen representa ta a evol evoluçãoda uçãoda velo velocidd ciddee instantânia do corredor. corredor. Fig 48 2009 CIN
Analisando _ _ esse _ gráfico, pode-se afirmar que as acelerações médias a1, a2 e a3 dos três corpos entre os instantes t = 0 e t = 6 s, _ é: _ _ a) a3 > a2 > a1. _ _ _ b) a2 > a1 > a3. _ _ _ c) a1 > a3 > a2 . _ _ _ *d) a1 > a2 > a3. (UFLA/MG-2009.1) - ALTERNATIVA: B
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(UFLA/MG-2009.1) - ALTERNATIVA: A O motor de um portão eletrônico possui uma polia dentada, também chamada de pinhão, com raio de 10 cm, a qual é aclopada a uma cremalheira de comprimento 4 m, presa ao portão. Ao acionar o motor, a polia gira com freqüência de 30 rpm. Considerando a polia dentada no início da cremalheira, o tempo necessário para abrir ou fechar o portão totalmente é *a) *a) 40/ 40/ s. b) 30 s. c) 7,5 7,5 s´ d) 3,14 s.
(UFLA/MG-2009.1) - ALTERNATIVA: B Uma pista de corrida tem sua forma indicada na figura abaixo, na qual os trechos AB e CD são retas, e os trechos BC e DA são arcos de circunferência de raio R.
Fig 49 2009 CIN
(UFLA/MG-2009.1) - ALTERNATIVA: C Um disco gira com aceleração angular constante em torno de um eixo que passa pelo seu centro O (figura abaixo). A distância do centro do disco ao ponto A é representada por R, e a do ponto B é representada por 2 R. Considerando a velocidade tangencial v, velocida velo cidade de angu angular lar e aceleraç aceleração ão cent centrípe rípeta ta a relativa aos pontos A e B, pode-se afirmar que
Um veículo, fazendo um teste nessa pista no trecho AB, mantém o módulo de sua velocidade constante, nos trechos BC e CD, tem o módulo de sua velocidade aumentando e, finalmente, no trecho DA, tem o módulo de sua velocidade diminuindo. A figura da alternativa que representa CORRETAMENTE os vetores velocidade e aceleração em todos os trechos da pista é:
a)
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(UNICENTRO/PR-2009.1) - ALTERNATIVA: C A partir do repouso, um carro carro percorreu o trecho retilíneo de uma avenida, desenvolvendo a velocidade média de 45 km/h. Este gráfico representa o comportamento da velocidade (v), em função do tempo (t), para os primeiros 18 segundos da situação descrita. A partir dessas informações, é CORRETO afirmar que a velocidade desse carro, no instante t = 13 s, foi de a) 45 km/h. b) 52 km/h. *c) 54 km/h.
(UCS/RS-2009.1) - ALTERNATIVA: B Para repor a bola em jogo rapidamente, um goleiro dá um chute e a bola sai de seus pés com uma velocidade inicial de 40 m/s, cuja direção faz um ângulo de 30° com o chão. Ela percorre, horizontalmente, 100 m do campo e entra no gol adversário. Quanto tempo ela levou para entrar no gol, desde que perdeu o contato com o pé do goleiro? (considere a aceleração da gravidade = 10 m/s 2, cos30° = 0,9 e sen30° = 0,5) a) 1,6 s *b) 2,8 s c) 3,2 s
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(UFAL/AL-2009.1) - ALTERNATIVA: E Um automóvel em movimento retilíneo tem sua velocidade, em m/s, em função do tempo, em segundos, dada pelo gráfico a seguir. Seu deslocamento, em metros, entre os instantes t = 2 s e t = 8 s, é igual a: a) 25 b) 18 c) 13 d) 12 *e) zero
(UEPG/PR-2009.1) - RESPOSTA: SOMA = 27 (01+02+08+16) Com base no gráfico abaixo, que mostra o movimento retilíneo descrito por uma partícula ao longo do eixo dos x, assinale o que for correto.
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(UNIMONTES/MG-2009.1) - ALTERNATIVA: B Um observador, observador, dentro de um ônibus estacionado, estacionado, nota que está chovendo e que as gotas de chuva caem verticalmente, com velocidade V 0, tal que V 0 = 6,0 m/s, deixando riscos na janela (veja a figura). Dentro de um ônibus que se move, em relação à terra, com velocidade V 1, sendo V 1 = 8,0 m/s, outro passageiro nota que as gotas de chuva, ao atingirem a janela, deixam riscos que formam formam ângulos ângulos com a vertica verticall (veja (veja a figura). figura). Determin Determinee o módulo da velocidade V das gotas de chuva para o passageiro do ônibus.
(UESPI/PI-2009.1) - ALTERNA ALTERNATIVA: TIVA: B Um corpo corpo movemove-se se numa numa trajetória trajetória circu circular lar de raio raio r = m, com uma velocidade de módulo constante, v = 4 m/s. Para tal situação, quanto tempo tal objeto leva para dar uma volta completa ao longo desta trajetória? a) (2/ 2) s *b) ( 2/2) s c) ( /2 /2)) s d) ( 2/4) s e) (2/ (2/ ) s
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(UFTM-2009.1) (UFTM-2009.1) - RESPOSTA: RESPOSTA: a) 2,88 m/s b) 1,80 m Para uma boa pescaria, além de um bom local e boas iscas, é fundamental, também, usar equipamentos adequados. Com a finalidade de facilitar o arremesso da isca e possibilitar maior força de tração depois da fisgada, muitos pescadores utilizam carretilhas, que consistem num carretel onde a linha de pesca é enrolada, e numa manivela que faz o carretel girar. Uma característica importante numa carretilha carretilha é a velocidade de giro que, em geral, vem impressa no equipamento com números representados, por exemplo, assim: 4:1, ou seja, com uma volta na manivela, o carretel gira quatro vezes.
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VESTIBULARES 2009.2 (UFPR-2009.2) - ALTERNATIVA: C Segundo Galileu Galilei, todos os movimentos descritos na cinemática são observados na natureza na forma de composição dos referidos movimentos. Nesse sentido quando um pequeno parapente sobrevoa Matinhos para leste com velocidade de 60 km/h em relação ao ar, ao mesmo tempo em que o vento sopra para o sul com velocidade de 80 km/h, é correto afirmar que a velocidade do parapente em relação ao solo e sua direção
(IFCE/CEFETCE-2009.2) (IFCE/CEFETCE-2009.2) - ALTERNA ALTERNATIVA: TIVA: D Uma partícula se move em uma trajetória semicircular de raio R, partindo do repouso no ponto A até atingir uma velocidade tangencial v = 2R/T no ponto B, como indica a figura. A partir de B, a partícula passa a frear com aceleração aceleração tangencial constante -a, até atingir o repouso repouso no ponto C. Sendo Sendo o ângulo AÔB=2 /3 radianos, o valor de a é a) 5R . 3T2
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(UNICENTRO/PR-2009.1) - ALTERNATIVA: A A figuramost figuramostra ra du duas as esfer esferas as quese des desloc locam am,, em senti sentido doss opo oposstos, sobre uma pista horizontal, plana, e sem atrito.
A esfera 1 tem massa m e velocidade de módulo módulo 3V, e a esfera 2 tem massa 2m e velocidade de módulo V. A colisão que ocorre entre as esferas é perfeitamente elástica. Considere | I 1 | o módulo do impulso sofrido pela esfera 1 na colisão, e | I2 | o módulo do impulso sofrido pela esfera 2 na colisão. É CORRETO afirmar que *a) | I1 | = | I2 | b) | I1 | > | I2 | c) | I1 | < | I2 | d) a quantidade de movimento do sistema vale 5mV. e) a quantidade de movimento do sistema é nula antes e depois da colisão. (PUCPR-2009.1) - ALTERNATIVA: E A produção de alimentos é uma atividade essencial para a existência humana que demanda efetivamente muita água. A chuva é a sua principal fonte. Para uma planta atingir o potencial produtivo, ela requer um volume de água para o respectivo metabolismo. Normalmente, quando a chuva cai sobre uma plantação, em geral as gotas não causam danos às plantas. Isso ocorre porque as gotas de chuva não estão em queda livre, mas sujeitas a um movimento movimento no qual a resistência do ar deve ser levada em consideração. Vamos supor que uma gota de chuva se forme numa altitude de 1000m e cuja massa vale aproximadamente 1,5 × 10 –3 g. Se na queda for considerada a resistência do ar, seu valor é tanto maior quanto maior a velocidade do corpo em movimento. Para uma gota em queda a partir do repouso, a velocidade aumenta aumenta até um valor máximo denominado velocidade limite, ou terminal, em média 18 km/h e atuam sobre a gota as seguintes forças: resistência do ar (F A), peso (P) e empuxo empuxo (E). A partir dessa dessa velocidade, a gota cai em movimento retilíneo uniforme. (Considere g = 9,8 m/s2). Com base no exposto, assinale a alternativa CORRETA. a) Se a resistência do ar e o empuxo fossem desprezados, a energia mecânica não se conservaria. b) Após atingir a velocidade limite, nenhuma força age sobre a gota. c) Considerando-se apenas a parte do percurso em que a gota está em movimento retilíneo uniforme, tem-se que ela sofre um acréscimo na sua energia cinética de 243 × 10 –6 J. d) Antes de a gota atingir a velocidade terminal a resultante das forças que agem sobre ela é F R = E + FA. *e) Se a resistência do ar e o empuxo fossem desprezados, a velocidade com que a gota chegaria à superfície da terra seria de v = 140 m/s. (PUCRIO-2009.1) - ALTERNATIVA: E Um astronauta flutuando no espaço lança horizontalmente um
(VUNESP/UNINOVE-2009.1) (VUNESP/UNINOVE-2009.1) - ALTERNA ALTERNATIVA: TIVA: C Num parque de diversões original, há um brinquedo que consta de dois carros A e B que podem deslizar livremente, sem atrito considerável, sobre uma pista retilínea. O carro A pode atingir uma mola de constante K = 103 N/m e deformá-la. Uma criança, de 30 kg de massa, sobe no carro A e outra, de 40 kg, no carro B. A partir de um estado de repouso, elas se empurempurram mutuamente e partem em sentidos opostos. Após o contato, o carro B percorre, então, 4,0 m em 1,0 s. Cada carro tem massa própria de 10 kg.
A máxima deformação que a mola sofre quando interage com o carro A vale a) 10 cm. b) 71 cm. *c) 1,0 m. d) 7,1 cm. e) 10 m. (VUNESP/UNINOVE-2009.1) (VUNESP/UNINOVE-2009.1) - ALTERNA ALTERNATIVA: TIVA: B Um operário ergue uma carga de 50 kg de massa trazendo-a do chão até uma altura de 6,0 m, onde ele se encontra. Para essa tarefa, o operário utiliza um moitão simples de uma roldana fixa e outra móvel, como ilustra a figura.
