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Prévia do material em texto

Ministério
da Educação
15Novembro/2014
Engenharia de Controle 
e Automação
LEIA COM ATENÇÃO AS INSTRUÇÕES ABAIXO.
ϭ͘��sĞƌŝĮƋƵĞ� ƐĞ͕� ĂůĠŵ� ĚĞƐƚĞ� ĐĂĚĞƌŶŽ͕� ǀŽĐġ� ƌĞĐĞďĞƵ� Ž� �ĂĚĞƌŶŽ� ĚĞ� ZĞƐƉŽƐƚĂƐ͕� ĚĞƐƟŶĂĚŽ� ă� ƚƌĂŶƐĐƌŝĕĆŽ� ĚĂƐ�
ƌĞƐƉŽƐƚĂƐ� ĚĂƐ� ƋƵĞƐƚƁĞƐ� ĚĞ� ŵƷůƟƉůĂ� ĞƐĐŽůŚĂ� ;ŽďũĞƟǀĂƐͿ͕� ĚĂƐ� ƋƵĞƐƚƁĞƐ� ĚŝƐĐƵƌƐŝǀĂƐ� Ğ� ĚŽ� ƋƵĞƐƟŽŶĄƌŝŽ� ĚĞ�
ƉĞƌĐĞƉĕĆŽ�ĚĂ�ƉƌŽǀĂ͘
Ϯ͘��ŽŶĮƌĂ�ƐĞ�ĞƐƚĞ�ĐĂĚĞƌŶŽ�ĐŽŶƚĠŵ�ĂƐ�ƋƵĞƐƚƁĞƐ�ĚŝƐĐƵƌƐŝǀĂƐ�Ğ�ĚĞ�ŵƷůƟƉůĂ�ĞƐĐŽůŚĂ�;ŽďũĞƟǀĂƐͿ͕�ĚĞ�ĨŽƌŵĂĕĆŽ�
ŐĞƌĂů�Ğ�ĚŽ�ĐŽŵƉŽŶĞŶƚĞ�ĞƐƉĞĐşĮĐŽ�ĚĂ�ĄƌĞĂ͕�Ğ�ĂƐ�ƌĞůĂƟǀĂƐ�ă�ƐƵĂ�ƉĞƌĐĞƉĕĆŽ�ĚĂ�ƉƌŽǀĂ͘��Ɛ�ƋƵĞƐƚƁĞƐ�ĞƐƚĆŽ�
ĂƐƐŝŵ�ĚŝƐƚƌŝďƵşĚĂƐ͗
Partes
Número das 
questões
Peso das 
questões no 
componente
Peso dos 
componentes no 
cálculo da nota
&ŽƌŵĂĕĆŽ�'ĞƌĂůͬ�ŝƐĐƵƌƐŝǀĂƐ �ϭ�Ğ��Ϯ 40%
25%
&ŽƌŵĂĕĆŽ�'ĞƌĂůͬKďũĞƟǀĂƐ ϭ�Ă�ϴ 60%
�ŽŵƉŽŶĞŶƚĞ��ƐƉĞĐşĮĐŽͬ�ŝƐĐƵƌƐŝǀĂƐ �ϯ�Ă��ϱ 15%
75%�ŽŵƉŽŶĞŶƚĞ��ƐƉĞĐşĮĐŽͬKďũĞƟǀĂƐ
EƷĐůĞŽ�ĚĞ��ŽŶƚĞƷĚŽƐ��ĄƐŝĐŽƐ
EƷĐůĞŽ�ĚĞ��ŽŶƚĞƷĚŽƐ�WƌŽĮƐƐŝŽŶĂůŝnjĂŶƚĞƐ
ϵ�Ă�ϭϴ
ϭϵ�Ă�ϯϱ
ϴϱй
YƵĞƐƟŽŶĄƌŝŽ�ĚĞ�WĞƌĐĞƉĕĆŽ�ĚĂ�WƌŽǀĂ� ϭ�Ă�ϵ - -
ϯ͘��sĞƌŝĮƋƵĞ�ƐĞ�Ă�ƉƌŽǀĂ�ĞƐƚĄ�ĐŽŵƉůĞƚĂ�Ğ�ƐĞ�Ž�ƐĞƵ�ŶŽŵĞ�ĞƐƚĄ�ĐŽƌƌĞƚŽ�ŶŽ��ĂĚĞƌŶŽ�ĚĞ�ZĞƐƉŽƐƚĂƐ͘��ĂƐŽ�ĐŽŶƚƌĄƌŝŽ͕�
ĂǀŝƐĞ�ŝŵĞĚŝĂƚĂŵĞŶƚĞ�Ƶŵ�ĚŽƐ�ƌĞƐƉŽŶƐĄǀĞŝƐ�ƉĞůĂ�ĂƉůŝĐĂĕĆŽ�ĚĂ�ƉƌŽǀĂ͘�sŽĐġ�ĚĞǀĞ�ĂƐƐŝŶĂƌ�Ž��ĂĚĞƌŶŽ�ĚĞ�ZĞƐƉŽƐƚĂƐ�
ŶŽ�ĞƐƉĂĕŽ�ƉƌſƉƌŝŽ͕�ĐŽŵ�ĐĂŶĞƚĂ�ĞƐĨĞƌŽŐƌĄĮĐĂ�ĚĞ�ƟŶƚĂ�ƉƌĞƚĂ͘
ϰ͘��KďƐĞƌǀĞ�ĂƐ�ŝŶƐƚƌƵĕƁĞƐ�ƐŽďƌĞ�Ă�ŵĂƌĐĂĕĆŽ�ĚĂƐ�ƌĞƐƉŽƐƚĂƐ�ĚĂƐ�ƋƵĞƐƚƁĞƐ�ĚĞ�ŵƷůƟƉůĂ�ĞƐĐŽůŚĂ�;ĂƉĞŶĂƐ�ƵŵĂ�ƌĞƐƉŽƐƚĂ�
ƉŽƌ�ƋƵĞƐƚĆŽͿ͕�ĞdžƉƌĞƐƐĂƐ�ŶŽ��ĂĚĞƌŶŽ�ĚĞ�ZĞƐƉŽƐƚĂƐ͘
ϱ͘��hƐĞ�ĐĂŶĞƚĂ�ĞƐĨĞƌŽŐƌĄĮĐĂ�ĚĞ�ƟŶƚĂ�ƉƌĞƚĂ͕�ƚĂŶƚŽ�ƉĂƌĂ�ŵĂƌĐĂƌ�ĂƐ�ƌĞƐƉŽƐƚĂƐ�ĚĂƐ�ƋƵĞƐƚƁĞƐ�ŽďũĞƟǀĂƐ�ƋƵĂŶƚŽ�ƉĂƌĂ�
ĞƐĐƌĞǀĞƌ�ĂƐ�ƌĞƐƉŽƐƚĂƐ�ĚĂƐ�ƋƵĞƐƚƁĞƐ�ĚŝƐĐƵƌƐŝǀĂƐ͘
ϲ͘�ZĞƐƉŽŶĚĂ� ĐĂĚĂ� ƋƵĞƐƚĆŽ� ĚŝƐĐƵƌƐŝǀĂ� Ğŵ͕� ŶŽ�ŵĄdžŝŵŽ͕� ϭϱ� ůŝŶŚĂƐ͘� YƵĂůƋƵĞƌ� ƚĞdžƚŽ� ƋƵĞ� ƵůƚƌĂƉĂƐƐĂƌ� Ž� ĞƐƉĂĕŽ�
ĚĞƐƟŶĂĚŽ�ă�ƌĞƐƉŽƐƚĂ�ƐĞƌĄ�ĚĞƐĐŽŶƐŝĚĞƌĂĚŽ͘
ϳ͘�EĆŽ�ƵƐĞ�ĐĂůĐƵůĂĚŽƌĂ͖�ŶĆŽ�ƐĞ�ĐŽŵƵŶŝƋƵĞ�ĐŽŵ�ŽƐ�ĚĞŵĂŝƐ�ĞƐƚƵĚĂŶƚĞƐ�ŶĞŵ�ƚƌŽƋƵĞ�ŵĂƚĞƌŝĂů�ĐŽŵ�ĞůĞƐ͖�
ŶĆŽ�ĐŽŶƐƵůƚĞ�ŵĂƚĞƌŝĂů�ďŝďůŝŽŐƌĄĮĐŽ͕�ĐĂĚĞƌŶŽƐ�ŽƵ�ĂŶŽƚĂĕƁĞƐ�ĚĞ�ƋƵĂůƋƵĞƌ�ĞƐƉĠĐŝĞ͘
ϴ͘�sŽĐġ�ƚĞƌĄ�ƋƵĂƚƌŽ�ŚŽƌĂƐ�ƉĂƌĂ�ƌĞƐƉŽŶĚĞƌ�ăƐ�ƋƵĞƐƚƁĞƐ�ĚĞ�ŵƷůƟƉůĂ�ĞƐĐŽůŚĂ�Ğ�ĚŝƐĐƵƌƐŝǀĂƐ�Ğ�ĂŽ�ƋƵĞƐƟŽŶĄƌŝŽ�ĚĞ�
ƉĞƌĐĞƉĕĆŽ�ĚĂ�ƉƌŽǀĂ͘
ϵ͘�YƵĂŶĚŽ�ƚĞƌŵŝŶĂƌ͕ �ĞŶƚƌĞŐƵĞ�ĂŽ��ƉůŝĐĂĚŽƌ�ŽƵ�&ŝƐĐĂů�Ž�ƐĞƵ��ĂĚĞƌŶŽ�ĚĞ�ZĞƐƉŽƐƚĂƐ͘
10. Atenção!�sŽĐġ�ĚĞǀĞƌĄ�ƉĞƌŵĂŶĞĐĞƌ͕ �ŶŽ�ŵşŶŝŵŽ͕�ƉŽƌ�ƵŵĂ�ŚŽƌĂ͕�ŶĂ�ƐĂůĂ�ĚĞ�ĂƉůŝĐĂĕĆŽ�ĚĂƐ�ƉƌŽǀĂƐ�Ğ�Ɛſ�ƉŽĚĞƌĄ�
ůĞǀĂƌ�ĞƐƚĞ��ĂĚĞƌŶŽ�ĚĞ�WƌŽǀĂ�ĂƉſƐ�ĚĞĐŽƌƌŝĚĂƐ�ƚƌġƐ�ŚŽƌĂƐ�ĚŽ�ŝŶşĐŝŽ�ĚŽ��džĂŵĞ͘
*R1520141*
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FORMAÇÃO GERAL
QUESTÃO DISCURSIVA 1
KƐ�ĚĞƐĂĨŝŽƐ�ĚĂ�ŵŽďŝůŝĚĂĚĞ�ƵƌďĂŶĂ�ĂƐƐŽĐŝĂŵͲƐĞ�ă�ŶĞĐĞƐƐŝĚĂĚĞ�ĚĞ�ĚĞƐĞŶǀŽůǀŝŵĞŶƚŽ�ƵƌďĂŶŽ�ƐƵƐƚĞŶƚĄǀĞů͘�
��KEh�ĚĞĮŶĞ�ĞƐƐĞ�ĚĞƐĞŶǀŽůǀŝŵĞŶƚŽ�ĐŽŵŽ�ĂƋƵĞůĞ�ƋƵĞ�ĂƐƐĞŐƵƌĂ�ƋƵĂůŝĚĂĚĞ�ĚĞ�ǀŝĚĂ͕�ŝŶĐůƵşĚŽƐ�ŽƐ�ĐŽŵƉŽŶĞŶƚĞƐ�
ĞĐŽůſŐŝĐŽƐ͕�ĐƵůƚƵƌĂŝƐ͕�ƉŽůşƟĐŽƐ͕�ŝŶƐƟƚƵĐŝŽŶĂŝƐ͕�ƐŽĐŝĂŝƐ�Ğ�ĞĐŽŶƀŵŝĐŽƐ�ƋƵĞ�ŶĆŽ�ĐŽŵƉƌŽŵĞƚĂŵ�Ă�ƋƵĂůŝĚĂĚĞ�ĚĞ�
ǀŝĚĂ�ĚĂƐ�ĨƵƚƵƌĂƐ�ŐĞƌĂĕƁĞƐ͘
K�ĞƐƉĂĕŽ�ƵƌďĂŶŽ�ďƌĂƐŝůĞŝƌŽ�Ġ�ŵĂƌĐĂĚŽ�ƉŽƌ�ŝŶƷŵĞƌŽƐ�ƉƌŽďůĞŵĂƐ�ĐŽƟĚŝĂŶŽƐ�Ğ�ƉŽƌ�ǀĄƌŝĂƐ�ĐŽŶƚƌĂĚŝĕƁĞƐ͘�hŵĂ�ĚĂƐ�
ŐƌĂŶĚĞƐ�ƋƵĞƐƚƁĞƐ�Ğŵ�ĚĞďĂƚĞ�Ěŝnj�ƌĞƐƉĞŝƚŽ�ă�ŵŽďŝůŝĚĂĚĞ�ƵƌďĂŶĂ͕�ƵŵĂ�ǀĞnj�ƋƵĞ�Ž�ŵŽŵĞŶƚŽ�Ġ�ĚĞ�ŵŽƚŽƌŝnjĂĕĆŽ�
ĚŽƐ�ĚĞƐůŽĐĂŵĞŶƚŽƐ�ĚĂ�ƉŽƉƵůĂĕĆŽ͕�ƉŽƌ�ŵĞŝŽ�ĚĞ�ƚƌĂŶƐƉŽƌƚĞ�ĐŽůĞƟǀŽ�Ğ�ŝŶĚŝǀŝĚƵĂů͘
�ŽŶƐŝĚĞƌĞ�ŽƐ�ĚĂĚŽƐ�ĚŽ�ƐĞŐƵŝŶƚĞ�ƋƵĂĚƌŽ͘
Mobilidade urbana em cidade com mais de 500 mil habitantes
Modalidade Tipologia Porcentagem (%)
EĆŽ�ŵŽƚŽƌŝnjĂĚŽ ��ƉĠ ϭϱ͕ϵ�ŝĐŝĐůĞƚĂ� Ϯ͕ϳ
DŽƚŽƌŝnjĂĚŽ�ĐŽůĞƟǀŽ
NŶŝďƵƐ�ŵƵŶŝĐŝƉĂů ϮϮ͕Ϯ
NŶŝďƵƐ�ŵĞƚƌŽƉŽůŝƚĂŶŽ ϰ͕ϱ
DĞƚƌŽĨĞƌƌŽǀŝĄƌŝŽ Ϯϱ͕ϭ
DŽƚŽƌŝnjĂĚŽ�ŝŶĚŝǀŝĚƵĂů �ƵƚŽŵſǀĞů Ϯϳ͕ϱDŽƚŽĐŝĐůĞƚĂ Ϯ͕ϭ
dĞŶĚŽ� Ğŵ� ǀŝƐƚĂ� Ž� ƚĞdžƚŽ� Ğ� Ž� ƋƵĂĚƌŽ� ĚĞ� ŵŽďŝůŝĚĂĚĞ� ƵƌďĂŶĂ� ĂƉƌĞƐĞŶƚĂĚŽƐ͕� ƌĞĚŝũĂ� Ƶŵ� ƚĞdžƚŽ� ĚŝƐƐĞƌƚĂƟǀŽ͕�
ĐŽŶƚĞŵƉůĂŶĚŽ�ŽƐ�ƐĞŐƵŝŶƚĞƐ�ĂƐƉĞĐƚŽƐ͗
ĂͿ� ĐŽŶƐĞƋƵġŶĐŝĂƐ͕�ƉĂƌĂ�Ž�ĚĞƐĞŶǀŽůǀŝŵĞŶƚŽ�ƐƵƐƚĞŶƚĄǀĞů͕�ĚŽ�ƵƐŽ�ŵĂŝƐ�ĨƌĞƋƵĞŶƚĞ�ĚŽ�ƚƌĂŶƐƉŽƌƚĞ�ŵŽƚŽƌŝnjĂĚŽ͖�
;ǀĂůŽƌ͗�ϱ͕Ϭ�ƉŽŶƚŽƐͿ
ďͿ� ĚƵĂƐ�ĂĕƁĞƐ�ĚĞ�ŝŶƚĞƌǀĞŶĕĆŽ�ƋƵĞ�ĐŽŶƚƌŝďƵĂŵ�ƉĂƌĂ�Ă�ĐŽŶƐŽůŝĚĂĕĆŽ�ĚĞ�ƉŽůşƟĐĂ�ƉƷďůŝĐĂ�ĚĞ�ŝŶĐƌĞŵĞŶƚŽ�ĂŽ�ƵƐŽ�
ĚĞ�ďŝĐŝĐůĞƚĂ�ŶĂ�ĐŝĚĂĚĞ�ŵĞŶĐŝŽŶĂĚĂ͕�ĂƐƐĞŐƵƌĂŶĚŽͲƐĞ�Ž�ĚĞƐĞŶǀŽůǀŝŵĞŶƚŽ�ƐƵƐƚĞŶƚĄǀĞů͘�;ǀĂůŽƌ͗�ϱ͕Ϭ�ƉŽŶƚŽƐͿ
RASCUNHO
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QUESTÃO DISCURSIVA 2
dƌġƐ�ũŽǀĞŶƐ�ĚĞ�ϭϵ�ĂŶŽƐ�ĚĞ�ŝĚĂĚĞ͕�ŵŽƌĂĚŽƌĞƐ�ĚĞ�ƌƵĂ͕�ĨŽƌĂŵ�ƉƌĞƐŽƐ�Ğŵ�ŇĂŐƌĂŶƚĞ͕�ŶĞƐƚĂ�ƋƵĂƌƚĂͲĨĞŝƌĂ͕�ƉŽƌ�ƚĞƌĞŵ�
ĂƚĞĂĚŽ�ĨŽŐŽ�Ğŵ�Ƶŵ�ũŽǀĞŵ�ĚĞ�ϭϳ�ĂŶŽƐ͕�ŐƵĂƌĚĂĚŽƌ�ĚĞ�ĐĂƌƌŽƐ͘�K�ŵŽƟǀŽ͕�ƐĞŐƵŶĚŽ�Ă�ϭϰ͘a��W͕ �ĨŽŝ�ƵŵĂ�͚͛ďƌŝŐĂ�ƉŽƌ�
ƉŽŶƚŽ͛͛͘ �hŵ�ŵŽƚŽƌŝƐƚĂ�ĚĞƵ�͚͛Ƶŵ�ƚƌŽĐĂĚŽ͛͛�ĂŽ�ŵĞŶŽƌ͕ �Ž�ƋƵĞ�ŝƌƌŝƚŽƵ�ŽƐ�ƚƌġƐ�ŵŽƌĂĚŽƌĞƐ�ĚĞ�ƌƵĂ͕�ƋƵĞ�ƚĂŵďĠŵ�
ŐƵĂƌĚĂǀĂŵ�ĐĂƌƌŽƐ�ŶŽ� ůŽĐĂů͘�K�ŵĞŶŽƌ�ĨŽŝ� ůĞǀĂĚŽ�ĂŽ�,ŽƐƉŝƚĂů�ĚĂƐ��ůşŶŝĐĂƐ� ;,�Ϳ�ƉŽƌ�WDƐ�ƋƵĞ�ƉĂƐƐĂǀĂŵ�ƉĞůŽ�
ůŽĐĂů͘�^ĞŐƵŶĚŽ�Ž�,�͕�ĞůĞ�ƚĞǀĞ�ƋƵĞŝŵĂĚƵƌĂƐ�ůĞǀĞƐ�ŶŽ�ŽŵďƌŽ�ĞƐƋƵĞƌĚŽ͕�ĨŽŝ�ŵĞĚŝĐĂĚŽ�Ğ͕�Ğŵ�ƐĞŐƵŝĚĂ͕�ůŝďĞƌĂĚŽ͘�
KƐ�ŝŶĚŝĐŝĂĚŽƐ�ƉŽĚĞŵ�ƉĞŐĂƌ�ĚĞ�ϭϮ�Ă�ϯϬ�ĂŶŽƐ�ĚĞ�ƉƌŝƐĆŽ͕�ƐĞ�ĮĐĂƌ�ĐŽŵƉƌŽǀĂĚŽ�ƋƵĞ�Ă�ŝŶƚĞŶĕĆŽ�ĞƌĂ�ŵĂƚĂƌ�Ž�ŵĞŶŽƌ͘ �
�ĂƐŽ�ĐŽŶƚƌĄƌŝŽ͕�ĐŽŶĨŽƌŵĞ�Ă�ϭϰ͘a��W͕ �ŽƐ�ƚƌġƐ�ƉŽĚĞƌĆŽ�ƉĞŐĂƌ�ĚĞ�Ƶŵ�Ă�ƚƌġƐ�ĂŶŽƐ�ĚĞ�ĐĂĚĞŝĂ͘
�ŝƐƉŽŶşǀĞů�Ğŵ͗фŚƩƉ͗ͬͬǁǁǁϭ͘ĨŽůŚĂ͘ƵŽů͘ĐŽŵ͘ďƌх͘��ĐĞƐƐŽ�Ğŵ͗�Ϯϴ�ũƵů͘�ϮϬϭϯ�;ĂĚĂƉƚĂĚŽͿ͘
��ƉĂƌƟƌ�ĚĂ�ƐŝƚƵĂĕĆŽ�ŶĂƌƌĂĚĂ͕�ĞůĂďŽƌĞ�Ƶŵ�ƚĞdžƚŽ�ĚŝƐƐĞƌƚĂƟǀŽ�ƐŽďƌĞ�ǀŝŽůġŶĐŝĂ�ƵƌďĂŶĂ͕�ĂƉƌĞƐĞŶƚĂŶĚŽ͗
ĂͿ��ĂŶĄůŝƐĞ�ĚĞ�ĚƵĂƐ�ĐĂƵƐĂƐ�ĚŽ�ƟƉŽ�ĚĞ�ǀŝŽůġŶĐŝĂ�ĚĞƐĐƌŝƚĂ�ŶŽ�ƚĞdžƚŽ͖�;ǀĂůŽƌ͗�ϳ͕Ϭ�ƉŽŶƚŽƐͿ
ďͿ��ĚŽŝƐ�ĨĂƚŽƌĞƐ�ƋƵĞ�ĐŽŶƚƌŝďƵŝƌŝĂŵ�ƉĂƌĂ�ƐĞ�ĞǀŝƚĂƌ�Ž�ĨĂƚŽ�ĚĞƐĐƌŝƚŽ�ŶĂ�ŶŽơĐŝĂ͘�;ǀĂůŽƌ͗�ϯ͕Ϭ�ƉŽŶƚŽƐͿ
RASCUNHO
1
2
ϯ
4
5
6
7
ϴ
9
10
11
12
ϭϯ
14
15
*R1520143*
4
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 01
K�ƚƌĞĐŚŽ�ĚĂ�ŵƷƐŝĐĂ�͞ EŽƐ��ĂŝůĞƐ�ĚĂ�sŝĚĂ͕͟ �ĚĞ�DŝůƚŽŶ�EĂƐĐŝŵĞŶƚŽ͕�͞ ƚŽĚŽ�ĂƌƟƐƚĂ�ƚĞŵ�ĚĞ�ŝƌ�ĂŽŶĚĞ�Ž�ƉŽǀŽ�ĞƐƚĄ͕͟ �Ġ�ĂŶƟŐŽ͕�
Ğ�Ă�ŵƷƐŝĐĂ͕�ĚĞ�ƚĆŽ�ƚŽĐĂĚĂ͕�ĂĐĂďŽƵ�ƉŽƌ�ƐĞ�ƚŽƌŶĂƌ�Ƶŵ�ĞƐƚĞƌĞſƟƉŽ�ĚĞ�ƚŽĐĂĚŽƌĞƐ�ĚĞ�ǀŝŽůƁĞƐ�Ğ�ĚĞ�ƌŽĚĂƐ�ĚĞ�ĂŵŝŐŽƐ�Ğŵ�
sŝƐĐŽŶĚĞ�ĚĞ�DĂƵĄ͕�ŶŽƐ�ĂŶŽƐ�ϭϵϳϬ͘��ŵ�ƚĞŵƉŽƐ�ĚŝŐŝƚĂŝƐ͕�ƉŽƌĠŵ͕�ĞůĂ�ĮĐŽƵ�ŵĂŝƐ�ĂƚƵĂů�ĚŽ�ƋƵĞ�ŶƵŶĐĂ͘���ĨĄĐŝů�ĞŶƚĞŶĚĞƌ�
Ž�ƉŽƌƋƵġ͗�ĂŶƟŐĂŵĞŶƚĞ͕�ƋƵĂŶĚŽ�Ă�ŝŶĨŽƌŵĂĕĆŽ�ƐĞ�ĐŽŶĐĞŶƚƌĂǀĂ�Ğŵ�ĐĞŶƚƌŽƐ�ĚĞ�ĞdžƉŽƐŝĕĆŽ͕�ǀĞşĐƵůŽƐ�ĚĞ�ĐŽŵƵŶŝĐĂĕĆŽ͕�
ĞĚŝƚŽƌĂƐ͕�ŵƵƐĞƵƐ�Ğ�ŐƌĂǀĂĚŽƌĂƐ͕�ĞƌĂ�ƉƌĞĐŝƐŽ�ƉĂƐƐĂƌ�ƉŽƌ�ƵŵĂ�ƐĠƌŝĞ�ĚĞ�ĐƵƌĂĚŽƌĞƐ͕�ƉĂƌĂ�ŐĂƌĂŶƟƌ�Ă�ƉƵďůŝĐĂĕĆŽ�ĚĞ�Ƶŵ�
ĂƌƟŐŽ�ŽƵ�ůŝǀƌŽ͕�Ă�ŐƌĂǀĂĕĆŽ�ĚĞ�Ƶŵ�ĚŝƐĐŽ�ŽƵ�Ă�ƉƌŽĚƵĕĆŽ�ĚĞ�ƵŵĂ�ĞdžƉŽƐŝĕĆŽ͘�K�ŵĞƐŵŽ�ĨƵŶŝů͕�ƋƵĞ�ƉŽĚĞƌŝĂ�ƐĞƌ�ŝŶũƵƐƚŽ�Ğ�
ĚĞŝdžĂƌ�ŐƌĂŶĚĞƐ�ƚĂůĞŶƚŽƐ�ĚĞ�ĨŽƌĂ͕�ƐŝŵƉůĞƐŵĞŶƚĞ�ƉŽƌƋƵĞ�ŶĆŽ�ƟŶŚĂŵ�ĂĐĞƐƐŽ�ăƐ�ĨĞƌƌĂŵĞŶƚĂƐ͕�ăƐ�ƉĞƐƐŽĂƐ�ŽƵ�ăƐ�ĨŽŶƚĞƐ�
ĚĞ�ŝŶĨŽƌŵĂĕĆŽ͕�ƚĂŵďĠŵ�ƐĞƌǀŝĂ�ĐŽŵŽ�ĮůƚƌŽ�ĚĞ�ƋƵĂůŝĚĂĚĞ͘�dŽĐĂƌ�ǀŝŽůĆŽ�ŽƵ�ĞŶĐĞŶĂƌ�ƵŵĂ�ƉĞĕĂ�ĚĞ�ƚĞĂƚƌŽ�Ğŵ�Ƶŵ�ŐƌĂŶĚĞ�
ĂƵĚŝƚſƌŝŽ�ĐŽƐƚƵŵĂǀĂ�ƚĞƌ�Ƶŵ�ƉĞƐŽ�ŵƵŝƚŽ�ŵĂŝŽƌ�ĚŽ�ƋƵĞ� ĨĂnjġͲůŽ�Ğŵ�Ƶŵ�ďĂƌ͕ �Ƶŵ�ĐĞŶƚƌŽ�ĐƵůƚƵƌĂů�ŽƵ�ƵŵĂ�ĐĂůĕĂĚĂ͘�
EĂƐ�ƌĂƌĂƐ�ŽĐĂƐŝƁĞƐ�Ğŵ�ƋƵĞ�ĞƐƐĞ�ǀĂůŽƌ�ƐĞ�ŝŶǀĞƌƟĂ͕�ĞƌĂ�ũƵƐƚĂŵĞŶƚĞ�ƉŽƌƋƵĞ͕�ƉĂƌĂ�ƵƐŽ�ĚŽ�ĞƐƉĂĕŽ�͞ĂůƚĞƌŶĂƟǀŽ͕͟ �ŚĂǀŝĂ�
ŵĞĐĂŶŝƐŵŽƐ�ĚĞ�ƐĞůĞĕĆŽ�ƚĆŽ�ŽƵ�ŵĂŝƐ�ƌşŐŝĚŽƐ�ƋƵĞ�ŽƐ�ĚŽ�ĞƐƉĂĕŽ�ŽĮĐŝĂů͘
Z��&�,Z�Z͕�>͘�dŽĚŽ�ĂƌƟƐƚĂ�ƚĞŵ�ĚĞ�ŝƌ�ĂŽŶĚĞ�Ž�ƉŽǀŽ�ĞƐƚĄ͘�ŝƐƉŽŶşǀĞů�Ğŵ͗�фŚƩƉ͗ͬͬŶŽǀŽ͘ŝƚĂƵĐƵůƚƵƌĂů͘ŽƌŐ͘ďƌх͘��ĐĞƐƐŽ�Ğŵ͗�Ϯϵ�ũƵů͘�ϮϬϭϰ�;ĂĚĂƉƚĂĚŽͿ͘
��ƉĂƌƟƌ�ĚŽ�ƚĞdžƚŽ�ĂĐŝŵĂ͕�ĂǀĂůŝĞ�ĂƐ�ĂƐƐĞƌĕƁĞƐ�Ă�ƐĞŐƵŝƌ�Ğ�Ă�ƌĞůĂĕĆŽ�ƉƌŽƉŽƐƚĂ�ĞŶƚƌĞ�ĞůĂƐ͘
/͘� K�ƉƌŽĐĞƐƐŽ�ĚĞ�ĞǀŽůƵĕĆŽ�ƚĞĐŶŽůſŐŝĐĂ�ĚĂ�ĂƚƵĂůŝĚĂĚĞ�ĚĞŵŽĐƌĂƟnjĂ�Ă�ƉƌŽĚƵĕĆŽ�Ğ�Ă�ĚŝǀƵůŐĂĕĆŽ�ĚĞ�ŽďƌĂƐ�
ĂƌơƐƟĐĂƐ͕�ƌĞĚƵnjŝŶĚŽ�Ă�ŝŵƉŽƌƚąŶĐŝĂ�ƋƵĞ�ŽƐ�ĐĞŶƚƌŽƐ�ĚĞ�ĞdžƉŽƐŝĕĆŽ�ƟŶŚĂŵ�ŶŽƐ�ĂŶŽƐ�ϭϵϳϬ͘
PORQUE
//͘� �Ɛ�ŶŽǀĂƐ�ƚĞĐŶŽůŽŐŝĂƐ�ƉŽƐƐŝďŝůŝƚĂŵ�ƋƵĞ�ĂƌƟƐƚĂƐ�ƐĞũĂŵ�ŝŶĚĞƉĞŶĚĞŶƚĞƐ͕�ŵŽŶƚĞŵ�ƐĞƵƐ�ƉƌſƉƌŝŽƐ�ĂŵďŝĞŶƚĞƐ�
ĚĞ�ƉƌŽĚƵĕĆŽ�Ğ�ĚŝƐƉŽŶŝďŝůŝnjĞŵ�ƐĞƵƐ�ƚƌĂďĂůŚŽƐ͕�ĚĞ�ĨŽƌŵĂ�ƐŝŵƉůĞƐ͕�ƉĂƌĂ�Ƶŵ�ŐƌĂŶĚĞ�ŶƷŵĞƌŽ�ĚĞ�ƉĞƐƐŽĂƐ͘
��ƌĞƐƉĞŝƚŽ�ĚĞƐƐĂƐ�ĂƐƐĞƌĕƁĞƐ͕�ĂƐƐŝŶĂůĞ�Ă�ŽƉĕĆŽ�ĐŽƌƌĞƚĂ͘
A �Ɛ�ĂƐƐĞƌĕƁĞƐ�/�Ğ�//�ƐĆŽ�ƉƌŽƉŽƐŝĕƁĞƐ�ǀĞƌĚĂĚĞŝƌĂƐ͕�Ğ�Ă�//�Ġ�ƵŵĂ�ũƵƐƟĮĐĂƟǀĂ�ĐŽƌƌĞƚĂ�ĚĂ�/͘
B �Ɛ�ĂƐƐĞƌĕƁĞƐ�/�Ğ�//�ƐĆŽ�ƉƌŽƉŽƐŝĕƁĞƐ�ǀĞƌĚĂĚĞŝƌĂƐ͕�ŵĂƐ�Ă�//�ŶĆŽ�Ġ�ƵŵĂ�ũƵƐƟĮĐĂƟǀĂ�ĐŽƌƌĞƚĂ�ĚĂ�/͘
C ��ĂƐƐĞƌĕĆŽ�/�Ġ�ƵŵĂ�ƉƌŽƉŽƐŝĕĆŽ�ǀĞƌĚĂĚĞŝƌĂ͕�Ğ�Ă�//�Ġ�ƵŵĂ�ƉƌŽƉŽƐŝĕĆŽ�ĨĂůƐĂ͘
D ��ĂƐƐĞƌĕĆŽ�/�Ġ�ƵŵĂ�ƉƌŽƉŽƐŝĕĆŽ�ĨĂůƐĂ͕�Ğ�Ă�//�Ġ�ƵŵĂ�ƉƌŽƉŽƐŝĕĆŽ�ǀĞƌĚĂĚĞŝƌĂ͘
E �Ɛ�ĂƐƐĞƌĕƁĞƐ�/�Ğ�//�ƐĆŽ�ƉƌŽƉŽƐŝĕƁĞƐ�ĨĂůƐĂƐ͘
QUESTÃO 02
�Žŵ�Ă�ŐůŽďĂůŝnjĂĕĆŽ�ĚĂ�ĞĐŽŶŽŵŝĂ�ƐŽĐŝĂů�ƉŽƌ�ŵĞŝŽ�ĚĂƐ�ŽƌŐĂŶŝnjĂĕƁĞƐ�ŶĆŽ�ŐŽǀĞƌŶĂŵĞŶƚĂŝƐ͕�ƐƵƌŐŝƵ�ƵŵĂ�ĚŝƐĐƵƐƐĆŽ�
ĚŽ�ĐŽŶĐĞŝƚŽ�ĚĞ�ĞŵƉƌĞƐĂ͕�ĚĞ�ƐƵĂ�ĨŽƌŵĂ�ĚĞ�ĐŽŶĐĞƉĕĆŽ�ũƵŶƚŽ�ăƐ�ŽƌŐĂŶŝnjĂĕƁĞƐ�ďƌĂƐŝůĞŝƌĂƐ�Ğ�ĚĞ�ƐƵĂƐ�ƉƌĄƟĐĂƐ͘�
�ĂĚĂ�ǀĞnj�ŵĂŝƐ͕�Ġ�ŶĞĐĞƐƐĄƌŝŽ�ĐŽŵďŝŶĂƌ�ĂƐ�ƉŽůşƟĐĂƐ�ƉƷďůŝĐĂƐ�ƋƵĞ�ƉƌŝŽƌŝnjĂŵ�ŵŽĚĞƌŶŝĚĂĚĞ�Ğ�ĐŽŵƉĞƟǀŝĚĂĚĞ�
ĐŽŵ�Ž�ĞƐĨŽƌĕŽ�ĚĞ�ŝŶĐŽƌƉŽƌĂĕĆŽ�ĚŽƐ�ƐĞƚŽƌĞƐ�ĂƚƌĂƐĂĚŽƐ͕�ŵĂŝƐ�ŝŶƚĞŶƐŝǀŽƐ�ĚĞ�ŵĆŽ�ĚĞ�ŽďƌĂ͘��ŝƐƉŽŶşǀĞů�Ğŵ͗�фŚƩƉ͗ͬͬƵŶƉĂŶϭ͘ƵŶ͘ŽƌŐх͘��ĐĞƐƐŽ�Ğŵ͗�ϰ�ĂŐŽ͘�ϮϬϭϰ�;ĂĚĂƉƚĂĚŽͿ͘
��ƌĞƐƉĞŝƚŽ�ĚĞƐƐĂ�ƚĞŵĄƟĐĂ͕�ĂǀĂůŝĞ�ĂƐ�ĂĮƌŵĂĕƁĞƐ�Ă�ƐĞŐƵŝƌ͘
/͘� K� ƚĞƌĐĞŝƌŽ� ƐĞƚŽƌ� Ġ� ƵŵĂ�ŵŝƐƚƵƌĂ� ĚŽƐ� ĚŽŝƐ� ƐĞƚŽƌĞƐ� ĞĐŽŶƀŵŝĐŽƐ� ĐůĄƐƐŝĐŽƐ� ĚĂ� ƐŽĐŝĞĚĂĚĞ͗� Ž� ƉƷďůŝĐŽ͕�
ƌĞƉƌĞƐĞŶƚĂĚŽ�ƉĞůŽ��ƐƚĂĚŽ͕�Ğ�Ž�ƉƌŝǀĂĚŽ͕�ƌĞƉƌĞƐĞŶƚĂĚŽ�ƉĞůŽ�ĞŵƉƌĞƐĂƌŝĂĚŽ�Ğŵ�ŐĞƌĂů͘
//͘� ��Ž�ƚĞƌĐĞŝƌŽ�ƐĞƚŽƌ�ƋƵĞ�ǀŝĂďŝůŝnjĂ�Ž�ĂĐĞƐƐŽ�ĚĂ�ƐŽĐŝĞĚĂĚĞ�ă�ĞĚƵĐĂĕĆŽ�Ğ�ĂŽ�ĚĞƐĞŶǀŽůǀŝŵĞŶƚŽ�ĚĞ�ƚĠĐŶŝĐĂƐ�
ŝŶĚƵƐƚƌŝĂŝƐ͕�ĞĐŽŶƀŵŝĐĂƐ͕�ĮŶĂŶĐĞŝƌĂƐ͕�ƉŽůşƟĐĂƐ�Ğ�ĂŵďŝĞŶƚĂŝƐ͘
///͘� ��ƌĞƐƉŽŶƐĂďŝůŝĚĂĚĞ�ƐŽĐŝĂů�ƚĞŵ�ƌĞƐƵůƚĂĚŽ�ŶĂ�ĂůƚĞƌĂĕĆŽ�ĚŽ�ƉĞƌĮů�ĐŽƌƉŽƌĂƟǀŽ�Ğ�ĞƐƚƌĂƚĠŐŝĐŽ�ĚĂƐ�ĞŵƉƌĞƐĂƐ͕�
ƋƵĞ�ƚġŵ�ƌĞĨŽƌŵƵůĂĚŽ�Ă�ĐƵůƚƵƌĂ�Ğ�Ă�ĮůŽƐŽĮĂ�ƋƵĞ�ŽƌŝĞŶƚĂŵ�ĂƐ�ĂĕƁĞƐ�ŝŶƐƟƚƵĐŝŽŶĂŝƐ͘
�ƐƚĄ�ĐŽƌƌĞƚŽ�Ž�ƋƵĞ�ƐĞ�ĂĮƌŵĂ�Ğŵ
A /͕�ĂƉĞŶĂƐ͘
B //͕�ĂƉĞŶĂƐ͘
C /�Ğ�///͕�ĂƉĞŶĂƐ͘
D //�Ğ�///͕�ĂƉĞŶĂƐ͘
E /͕�//�Ğ�///͘
*R1520144*
5
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 03
WeŐĂĚĂ�ĞĐŽůſŐŝĐĂ�Ġ�Ƶŵ� ŝŶĚŝĐĂĚŽƌ�ƋƵĞ�ĞƐƟŵĂ�Ă�ĚĞŵĂŶĚĂ�ŽƵ�Ă� ĞdžŝŐġŶĐŝĂ�ŚƵŵĂŶĂ� ƐŽďƌĞ�Ž�ŵĞŝŽ� ĂŵďŝĞŶƚĞ͕�
ĐŽŶƐŝĚĞƌĂŶĚŽͲƐĞ�Ž�ŶşǀĞů�ĚĞ�ĂƟǀŝĚĂĚĞ�ƉĂƌĂ�ĂƚĞŶĚĞƌ�ĂŽ�ƉĂĚƌĆŽ�ĚĞ�ĐŽŶƐƵŵŽ�ĂƚƵĂů�;ĐŽŵ�Ă�ƚĞĐŶŽůŽŐŝĂ�ĂƚƵĂůͿ͘��͕�ĚĞ�
ĐĞƌƚĂ�ĨŽƌŵĂ͕�ƵŵĂ�ŵĂŶĞŝƌĂ�ĚĞ�ŵĞĚŝƌ�Ž�ŇƵdžŽ�ĚĞ�ĂƟǀŽƐ�ĂŵďŝĞŶƚĂŝƐ�ĚĞ�ƋƵĞ�ŶĞĐĞƐƐŝƚĂŵŽƐ�ƉĂƌĂ�ƐƵƐƚĞŶƚĂƌ�ŶŽƐƐŽ�ƉĂĚƌĆŽ�
ĚĞ�ĐŽŶƐƵŵŽ͘��ƐƐĞ�ŝŶĚŝĐĂĚŽƌ�Ġ�ŵĞĚŝĚŽ�Ğŵ�ŚĞĐƚĂƌĞ�ŐůŽďĂů͕�ŵĞĚŝĚĂ�ĚĞ�ĄƌĞĂ�ĞƋƵŝǀĂůĞŶƚĞ�Ă�ϭϬ�ϬϬϬ�ŵϸ͘�EĂ�ŵĞĚŝĚĂ�
ŚĞĐƚĂƌĞ�ŐůŽďĂů͕�ƐĆŽ�ĐŽŶƐŝĚĞƌĂĚĂƐ�ĂƉĞŶĂƐ�ĂƐ�ĄƌĞĂƐ�ƉƌŽĚƵƟǀĂƐ�ĚŽ�ƉůĂŶĞƚĂ͘���ďŝŽĐĂƉĂĐŝĚĂĚĞ�ĚŽ�ƉůĂŶĞƚĂ͕�ŝŶĚŝĐĂĚŽƌ�
ƋƵĞ�ƌĞŇĞƚĞ�Ă�ƌĞŐĞŶĞƌĂĕĆŽ�;ŶĂƚƵƌĂůͿ�ĚŽ�ŵĞŝŽ�ĂŵďŝĞŶƚĞ͕�Ġ�ŵĞĚŝĚĂ�ƚĂŵďĠŵ�Ğŵ�ŚĞĐƚĂƌĞ�ŐůŽďĂů͘�hŵĂ�ƌĂnjĆŽ�ĞŶƚƌĞ�
ƉĞŐĂĚĂ�ĞĐŽůſŐŝĐĂ�Ğ�ďŝŽĐĂƉĂĐŝĚĂĚĞ�ĚŽ�ƉůĂŶĞƚĂ�ŝŐƵĂů�Ă�ϭ�ŝŶĚŝĐĂ�ƋƵĞ�Ă�ĞdžŝŐġŶĐŝĂ�ŚƵŵĂŶĂ�ƐŽďƌĞ�ŽƐ�ƌĞĐƵƌƐŽƐ�ĚŽ�
ŵĞŝŽ�ĂŵďŝĞŶƚĞ�Ġ�ƌĞƉŽƐƚĂ�ŶĂ�ƐƵĂ�ƚŽƚĂůŝĚĂĚĞ�ƉĞůŽ�ƉůĂŶĞƚĂ͕�ĚĞǀŝĚŽ�ă�ĐĂƉĂĐŝĚĂĚĞ�ŶĂƚƵƌĂů�ĚĞ�ƌĞŐĞŶĞƌĂĕĆŽ͘�^Ğ�ĨŽƌ�
ŵĂŝŽƌ�ƋƵĞ�ϭ͕�Ă�ƌĂnjĆŽ�ŝŶĚŝĐĂ�ƋƵĞ�Ă�ĚĞŵĂŶĚĂ�ŚƵŵĂŶĂ�Ġ�ƐƵƉĞƌŝŽƌ�ă�ĐĂƉĂĐŝĚĂĚĞ�ĚŽ�ƉůĂŶĞƚĂ�ĚĞ�ƐĞ�ƌĞĐƵƉĞƌĂƌ�Ğ͕�ƐĞ�ĨŽƌ�
ŵĞŶŽƌ�ƋƵĞ�ϭ͕�ŝŶĚŝĐĂ�ƋƵĞ�Ž�ƉůĂŶĞƚĂ�ƐĞ�ƌĞĐƵƉĞƌĂ�ŵĂŝƐ�ƌĂƉŝĚĂŵĞŶƚĞ͘
Razão entre a pegada ecológica
e a biocapacidade do planeta1.60
1.50
1.40
1.30
1.20
1.10
1.00
0.90
0.80
0.70
0.60
19
61
19
65
19
70
19
75
19
80
19
85
19
90
19
95
20
00
20
05
20
08
0.74
0.85
1.00
1.08
1.16 1.14
1.25 1.27
1.30
1.45
1.52
�ŝƐƉŽŶşǀĞů�Ğŵ͗фŚƩƉ͗ͬͬĨŝŶĂŶĐĂƐĨĂĐĞŝƐ͘ǁŽƌĚƉƌĞƐƐ͘ĐŽŵх͘��ĐĞƐƐŽ�Ğŵ͗�ϭϬ�ĂŐŽ͘�ϮϬϭϰ͘
K�ĂƵŵĞŶƚŽ�ĚĂ�ƌĂnjĆŽ�ĞŶƚƌĞ�ƉĞŐĂĚĂ�ĞĐŽůſŐŝĐĂ�Ğ�ďŝŽĐĂƉĂĐŝĚĂĚĞ�ƌĞƉƌĞƐĞŶƚĂĚŽ�ŶŽ�ŐƌĄĨŝĐŽ�ĞǀŝĚĞŶĐŝĂ
A ƌĞĚƵĕĆŽ�ĚĂƐ�ĄƌĞĂƐ�ĚĞ�ƉůĂŶƚŝŽ�ĚŽ�ƉůĂŶĞƚĂ�ƉĂƌĂ�ǀĂůŽƌĞƐ�ŝŶĨĞƌŝŽƌĞƐ�Ă�ϭϬ�ϬϬϬ�ŵ2�ĚĞǀŝĚŽ�ĂŽ�ƉĂĚƌĆŽ�ĂƚƵĂů�
ĚĞ�ĐŽŶƐƵŵŽ�ĚĞ�ƉƌŽĚƵƚŽƐ�ĂŐƌşĐŽůĂƐ͘
B ĂƵŵĞŶƚŽ�ŐƌĂĚƵĂů�ĚĂ�ĐĂƉĂĐŝĚĂĚĞ�ŶĂƚƵƌĂů�ĚĞ�ƌĞŐĞŶĞƌĂĕĆŽ�ĚŽ�ƉůĂŶĞƚĂ�Ğŵ�ƌĞůĂĕĆŽ�ăƐ�ĞdžŝŐġŶĐŝĂƐ�ŚƵŵĂŶĂƐ͘
C ƌĞƉŽƐŝĕĆŽ�ĚŽƐ�ƌĞĐƵƌƐŽƐ�ŶĂƚƵƌĂŝƐ�ƉĞůŽ�ƉůĂŶĞƚĂ�Ğŵ�ƐƵĂ�ƚŽƚĂůŝĚĂĚĞ�ĨƌĞŶƚĞ�ăƐ�ĞdžŝŐġŶĐŝĂƐ�ŚƵŵĂŶĂƐ͘
D ŝŶĐĂƉĂĐŝĚĂĚĞ�ĚĞ�ƌĞŐĞŶĞƌĂĕĆŽ�ŶĂƚƵƌĂů�ĚŽ�ƉůĂŶĞƚĂ�ĂŽ�ůŽŶŐŽ�ĚŽ�ƉĞƌşŽĚŽ�ϭϵϲϭͲϮϬϬϴ͘
E ƚĞŶĚġŶĐŝĂ�Ă�ĚĞƐĞƋƵŝůşďƌŝŽ�ŐƌĂĚƵĂů�Ğ�ĐŽŶƚşŶƵŽ�ĚĂ�ƐƵƐƚĞŶƚĂďŝůŝĚĂĚĞ�ĚŽ�ƉůĂŶĞƚĂ͘
*R1520145*
6
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 04
/ŵƉŽƌƚĂŶƚĞ�website� ĚĞ� ƌĞůĂĐŝŽŶĂŵĞŶƚŽ� ĐĂŵŝŶŚĂ� ƉĂƌĂ�
ϳϬϬ�ŵŝůŚƁĞƐ�ĚĞ�ƵƐƵĄƌŝŽƐ͘�KƵƚƌŽ�ĐŽŶŚĞĐŝĚŽ�ƐĞƌǀŝĚŽƌ�ĚĞ�
microblogging�ĂĐƵŵƵůĂ�ϭϰϬ�ŵŝůŚƁĞƐ�ĚĞ�ŵĞŶƐĂŐĞŶƐ�ĂŽ�
ĚŝĂ͘���ĐŽŵŽ�ƐĞ�ϳϱй�ĚĂ�ƉŽƉƵůĂĕĆŽ�ďƌĂƐŝůĞŝƌĂ�ƉŽƐƚĂƐƐĞ�Ƶŵ�
ĐŽŵĞŶƚĄƌŝŽ�Ă�ĐĂĚĂ�Ϯϰ�ŚŽƌĂƐ͘��Žŵ�ĂƐ�ƌĞĚĞƐ�ƐŽĐŝĂŝƐ�ĐĂĚĂ�
ǀĞnj�ŵĂŝƐ�ƉƌĞƐĞŶƚĞƐ�ŶŽ�ĚŝĂ�Ă�ĚŝĂ�ĚĂƐ�ƉĞƐƐŽĂƐ͕�Ġ�ŝŶĞǀŝƚĄǀĞů�
ƋƵĞ� ŵƵŝƚĂ� ŐĞŶƚĞ� ĞŶĐŽŶƚƌĞ� ŶĞůĂƐ� ƵŵĂ� ŵĂŶĞŝƌĂ� ĨĄĐŝů͕�
ƌĄƉŝĚĂ�Ğ�ĂďƌĂŶŐĞŶƚĞ�ĚĞ�ƐĞ�ŵĂŶŝĨĞƐƚĂƌ͘
hŵĂ�ƌĞĚĞ�ƐŽĐŝĂů�ĚĞ�ƌĞĐƌƵƚĂŵĞŶƚŽ�ƌĞǀĞůŽƵ�ƋƵĞ�ϵϮй�
ĚĂƐ� ĞŵƉƌĞƐĂƐ� ĂŵĞƌŝĐĂŶĂƐ� ũĄ� ƵƐĂƌĂŵ� ŽƵ� ƉůĂŶĞũĂŵ�
ƵƐĂƌ� ĂƐ� ƌĞĚĞƐ� ƐŽĐŝĂŝƐ� ŶŽ� ƉƌŽĐĞƐƐŽ� ĚĞ� ĐŽŶƚƌĂƚĂĕĆŽ͘�
�ĞƐƚĂƐ͕� ϲϬй� ĂƐƐƵŵĞŵ� ƋƵĞ� ďŝƐďŝůŚŽƚĂŵ� Ă� ǀŝĚĂ� ĚŽƐ�
ĐĂŶĚŝĚĂƚŽƐ�Ğŵ�websites�ĚĞ�ƌĞĚĞ�ƐŽĐŝĂů͘
ZĞĂůŝnjĂĚĂ� ƉŽƌ� ƵŵĂ� ĂŐġŶĐŝĂ� ĚĞ� ƌĞĐƌƵƚĂŵĞŶƚŽ͕� ƵŵĂ�
ƉĞƐƋƵŝƐĂ� ĐŽŵ� Ϯ� ϱϬϬ� ĞdžĞĐƵƟǀŽƐ� ďƌĂƐŝůĞŝƌŽƐ� ŵŽƐƚƌŽƵ�
ƋƵĞ�ϰϰй�ĚĞƐĐůĂƐƐŝĮĐĂƌŝĂŵ͕�ŶŽ�ƉƌŽĐĞƐƐŽ�ĚĞ�ƐĞůĞĕĆŽ͕�Ƶŵ�
ĐĂŶĚŝĚĂƚŽ�ƉŽƌ�ƐĞƵ�ĐŽŵƉŽƌƚĂŵĞŶƚŽ�Ğŵ�ƵŵĂ�ƌĞĚĞ�ƐŽĐŝĂů͘
DƵŝƚĂƐ� ƉĞƐƐŽĂƐ� ũĄ� ĞŶĨƌĞŶƚĂƌĂŵ� ƉƌŽďůĞŵĂƐ� ƉŽƌ�
ĐĂƵƐĂ� ĚĞ� ŝŶĨŽƌŵĂĕƁĞƐ� online͕� ƚĂŶƚŽ� ŶŽ� ĐĂŵƉŽ�
ƉĞƐƐŽĂů� ƋƵĂŶƚŽ� ŶŽ� ƉƌŽĮƐƐŝŽŶĂů͘� �ůŐƵŵĂƐ� ĞŵƉƌĞƐĂƐ�
Ğ� ŝŶƐƟƚƵŝĕƁĞƐ͕� ŝŶĐůƵƐŝǀĞ͕� ũĄ� ĂĚŽƚĂƌĂŵ� ĐĂƌƟůŚĂƐ� ĚĞ�
ĐŽŶĚƵƚĂ�Ğŵ�ƌĞĚĞƐ�ƐŽĐŝĂŝƐ͘
WK>KE/͕�'͘�K�ůĂĚŽ�ƉĞƌŝŐŽƐŽ�ĚĂƐ�ƌĞĚĞƐ�ƐŽĐŝĂŝƐ͘�ZĞǀŝƐƚĂ�/E&K͕�
Ɖ͘�ϳϬ�Ͳ�ϳϱ͕�ũƵůŚŽ�ϮϬϭϭ�;ĂĚĂƉƚĂĚŽͿ͘
�Ğ�ĂĐŽƌĚŽ�ĐŽŵ�Ž�ƚĞdžƚŽ͕
A ŵĂŝƐ�ĚĂ�ŵĞƚĂĚĞ�ĚĂƐ�ĞŵƉƌĞƐĂƐ�ĂŵĞƌŝĐĂŶĂƐ�ĞǀŝƚĂ�
ĂĐĞƐƐĂƌ�websites ĚĞ�ƌĞĚĞƐ�ƐŽĐŝĂŝƐ�ĚĞ�ĐĂŶĚŝĚĂƚŽƐ�
Ă�ĞŵƉƌĞŐŽ͘
B ĞŵƉƌĞƐĂƐ� Ğ� ŝŶƐƟƚƵŝĕƁĞƐ� ĞƐƚĆŽ� ĂƚĞŶƚĂƐ� ĂŽ�
ĐŽŵƉŽƌƚĂŵĞŶƚŽ�ĚĞ� ƐĞƵƐ� ĨƵŶĐŝŽŶĄƌŝŽƐ� Ğŵ�websites
ĚĞ�ƌĞĚĞƐ�ƐŽĐŝĂŝƐ͘
C Ă� ĐŽŵƉůĞdžŝĚĂĚĞ� ĚŽƐ� ƉƌŽĐĞĚŝŵĞŶƚŽƐ� ĚĞ� ƌĂƐƚƌĞŝŽ� Ğ�
ŵŽŶŝƚŽƌĂŵĞŶƚŽ� ĚĞ� ƵŵĂ� ƌĞĚĞ� ƐŽĐŝĂů� ŝŵƉĞĚĞ� ƋƵĞ�
ĂƐ� ĞŵƉƌĞƐĂƐ� ƚĞŶŚĂŵ� ĂĐĞƐƐŽ� ĂŽ� ƉĞƌĮů� ĚĞ� ƐĞƵƐ�
ĨƵŶĐŝŽŶĄƌŝŽƐ͘
D ĂƐ� ĐĂƌƟůŚĂƐ� ĚĞ� ĐŽŶĚƵƚĂ� ĂĚŽƚĂĚĂƐ� ŶĂƐ� ĞŵƉƌĞƐĂƐ�
ƉƌŽşďĞŵ�Ž�ƵƐŽ�ĚĞ�ƌĞĚĞƐ�ƐŽĐŝĂŝƐ�ƉĞůŽƐ�ĨƵŶĐŝŽŶĄƌŝŽƐ �͕Ğŵ�
ǀĞnj�ĚĞ�ƌĞĐŽŵĞŶĚĂƌ�ŵƵĚĂŶĕĂƐ�ĚĞ�ĐŽŵƉŽƌƚĂŵĞŶƚŽ͘
E Ă� ŵĂŝŽƌŝĂ� ĚŽƐ� ĞdžĞĐƵƟǀŽƐ� ďƌĂƐŝůĞŝƌŽƐ� ƵƟůŝnjĂƌŝĂ�
ŝŶĨŽƌŵĂĕƁĞƐ� ŽďƟĚĂƐ� Ğŵ� websites ĚĞ� ƌĞĚĞƐ�
ƐŽĐŝĂŝƐ͕� ƉĂƌĂ� ĚĞƐĐůĂƐƐŝĮĐĂƌ� Ƶŵ� ĐĂŶĚŝĚĂƚŽ� Ğŵ�
ƉƌŽĐĞƐƐŽ�ĚĞ�ƐĞůĞĕĆŽ͘
QUESTÃO 05
hŵĂ� ŝĚĞŝĂ� Ğ� Ƶŵ� ĂƉĂƌĞůŚŽ� ƐŝŵƉůĞƐ� ĚĞǀĞŵ͕� Ğŵ� ďƌĞǀĞ͕�
ĂũƵĚĂƌ�Ă�ƐĂůǀĂƌ�ǀŝĚĂƐ�ĚĞ�ƌĞĐĠŵͲŶĂƐĐŝĚŽƐ͘�/ĚĞĂůŝnjĂĚŽ�ƉĞůŽ�
ŵĞĐąŶŝĐŽ�ĂƌŐĞŶƟŶŽ�:ŽƌŐĞ�KĚſŶ͕�Ž�ĚŝƐƉŽƐŝƟǀŽ�ƋƵĞ�ůĞǀĂ�ƐĞƵ�
ƐŽďƌĞŶŽŵĞ�ĚĞƐĞŶƚĂůĂ�Ƶŵ�ďĞďġ�ƉƌĞƐŽ�ŶŽ�ĐĂŶĂů�ǀĂŐŝŶĂů�ͷ
Ğ͕�ƉŽƌ�ŵĂŝƐ�ŝŶƵƐŝƚĂĚŽ�ƋƵĞ�ƉĂƌĞĕĂ͕�ĨŽŝ�ĐƌŝĂĚŽ�ĐŽŵ�ďĂƐĞ�Ğŵ�
ƚĠĐŶŝĐĂ�ƵƐĂĚĂ�ƉĂƌĂ�ƌĞŵŽǀĞƌ�ƌŽůŚĂƐ�ĚĞ�ĚĞŶƚƌŽ�ĚĞ�ŐĂƌƌĂĨĂƐ͘�
K�ĂƉĂƌĞůŚŽ�ĐŽŶƐŝƐƚĞ�Ğŵ�ƵŵĂ�ďŽůƐĂ�ƉůĄƐƟĐĂ�ŝŶƐĞƌŝĚĂ�Ğŵ�
ƵŵĂ�ƉƌŽƚĞĕĆŽ�ĨĞŝƚĂ�ĚŽ�ŵĞƐŵŽ�ŵĂƚĞƌŝĂů�Ğ�ƋƵĞ�ĞŶǀŽůǀĞ�Ă�
ĐĂďĞĕĂ� ĚĂ� ĐƌŝĂŶĕĂ͘� �ƐƚĂŶĚŽ�Ž� ĚŝƐƉŽƐŝƟǀŽ� ĚĞǀŝĚĂŵĞŶƚĞ�
ƉŽƐŝĐŝŽŶĂĚŽ͕�Ă�ďŽůƐĂ�Ġ� ŝŶŇĂĚĂ�ƉĂƌĂ�ĂĚĞƌŝƌ�ă�ĐĂďĞĕĂ�ĚŽ�
ďĞďġ�Ğ�ƐĞƌ�ƉƵdžĂĚĂ�ĂŽƐ�ƉŽƵĐŽƐ͕�ĚĞ�ĨŽƌŵĂ�Ă�ŶĆŽ�ŵĂĐŚƵĐĄͲ
ůŽ͘�K�ŵĠƚŽĚŽ�ĚĞ�KĚſŶ�ĚĞǀĞ�ƐƵďƐƟƚƵŝƌ�ŽƵƚƌŽƐ�ũĄ�ĂƌĐĂŝĐŽƐ͕�
ĐŽŵŽ�Ž�ĚĞ�ĨſƌĐĞƉƐ�Ğ�Ž�ĚĞ�ƚƵďŽƐ�ĚĞ�ƐƵĐĕĆŽ͕�ŽƐ�ƋƵĂŝƐ͕�ƐĞ�
ƵƐĂĚŽƐ� ƉŽƌ� ŵĆŽƐ� ŵĂůƚƌĞŝŶĂĚĂƐ͕� ƉŽĚĞŵ� ĐŽŵƉƌŽŵĞƚĞƌ�
Ă�ǀŝĚĂ�ĚŽ�ďĞďġ͕�Ž�ƋƵĞ͕�ƐĞŐƵŶĚŽ�ĞƐƉĞĐŝĂůŝƐƚĂƐ͕�ŶĆŽ�ĚĞǀĞ�
ĂĐŽŶƚĞĐĞƌ�ĐŽŵ�Ž�ŶŽǀŽ�ĞƋƵŝƉĂŵĞŶƚŽ͘
^ĞŐƵŶĚŽ�Ž�dŚĞ�EĞǁ�zŽƌŬ�dŝŵĞƐ͕�Ă�ŝĚĞŝĂ�ƌĞĐĞďĞƵ�ĂƉŽŝŽ�
ĚĂ�KƌŐĂŶŝnjĂĕĆŽ�DƵŶĚŝĂů�ĚĞ�^ĂƷĚĞ�;KD^Ϳ�Ğ� ũĄ� ĨŽŝ�ĂƚĠ�
ůŝĐĞŶĐŝĂĚĂ� ƉŽƌ� ƵŵĂ� ĞŵƉƌĞƐĂ� ŶŽƌƚĞͲĂŵĞƌŝĐĂŶĂ� ĚĞ�
ƚĞĐŶŽůŽŐŝĂ�ŵĠĚŝĐĂ͘�EĆŽ�ƐĞ�ƐĂďĞ�ƋƵĂŶĚŽ�Ž�ĞƋƵŝƉĂŵĞŶƚŽ�
ĐŽŵĞĕĂƌĄ�Ă�ƐĞƌ�ƉƌŽĚƵnjŝĚŽ�ŶĞŵ�Ž�ƉƌĞĕŽ�Ă�ƐĞƌ�ĐŽďƌĂĚŽ͕�
ŵĂƐ�ƉƌĞƐƵŵĞͲƐĞ�ƋƵĞ�ĞůĞ�ŶĆŽ�ƉĂƐƐĂƌĄ�ĚĞ�ϱϬ�ĚſůĂƌĞƐ͕�
ĐŽŵ�ƌĞĚƵĕĆŽ�ĚŽ�ƉƌĞĕŽ�Ğŵ�ƉĂşƐĞƐ�ŵĂŝƐ�ƉŽďƌĞƐ͘
'h^D�K͕�'͘��ƉĂƌĞůŚŽ�ĚĞǀĞ�ĨĂĐŝůŝƚĂƌ�ƉĂƌƚŽƐ�Ğŵ�ƐŝƚƵĂĕƁĞƐ�ĚĞ�
emergência͘��ŝƐƉŽŶşǀĞů�Ğŵ͗�фŚƩƉ͗ͬͬĞdžĂŵĞ͘Ăďƌŝů͘ĐŽŵ͘ďƌх͘�
�ĐĞƐƐŽ�Ğŵ͗�ϭϴ�ŶŽǀ͘ �ϮϬϭϯ�;ĂĚĂƉƚĂĚŽͿ͘
�Žŵ�ƌĞůĂĕĆŽ�ĂŽ�ƚĞdžƚŽ�ĂĐŝŵĂ͕�ĂǀĂůŝĞ�ĂƐ�ĂĮƌŵĂĕƁĞƐ�Ă�ƐĞŐƵŝƌ͘
/͘� �� ƵƟůŝnjĂĕĆŽ� ĚŽ� ŵĠƚŽĚŽ� ĚĞ� KĚſŶ� ƉŽĚĞƌĄ�
ƌĞĚƵnjŝƌ�Ă� ƚĂdžĂ�ĚĞ�ŵŽƌƚĂůŝĚĂĚĞ�ĚĞ�ĐƌŝĂŶĕĂƐ�ĂŽ�
ŶĂƐĐĞƌ͕ �ŵĞƐŵŽ�Ğŵ�ƉĂşƐĞƐ�ƉŽďƌĞƐ͘
//͘� WŽƌ� ƐĞƌ� ƵŵĂ� ǀĂƌŝĂŶƚĞ� ĚŽƐ� ƚƵďŽƐ� ĚĞ� ƐƵĐĕĆŽ͕� Ž�
ĂƉĂƌĞůŚŽ�ĚĞƐĞŶǀŽůǀŝĚŽ�ƉŽƌ�KĚſŶ�Ġ�ƌĞƐƵůƚĂĚŽ�ĚĞ�
ĂƉĞƌĨĞŝĕŽĂŵĞŶƚŽ�ĚĞ�ĞƋƵŝƉĂŵĞŶƚŽƐ�ĚĞ�ƉĂƌƚŽ͘
///͘� WŽƌ�ƐĞƵ�ƵƐŽ�ƐŝŵƉůĞƐ͕�Ž�ĚŝƐƉŽƐŝƟǀŽ�ĚĞ�MĚŽŶ�ƚĞŵ�
ŐƌĂŶĚĞ�ƉŽƚĞŶĐŝĂů�ĚĞ�ƐĞƌ�ƵƐĂĚŽ�Ğŵ�ƉĂşƐĞƐ�ŽŶĚĞ�
Ž�ƉĂƌƚŽ�Ġ�ƵƐƵĂůŵĞŶƚĞ�ƌĞĂůŝnjĂĚŽ�ƉŽƌ�ƉĂƌƚĞŝƌĂƐ͘
/s͘ � �� ƉŽƐƐŝďŝůŝĚĂĚĞ� ĚĞ͕� Ğŵ� ƉĂşƐĞƐ� ŵĂŝƐ� ƉŽďƌĞƐ͕�
ƌĞĚƵnjŝƌͲƐĞ� Ž� ƉƌĞĕŽ� ĚŽ� ĂƉĂƌĞůŚŽ� ŝĚĞĂůŝnjĂĚŽ�
ƉŽƌ� KĚſŶ� ĞǀŝĚĞŶĐŝĂ� ƉƌĞŽĐƵƉĂĕĆŽ� ĐŽŵ� Ă�
ƌĞƐƉŽŶƐĂďŝůŝĚĂĚĞ�ƐŽĐŝĂů͘
��ĐŽƌƌĞƚŽ�ĂƉĞŶĂƐ�Ž�ƋƵĞ�ƐĞ�ĂĮƌŵĂ�Ğŵ
A /�Ğ�//͘
B /�Ğ�/s͘
C //�Ğ�///͘
D /͕�///�Ğ�/s͘
E //͕�///�Ğ�/s͘
*R1520146*
7
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 06
�Ɛ�ŵƵůŚĞƌĞƐ�ĨƌĞƋƵĞŶƚĂŵ�ŵĂŝƐ�ŽƐ�ďĂŶĐŽƐ�ĞƐĐŽůĂƌĞƐ�ƋƵĞ�ŽƐ�ŚŽŵĞŶƐ͕�ĚŝǀŝĚĞŵ�ƐĞƵ�ƚĞŵƉŽ�ĞŶƚƌĞ�Ž�ƚƌĂďĂůŚŽ�Ğ�ŽƐ�
ĐƵŝĚĂĚŽƐ�ĐŽŵ�Ă�ĐĂƐĂ͕�ŐĞƌĂŵ�ƌĞŶĚĂ�ĨĂŵŝůŝĂƌ͕ �ƉŽƌĠŵ�ĐŽŶƟŶƵĂŵ�ŐĂŶŚĂŶĚŽ�ŵĞŶŽƐ�Ğ�ƚƌĂďĂůŚĂŶĚŽ�ŵĂŝƐ�ƋƵĞ�ŽƐ�
ŚŽŵĞŶƐ͘
�Ɛ�ƉŽůşƟĐĂƐ�ĚĞ�ďĞŶĞİĐŝŽƐ�ŝŵƉůĞŵĞŶƚĂĚĂƐ�ƉŽƌ�ĞŵƉƌĞƐĂƐ�ƉƌĞŽĐƵƉĂĚĂƐ�Ğŵ�ĨĂĐŝůŝƚĂƌ�Ă�ǀŝĚĂ�ĚĂƐ�ĨƵŶĐŝŽŶĄƌŝĂƐ�ƋƵĞ�
ƚġŵ�ĐƌŝĂŶĕĂ�ƉĞƋƵĞŶĂ�Ğŵ�ĐĂƐĂ�ũĄ�ĞƐƚĆŽ�ĐŚĞŐĂŶĚŽ�ĂŽ��ƌĂƐŝů͘��ĐŽƌĚŽƐ�ĚĞ�ŚŽƌĄƌŝŽƐ�ŇĞdžşǀĞŝƐ͕�ƉƌŽŐƌĂŵĂƐ�ĐŽŵŽ�
ĂƵdžşůŝŽͲĐƌĞĐŚĞ͕�ĂƵdžşůŝŽͲďĂďĄ�Ğ�ĂƵdžşůŝŽͲĂŵĂŵĞŶƚĂĕĆŽ�ƐĆŽ�ĂůŐƵŶƐ�ĚŽƐ�ďĞŶĞİĐŝŽƐ�ŽĨĞƌĞĐŝĚŽƐ͘
�ŝƐƉŽŶşǀĞů�Ğŵ͗фŚƩƉ͗ͬͬǁǁǁϭ͘ĨŽůŚĂ͘ƵŽů͘ĐŽŵ͘ďƌх͘��ĐĞƐƐŽ�Ğŵ͗�ϯϬ�ũƵů͘�ϮϬϭϯ�;ĂĚĂƉƚĂĚŽͿ͘
30,3 36,5
10,1 44,4
31,7 34
15,5 41,4
JORNADA MÉDIA TOTAL DE TRABALHO POR
SEMANA NO BRASIL - (EM HORAS)mãe com filhos
pai com filhos
mulher chefe de casal
com filhos
homem chefe de casal
com filhos
mulher cônjuge em
casal com filhos
tempo médio por semana dedicado aos afazeres domésticos
0 10 20 30 40 50 60 70
tempo médio por semana dedicado ao trabalho remunerado
25,9 36,8
�ŝƐƉŽŶşǀĞů�Ğŵ͗�фŚƩƉ͗ͬͬŝƉĞĂ͘ŐŽǀ͘ ďƌх͘��ĐĞƐƐŽ�Ğŵ͗�ϯϬ�ũƵů͘�ϮϬϭϯ͘�
�ŽŶƐŝĚĞƌĂŶĚŽ�Ž�ƚĞdžƚŽ�Ğ�Ž�ŐƌĄĮĐŽ͕�ĂǀĂůŝĞ�ĂƐ�ĂĮƌŵĂĕƁĞƐ�Ă�ƐĞŐƵŝƌ͘
/͘� K�ƐŽŵĂƚſƌŝŽ�ĚŽ�ƚĞŵƉŽ�ĚĞĚŝĐĂĚŽ�ƉĞůĂƐ�ŵƵůŚĞƌĞƐ�ĂŽƐ�ĂĨĂnjĞƌĞƐ�ĚŽŵĠƐƟĐŽƐ�Ğ�ĂŽ�ƚƌĂďĂůŚŽ�ƌĞŵƵŶĞƌĂĚŽ�
Ġ�ƐƵƉĞƌŝŽƌ�ĂŽ�ĚĞĚŝĐĂĚŽ�ƉĞůŽƐ�ŚŽŵĞŶƐ͕�ŝŶĚĞƉĞŶĚĞŶƚĞŵĞŶƚĞ�ĚŽ�ĨŽƌŵĂƚŽ�ĚĂ�ĨĂŵşůŝĂ͘
//͘� K�ĨƌĂŐŵĞŶƚŽ�ĚĞ�ƚĞdžƚŽ�Ğ�ŽƐ�ĚĂĚŽƐ�ĚŽ�ŐƌĄĮĐŽ�ĂƉŽŶƚĂŵ�ƉĂƌĂ�Ă�ŶĞĐĞƐƐŝĚĂĚĞ�ĚĞ�ĐƌŝĂĕĆŽ�ĚĞ�ƉŽůşƟĐĂƐ�ƋƵĞ�
ƉƌŽŵŽǀĂŵ�Ă�ŝŐƵĂůĚĂĚĞ�ĞŶƚƌĞ�ŽƐ�ŐġŶĞƌŽƐ�ŶŽ�ƋƵĞ�ĐŽŶĐĞƌŶĞ͕�ƉŽƌ�ĞdžĞŵƉůŽ͕�Ă�ƚĞŵƉŽ�ŵĠĚŝŽ�ĚĞĚŝĐĂĚŽ�
ĂŽ�ƚƌĂďĂůŚŽ�Ğ�ƌĞŵƵŶĞƌĂĕĆŽ�ƌĞĐĞďŝĚĂ͘�
///͘� EŽ� ĨƌĂŐŵĞŶƚŽ� ĚĞ� ƌĞƉŽƌƚĂŐĞŵ� ĂƉƌĞƐĞŶƚĂĚŽ͕� ƌĞƐƐĂůƚĂͲƐĞ� Ă� ĚŝĨĞƌĞŶĕĂ� ĞŶƚƌĞ� Ž� ƚĞŵƉŽ� ĚĞĚŝĐĂĚŽ� ƉŽƌ�
ŵƵůŚĞƌĞƐ�Ğ�ŚŽŵĞŶƐ�ĂŽ�ƚƌĂďĂůŚŽ�ƌĞŵƵŶĞƌĂĚŽ͕�ƐĞŵ�ĂůƵƐĆŽ�ĂŽƐ�ĂĨĂnjĞƌĞƐ�ĚŽŵĠƐƟĐŽƐ͘�
��ĐŽƌƌĞƚŽ�Ž�ƋƵĞ�ƐĞ�ĂĮƌŵĂ�Ğŵ
A /͕�ĂƉĞŶĂƐ͘
B ///͕�ĂƉĞŶĂƐ͘
C /�Ğ�//͕�ĂƉĞŶĂƐ͘
D //�Ğ�///͕�ĂƉĞŶĂƐ͘
E /͕�//�Ğ�///͘
*R1520147*
ϴ
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 07
K� ƋƵĂĚƌŽ� Ă� ƐĞŐƵŝƌ� ĂƉƌĞƐĞŶƚĂ� Ă� ƉƌŽƉŽƌĕĆŽ� ;йͿ�
ĚĞ� ƚƌĂďĂůŚĂĚŽƌĞƐ� ƉŽƌ� ĨĂŝdžĂ� ĚĞ� ƚĞŵƉŽ� ŐĂƐƚŽ� ŶŽ�
ĚĞƐůŽĐĂŵĞŶƚŽ� ĐĂƐĂͲƚƌĂďĂůŚŽ͕� ŶŽ� �ƌĂƐŝů� Ğ� Ğŵ� ƚƌġƐ�
ĐŝĚĂĚĞƐ�ďƌĂƐŝůĞŝƌĂƐ͘
Tempo de 
deslocamento Brasil
Rio de 
Janeiro
São
Paulo �ƵƌŝƟďĂ�
Até cinco minutos ϭϮ͕ϳϬ ϱ͕ϴϬ ϱ͕ϭϬ ϳ͕ϴϬ
De seis minutos 
até meia hora ϱϮ͕ϮϬ ϯϮ͕ϭϬ ϯϭ͕ϲϬ ϰϱ͕ϴϬ
Mais de meia hora 
até uma hora Ϯϯ͕ϲϬ ϯϯ͕ϱϬ ϯϰ͕ϲϬ ϯϮ͕ϰϬ
Mais de uma hora 
até duas horas ϵ͕ϴϬ Ϯϯ͕ϮϬ Ϯϯ͕ϯϬ ϭϮ͕ϵϬ
Mais de duas 
horas ϭ͕ϴϬ ϱ͕ϱϬ ϱ͕ϯϬ ϭ͕ϮϬ
��E^K�ϮϬϭϬͬ/�'��;ĂĚĂƉƚĂĚŽͿ͘�
�Žŵ� ďĂƐĞ� ŶŽƐ� ĚĂĚŽƐ� ĂƉƌĞƐĞŶƚĂĚŽƐ� Ğ� ĐŽŶƐŝĚĞƌĂŶĚŽ� Ă�
ĚŝƐƚƌŝďƵŝĕĆŽ� ĚĂ� ƉŽƉƵůĂĕĆŽ� ƚƌĂďĂůŚĂĚŽƌĂ� ŶĂƐ� ĐŝĚĂĚĞƐ� Ğ�
ĂƐ�ƉŽůşƟĐĂƐ�ƉƷďůŝĐĂƐ�ĚŝƌĞĐŝŽŶĂĚĂƐ�ă�ŵŽďŝůŝĚĂĚĞ�ƵƌďĂŶĂ͕�
ĂǀĂůŝĞ�ĂƐ�ĂĮƌŵĂĕƁĞƐ�Ă�ƐĞŐƵŝƌ͘
/͘� ��ĚŝƐƚƌŝďƵŝĕĆŽ�ĚĂƐ�ƉĞƐƐŽĂƐ�ƉŽƌ� ĨĂŝdžĂ�ĚĞ� ƚĞŵƉŽ�
ĚĞ� ĚĞƐůŽĐĂŵĞŶƚŽ� ĐĂƐĂͲƚƌĂďĂůŚŽ� ŶĂ� ƌĞŐŝĆŽ�
ŵĞƚƌŽƉŽůŝƚĂŶĂ�ĚŽ�ZŝŽ�ĚĞ�:ĂŶĞŝƌŽ�Ġ�ƉƌſdžŝŵĂ�ă�ƋƵĞ�
ƐĞ�ǀĞƌŝĮĐĂ�Ğŵ�^ĆŽ�WĂƵůŽ͕�ŵĂƐ�ŶĆŽ�Ğŵ��ƵƌŝƟďĂ�Ğ�
ŶĂ�ŵĠĚŝĂ�ďƌĂƐŝůĞŝƌĂ͘
//͘� EĂƐ�ŵĞƚƌſƉŽůĞƐ͕�Ğŵ�ŐĞƌĂů͕�Ă�ŵĂŝŽƌŝĂ�ĚŽƐ�ƉŽƐƚŽƐ�
ĚĞ� ƚƌĂďĂůŚŽ� ĞƐƚĄ� ůŽĐĂůŝnjĂĚĂ� ŶĂƐ� ĄƌĞĂƐ� ƵƌďĂŶĂƐ�
ĐĞŶƚƌĂŝƐ͕�Ğ�ĂƐ�ƌĞƐŝĚġŶĐŝĂƐ�ĚĂ�ƉŽƉƵůĂĕĆŽ�ĚĞ�ďĂŝdžĂ�
ƌĞŶĚĂ�ĞƐƚĆŽ� ĐŽŶĐĞŶƚƌĂĚĂƐ� Ğŵ�ĄƌĞĂƐ� ŝƌƌĞŐƵůĂƌĞƐ�
ŽƵ�ŶĂ�ƉĞƌŝĨĞƌŝĂ͕�Ž�ƋƵĞ�ĂƵŵĞŶƚĂ�Ž�ƚĞŵƉŽ�ŐĂƐƚŽ�ƉŽƌ�
ĞƐƚĂ�ƉŽƉƵůĂĕĆŽ�ŶŽ�ĚĞƐůŽĐĂŵĞŶƚŽ�ĐĂƐĂͲƚƌĂďĂůŚŽ�Ğ�
Ž�ĐƵƐƚŽ�ĚŽ�ƚƌĂŶƐƉŽƌƚĞ͘
///͘� �Ɛ� ƉŽůşƟĐĂƐ� ƉƷďůŝĐĂƐ� ƌĞĨĞƌĞŶƚĞƐ� Ă� ƚƌĂŶƐƉŽƌƚĞƐ�
ƵƌďĂŶŽƐ͕� ĐŽŵŽ͕� ƉŽƌ� ĞdžĞŵƉůŽ͕� �ŝůŚĞƚĞ� jŶŝĐŽ�
Ğ� sĞşĐƵůŽ� >ĞǀĞ� ƐŽďƌĞ� dƌŝůŚŽƐ� ;s>dͿ͕� ĂŽ� ƐĞƌĞŵ�
ŝŵƉůĞŵĞŶƚĂĚĂƐ͕� ĐŽŶƚƌŝďƵĞŵ� ƉĂƌĂ� ƌĞĚƵĕĆŽ� ĚŽ�
ƚĞŵƉŽ�ŐĂƐƚŽ�ŶŽ�ĚĞƐůŽĐĂŵĞŶƚŽ� ĐĂƐĂͲƚƌĂďĂůŚŽ�Ğ�
ĚŽ�ĐƵƐƚŽ�ĚŽ�ƚƌĂŶƐƉŽƌƚĞ͘
��ĐŽƌƌĞƚŽ�Ž�ƋƵĞ�ƐĞ�ĂĮƌŵĂ�Ğŵ
A /͕�ĂƉĞŶĂƐ͘
B ///͕�ĂƉĞŶĂƐ͘
C /�Ğ�//͕�ĂƉĞŶĂƐ͘
D //�Ğ�///͕�ĂƉĞŶĂƐ͘
E /͕�//�Ğ�///͘
QUESTÃO 08
�ŽŶƐƚĂŶƚĞƐ� ƚƌĂŶƐĨŽƌŵĂĕƁĞƐ� ŽĐŽƌƌĞƌĂŵ� ŶŽƐ� ŵĞŝŽƐ�
ƌƵƌĂů�Ğ�ƵƌďĂŶŽ͕�Ă�ƉĂƌƟƌ�ĚŽ�ƐĠĐƵůŽ�yy͘��Žŵ�Ž�ĂĚǀĞŶƚŽ�
ĚĂ�ŝŶĚƵƐƚƌŝĂůŝnjĂĕĆŽ͕�ŚŽƵǀĞ�ŵƵĚĂŶĕĂƐ�ŝŵƉŽƌƚĂŶƚĞƐ�ŶŽ�
ŵŽĚŽ�ĚĞ�ǀŝĚĂ�ĚĂƐ�ƉĞƐƐŽĂƐ͕�Ğŵ�ƐĞƵƐ�ƉĂĚƌƁĞƐ�ĐƵůƚƵƌĂŝƐ͕�
ǀĂůŽƌĞƐ� Ğ� ƚƌĂĚŝĕƁĞƐ͘�K� ĐŽŶũƵŶƚŽ�ĚĞ� ĂĐŽŶƚĞĐŝŵĞŶƚŽƐ�
ƉƌŽǀŽĐŽƵ͕� ƚĂŶƚŽ� ŶĂ� njŽŶĂ� ƵƌďĂŶĂ� ƋƵĂŶƚŽ� ŶĂ� ƌƵƌĂů͕�
ƉƌŽďůĞŵĂƐ�ĐŽŵŽ�ĞdžƉůŽƐĆŽ�ĚĞŵŽŐƌĄĮĐĂ͕�ƉƌĞũƵşnjŽ�ŶĂƐ�
ĂƟǀŝĚĂĚĞƐ�ĂŐƌşĐŽůĂƐ�Ğ�ǀŝŽůġŶĐŝĂ͘
/ŶŝĐŝĂƌĂŵͲƐĞ� ŝŶƷŵĞƌĂƐ� ƚƌĂŶƐĨŽƌŵĂĕƁĞƐ� ŶĂ� ŶĂƚƵƌĞnjĂ͕�
ĐƌŝĂŶĚŽͲƐĞ�ƚĠĐŶŝĐĂƐ�ƉĂƌĂ�ŽďũĞƚŽƐ�ĂƚĠ�ĞŶƚĆŽ�ƐĞŵ�ƵƟůŝĚĂĚĞ�
ƉĂƌĂ� Ž� ŚŽŵĞŵ͘� /ƐƐŽ� Ɛſ� ĨŽŝ� ƉŽƐƐşǀĞů� Ğŵ� ĚĞĐŽƌƌġŶĐŝĂ�
ĚŽƐ� ƌĞĐƵƌƐŽƐ� ŶĂƚƵƌĂŝƐ� ĞdžŝƐƚĞŶƚĞƐ͕� ƋƵĞ� ƉƌŽƉŝĐŝĂƌĂŵ�
ĞƐƚƌƵƚƵƌĂ�ĚĞ�ĐƌĞƐĐŝŵĞŶƚŽ�Ğ�ďƵƐĐĂ�ĚĞ�ƉƌŽƐƉĞƌŝĚĂĚĞ͕�Ž�
ƋƵĞ�ĨĂnj�ĚĂ�ĞdžƉĞƌŝŵĞŶƚĂĕĆŽ�Ƶŵ�ŵĠƚŽĚŽ�ĚĞ�ƚƌĂŶƐĨŽƌŵĂƌ�
ŽƐ�ƌĞĐƵƌƐŽƐ�Ğŵ�ďĞŶĞİĐŝŽ�ƉƌſƉƌŝŽ͘
^�EdK^͕�D͘�DĞƚĂŵŽƌĨŽƐĞƐ�ĚŽ�ĞƐƉĂĕŽ�ŚĂďŝƚĂĚŽ.