Desprezando Desprezando a inércia das roldanas e do cabo e considerando a aceleração da gravidade com o valor 10 m/s 2, pode-se afirmar que o trabalho realizado a) pelo peso da carga é de 3 000 J. *b) pelo peso da carga é de –3 000 J. c) pela força exercida pelo operário é de 1 500 J. d) pela força exercida pelo operário é de –1 500 J. e) pe pela la força força exe exerci rcida da pelo pelo ope operár rário io dep depen ende de da veloc velocida idade de con consstante com que a carga é erguida. (UDESC-2009.1) - ALTERNATIVA: C O Sistema Internacional de unidades (SI) adota sete unidades fundamentais fundament ais para grandezas físicas. Por exemplo, a unidade da intensidade de corrente elétrica é o ampère, cujo símbolo é “A”. Para o estudo da Mecânica usam-se três unidades fundamentais associadas às grandezas físicas: comprimento, massa e tempo. Nesse sistema, a unidade de potência mecânica é:
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(UDESC-2009.1) - ALTERNATIVA: D Um jogador de futebol, ao cobrar uma falta, chuta a bola de forma que ela deixa seu pé com uma velocidade de 25 m/s. Sabendo que a massa da bola é igual a 400 g e que o tempo de contato entre o pé do jogador e a bola, durante o chute, foi de 0,01 s, a força média exercida pelo pé sobre a bola é igual a: a) 100 N b) 6250 N c) 2500 N *d) 1000 N e) 10000 N (UFCG/PB-2009) - ALTERNATIVA: B Em um laborató.1rio de Física, uma plataforma move-se sobre trilhos com movimento retilíneo uniforme com velocidade de módulo igual a 20 m/s em relação ao laboratório. Sara, na plataforma, observa que um corpo de 2,0 kg, sujeito a uma força resultante constante de 10N, move-se a partir do repouso. José, sobre o piso do laboratório, observa o mesmo fenômeno fenômeno vendo o corpo se mover na mesma direção do movimento da plataforma. Após um intervalo de tempo de 4,0 segundos, medido a partir do início do movimento do bloco na plataforma, pode-se afirmar que a) com comoo o Princí Princípio pio da Con Conse serva rvaçãoda çãoda Energi Energiaa é válido válido em qua quallquer referencial, o trabalho medido por Sara e José tem o mesmo valor. *b) a variação da energia cinética do bloco, medida por José, é de 1,2 x 10 3 J. c) o trabalho realizado pela força sobre o bloco, medido por Sara, vale 1,0 x 102 J. d) Sara e José verificarão, independentemente, que a variação da energia cinética do bloco é de 4,0 x 10 2 J. e) o trabalho realizado pela força sobre o bloco, medido por José vale 8,0 x 10 2 J. (UFCG/PB-2009.1) - ALTERNATIVA: D A idéia sempre difundida de que a conversão de energia mecânica em energia elétrica é “limpa” tem sido amplamente contestada por estudos de impactos ambientais ambientais em diversos casos. Para se avaliar a situação, veja o exemplo da hidrelétrica de Tucuruí, no RioToca RioTocanti ntins ns,, com com que queda da verti vertica call de águ águaa de 60m 60m.. Const Constru ruída ída na década de 1980, apresenta em seu lago uma produção de metano (CH4), a 30m de profundidade, profundidade, de 6 x 10 –3 kg/m3, causada pelos restos vegetais submersos que não foram adequadamente tratados quando de sua construção. Em 1991, para gerar 18 TWh (6,5 x 1016 joules) de energia elétrica, pode-se afirmar que a quantidade, em toneladas, de CH4 exportada do reservatório pelas turbinas, vale (DADOS: g = 10,0 m/s 2 e dágua = 1000 kg/ m3) a) 6,5 x 1016. b) 1,1 x 1014. c) 1,8 x 10 13. *d) 6,6 x 105. e) 1,8 x 103. (UFCG/PB-2009.1) (UFCG/PB-2009.1) - RESPOSTA: RESPOSTA: a) –28O em relação ao eixo +X 3 b) 2,3 × 10 m/s Num laboratório de Física Nuclear observa-se que um núcleo, inicialme inicialmente nte em repouso, repouso, desintegra desintegra-se -se emiti emitindo ndo um elétron elétron e um neutrino. A quantidade de movimento movimento do elétron é 1,2 x 10 –22
(UNICAMP-2009.1) (UNICAMP-2009.1) - RESPOSTA: RESPOSTA: a) 32,0 kJ b) 15,0 CV CV A tração animal pode ter sido a primeira fonte externa de energia usada pelo homem e representa um aspecto marcante da sua relação com os animais. a) O gráfico ao lado mostra a força de tração exercida por um cavalo como função do deslocamento de uma carroça. O trabalho realizado pela força é dado pela área sob a curva F × d. Calcule o trabalho realizado pela força de tração do cavalo na região em que ela é constante. Fig 6 2009 ENR
b) No sistema internacional, a unidade de potência é o watt (1 W = 1 J/s). O uso de tração animal era tão difundido no passado que James Watt, aprimorador da máquina a vapor, definiu uma unidade de potência tomando os cavalos como referência. O cavalo-vapor (CV), definido a partir da idéia de Watt, vale aproximadamente 740 W. Suponha que um cavalo, transportando uma pessoa ao longo do dia, realize um trabalho total de 444000 J. Sabendo que o motor de uma moto, operando na potência máxima, executa esse mesmo trabalho em 40 s, calcule a potência máxima do motor da moto em CV. (UECE-2009.1) - ALTERNATIVA: A A força resultante que age sobre um corpo de massa 2 kg, que está se movendo no sentido positivo do eixo –x, é dada, em Newtons, pela expressão F = –6x, sendo x dado em metros. Se a velocidade do corpo, para x = 3,0 m, é v = 8,0 m/s, então, para x = 4,0 m, sua velocidade será, aproximadamente, *a) 6,5 m/s. b) 8,0 m/s. c) 9,0 m/s. d) –6,5 m/s. (UECE-2009.1) - ALTERNATIVA: D Um grupo de alunos, no laboratório de física, afirma que observaram uma colisão perfeitamente elástica entre duas esferas metálicas bem polidas, em uma superfície horizontal, que resultou nas duas esferas terminarem em repouso. Nenhuma força externa horizontal estava agindo nas esferas no instante da colisão. Sobre o fato, assinale o correto. a) As velocidades escalares escalares iniciais das duas duas esferas eram iguais e suas massas eram idênticas. b) As velocidades escalares iniciais das duas esferas eram diferentes e suas massas eram, também, diferentes. c)As velo velocida cidades des escalare escalaress iniciais iniciais das duasesferas eramiguais, mas suas massas não necessariamente eram idênticas. *d) A colisão não pode ter ocorrido como afirmado pelo grupo. (UFOP-2009.1) - ALTERNATIVA: C Um projétil de massa de 20,0kg disparado pelo canhão do veículo caça-tanques brasileiro Sucuri-II possui uma velocidade inicial de 1450,0 m/s. Sabendo que, em determinado momento, a cadência de tiro do equipamento é de 6,0 tiros/min, podemos afirmar que, nessa situação, a potência aproximada, em Watts, dis-
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(UFPR-2009.1) - ALTERNATIVA: B Em um cruzamento mal sinalizado, houve uma colisão de dois automóveis, que vinham inicialmente de direções perpendiculares, em linha reta. Em módulo, a velocidade do primeiro é exatamente o dobro da velocidade do segundo, ou seja, v 1 = 2v 2. Ao fazer o boletim de ocorrência, o policial responsável verificou que após a colisão os automóveis ficaram presos nas ferragens (colisão inelástica) e se deslocaram em uma direção de 45º em relação à direção inicial de ambos. Considere que a massa do segundo automóvel é exatamente o dobro da massa do primeiro, isto é, m2 = 2m1 e que a perícia constatou que o módulo da velocidade dos automóveis unidos, imediatamente após a colisão, foi de 40 km/h. Assinale a alternativa que apresenta apresenta a velocidade correta, em módulo, do automóvel 2, isto é, v2, imediatamente antes da colisão. a) 15 km/h. /h. *b) *b) 30 km/h km/h.. c) 60 km/h km/h.. d) 15 km/h. e) 30 km/h. (UFERJ/UNIRIO-2009.1) - ALTERNATIVA: A Um megaton de TNT (Trinitrotolueno), que é um explosivo, equivale a 4,2 × 1015 J. Admita que o asteróide 99942Apophis que, segundo cálculos confiáveis da NASA passará próximo à Terra por volta de 2040, sofresse um desvio em sua trajetória e viesse a se chocar com o nosso planeta. Considerando que sua massa é de aproximadamente 3 × 10 10 kg e que sua velocidade de impacto, suposta constante, seja de 12 km/s, a quantidade de energia que seria liberada durante o choque, em megatons de TNT, é, aproximadamente, igual a *a) 514. b) 857. c)1029. d) 1080. e) 2160. (FUVEST-2009.1) - ALTERNATIVA: A Um caminhão, parado em um semáforo, teve sua traseira atingida por um carro. Logo após o choque, ambos foram lançados juntos para frente (colisão inelástica), com uma velocidade estimada em 5 m/s (18 km/h), na mesma direção em que o carro vinha. Sabendose que a massa do caminhão era cerca de três vezes a massa do carro, foi possível concluir que o carro, no momento da colisão, trafegava a uma velocidade aproximada de *a) 72 km/h b) 60 km/h c) 54 km/h d) 36 km/h e) 18 km/h (UFPB-2009.1) - RESPOSTA: afirmativas corretas: I e II No man manual ual de instruç instruções ões de umadeterminad umadeterminadaa cam caminho inhonet nete, e, consconstam as seguintes especificações: Massa de 1.000 kg. Potência máxima de 5.10 4 W. Considerando que, na caminhonete, atuam apenas forças conservativas, que ela parte do repouso e que foram decorridos 9 segundos do movimento desse veículo, identifique as afirmati-
(UFPB-2009.1) - ALTERNATIVA: B Sobre um bloco com massa 1,0 kg, apoiado sobre uma mesa horizontal (figura abaixo), existe uma força dada pela equação cartesiana F = 1i + 3k , expressa no Sistema Internacional de Unidades (S.I.).
Considerando que o coeficiente de atrito cinético entre o bloco e a mesa é 0,2 e admitindo que, inicialmente, foi fornecida ao bloco uma velocidade velocidade de 4,0 m/s ao longo do eixo , é correto correto afirmar que o bloco, até parar, percorreu uma distância de: a) 16 m c) 32 m e) 80 m *b) 20 m d) 40 m (UFPB-2009.1) - RESPOSTA: afirmativas corretas: I, III e IV Em um laboratório de Física, um estudante resolve analisar processos envolvendo envolvendo colisões frontais entre corpos. corpos. Para isso prepara a experiência descrita e representada a seguir: sobre uma mesa lisa e sem atrito, o estudante imprime a um corpo A de massa M uma velocidade v 1; esse esse corpo corpo chocachoca-se, se, de forma forma perfeit perfeitame amente nte inelásti inelástica, ca, com o corpo B em repouso e também de massa M; em seguida, o conjunto (corpos A e B) colide com um terceiro corpo C , também em repouso e com massa 2M.
Nesse contexto, com relação às velocidades v 1, v2 e v3, representadas na figura, identifique as afirmativas corretas: I. v 3 corresponde a 25% de v 1. II. v2 corresponde a 30% de v 1. III. v3 corresponde a 50% de v2. IV. v2 corresponde a 50% de v1. V. v3 é igual a v2. (UFPB-2009.1) - ALTERNATIVA: B Em uma partida de tênis, um jogador rebate uma bola com 60 gramas de massa, que chega a sua raquete com velocidade de
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(UFPB-2009.1) - ALTERNATIVA: D Para analisar mudanças entre energias cinética e potencial elástica em um sistema mecânico massa-mola, um estudante de Física realiza o experimento descrito e representado abaixo: fixa duas molas idênticas em paredes verticais opostas; assinala o ponto O como o de referência e as posições das extremidades livres das molas por X 1 e –X 1; comprime a mola da direita com um bloco até um ponto assinalado por X2; verifica que a energia potencial do sistema é de 16J; libera o bloco a partir do repouso.
A partir desse momento, momento, o estudante observa que o bloco é arremessado em direção à mola da esquerda, que sofre uma compressão até a posição –X 2. Dessa forma, o bloco fica oscilando entre as molas. Desprezando as perdas de energia, verifica-se que o comportamento da energia cinética do bloco, em função da sua posição, está melhor representado no gráfico:
a)
(UNIOESTE/PR-2009.1) (UNIOESTE/PR-2009.1) - ALTERNA ALTERNATIVA: TIVA: C Uma criança empurra e solta um carrinho sobre uma superfície plana, imprimindo neste uma certa velocidade inicial. Ela observa que, depois de abandonado, o carrinho percorre 2 m até parar. Se a massa do carrinho fosse o dobro e a criança o empurrasse imprimindo nele a mesma velocidade inicial, qual a distância percorrida pelo carrinho até parar? a) 1 m b) 1,5 m *c) 2 m d) 3 m e) 4 m (UFTM-2009.1) - ALTERNATIVA OFICIAL: E Dois amigos, o primeiro com peso de 490 N e o segundo com peso de 539 N, disputavam para ver quem pulava mais alto ao realizarem saltos verticalmente verticalmente para cima. cima. A partir do solo, o primeiro tomou impulso e elevou seu centro de massa em 0,4 m relativamente ao chão, enquanto que o segundo, sob as mesmas condições do anterior, conseguiu elevar seu centro de massa em 0,5 m, também relativamente ao chão. Desconsiderando a existência de forças dissipativas como a resistência do ar, a energia que faltou ao saltador que deu o pulo mais baixo, para que a altura por ele atingida se equiparasse à do vencedor, corresponde em J, aproximadamente, a a) 30. b) 40. c) 50. d) 60. e) 70. (UFTM-2009.1) - ALTERNATIVA: D O bloco sobre a superfície plana e horizontal encontra-se inicialmente em repouso em um trecho perfeitamente liso, devido a umaação exte externa rna que impede impede seumovimento seumovimento.. Qua Quando ndo essa essa ação ação deixa de existir, o sistema passa a se movimentar.
b)
c)
*d)
e)
Dois segundos após o início do movimento, o bloco sobre o plano entra em uma região rugosa, surgindo, por conta disso, uma força de atrito que, atuando uniformemente sobre o corpo apoiado, dissipa toda a energia cinética do sistema. Sob essas condições, pode-se concluir que o módulo da energia dissipada durante o movimento sobre a superfície rugosa, em J, é Dado: aceleração da gravidade = 10 m/s 2 a) 960. b) 1 080. c) 1 460. *d) 1 600. e) 1 820. (UTFPR-2009.1) - ALTERNATIVA: B Um corpo de 500 g é lançado para cima com uma velocidade inicial de 8,0 m/s e atinge uma altura máxima de 2,8 m. Calcule a quantidade de energia dissipada pela resistência do ar
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(CETETMG-2009.1) - ALTERNATIVA: B Um malabarista lança uma de suas bolinhas com velocidade inicial cial v = 3 m/s com com ângu ângulo lo = 45 45O em relação a horizontal, conforme representado representado abaixo. Adote sen 45 O = cos 45O = 0,71 e g = 10 m/s2.
Desprezando a resistência do ar, é correto afirmar que a(o) a) altura máxima h é 45 cm. *b) alcance horizontal máximo d é 90 cm. c) energia cinética da bolinha, no ponto h, é máxima. d) tempo para atingir a altura máxima h é igual a 0,6 s. e) energia mecânica da bolinha, ao atingir a outra mão do malabarista, é nula. (UTFPR-2009.1) - ALTERNATIVA: C Um jogador de ping-pong recebe a bola, que se desloca com módulo 6 m/s. Aplicando com sua raquete uma força de contato de 1,5 N na bola, faz com que sua velocidade inverta de sentido e que seu módulo se altere para 9 m/s. Sabendo que a massa da bola vale 3 g, pode-se estimar o tempo de contato entre a raquete e a bola, em segundos, como sendo: a) 0,006. b) 0,018. *c) 0,030. d) 0,180. e) 0,360.
(FGVSP-2009.1) - ALTERNATIVA: D Num sistema isolado de forças externas, em repouso, a resultante das forças internas e a quantidade de movimento movimento total, são, ao longo do tempo, respectivamente, a) crescente e decrescente. b) decrescente e crescente. c) decrescente e nula. *d) nula e constante. e) nula e crescente. (CEFETMG-2009.1) - ALTERNATIVA: C Um bloco de massa igual a 2,0 kg é empurrado por uma pessoa sobre uma superfície horizontal. Ao adquirir a velocidade de 10 m/s, ele é solto e pára a uma distância de 20 m. Considerando g = 10 m/s 2, o coeficiente de atrito entre esse bloco e a superfície
(FGVSP-2009.1) - ALTERNATIVA: B Devido a forças dissipativas, parte da energia mecânica de um sistema foi convertida em calor, circunstância caracterizada pelo gráfico apresentado. apresentado.
Sabendo-se que a variação da energia potencial desse sistema foi nula, o trabalho realizado sobre o sistema nos primeiros 4 segundos, em J, foi, em módulo, a) 3 600. *b) 1 200. c) 900. d) 800. e) 600. (UNEMAT/MT-2009.1) - ALTERNATIVA: A Um motor com potência de 150 KW impulsiona um veículo por um períod períodoo de 30 min minuto utos. s. O trabal trabalho ho realiz realizadopela adopela força força mo motor toraa medida em Kwh e J é igual a: *a) 75 Kwh e 270 × 10 6 J b) 150 Kwh e 260 × 10 6 J c) 500 Kwh e 270 × 10 6 J d) 75 Kwh e 300 × 10 6 J e) 75 Kwh e 500 × 10 6 J
(UNEMAT/MT-2009.1) - ALTERNATIVA: A A figura abaixo mostra o esquema de um tobogã. No ponto A da figura é abandonado um corpo com massa de 15 Kg, que se movimenta e chega ao ponto B do plano horizontal com velocidade de 10 m/s. Adote g = 10 m/s 2
Com base nos dados e na figura, pode-se dizer que a quantidade
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(PUCSP-2009.1) - ALTERNATIVA: C
Fig 16 2009 NEW
Suponha que, na tirinha acima, tenha ocorrido o “beijinho”, e na falta de outra melancia de 5 kg, o marido ciumento ciumento tenha largado uma maçã de 50 g. Comparando as grandezas velocidade e força peso nas duas situações, pode-se afirmar que (considere g = 9,8 m/s2 e a altura da queda = 10 m) a) a velocidade seria a mesma, valendo 196 m/s, mas a força pe peso so seria seria difere diferente nte,, valen valendo do 10 vezesmeno vezesmenoss na que queda da da maçã maçã.. b) a velocidade seria a mesma, valendo 14 m/s, mas a força peso seria diferente, valendo 10 vezes mais na queda da maçã. *c) a velocidade seria a mesma, valendo 14 m/s, mas a força peso peso seria seria dife diferen rente, te, valend valendoo 100vezes men menos os na que queda da da ma maçã. çã. d) a força peso seria a mesma, valendo 14 N, mas a velocidade de queda seria diferente, valendo 10 vezes mais na queda da maçã. e) a força peso seria a mesma, valendo 49 N, mas a velocidade de queda seria diferente, valendo 100 vezes menos na queda da maçã.
(UEM/PR-2009.1) (UEM/PR-2009.1) - RESPOSTA: SOMA = 00 (nenhuma é correta) Um bloco de massa 1,0 kg é solto do ponto mais alto de um plano inclinado de 30O e a 2,5 m de altura, ambos em relação a horizontal. Considere g = 10,0 m/s 2 e assinale o que for correto. 01) Se não houver atrito entre o bloco e a superfície do plano inclinado, o bloco atinge a base do plano a uma velocidade de 10,0 m/s. 02) O módulo da força de reação normal do plano inclinado é igual ao módulo da força peso do bloco. 04) Se houver atrito entre o bloco e a superfície do plano inclinado, com coeficiente de atrito cinético 0,2, o trabalho realizado pela pela força força de atrito atrito será será J. 08) Se há atrito entre o bloco e a superfície do plano inclinado, há conservação de energia mecânica. 16) A força resultante que age sobre o bloco e o faz se deslocar sobre o plano inclinado quando não há atrito entre o bloco e a superfície do plano é igual a mgcos(30 O ). (UEPB-2009.1) - ALTERNATIVAS: ALTERNATIVAS: 21 A e 22 B Leia o texto I para responder às questões 21 e 22. Texto I A esteira é o aparelho mais usado nas academias. As mais modernas possuem um computador com visor que informa o tempo, a distância, a velocidade, os batimentos cardíacos e as calorias gastas, entre outras funções. Fig 18 2009 ENR
(UEM/PR-2009.1) - RESPOSTA: 09 (01+08) Projéteis de 100,0 g são disparados por uma metralhadora metralhadora presa a um dispos dispositiv itivoo que que,, efet efetuan uando do umaforça men mensur suráve ávell e regulá regulável vel,, impede que a arma recue quando a metralhadora é acionada. A velocidade de saída dos projéteis é 100,0 m/s. Despreze a resistência do ar e considere g = 10,0 m/s 2. Assinale o que for correto. 01) Se a força exercida pelo dispositivo que prende a arma for 50,0 N, a metralhadora disparará 5 balas por segundo. 02) Se a força exercida pelo dispositivo que prende a arma for 50,0 N, o conjunto de projéteis disparados possuirá uma energia cinética de 5000,0 J. 04) Um atirador aciona a metralhadora e dispara 5 balas contra um bloco de madeira de massa 99,5 kg, inicialmente em repouso sobre uma superfície plana e sem atrito. Se todos os projéteis ficarem incrustados no interior do bloco, sua velocidade, ao final dos disparos, será 1,0 m/s. 08) Um atirador aciona a metralhadora e dispara 5 balas contra um bloco de madeira de massa 99,5 kg, inicialmente em repouso sobre uma superfície plana e com coeficiente de atrito cinético 0,0625. Se todos os projéteis ficarem incrustados no interior do bloco, ele percorrerá uma distância de 0,2 m sobre a superfície até parar.
Em uma academia de ginástica, uma jovem anda sobre uma esteira rolante horizontal que não dispõe de motor [figura ao lado], mo movim vimen entan tandodo-a. a. O visor visor da estei esteira ra inform informaa qu quee elaandoua um umaa velocidade constante de 5,4 km/h e que, durante 30 minutos, foram consumidas 202,5 quilocalorias. Adote 1,0 cal = 4,0 J. 21ª QUESTÃO - ALTERNATIVA: A Acerca do assunto tratado no texto I, responda à seguinte situação-problema: Qual é a distância, em km, percorrida pela jovem
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(FATECSP-2009.1) - ALTERNATIVA: C Os modelos disponíveis da linha de motocicletas de 125 cilindradas de um determinado fabricante apresentam uma das menor menores es mass massas as da catego categoria ria,, 83 kg, e um melho melhor r posicionamento do centro de gravidade. Resumindo, Resumindo, diversão garantida para pilotos de qualquer peso ou estatura. O gráfico mostra a variação da energia cinética do conjunto motociclista e uma dessas motocicletas em função do quadrado de sua velocidade, sobre uma superfície plana e horizontal.
(UFPR-20 (UFPR-2009.1 09.1)) - RESPOST RESPOSTA: A: t = 2,8 s Na construção de um prédio, os operários utilizam um pequeno motor, associado a uma roldana e corda, para transportar objetos pesados para as partes mais altas. Suponha que em dada situação seja necessário elevar a uma altura de 27,5 m um recipiente contendo reboco cuja massa total seja igual a 38 kg. Despreze a massa da corda e considere que 1hp é igual a 746W. Calcule o tempo, em segundos, para levantar esse recipiente a uma velocidade constante se o motor tiver 5 hp. (Considere g = 10 m/s2 - dado não disponível na prova) (PUCMINAS-2009.1) - ALTERNATIVA: D São apresentadas a seguir diversas afirmativas sobre o conceito de energia. É CORRETO afirmar: a) O fato de a energia não se conservar justifica a necessidade que temos de economizar energia. b) O calor é uma forma de energia mecânica. c) Todos os corpos têm energia térmica que aparece na forma de calor quando são colocados em ambientes de altas temperaturas. *d) Se forem consideradas todas as suas modalidades, a energia de um sistema isolado sempre se conserva.
Analisando os dados do gráfico, pode-se determinar a massa do motociclista que, em kg, vale a) 45. b) 52. *c) 67. d) 78. e) 90.
(UFSC-2009.1) - RESPOSTA: SOMA = 17 (01+16) Uma tábua homogênea encontra-se em repouso sobre um lago de águas calmas. Dois sapos estão parados nas extremidades desta tábua, como é mostrado na figura. A massa do sapo da esquerda (sapo 1) é maior do que a do sapo da direita (sapo 2). Em determinado momento, os sapos pulam e trocam de posição. Suponha que o atrito da tábua com a água seja desprezível.
(UFSCar-2009.1) - ALTERNATIVA: E Quase terminada a arrumação do novo escritório, o engenheiro lamenta profundamente o acontecido... acontecido...
Fig 21 2009 HDR
Considerando o sistema formado pelos dois sapos e a tábua, e as margens do lago como referencial, é CORRETO afirmar que: 01. a quantidade de movimento do sistema constituído pelos dois sapos e a tábua se conserva. 02. a quantidade de movimento do sapo 1 é igual, em módulo, à quantidade de movimento do sapo 2, durante a troca de suas posições. 04. a tábua fica em repouso enquanto os sapos estão no ar.
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(UFSC-2009.1) - RESPOSTA: SOMA = 20 (04+16) Em um parque de diversões, um pêndulo de brinquedo é constituído por uma esfera metálica de massa m, amarrada a uma barra fina, fina, de m massa assa desprezível desprezível e com comprimento primento . O pêndulo deve ser lançado da altura máxima máxima no ponto A, girando em um plano vertical, com o objetivo de tentar completar a volta e se aproximar, o máximo possível, novamente, novamente, do ponto A. Suponha que o pêndulo seja lançado com velocidade de módulo , a partir do ponto A, chegando só até o ponto D, na primeira oscilação. Após oscilar repetidas vezes, pára no ponto C. Despreze o atrito da esfera com o ar. Considere:
cos 37 O sen 37 O
(UFU-2009.1) - RESPOSTA: 1F; 2F; 3V; 4F Um astronauta de massa 100 kg carrega um equipamento de massa igual a 5 kg para tentar consertar um satélite, em órbita ao redor da Terra. Em determinado momento, esse astronauta se solta da nave espacial, permanecendo em repouso em relação ao sistema de referência mostrado na figura abaixo.
0,8 0,6
Assinale a(s) proposição(ões) proposição(ões) CORRETA(S). 01. Se o atrito entre a barra e o eixo de suspensão fosse desprezível, a tensão na barra, no ponto C, seria três vezes o peso da esfera. 02. Se o atrito entre a barra e o eixo de suspensão fosse desprezível, o módulo da velocidade que a esfera teria ao passar pelo ponto D seria . 04. Durante todo o movimento do pêndulo, a tensão não realiza trabalho. 08. O trabalho realizado pelo atrito entre os pontos A e D é 0, 0,4. 4.m. m.g. g. . 16. O trabalho realizado realizado pelo atrito desde desde o ponto A até a parada definitiva defin itiva do do pêndulo pêndulo no ponto ponto C é –3mg –3mg .
(MACKENZIE-2009.1) - ALTERNATIVA: B Certo garoto, com seu “skate”, desliza pela rampa, descrevendo o segmento de reta horizontal AB, com movimento uniforme, em 2,0 s. As resistências ao movimento são desprezíveis. Considerando d igual a 20 m e o módulo de g igual a 10 m/s 2, o intervalo de tempo gasto por esse garoto para descrever o segmento CD é, aproximadamente, de a) 1,0 s. *b) 1,4 s. c) 1,6 s. d) 2,0 s. e) 2,8 s.
A nave de comprimento 30 m possui uma velocidade constante constante v = 5 m/s, no sentido contrário ao do eixo y da figura e, no instante t = 0 s, o bico da nave possui coordenadas (10 m, 30 m), conforme representadas na figura. O astronauta, para tentar alcançar a nave de volta, volta, lança lança o equi equipam pamento ento paralelam paralelamente ente ao eixo x, com velocidade vxequipamento = – 4m/s. Desprezando as forças que os planetas exercem sobre o astronauta e sobre a nave espacial, marque para as alternativas abaixo (V) Verdadeira ou (F) Falsa. 1 ( ) O astronauta não alcançará a nave, pois ele continuará em repouso após arremessar o equipamento. 2 ( ) Após arremessar o equipamento, o astronauta alcançará uma velocidade igual a 4 m/s no sentido do eixo x. 3 ( ) Após 6 s, o bico da nave espacial estará na posição posição (10 m, 0 m ). 4 ( ) O astronauta irá se deslocar no sentido positivo de x, mas não conseguirá alcançar a nave. (UFSCar-2009.1) - ALTERNATIVA: E
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(UNESP-2009.1) - ALTERNATIVA: E Um madeireiro tem a infeliz idéia de praticar tiro ao alvo disparando seu revólver contra um tronco de árvore caído no solo. Os projéteis alojam-se no tronco, que logo fica novamente imóvel sobre o solo. Nessa situação, considerando um dos disparos, pode-se afirmar que a quantidade de movimento do sistema pro jétil-tronco a) não se conserva, conserva, porque a energia cinética do projétil se transt ransforma em calor. b) se conserva e a velocidade final do tronco é nula, pois a sua massa é muito maior do que a massa do projétil. c) não se conserva, porque a energia não se conserva, já que o choque é inelástico. d) se conserva, pois a massa total do sistema projétil-tronco não foi alterada. *e) não se conserva, porque o sistema projétil-tronco não é isolado. (UNESP-2009.1) - ALTERNATIVA: C Suponha que os tratores 1 e 2 da figura arrastem toras de mesma massa pelas rampas correspondentes, elevando-as à mesma altura h. Sabe-se que ambos se movimentam com velocidades constantes e que o comprimento da rampa 2 é o dobro do comprimento da rampa 1. Fig 26 2009 ENR
Chamando de 1 e 2 os trabalhos realizados pela força gravitacional sobre essas toras, pode-se afirmar que: a) 1 = 2 2 ; 1 > 0 e 2 < 0 . b) 1 = 2 2 ; 1 < 0 e 2 > 0 . *c) 1 = 2 ; 1 < 0 e 2 < 0 . d) 2 1 = 2 ; 1 > 0 e 2 > 0 . e) 2 1 = 2 ; 1 < 0 e 2 < 0 . (UNESP-2009.1) - RESPOSTA: P = 4,0 × 105 W Segundo informação da empresa fabricante, um trator florestal (Trator Florestal de Rodas 545C) é capaz de arrastar toras por meio do seu cabo exercendo sobre elas uma força de módulo 2,0×10 5 N, com velocidade constante de módulo 2,0 m/s. Desprezando a massa do cabo e supondo que a força por ele exercida seja horizontal e paralela ao solo, determine a potência útil desenvolvida pelo trator. (UNESP-2009.1) - RESPOSTA: x = 1,4 m A f ig ig uurr a m o st st ra ra , e m c or or te te , u m
t ra ra to to r
f lo lo re re st st al al
(UNESP-2009.1) - RESPOSTA: F = 10,0 N Buriti é uma palmeira alta, comum no Brasil central e no sul da planície amazônica. Um fruto do buriti – eles são pequenos e têm em média massa de 30 g – cai de uma altura de 20 m e pára, amortecido pelo solo (o buriti dá em solos fofos e úmidos). Suponha que na interação do fruto com o solo, sua velocidade se reduza até o repouso durante o tempo tempo t = 0,060 s. ConsideranConsiderando desprezível a resistência do ar, determine o módulo da força resultante média exercida sobre o fruto durante a sua interação com o solo. Adote g = 10 m/s2. (ITA-2009.1) - ALTERNATIVA: D Sabe-se que o momento angular de uma massa pontual é dado pelo produto vetorial do vetor posição dessa massa pelo seu momento linear. Então, em termos das dimensões de comprimento (L), de massa (M), e de tempo (T), um momento angular qualquer tem sua dimensão dada por a) L 0MT –1. b) LM0T –1. c) LMT –1. *d) L2MT –1. e) L 2MT –2. (ITA-2009.1) - ALTERNATIVA: C A partir do repouso, um carrinho de montanha russa desliza de uma altura altura H = 20 20 m sobre sobre uma uma rampa rampa de 60° 60° de inclina inclinação ção e corre 20 m num trecho horizontal antes de chegar em um loop circular, de pista sem atrito. Sabendo que o coeficiente de atrito da rampa e do plano horizontal é 1 2, assinale o valor valor do raio máximo máximo que pode ter esse esse loop para que o carrinho faça todo o percurso sem perder o contato com a sua pista.
a) R = 8 m b) R = 4( - 1) m *c) *c) R = 8( - 1) m
d) R = 4(2 e) R = 40(
- 1) m - 1) 3 m
(ITA-2009.1) - ALTERNATIVA: C Considere um pêndulo simples de comprimento L e massa m
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(ITA-2009.1) (ITA-2009.1) - ALTERNA ALTERNATIVA: TIVA: E (RESOLUÇÃO NO FINAL) Considere uma bola de basquete de 600 g a 5 m de altura e, logo acima dela, uma de tênis de 60 g. A seguir, num dado instante, ambas as bolas são deixadas cair. Supondo choques perfeitamente elásticos e ausência de eventuais resistências, resistências, e considerando g = 10 m/s 2, assinale o valor que mais se aproxima da altura máxima alcançada pela bola de tênis em sua ascenção [sic] após o choque. a) 5 m b) 10 m c) 15 m d) 25 m *e) 35 m RESOLUÇÃO ITA - 2009.1 A velocidade com que ambas as bolas chegam ao solo, tendo partid partidoo do repous repouso, o, é 10 m/s(conser m/s(conservaç vação ão da ene energi rgiaa mecân mecâncic cicaa
(ITA-2009.1) - RESPOSTA: h = 2E2 (gm2c2) RESOLUÇÃO NO FINAL Um feixe de laser com energia E incide sobre um espelho de massa m dependurado por um fio. Sabendo que o momentum do feixe de luz laser é E/c, em que c é a velocidade da luz, calcule a que altura h o espelho subirá.
RESOLUÇÃO: ITA-2009.1 ITA-2009.1 Caráter corpuscular da radiação e analisar a interação entre o espelho e o feixe de luz como uma colisão elástica
ou equa equaçã çãoo de Torri orrice celllli:i: v = . Sendo os choques perfeitamente elásticos, tem-se que a velocidade relativa de aproximação é igual à velocidade relativa de afastamento. Assim:
Já que V aproximação = 20 m/s Vafastamento = 20 m/s (colisão perfeitamente elástica) e como a massa da bola de tênis é m e a massa da bola de basquete é 10m, pela conservação daquantidade de movimento m(-10) m(-10) + 10m× 10m×10 10 = (10m)v (10m)v + m(v + 20) v = 70/1 70/111 m/s m/s Daí, a velocidade da bola de tênis é v + 20 = 290/11 m/s. Portanto, hmáx = v2/2g = 34,75 m. (UNIFESP-2009.1) - ALTERNATIVA: B Uma pessoa de 70 kg desloca-se do andar térreo ao andar superior de uma grande loja de departamentos, utilizando uma escada rolante. A figura fornece a velocidade e a inclinação da escada em relação ao piso horizontal da loja.
Qdepois = Q antes
mV + (-E/c) (-E/c) = E/c V = 2E/mc 2E/mc 2 2 mV /2 = mgh h = 2E (gm2c2)
(UNIFESP-2009.1) - ALTERNATIVA: B No quadriculado da figura estão representados, em seqüência, os vetores quantidade de movimento da partícula A antes e depois de ela colidir elasticamente com a partícula B, que se encontrava em repouso.
Sabe-se que a soma das energias cinéticas das partículas A e B manteve-se constante, antes e depois do choque, e que nenhuma interação ocorreu com outros corpos. O vetor quantidade de movimento da partícula B após o choque está melhor representado por a) d) *b)
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(UNIESP-2009.1) - RESPOSTA: a) 6,0 × 10 –2J b) 3,0 3,0 × 10 –2m Uma pequena esfera A, com massa de 90 g, encontra-se em repouso e em contato com a mola comprimida de um dispositivo lançador, lançador, sobre uma mesa plana e horizontal. Quando o gatilho é acionado, a mola se descomprime e a esfera é atirada horizontalmente, com velocidade de 2,0 m/s, em direção frontal a uma outra esfera B, com massa de 180 g, em repouso sobre a mesma mesa. No momento da colisão, as esferas se conectam e passam a se deslocar juntas. O gráfico mostra a intensidade da força elástica da mola em função de sua elongação.
Considerando que as esferas não adquirem movimento de rotação, que houve conservação da quantidade de movimento na colisão e que não há atrito entre as esferas e a mesa, calcule: a) a energia cinética da composição de esferas AB após a colisão. b) quanto a mola estava comprimida no instante em que o gatilho do dispositivo lançador é acionado. (EAFI/MG-2009.1) - ALTERNATIVA: D Três esferas de massas M1, M2 e M3 tal que M1 < M2 < M3 são abandonada abandonadass simultaneamente em três planos inclinados distintos, possuindo ângulos de inclinações diferentes, porém com a mesma altura de elevação, conforme figura:
(UFU/MG-2009.1) - ALTERNATIVA: D Um bloco de 2 Kg de massa desloca-se, inicialmente, ao longo de um plano horizontal sem atrito com uma energia cinética inicial de 100 J. Durante um intervalo de tempo de 4s, uma força variável, como mostra o gráfico abaixo, é aplicada sobre o bloco, na mesma direção e no mesmo sentido da velocidade inicial.
Após a aplicação dessa força (t = 4 s), a velocidade final do bloco será a) 60 m/s b) 30 m/s c) 80 m/s *d) 50 m/s (UFF/RJ-2009.1) (UFF/RJ-2009.1) - RESPOSTA: a) 1,0 b) 1,0 m/s (horizontal) c) 4, 4,11 m/ m/ss d) 40 cm Um projétil de massa m = 10 g viaja horizontalmente horizontalmente com a velo2 cidade v = 1,0 x 10 m/s. Com esta velocidade, o mesmo atinge um bloco de massa M = 0,99 kg, que está em repouso na beirada de uma mesa cujo tampo encontra-se a uma altura h = 80 cm do chão, como mostra a figura. O projétil se aloja no bloco e o con junto cai da mesa. Considere desprezíveis desprezíveis as dimensões do bloco e do projétil quando comparadas comparadas com as da mesa. Suponha g = 10 m/s2.
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(UDESC-2009.1) - RESPOSTA: a) Q = +400 kg.m/s b) a = –7,0 m/s 2 c) v = +5,0 m/s O movimento retilíneo de um móvel de massa 10,0 kg acontece ao longo de uma pista horizontal. O módulo de sua velocidade constante é de 5,0 m/s, quando uma força dependente do tempo, inicialmente na mesma direção e no mesmo sentido do movimento do móvel, passa a atuar. Essa força, indicada no gráfico abaixo, atua sobre o móvel durante o intervalo de 10,0 s, sempre na mesma direção do movimento.
Considerando que não há atrito entre o móvel e a pista, calcule: a) a quantidade de movimento do móvel, 5,0 s após o início de atuação da força; b) a aceleração do móvel, 7,5 s após o início de atuação da força; c) o valor da velocidade do móvel, imediatamente após cessar a atuação da força. (UFMS-2009.1) - RESPOSTA: SOMA = 010 (002+008) Um pêndulo rígido, na forma de haltere com duas esferas de
(UFV/MG-2009.1) - ALTERNATIVA: B Todo atirador profissional sabe que, ao dar um tiro com um rifle, este sofrerá um recuo no instante do disparo. Dentre as leis da Física abaixo relacionadas, a que explica este fenômeno é: a) a primeira lei da termodinâmica. *b) a lei da conservação da quantidade de movimento. c) a primeira lei de Newton. d) a lei da conservação da energia. (UFMS-2009.1) - ALTERNATIVA: A O Triatlo é uma modalidade esportiva que combina, de forma seqüencial e sem interrupção, natação, ciclismo e corrida. Com relação à parte do ciclismo, uma das preocupações dos treinadores e dos atletas é a resistência do ar que aplica força de arrasto Fa contrária ao movimento. Essa força depende da seção transversal à direção do movimento, e aumenta com a velocidade v. Um dos modelos teóricos para expressar essa força é dado pela expressão vetorial F a = –bv, onde b é uma constante de proporcionalidade. Um dos recursos utilizados pelo ciclista para diminuir essa força, durante o movimento, é curvar o seu corpo para a frente diminuindo a seção transversal. Um treinador, na tentativa de analisar a dependência entre essa força e a maneira como o ciclista curva o corpo, faz um experimento com um ciclista. Na primeira parte do experimento, o ciclista desce ao longo de um declive, numa trajetória retilínea, a partir do repouso no ponto A, com a bicicleta livre e sem pedalar, e sem curvar o corpo, veja a figura 1. Na 2 a parte do experimento, repete todo o procedimento da 1a parte e nas mesmas condições, no mesmo declive. A única diferença é que o ciclista curva o corpo para a frente diminuindo a seção transversal, veja a figura 2. Para análise, o treinador escolhe o modelo teórico da força proporcional à velocidade como citada acima, e verifica que a bicicleta atinge uma velocidade constante antes de chegar ao final do plano nas duas partes do experimento, só que, no segundo caso, o tempo de descida do ponto A ao B é menor que na 1 a parte do experimento. Considere que a massa de todo o sistema é invariável e que a única força contrária ao movimento é a força de arrasto
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(UFV/MG-2009.1) - ALTERNATIVA: B Uma pedra é lançada verticalmente para cima. Desprezando-se a resistência do ar, o gráfico que representa CORRETAMENTE os comportamentos da energia potencial gravitacional U e da energia cinética K da pedra em função do tempo t é: a)
c)
*b)
d)
(UFV/MG-2009.1) - ALTERNATIVA: A Uma pessoa aplica uma força horizontal sobre um corpo de massa M, inicialmente em repouso, fazendo-o adquirir uma velocidade de módulo v. Uma segunda pessoa também aplica uma força horizontal sobre outro corpo igual ao primeiro, mas que possui velocidade inicial de módulo v. Neste segundo caso, a ação da força aplicada faz com que o corpo entre em estado de repouso. Nos dois casos os corpos se movem sobre uma superfície horizontal sem atrito. Com relação aos módulos dos trabalhos realizados pelas duas pessoas, é CORRETO afirmar que: *a) são iguais. b) o realizado pela segunda pessoa é nulo. c) o realizado pela primeira pessoa é maior que o realizado pela
(UNIFOR/CE-2009.1) - ALTERNATIVA: A Uma esfera de massa m = 200 g é presa à extremidade de um fio, de comprimento comprimento 0,50 m, com sua outra extremidade fixa conforme a figura a seguir. Com o fio esticado na horizontal, abandona-se a esfera. Adote g = 10 m/s 2 e despreze forças resistentes ao movimento. Ao passar pelo ponto inferior de sua trajetória, a tração no fio vale, em newtons, m *a) 6,0 b) 4,0 c) 0,60 d) 0,40 e) 0,20 (UFPE-2009.1) - ALTERNATIVA: C A aplicação da chamada “lei seca” diminuiu significativamente o percentual de acidentes de trânsito em todo o país. Tentando chamar a atenção dos seus alunos para as conseqüências dos acidentes de trânsito, um professor de Física solicitou que considerassem um automóvel de massa 1000 kg e velocidade igual a 54 km/h, colidindo com uma parede rígida. Supondo que ele atinge o repouso em um intervalo de tempo de 0,50 s, determine a força média que a parede exerce sobre o automóvel durante a colisão. a) 1,0 × 10 4 N b) 2,0 × 10 4 N *c) 3,0 × 10 4 N d) 4,0 × 10 4 N e) 5,0 × 10 4 N (UFPE-2009.1) - ALTERNATIVA: D Um pequeno bloco de massa m é largado, a partir do repouso, do ponto A, como mostrado na figura. O bloco desliza, com atrito, dentro de uma calota esférica de raio R até o ponto B, onde atinge o repouso. Considerando g, a aceleração da gravidade, calcule o trabalho
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(UFPE-20 (UFPE-2009.1) 09.1) - RESPOST RESPOSTA: A: = 88,0 88,0 J Um bloco de massa m = 4,0 kg é empurrado, através da aplicação de uma força F constante ao longo de um plano inclinado, como mostra a figura. O bloco parte do repouso no ponto 1 e chega ao ponto 2 com velocidade v = 2,0 m/s.
Calcule o trabalho realizado pela força F, ao longo do trajeto de 1 a 2, em joules. Despreze o atrito com o plano, a resistência do ar e considere g = 10,0 m/s2.
(CEFETSP-2009.1) - ALTERNATIVA: B Considere uma colisão frontal unidimensional entre um átomo de Hidrogênio (H) que se move com velocidade de módulo V e uma molécula de Hidrogênio (H 2), em repouso. Sabe-se que após a colisão a molécula adquire velocidade de módulo V/3. Sendo E 1 e E 2 as energias cinéticas do sistema antes e depois da colisão, respectivamente, a relação E2 / E 2 vale a) 1/4. *b) 1/3. c) 1/2. d) 2/3. e) 3/4. (VUNESP/FMJ-2009.1) (VUNESP/FMJ-2009.1) - ALTERNA ALTERNATIVA: TIVA: B Dois blocos de massas m e 3m colidem frontalmente sobre uma superfície plana, horizontal e perfeitamente lisa. As figuras mostram dois instantes imediatamente antes e imediatamente depois da colisão.
(UFPE-2009.1) - RESPOSTA: F = 2,0 N Uma torneira colocada a uma altura H = 0,8 m do solo, não estando bem fechada, goteja. Cada gota tem em média a massa m = 0,5 g.
Pode-se afirmar que nesse processo a) houve conservação da quantidade de movimento e da energia cinética do sistema. *b) houve conservação da quantidade de movimento e a energia cinética do sistema diminuiu. c) houve conservação da quantidade de movimento e a energia cinética do sistema aumentou. d) nãohouv nãohouvee con conser servaç vação ão da qua quanti ntida dade de de mo movim viment entoo e a en enerer-
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VUNESP/FMJ-2009.1) - RESPOSTA: a) | W | = 36000 J b) v = 1,6 m/s Gruas são equipamentos largamente utilizados em construção civil, pois podem movimentar objetos pesados tanto na direção horizontal quanto na vertical, além de poderem girar em torno de um eixo vertical vertical,, passand passandoo por sua torre. torre. PretendePretende-se se utilizar utilizar uma grua para levar uma caixa de massa m = 200 kg do ponto A, no solo, ao ponto C, no topo de um edifício em obras, pelo percurso ABC mostrado mostrado na Figura 1. 1. Do ponto A até o ponto B, ela é levada em linha reta com velocidade constante de 0,5 m/s, em 60 s.
(FUVEST-2009.1) (FUVEST-2009.1) - RESPOSTA RESPOSTA NO FINAL Para testar a elasticidade de uma bola de basquete, ela é solta, a partir de uma altura H 0, em um equipamento no qual seu movimento é monitorado por um sensor. sensor. Esse equipamento registra a altura do centro de massa da bola, a cada instante, acompanhando seus sucessivos choques com o chão. Fig 35 2009 ENR Fig 34 2009 ENR
Fig 32 2009 ENR
NOTE E ADOTE: Desconsi Desconsiderea derea deformaçã deformaçãoo da bola bola e a resist resistênc ência ia do ar. ar. Aceleraçãoda Aceleraçãoda gravidade gravidade na Terra, g = 10 m/s2
Para ir verticalmente do ponto B ao ponto C, ela demora 10 s, com sua velocidade variando segundo o gráfico mostrado na Figura 2.
A pa parti rtirr da aná anális lisee dosregistro dosregistros, s, é pos possív sível, el, en então tão,, estim estimar ar a elaselasticidade da bola, caracterizada pelo coeficiente de restituição CR. O gráfico apresenta os registros de alturas, em função do tempo, para uma bola de massa M = 0,60 kg, quando ela é solta e inicia o movimento com seu centro de massa a uma altura H 0 = 1,6 m, chocando-se sucessivas vezes com o chão. A partir dessas informações: a) Represente, no Gráfico I da folha de respostas, a energia potencial da bola, EP, em joules, em função do tempo, t empo, indicando os valores na escala. b) Represente, no Gráfico II da folha de respostas, a energia mecânica total da bola, ET, em joules, em função do tempo, indicando os valores na escala. c) Estime o coeficiente de restituição CR dessa bola, utilizando a
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(FUVEST-2009.1) -RESPOSTA: a) 3,4 × 108J b) 14 1488 km/h km/h c) 0,53 A Com o objetivo de criar novas partículas, a partir de colisões entre prótons, está sendo desenvolvido, no CERN (Centro Europeu de Pesquis Pesquisas as Nuclea Nucleares res), ), um grande grande acelera acelerador(LHC) dor(LHC).. Nele, Nele, atraatravés de um conjunto de ímãs, feixes de prótons são mantidos em órbita circular, com velocidades muito próximas à velocidade c da luz no vácuo. Os feixes percorrem longos tubos, que juntos formam uma circunferência de 27 km de comprimento, onde é feito vácuo. Um desses feixes contém N = 3,0 x 10 14 prótons, distribuídos uniformemente ao longo dos tubos, e cada próton tem uma energia cinética E de 7,0 x 10 12 eV. Os prótons repassam inúmeras vezes por cada ponto de sua órbita, estabelecendo, dessa forma, uma corrente elétrica elétrica no interior dos tubos. Analisando a operação desse sistema, estime: a) A energia cinética total E c, em joules, do conjunto de prótons contidos no feixe. b) A velocidade V, em km/h, de um trem de 400 toneladas que teria uma energia cinética equivalente à energia do conjunto de prótons contidos no feixe. c) A corrente elétrica I, em ampères, que os prótons em movimento estabelecem no interior do tubo onde há vácuo.
(UFC/CE-2009.1) - RESPOSTA NO FINAL Duas partículas A e B, de massa m, executam movimentos circulares uniformes sobre o plano x y (x e y representam eixos perpendiculares) com equações horárias dadas por x A ( t ) = 2 a + a cos( t ), ), y A ( t ) = a sen( t ) e x B ( t ) = –2a + a cos( t ), ), y B( t ) = ) , sen enddo e a constantes positivas. a sen( t ), a) Determine as coordenadas das posições iniciais, em t = 0 , das partículas A e B. b) Determine as coordenadas do centro de massa do sistema formado pelas partículas A e B no instante t = 0 . c) Determine as coordenadas do centro de massa do sistema formado pelas partículas A e B em um instante qualquer t . d) Mostre que a trajetória do centro de massa é uma circunferência de raio a , com centro no ponto ( x = 0, y = 0 ). ). RESPOSTA: RESPOSTA: UFC/CE-2009.1 a) xA = +2a e yA = 0: xB = –a e yB = 0 b) x = a e y = 0 c) x = acos( t ) e y = asen ( t ) d) equação da trajetória do CM: x 2 + y2 = a2 (circunferência de raio a e centro em x = 0 e y = 0) (UFC/CE-2009.1) - RESPOSTA: a) FR = 25 N b) Q = 70 N·s N·s A única força horizontal (ao longo do eixo x) que atua em uma partícula de massa m = 2 kg é descrita, em um dado intervalo de
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(UNICAMP-2009.1) - RESPOSTA: a) Para v = 900 km/h e L = 50 m R 8,3×108 b) E = 7,5×10 –27 J O aperfeiçoamento de aeronaves que se deslocam em altas velocidades exigiu o entendimento das forças que atuam sobre um corpo em movimento num fluido. Para isso, projetistas realizam testes aerodinâmicos com protótipos em túneis de vento. Para que o resultado dos testes corresponda corresponda à situação real das aeronaves em vôo, é preciso que ambos sejam caracterizados por valores similares de uma quantidade conhecida como número de Reynolds R . Esse número é definido como R = VL b, onde V é uma velocidade típica do movimento, L é um comprimento característico do corpo que se move e b é uma constante que depende do fluido. a) Faça uma estimativa do comprimento total das asas e da velocidade de um avião e calcule o seu número de Reynolds. Para o ar, bar 1,5×10 –5 m2/s. b) Uma situação de importância biotecnológica é o movimento de um micro-organismo num meio aquoso, que determina seu gasto energético e sua capacidade de encontrar alimento. O valor típico do número de Reynolds nesse caso é de cerca de 1,0×10 –5, bastante diferente daquele referente ao movimento de um avião no ar. ar. Sabendo que uma uma bactéria de 2,0 m de compricompri –16 mento tem massa de 6,0×10 kg , encontre a sua energia –6
2
(UNICAMP(UNICAMP-2009 2009.1) .1) - RESPOS RESPOST TA: a) 5,0 W b) 1050 nm Thomas Edison inventou a lâmpada utilizando filamentos que, quando quan do percorri percorridos dos por corrente corrente elétrica, elétrica, tornam-s tornam-see incandescentes, emitindo luz. Hoje em dia, os LEDs (diodos emissores de luz) podem emitir luz de várias cores e operam com eficiência muito superior à das lâmpadas incandescentes. a) Em uma residência, uma lâmpada incandescente acesa durante um dia consome uma quantidade de energia elétrica igual a 1,2 kWh. Uma lâmpada de LEDs com a mesma capacidade de iluminação consome a mesma energia elétrica em 10 dias. Calcule a potência da lâmpada de LEDs em watts. b) O gráfico da figura 1 mostra como a potência elétrica varia em função da temperatura para duas lâmpadas de filamento de Tungstênio, uma de 100 W e outra de 60 W. A potência elétrica diminui com a temperatura devido ao aumento da resistência do filamento. No mesmo gráfico é apresentado o comportamento da potência emitida por radiação para cada lâmpada, mostrando que quanto maior a temperatura, maior a potência radiada. Na prática, quando uma lâmpada é ligada, sua temperatura aumenta até que toda a potência elétrica seja convertida em radiação (luz visível e infravermelha). Obtenha, a partir do gráfico da figura 1, a temperatura de operação da lâmpada de 100 W. Em seguida, use a figura 2 para encontrar o comprimento de onda de máxima intensidade radiada por essa lâmpada.
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(FURG/RS-2009.1) (FURG/RS-2009.1) - ALTERNA ALTERNATIVAS: TIVAS: 19 A e 20 D O enunciado a seguir refere-se às questões 19 e 20. Um objeto de massa m = 1kg, ao passar pelo ponto 1 de uma rampa, livre de atrito, tem energia cinética igual a 2 Joules. O ponto 1 está a uma altura de h = 20 cm em relação ao ponto 2, situado na base da rampa. Considerando g = 10m/s 2:
19) Qual a velocidade do objeto ao passar pelo ponto 2? *a) 2 m/s b) 8 m/s c) m/s d) 2 m/s e) 20 m/s
(CEFETRJ-2009.1) - RESOLUÇÃO NO FINAL Um acrobata de massa m = 50 kg está fazendo uma exibição pública. Ele encontra-se inicialmente em repouso na extremidade esquerda de uma tora de madeira de massa M = 200 kg e comprimento L = 4 m, que flutua sobre a superfície de um lago tranqüilo. Em determinado instante, o acrobata dá um salto em direção à extremidade direita da tora com uma velocidade que fo form rmaa um um ân ângu gulo lo = 15o com a horizontal. Despreze o atrito entre a tora e a água, bem como os efeitos de resistência do ar durante todo o movimento do sistema acrobata + tora. Considere g = 10 m/s 2 a aceleração da gravidade local e admita que você possa considerar o acrobata como uma partícula. (Rigorosamente gorosamente falando, você está analisando o movimento do centro de massa do acrobata). a) Descreva qualitativamente o movimento do sistema acrobata + tora de madeira. b) Determine a velocidade inicial do acrobata necessária para que ele atinja exatamente a extremidade direita da tora de madeira. RESOLUÇÃO CEFETRJ-2009.1: a) Quando o acrobata pula, ele aplica sobre a tora uma força interna (estamos considerando considerando o acrobata + a tora como o nosso sistema). Portanto, a soma das forças externas que atuam sobre o sistema na direção horizontal é nula e o momento linear total
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(CEFETCE-2009.1) - RESPOSTA: a) Wa = ECa = 5,5 J b) W b = ECb = 7,2 J Em um elevador de altura 1,8 m, que se desloca para baixo com velocidade constante de 1,0 m/s, uma lâmpada de massa 300 g se desprende do teto e cai até o piso. Calcule o trabalho da força peso e a variação de energia cinética da lâmpada no deslocamento do teto ao piso do elevador a) em relação ao referencial do elevador. b) em relação ao referencial do solo. Despreze a resistência do ar e adote g = 10,0 m/s 2. (UFRN-2009.1) - ALTERNATIVA: D A produção de energia proveniente de maré, sistema maré-motriz (no qual se utiliza o fluxo das marés para movimentar uma turbina reversível capaz de converter em energia elétrica a energia potencial gravitacional da água), constitui-se numa alternativa de produção de energia de baixo impacto ambiental. Um sistema desse tipo encontra-se em funcionamento na localidade de La Rance, França, desde 1966, com capacidade instalada de 240 megawatts. As figuras abaixo mostram, esquematicamente, um corte transversal da barragem de um sistema maré-motriz, em quatro situações distintas, evidenciando os níveis da água, nos dois lados
(UFRN-2009.1) - ALTERNATIVA: C Para demonstrar a aplicação das leis de conservação conservação da energia e da quantidade de movimento, um professor realizou o experimento ilustrado nas Figuras 1 e 2, abaixo.
Inicialmente, ele fez colidir um carrinho de massa igual a 1,0 kg, com velocidade de 2,0 m/s, com um outro de igual massa, porém em repouso, conforme ilustrado na Figura 1. No segundo carrinho, existia uma cera adesiva de massa desprezível. Após a colisão, os dois carrinhos se mantiveram unidos, deslocando-se com velocidade igual a 1,0 m/s, conforme ilustrado na Figura 2. Considerando-se que a quantidade de movimento e a energia cinética iniciais do sistema eram, respectivamente, 2,0 kg.m/s e
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(UFRGS-2009.1) - ALTERNATIVA: B Você sobe uma escada e, a meio caminho do topo, de uma altura y, você deixa cair uma pedra. Ao atingir o topo da escada, de uma altura 2y, você solta uma outra pedra. Sendo v1 e v2 os módulos das velocidades de impacto no solo da prime primeira ira e da segun segunda da ped pedra, ra, respc respctim timam ament ente, e, a razão razão v 1 v 2 vale a) 1/2 . *b) 1 . c) 1 . d) . e) 2 . (UFRGS-2009.1) - ALTERNATIVA: B Na modal modalida idade de espor esportiv tivaa de salto salto com com vara, vara, o atlet atletaa salta salta e apó apóiaiase na vara para ultrapassar o sarrafo. Mesmo assim, é uma exelente aproximação considerar que a impulsão do atleta para ultrapassar o sarrafo resulta apenas da energia cinética adquirida na corrida, que é totalmente armazenada armazenada na forma de energia de deformação da vara. Na situação ideal – em que a massa da vara é desprezível e a energia potencial da deformação da vara é toda convertida em energia potencial gravitacional do atleta –, qual é o valor aproximado do deslocamento vertical do centro de massa do atleta,
(UFLA/MG-2009.1) - ALTERNATIVA: D Num parque parque de dive diversõ rsões, es, um carrinho carrinho,, sobre sobre trilhos, trilhos, é traciona tracionado do por um motor de potência média 20.000 W, num trecho reto e plano, de forma que o carrinho, partindo do repouso, atinja a velocidade de 25 m/s em 10 s. A massa do carrinho é a) 1000 kg. b) 820 kg. c) 2000 kg. *d) 640 kg. (UFLA/MG-2009.1) - ALTERNATIVA: A Um carrinho de massa 6 kg desloca-se horizontalmente, sem atrito, com velocidade vA de 4 m/s, quando um bloco de massa 2 kg cai verticalmente sobre o carrinho, atingindo-o com velocidade vB de 5 m/s (ver figura) e agregando-se agregando-se a ele. Após o choque, a velocidade do conjunto carrinho-bloco será *a) 3 m/s. b) 2 m/s. c) 6 m/s. d) 9 m/s.
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(UNIFEI/MG-2009.1) (UNIFEI/MG-2009.1) - RESPOSTA: a) 2,0 m/s b) 1,2 N (direção: vertical, sentido: para cima) Um cubo de gelo de 40 g de massa desliza sem atrito e oscila entre os dois extremos da figura. O raio do semicilindro é igual a 20 cm.
(CESGRANRIO-2009.1) - ALTERNATIVA: C Uma bola de raio muito pequeno é abandonada, no vácuo, a uma altura de 5 metros, chocando-se com uma superfície horizontal. Esse choque é parcialmente elástico, com coeficiente de restituição e = /2. Imaginando-se que essa bola possa quicar infinitamente, e considerando-se a aceleração da gravidade igual a 10 m/s2, a distância total percorrida pela bola, em metros, valerá a) 10,0 b) 12,5 *c) 15,0
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(UFBA-2009.1) - RESOLUÇÃO NO FINAL Buscando melhorar a segurança de seus veículos, as fábricas de automóveis fazem testes de impacto, a fim de avaliar os efeitos sobre a estrutura dos carros e sobre seus ocupantes. Como resultado dessa iniciativa, as pesquisas têm conduzido à construção de carros com carroceria menos rígida, que se deformam mais facilmente em caso de colisão. Em um teste realizado, um veículo de 1000,0 kg, movendo-se com velocidade igual a 72,0 km/h e dirigido por controle remoto foi arremessado contra contra uma parede de concreto. A colisão, completamente inelástica, durou 0,05 segundos.
(UECE-2009.1) - ALTERNATIVA: A O corpo A, de massa 2 kg, move-se com velocidade constante de 4 m/s, com direção ao longo do eixo x , no sentido positivo desse eixo. O corpo B, de massa 6 kg, move-se com velocidade constante de 3 m/s, com direção ao longo do eixo y , no sentido negativo desse eixo. O módulo da velocidade do centro de massa do sistema composto pelos dois corpos A e B, em m/s, é aproximadamente *a) 2,5. b) 5,5. c) 10,5.
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(UEPG/PR-2009 (UEPG/PR-2009.1) .1) - RESPOSTA: RESPOSTA: SOMA= 31 (01+02+04+0 (01+02+04+08+16) 8+16) Um bloco de massa m é solto, a partir do repouso, do topo de um plano plan o inclinado inclinado de de altura altura h que forma forma um âângul nguloo com a horihorizontal, como como mostra a figura abaixo. abaixo. A respeito deste deste evento físico, considerando que não existe atrito entre o bloco e a superfície do plano inclinado, assinale o que for correto.
(UESPI/PI-2009.1) - ALTERNA ALTERNATIVA: TIVA: A Para levar uma uma partícula material material de um ponto ponto A até um ponto B, a força resultante agindo sobre ela realiza trabalho igual a 5 J. Sabe-se também que, nesse percurso, 5 J de energia são dissipa pados dos.. A variaç variação ão da ene energi rgiaa po poten tencia ciall da pa partí rtícul cula, a, ent entre re os pon pon-tos A e B, vale, em joules, *a) –10. b) –5. c) 0. d) 5. e) 10.
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(UEPG/PR-2009.1) - ALTERNATIVA: B Em que consiste o Teorema do Impulso? a) Se corpos de massas diferentes forem submetidos a um impulso de igual intensidade, as suas velocidades serão iguais. *b) O impulso aplicado a um corpo num certo intervalo de tempo mede a variação da quantidade de movimento no mesmo intervalo de tempo. c) Se a força aplicada em um corpo for variável, a quantidade de movimento desse corpo é constante. d) Sendo o impulso uma grandeza vetorial, quando aplicado num corpo, ele altera a sua trajetória.
(UFG/GO-2009.1) - ALTERNATIVA: 41 E e 42 C O texto a seguir refere-se às questões 41 e 42. A saltadora brasileira Fabiano Murer terminou as Olimpíadas de Pequim em décimo lugar, após descobrir, no meio da competição, que o Comitê Organizador do Jogos havia perdido uma de suas varas, a de flexibilidade 21. Fig 55 2009 ENR
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(UFMG (UFMG-20 -2009. 09.1) 1) - RESPOS RESPOST TA: a) v 0,5 m/s m/s b) E 0,3 0,366 J Uma bola é lançada horizontalmente, de certa altura, e cai sobre uma superfície rígida, plana e horizontal. Uma parte da trajetória dessa bola está mostrada nesta fotografia estroboscópica, que consiste na superposição de diversas imagens registradas em instantes consecutivos: Fig 56 2009 ENR
(UFOP-2009.1) - RESPOSTA: a) 1,0 m/s b) conserv. quant. mov. c) Sim Sim d) Não Não Um jovem de massa 60,0kg está parado sobre uma pista de patinação no gelo, perfeitamente lisa, quando apanha seu cachorro de massa 20,0kg, que se movia horizontalmente, em sua direção, com velocidade de 4,0m/s. Sabendo que g = 10,0 m.s –2, faça o que se pede. a) Calcule a velocidade do jovem e de seu cachorro, depois que o cachorro foi apanhado pelo jovem. b) Explicite qual princípio da Física é exemplificado pelo fenômeno acima.
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VESTIBULARES 2009.2 (UFPR-2009.2) - ALTERNATIVA: A Arquimedes de Siracusa descobriu que dois corpos não podem ocupar o mesmo espaço num mesmo tempo e, além disso, todo corpo mergulhado em um fluido experimenta uma força contrária ao seu peso denominada “Empuxo”. Dentro desse contexto, observa-se que um bloco cúbico de madeira (d = 0,65 g/cm 3), com 20 cm de aresta, flutua na água (d = 1,0 g/cm3). A altura do cubo que permanece permanece dentro da água tem o valor de: *a) 13 cm. b) 20 cm. c) 15 cm. d) 18 cm. e) 16 cm. (UNIFOR/CE-2009.2) - ALTERNATIVA: B Uma haste maciça de alumínio tem 2,0 m de comprimento e secção transversal em forma de T, com as dimensões abaixo dadas em cm.
A densidade do alumínio alumínio é d = 2,7 × 103 kg/m3. A mas massa sa da hast hastee é, em kg, a) 81 *b) 54 c) 41 d) 27 e) 14 (UNIFOR/CE-2009.2) - ALTERNATIVA: D Um balão abandonado no ar desce com aceleração de 0,20 m/ s2. Retirando-se do balão a massa de 2,0 kg, quando solto, ele passa a subir com aceleração de 0,20 m/s 2. Considere o empuxo do ar constante nas duas situações e adote g = 9,8 m/s2. A massa original do balão era, em kg, a) 20 b) 30 c) 40 *d) 50 e) 60 (IFCE/CEFETCE-2009.2) (IFCE/CEFETCE-2009.2) - ALTER A LTERNAT NATIVA: IVA: C O aquecimento global vem causando o derretimento das calotas polares, responsáveis pelo equilíbrio climático do planeta. Se a área coberta pelos mares mares e pelos oceanos for expressa expressa por A e a profundid profundidade ade média média dos mesmo mesmoss por P, P, um aum aumento ento V, em seu volume, devido ao derretimento das calotas polares, consi-
(IFCE/CEFETCE-2009.2) (IFCE/CEFETCE-2009.2) - ALTERNA ALTERNATIVA: TIVA: B A parte visível de um iceberg, acima acima da superfície do mar, representa apenas uma fração de seu volume total. Sabendo-se que a densidade do gelo é 0,92 g/cm3 e a da água do mar é 1,0 g/cm3, a razão entre o volume total e o volume da parte submersa de um iceberg é mais próxima de a) 0,92. *b) 1,1. c) 1,2. d) 1,9. e) 2,1. (IFGO/CEFETGO-2009.2) - ALTERNATIVA: A
Pra Ser Sincero
Fig 61 2009 HDR
(Engenheiros do Hawaii)
“...Sabemos tudo A nosso respeito Somos suspeitos De um crime perfeito Mas crimes perfeitos Nunca deixam suspeitos...” Houve uma tentativa de cometer um crime perfeito em Siracusa, mas Arquimedes lá estava e não só descobriu o crime como também a quantidade de ouro roubada. Suponha que havia 800 g de ouro para fazer uma coroa, cuja densidade era 20 g/cm 3. O desonesto joalheiro substituiu 200 g de ouro pela mesma massa de prata, cuja densidade era de 10 g/cm3. Arquimedes foi chamado para descobrir se havia ou não mistura de prata nesta coroa, aqui chamada de Coroa de Arquimedes. Indique a conclusão correta. Considere g = 10 m/ s2, d água = 1 g/cm3 e d mercúrio = 13,6 g/cm3. *a) Quando totalmente mergulhada em água e abandonada, a Coroa de Arquimedes ficará sujeita a uma força resultante de módulo 7,5 N. b) O volume de ouro na coroa era de 25 cm 3. c) Qua QuandoArqui ndoArquimed medes es mergulh mergulhou ou tota totalme lmente nte a tal coroa coroa em água água,, o empuxo foi de 0,75 N. d) Se a coroa for totalmente mergulhada em mercúrio, ela flutuará. e) Uma outra coroa, toda feita em prata, também com 800 g, deslocará menos água que a Coroa de Arquimedes, se ambas forem totalmente mergulhadas. (IFCE/CEFETCE-2009.2) (IFCE/CEFETCE-2009.2) - RESPOSTA: RESPOSTA: a) 7,1 N b) 850 kg/m3 3 c) 1000 kg/m Um cubo maciço de madeira, com aresta aresta h = 10,0 cm, flutua com 85,0% de seu volume submerso no líquido A (ver figura do lado esquerdo). Ao ser colocado no líquido B, o cubo afunda, repousando em uma balança que, então, indica um peso de 0,140 kgf (ver figura do lado direito). A densidade do do líquido B, B é 710 kg/ m3. Determine:
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(VUNESP/UNICID-2009.2) - ALTERNATIVA: A Devido a uma dificuldade espacial, a tubulação de água limpa de um banheiro assume em certo ponto do interior da parede uma estranha estranha geom geometria etria que, entre outras outras coisas, coisas, foi responsá responsável vel pela rachadura acidental ocorrida durante uma reforma, provocando o vazamento da água do interior do cano.
Como os canos estavam cheios de água, deve-se esperar que no interior deles, a água, representada em cor acinzentada, permanecerá em repouso conforme o indicado em
*a)
b)
c)
d)
e)
(UFOP/MG-2009.2) - ALTERNATIVA: C Para que seja possível emergir e submergir, os submarinos utilizam-se de “tanques de lastro”, que são enchidos com água ou esvaziados de acordo com a necessidade. Com base nesse fato, é correto afirmar: a) Para emergir o submarino, enche-se o tanque de lastro, pois assim aumenta seu volume. b) Para emergir o submarino, esvazia-se o tanque de lastro, pois assim diminui o seu volume. *c) Para submergir o submarino, enche-se o tanque de lastro, pois assim aumenta sua densidade. d) Para submergir o submarino, esvazia-se o tanque de lastro, pois assim diminui sua densidade. (IFMG/CEFETMG-2009.2) (IFMG/CEFETMG-2009.2) - ALT A LTERNA ERNATIVA: TIVA: D Um cilindro de madeira de massa igual a 600 g flutua com 3/4 do seu volume submerso em água. Nessas condições, a(o) (Dados: g = 10 m/s 2 e densidade da água = 1,0 g/cm 3) a) peso do cilindro é igual a 8,0 N. b) volume do cilindro é igual a 750 cm 3. c) empuxo sobre o cilindro vale 0,60 N. *d) densidade do cilindro vale 0,75 g/cm3. e) volume de água deslocado é igual a 800 cm 3. (UFV/MG-2009.2) - ALTERNATIVA: A A figura abaixo ilustra uma pessoa equilibrando um caminhão por meio de um elevador hidráulico. O caminhão tem 10 toneladas de massa e está apoiado sobre um pistão cuja área é de 6 m2. Sabendo que a área do pistão no qual a pessoa atua é de 30 cm2, é CORRETO afirmar que o valor do módulo da força que esta pessoa exerce sobre o pistão é de: (Considere a aceleração da gravidade local g = 10 m/s 2.) *a) 50 N b) 150 N c) 200 N d) 500 N
(UEG/GO-2009.2) - ALTERNATIVA: A O sistema cardiovascular dos humanos é constituído de um tubo fechado através do qual o sangue flui devido ao bombeamento exercido pelo coração. Para bombear o sangue, as paredes do coração coração se contraem contraem (sístole) (sístole) e relaxam relaxam (diástole) (diástole) periodicame periodicamente, nte, batendo em média 100 vezes por minuto. Considere que a densidade do sangue seja igual à densidade da água (d água = 1,0 kg/ m3) e que o coração consiga bombear o sangue a uma pressão de 150 mmHg acima da pressão atmosférica. Para efeito de cálculo, considere 1 atm = 750 mmHg. Fazendo a analogia entre o sistema cardiovascular cardiovascular e uma coluna de líquido, até que altura o coração consegue bombear o sangue? *a) 2,0 metros b) 1,5 metros c) 1,0 metro d) 0,5 metro (UERJ/RJ-2009.2) - ALTERNATIVA: B A maior profundidade de um determinado lago de água doce,
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(UERJ/RJ-2009.2) - ALTERNATIVA: C A figura a seguir representa um fio AB de comprimento igual a 100 cm, formado de duas partes homogêneas sucessivas: uma de alumínio e outra, mais densa, de cobre. Uma argola P que envolve o fio é deslocada de A para B.
Durante esse deslocamento, a massa de cada pedaço de comprimento AP é medida. Os resultados estão representados no gráfico abaixo:
A razão entre a densidade do alumínio e a densidade do cobre é aproximadamente aproximadamente igual a: a) 0,1 b) 0,2 *c) 0,3 d) 0,4 (UFU/MG-2009.2) - ALTERNATIVA: A A superfície de um planeta, recentemente descoberto, foi analisada por um grupo de astronautas por meio de uma sonda mecânica. Foi verificado que a maior parte do planeta era composta por certo líquido “X” até então desconhecido. A sonda utilizada consistia de um cilindro reto maciço, de base circular, que foi imersa verticalmente (direção z) dentro do líquido “X”, conforme indicado nas figuras apresentadas a seguir.
(UCS/RS-2009.2) - ALTERNATIVA: B Os samurais são antigos guerreiros japoneses que, pelas lendas, apresentavam grande habilidade como espadachins e dispunham punh am de espadasafiadíss espadasafiadíssimas imas,, que lhespermitiam lhespermitiam cortar cortar grosgrossosobjetos sosobjetos rapida rapidamen mente. te. Suponh Suponham amos os queo golpe golpe de um sam samura uraii com sua espada afiada aplique a mesma força que o golpe de um soldado com uma espada não tão afiada, mas que o golpe do samurai resulte num corte melhor do que o do soldado. Por que isso acontece? a) A lâmina da espada do samurai samurai tem uma área de contato menor e por isso exerce uma menor pressão. *b) A lâmina da espada do samurai tem uma área de contato menor e por isso exerce uma pressão maior. c) A espada do samurai tem menos massa que a do soldado, portanto, por definição, terá sempre mais energia cinética que a do soldado. d) A espada do soldado é mais rígida do que a do samurai, portanto, por definição, terá sempre menos energia cinética que a do samurai. e) A espada do soldado soldado é menos rígida que a do samurai, portanto, por definição, terá sempre menos energia cinética que a do samurai. (UERJ/RJ-2009.2) - ALTERNATIVA: C Uma pessoa totalmente imersa em uma piscina sustenta, com uma das mãos, uma esfera maciça de diâmetro igual a 10 cm, também totalmente imersa. Observe a ilustração:
A massa específica do material da esfera é igual a 5,0 g/cm 3 e a da água da piscina é igual a 1,0 g/cm3. A razãoentr razãoentree a força força quea pes pesso soaa ap aplic licaa na esfer esferaa pa para ra suste sustentá ntá-la e o peso da esfera é igual a: a) 0,2 b) 0,4 *c) 0,8 d) 1,0 (UTFPR-2009.2) - ALTERNATIVA: D Um barômetro é um instrumento usado para medir a pressão atmosférica. A figura abaixo representa um destes instrumentos numa forma simples. Ele é constituído de um tubo de vidro fechado em uma de suas extremidades e preenchido com mercúrio, que é mergulhado em um prato contendo também mercúrio. A coluna desce até uma altura de 76 cm acima do nível do mercúrio do prato. Por que isto ocorre?
Analisando-se a força de empuxo sobre a sonda, em função do deslocamento deslocamento em z, os astronautas concluíram que a densidade do líquido líquido era era diretamente diretamente proporcional proporcional a z, isto é, = 0.z, onde é constante. Nesse caso, assinale a alternativa que melhor 0 representa a força de empuxo observada, em função da posição vertical z da sonda. *a)
b)
a) Por causa da capilaridade, que provoca uma adesão das moléculas de mercúrio nas paredes do vidro que impede o seu escoamento. b) Porque quando o líquido descer, a coluna de mercúrio formará um vácuo na parte de cima do tubo que impedirá que o líquido escoe. c) Porque o vácuo formado na parte de cima do tubo produz uma pressão negativa que suporta todo o peso da coluna de mercú-
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(IFMG/EAFI-2009.2) - ALTERNA ALTERNATIVA: B Existem regiões do litoral brasileiro em que é comum, perto das praias, encontrarmos lagoas de água doce. Considere um mergulhador mergulhando a 5,0 m de profundidade no mar e depois mergulhando mergulhando também a 5,0 m de profundidade em uma lagoa no mesmo nível do mar. Sendo Pmar a pressão no mergulhador no mar e P la a pressão no fundo da lagoa, podemos dizer que: a) Pmar = P la *b) Pmar > P la c) P mar < P la d) Só é possível fazer comparações abaixo de 10m de profundidade. e) Só é possível fazer comparações abaixo de 20m de profundidade. (UDESC-2009.2) (UDESC-2009.2) - RESPOSTA: a) 1,04 × 10 5 N/m2 b) 1,2 g/cm3 c) 25 cm O tubo em forma de U da figura abaixo contém 3 líquidos diferentes L1, L 2 e L 3. As densidades dos líquidos L 2 e L3 são 1,6 g/cm3 e 1,0 g/cm3, respectivamente. Considere Patm = 10 5 N/m2 e g = 10 m/s2.
Em relação a isso determine: a) a pressão na superfície de separação entre os líquidos L 2 e L3; b) a densidade do líquido L1; c) a altura da coluna de L 2 acima da superfície de separação entre L2 e L 3 após o equilíbrio, caso o líquido L1 seja retirado do tubo em forma de U. (UDESC-2009.2) - RESPOSTA: a) 160 cm3 e 2,4 N b) 3,0 3,0 N e 0,6 N c) 2,25 2,25 × 103 Pa Um cilindro, cuja área da base é igual a 20 cm 2, está flutuando em um líquido de densidade igual a 1,5 × 10 3 kg/m3, conforme ilustra a figura abaixo. Considere g = 10 m/s 2.
(UFMS-2009.2) - ALTERNATIVA: D A figura mostra um recipiente em repouso com água sobre uma mesa, e dois balões, sendo o da esquerda de vidro (inflexível), e o da direita de borracha (flexível), e estão totalmente imersos na água mantendo suspensos, suspensos, em equilíbrio, dois blocos sólidos de densidade maior que a água, impermeáveis e de massa igual a 1,0 kg cada. Todo esse sistema se encontra no alto de uma montanha acima do nível do mar onde a pressão atmosférica é P. Considere a aceleração da gravidade igual a 10 m/s 2 e, com fundamentos na mecânica dos fluidos, assinale a alternativa correta.
a) A força de empuxo aplicada aplicada pela água em cada cada balão é igual a 10N. b) A força de empuxo aplicada pela água em cada bloco é igual ao peso da água que os balões deslocaram. c) Se esse sistema for levado até o nível do mar onde a pressão atmosférica é maior que P, a pressão da água aumentará apenas na sua superfície. *d) Se esse sistema for levado até o nível do mar, onde a pressão atmosférica é maior que P, a força de empuxo no balão de borracha diminuirá, e o bloco puxará o balão para o fundo. e) Se esse sistema for levado até o nível do mar, onde a pressão atmosférica é maior que P, a força de empuxo no balão de vidro aumentará e puxará o bloco para cima. (UNESP-2009.2) - RESPOSTA: 1560 mm e 1040 mm O esfignomanômetro de Riva-Rocci foi um dos primeiros aparelhos desenvolvidos para se medir a pressão arterial. Atualmente, devido ao mercúrio presente nesses aparelhos, eles vêm sendo substituídos por esfignomanômetros eletrônicos, sem mercúrio, para reduzir impactos ambientais. Para uma pessoa saudável, a pressão arterial máxima equilibra a coluna de mercúrio a uma altura máxima de 120 mm e a pressão arterial mínima equilibra a coluna de mercúrio a uma altura mínima de 80 mm. Se o esfignomanômetro de Riva-Rocci utilizasse água ao invés de mercúrio, quais seriam as alturas máxima e mínima, em milímetros, da coluna de água que seria equilibrada pelos valores máximos e mínimos da pressão arterial de uma pessoa saudável? Considere que a densidade do mercúrio é 13 vezes maior que a da água. (UNESP-2009.2) - RESPOSTA: 1,2 × 105 Pa e 780 mmHg Dois mergulhadores, A e B, estão submersos em um tanque, a diferentes profundidades, de forma que a distância vertical entre eles é de 1,3 metro, como indica a figura. Sabendo-se que o manômetro localizado no pulso do mergulhador B indica uma pressão de 880 mmHg, determine essa pressão, em pascal, e a indicação do manômetro do mergulhador A, em mmHg.
a) Calcu Calcule le o volum volumee do líquid líquidoo des desloc locadopelo adopelo cilind cilindro ro e o em empux puxoo
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(VUNESP/UFTM-2009.2) - RESPOSTA: a) 20 kg b) 300 N Abandonado à deriva nas águas tranquilas de um lago, um tonel de 50 litros flutua em posição vertical, mantendo 3/5 de seu volume fora da água, como mostra o desenho.
Para esse tonel, admitindo que a densidade da água do lago tem valor 1.103 kg/m3 e que a aceleração da gravidade tem valor g = 10 m/s2, determine: a) sua massa, em kg. b) a intensidade da menor força que se deve aplicar verticalmenverticalmente e para baixo, sobre o centro do tonel, de modo a torná-lo completamente submerso. submerso. (UFPel-2009.2) - ALTERNATIVA: A De acordo com a Hidrostática, analise as afirmações abaixo. I) O empuxo que atua em um corpo é tanto maior quanto maior for a quantidade de líquido que ele desloca. II) O valor do empuxo que atua em um corpo mergulhado em um líquido é igual ao peso do líquido deslocado pelo corpo. III) Todo corpo mergulhado em um líquido e que não esteja em contato com as paredes do recipiente que o contém, recebe um empuxo vertical, para cima, igual ao peso do líquido deslocado pelo corpo. IV) Um balão sobe na atmosfera porque sua densidade média é menor do que a do ar. Como a densidade do ar diminui com a altitude, o valor do empuxo sobre o balão diminuirá enquanto ele sobe. V) Um objeto pendurado em um dinamômetro está totalmente mergulhado num líquido sem encostar no fundo do recipiente. Em relação à situação descrita, se o objeto estiver parado, a indicação do dinamômetro é igual ao empuxo que o corpo recebe do líquido. Quantas afirmativas estão INCORRETAS? *a) Uma. b) Duas. c) Três. d) Quatro. e) Cinco. (UFLA/MG-2009.2) - ALTERNATIVA: D Um corpo C, no ar, pesa 0,185 N. Quando esse corpo é preso a um dinamômetro D fixado no fundo de um reservatório de água, o dinamômetro passa a indicar a leitura de 0,815 N (figura abaixo). Considerando a densidade da água 10 3 kg/m3, pode-se afirmar que a densidade do corpo é: a) 1,2 × 103 kg/m3 b) 1,0 × 103 kg/m3 c) 3,14 × 103 kg/m3 *d) 0,185 × 103 kg/m3
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MECÂNICA: HIDRODINÂMICA VESTIBULARES 2009.1 VESTIBULARES VESTIBULARES 2009.2 2009.2 PÁG. PÁG. 128 (UFCG/PB-2009.1) - ALTERNATIVA: D O perfil da asa de um avião está sob a ação de um fluxo de ar como mostra a simulação na figura. Fig 4 2009 HDR
(UFMS-2009.1) - RESPOSTA OFICIAL: SOMA = 005 (001+004) A roda d’água de uma bomba hidráulica está girando com velocidade angular constante constante igual a W. A roda d’água possui possui diâmetro D e está sendo alimentada pelo topo, no ponto A, por uma vazão constante de água. Depois de meia volta, a água é despejada na parte inferior da roda, no ponto B, com a mesma vazão e velocidade do ponto A. A bomba hidráulica retira água, no ponto E, de um reservatório, a uma vazão constante e igual a 2 (kg/s), cujo nível de água está a uma altura Y1 do solo, e a bombeia até uma altura Y2 do solo, no ponto S, com a mesma vazão e velocidade no ponto E, veja a figura. Considere a água como um fluido ideal e com fundamentos na mecânica dos fluidos, assinale a(s) proposição(ões) proposição(ões) correta(s). correta(s). Fig 31 2009 HDR
Em relação ao experimento é CORRETO afirmar que a) o módulo da velocidade do ar é maior acima do perfil do que abaixo dele porque, aí, o ar percorre uma distância maior. b) a pressão exercida pelo ar sobre o perfil na parte de baixo é menor do que a pressão exercida por ele na parte de cima do perfil. c) a pressão do ar sobre o perfil é menor na parte de cima porque a velocidade do ar nessa região é maior. *d) a pressão exercida pelo ar sobre a parte superior do perfil é menor e, como conseqüência, sua velocidade é maior nessa região. e) nenhuma das alternativas anteriores é satisfatória no contexto da análise do experimento. (UFBA-2009.1) - RESOLUÇÃO NO FINAL Um experimento interessante interessante e de fácil execução pode ser realizado com uma fita de papel. Esse experimento consiste em aproximar a fita do lábio inferior e soprá-la, verificando-se, então, que ela se eleva.
(001) O trabalho realizado pelo campo gravitacional, em um elemento de massa de água que foi despejado no topo superior da roda, no ponto A, até ser despejado na parte parte inferior da roda, no ponto B, não depende da velocidade angular W da roda d`água. (002) A potência motriz média, realizada pela roda d’água, depende da velocidade angular W da roda. (004) O torque motriz médio, realizado pela roda com relação ao eixo de rotação, depende do diâmetro da roda. (008) O trabalho realizado pelo campo gravitacional em um elemento de massa que foi bombeado desde a entrada na bomba, no ponto E, até a saída do condutor, no ponto S, depende da vazão 2 em que a água é bombeada e do desnível (Y 2 – Y 1). (016) Se multiplicarmos a vazão 2 (kg/s) pela altura Y 2 (m), e pela aceleração da gravidade (m/s 2), teremos um resultado em unidades de energia em Joules. (FEI/SP-2009.1) - ALTERNAT ALTERNATIVA: IVA: A Em uma caixa d’água havia uma rachadura por onde escoaram 105,135 litros de água em 10,0 s. Qual é a vazão deste vazamento em L/s? *a) 10,5135 b) 105,315 c) 1,531 d) 1005,31 e) 15,315
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VESTIBULARES 2009.2 (UFMS-2009.2) - RESPOSTA: SOMA = 014 (002+004+008) As formigas constroem seus formigueiros, com várias galerias subterrâneas, que se comunicam entre si e com a superfície do solo. A figura abaixo mostra uma galeria que possui duas comunicações externas externas em alturas diferentes, diferentes, sendo a abertura abertura A mais alta e a B mais baixa. O gráfico ao lado mostra a distribuição da velocidade do vento com a altura y nessa região, e nota-se que, devido ao atrito entre o solo e o ar, a velocidade do vento aumenta com a altura y atingindo um valor limite a partir de uma determinada altura. As aberturas A e B possuem secções planas e paralelas ao plano horizontal e as velocidades do vento nessas aberturas também são horizontais. Considere todo o ar na mesma temperatura e como um fluido ideal, a abertura A muito distante da abertura B, e, com fundamentos na mecânica dos fluidos, assinale a(s) afirmação(ões) correta(s).
(001) A velocidade velocidade do ar, na abertura abertura A, é menor que a velocidade do ar na abertura B. (002) A pressão do ar, na abertura A, é menor que a pressão do ar na abertura B. (004) O ar circulará pela galeria, entrando pela abertura B e saindo pela abertura A. (008) Se o vento nessa região estiver com a mesma distribuição de velocidades, não importa o seu sentido, isto é, da direita para a esquerda ou da esquerda para a direita, a diferença entre a pressão da abertura A e a pressão da abertura B será a mesma. (016) Se as aberturas A e B estivessem na mesma altura, circularia ar pela galeria, da abertura A para a abertura B.