^ĆŽ�WĂƵůŽ͗�,ƵĐŝƚĞĐ͕�ϭϵϴϴ�;ĂĚĂƉƚĂĚŽͿ͘
��ƉĂƌƟƌ�ĚĂƐ�ŝĚĞŝĂƐ�ĞdžƉƌĞƐƐĂƐ�ŶŽ�ƚĞdžƚŽ�ĂĐŝŵĂ͕�ĐŽŶĐůƵŝͲƐĞ�
ƋƵĞ͕�ŶŽ��ƌĂƐŝů�ĚŽ�ƐĠĐƵůŽ�yy͕
A Ă� ŝŶĚƵƐƚƌŝĂůŝnjĂĕĆŽ� ŽĐŽƌƌĞƵ� ŝŶĚĞƉĞŶĚĞŶƚĞŵĞŶƚĞ�
ĚŽ�ġdžŽĚŽ�ƌƵƌĂů�Ğ�ĚŽƐ�ƌĞĐƵƌƐŽƐ�ŶĂƚƵƌĂŝƐ�ĚŝƐƉŽŶşǀĞŝƐ͘
B Ž�ġdžŽĚŽ�ƌƵƌĂů�ƉĂƌĂ�ĂƐ�ĐŝĚĂĚĞƐ�ŶĆŽ�ƉƌĞũƵĚŝĐŽƵ�ĂƐ�
ĂƚŝǀŝĚĂĚĞƐ�ĂŐƌşĐŽůĂƐ�ŶĞŵ�Ž�ŵĞŝŽ�ƌƵƌĂů�ƉŽƌƋƵĞ�
ŶŽǀĂƐ� ƚĞĐŶŽůŽŐŝĂƐ� ŚĂǀŝĂŵ� ƐŝĚŽ� ŝŶƚƌŽĚƵnjŝĚĂƐ�
ŶŽ�ĐĂŵƉŽ͘
C ŚŽŵĞŶƐ�Ğ�ŵƵůŚĞƌĞƐ�ĂĚǀŝŶĚŽƐ�ĚŽ�ĐĂŵƉŽ�ĚĞŝdžĂƌĂŵ�
ƐƵĂ� ĐƵůƚƵƌĂ� Ğ� ƐĞ� ĂĚĂƉƚĂƌĂŵ� Ă� ŽƵƚƌĂ͕� ĐŝƚĂĚŝŶĂ͕�
ƚŽƚĂůŵĞŶƚĞ�ĚŝĨĞƌĞŶƚĞ�Ğ�ŽƉŽƐƚĂ�ĂŽƐ�ƐĞƵƐ�ǀĂůŽƌĞƐ͘
D ƚĂŶƚŽ�Ž�ĞƐƉĂĕŽ�ƵƌďĂŶŽ�ƋƵĂŶƚŽ�Ž� ƌƵƌĂů� ƐŽĨƌĞƌĂŵ�
ƚƌĂŶƐĨŽƌŵĂĕƁĞƐ� ĚĞĐŽƌƌĞŶƚĞƐ� ĚĂ� ĂƉůŝĐĂĕĆŽ� ĚĞ�
ŶŽǀĂƐ� ƚĞĐŶŽůŽŐŝĂƐ� ăƐ� ĂƟǀŝĚĂĚĞƐ� ŝŶĚƵƐƚƌŝĂŝƐ� Ğ�
ĂŐƌşĐŽůĂƐ͘
E ŽƐ� ŵŝŐƌĂŶƚĞƐ� ĐŚĞŐĂƌĂŵ� ăƐ� ŐƌĂŶĚĞƐ� ĐŝĚĂĚĞƐ�
ƚƌĂnjĞŶĚŽ� ĐŽŶƐŝŐŽ� ǀĂůŽƌĞƐ� Ğ� ƚƌĂĚŝĕƁĞƐ͕� ƋƵĞ� ůŚĞƐ�
ƉŽƐƐŝďŝůŝƚĂƌĂŵ� ŵĂŶƚĞƌ� ŝŶƚĂĐƚĂ� ƐƵĂ� ĐƵůƚƵƌĂ͕� ƚĂů�
ĐŽŵŽ�ƐĞ�ŵĂŶŝĨĞƐƚĂǀĂ�ŶĂƐ�ƉĞƋƵĞŶĂƐ�ĐŝĚĂĚĞƐ�Ğ�ŶŽ�
ŵĞŝŽ�ƌƵƌĂů͘
*R1520148*
9
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COMPONENTE ESPECÍFICO
QUESTÃO DISCURSIVA 3
�ŽŶƐŝĚĞƌĞ�Ƶŵ�ĐŚƵǀĞŝƌŽ�ĞůĠƚƌŝĐŽ�ŶŽ�ƋƵĂů�Ă�ƚĞŵƉĞƌĂƚƵƌĂ�ĚĂ�ĄŐƵĂ�ƉŽĚĞ�ƐĞƌ�ƐĞůĞĐŝŽŶĂĚĂ�ƉĞůŽ�ƵƐƵĄƌŝŽ�ĞŶƚƌĞ�Ă�
ƚĞŵƉĞƌĂƚƵƌĂ�ĂŵďŝĞŶƚĞ�Ğ�ϱϬ�Ǒ�͘���ƌĞƐŝƐƚġŶĐŝĂ�ĚŽ�ĐŚƵǀĞŝƌŽ�ĚŝƐƐŝƉĂ�ĞŶĞƌŐŝĂ�ĞůĠƚƌŝĐĂ�Ğŵ�ĨŽƌŵĂ�ĚĞ�ĐĂůŽƌ�ƉĂƌĂ�
ĂƋƵĞĐĞƌ�Ă�ĄŐƵĂ͕�Ğ�Ġ�ĂůŝŵĞŶƚĂĚĂ�ƉŽƌ�Ƶŵ�ĐŽŶǀĞƌƐŽƌ���ͬ��͕�ĚĞ�ŵŽĚŽ�ƋƵĞ�Ă�ƚĞŶƐĆŽ�ƉŽĚĞ�ƐĞƌ�ĂůƚĞƌĂĚĂ͕�ǀĂƌŝĂŶĚŽ͕�
ĂƐƐŝŵ͕�Ă�ƉŽƚġŶĐŝĂ͘�
WĂƌĂ� ůĞǀĂŶƚĂƌ� Ă� ĐĂƌĂĐƚĞƌşƐƟĐĂ� ĚŝŶąŵŝĐĂ� ĚŽ� ƐŝƐƚĞŵĂ͕� Ƶŵ�ĞŶŐĞŶŚĞŝƌŽ� ĂƉůŝĐŽƵ� Ƶŵ�ĚĞŐƌĂƵ� ĚĞ� Ϭ�s� Ă� ϰϬ�s� ŶŽ�
ŝŶƐƚĂŶƚĞ�ϭϬ�ƐĞŐƵŶĚŽƐ͕�ĐŽŵ�ǀĂnjĆŽ�ĚĞ�ĄŐƵĂ�ĐŽŶƐƚĂŶƚĞ͕�ŽďƚĞŶĚŽ�Ă�ƌĞƐƉŽƐƚĂ�ĚĞ�ƚĞŵƉĞƌĂƚƵƌĂ�ŵŽƐƚƌĂĚĂ�ŶĂ�ĮŐƵƌĂ�
Ă�ƐĞŐƵŝƌ͘ �WŽĚĞͲƐĞ�ŽďƐĞƌǀĂƌ�ƋƵĞ͕�ŝŶŝĐŝĂůŵĞŶƚĞ͕�Ă�ĄŐƵĂ�ĞƐƚĄ�Ğŵ�ƚĞŵƉĞƌĂƚƵƌĂ�ĂŵďŝĞŶƚĞ͘
0 5 10 15 20 25 30 35 40 45 50
Tempo (s)
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Te
m
pe
ra
tu
ra
 (°
C
)
Resposta ao degrau
ZĞƐƉŽƐƚĂ�ĂŽ�ĚĞŐƌĂƵ�ĚŽ�ƐŝƐƚĞŵĂ�Ğŵ�ŵĂůŚĂ�ĂďĞƌƚĂ�ŶĆŽ�ĐŽŶƚƌŽůĂĚŽ͘
WŽƐƚĞƌŝŽƌŵĞŶƚĞ͕�Ž�ĞŶŐĞŶŚĞŝƌŽ�ĚĞĐŝĚŝƵ�ŝŵƉůĞŵĞŶƚĂƌ�Ƶŵ�ĐŽŶƚƌŽůĞ�ĚĞ�ƚĞŵƉĞƌĂƚƵƌĂ�Ğŵ�ŵĂůŚĂ�ĨĞĐŚĂĚĂ�ƵƟůŝnjĂŶĚŽ�
Ƶŵ�ĐŽŵƉĞŶƐĂĚŽƌ�ƉƌŽƉŽƌĐŝŽŶĂůͲŝŶƚĞŐƌĂů͗�'Đ;ƐͿ�с�<Ɖ�н�<iͬƐ͘
�Žŵ�ďĂƐĞ�ŶŽƐ�ĚĂĚŽƐ�ĂƉƌĞƐĞŶƚĂĚŽƐ͕�Ğ�ĐŽŶƐŝĚĞƌĂŶĚŽ�ƋƵĞ�Ž�ƐŝƐƚĞŵĂ�Ġ�ůŝŶĞĂƌ�Ğ�ĚĞ�ƉƌŝŵĞŝƌĂ�ŽƌĚĞŵ͕�ĨĂĕĂ�Ž�ƋƵĞ�
ƐĞ�ƉĞĚĞ�ŶŽƐ�ŝƚĞŶƐ�Ă�ƐĞŐƵŝƌ͘
ĂͿ� KďƚĞŶŚĂ�Ă�ĨƵŶĕĆŽ�ĚĞ�ƚƌĂŶƐĨĞƌġŶĐŝĂ�ĚĞ�ŵĂůŚĂ�ĂďĞƌƚĂ�;ƐĞŵ�Ž�ĐŽŶƚƌŽůĂĚŽƌͿ�ƋƵĞ�ƌĞůĂĐŝŽŶĂ�Ă�ƚĞŶƐĆŽ�ĚĞ�ĞŶƚƌĂĚĂ�
ĐŽŵ�Ă�ƚĞŵƉĞƌĂƚƵƌĂ�ĚĞ�ƐĂşĚĂ͘�;ǀĂůŽƌ͗�ϲ͕Ϭ�ƉŽŶƚŽƐͿ
ďͿ� YƵĂů�Ġ�Ž�ĞĨĞŝƚŽ�ĚĂ�ĂĕĆŽ�ŝŶƚĞŐƌĂĚŽƌĂ�ĚŽ�ĐŽŵƉĞŶƐĂĚŽƌ�ŶŽ�ƐŝƐƚĞŵĂ�Ğŵ�ŵĂůŚĂ�ĨĞĐŚĂĚĂ͍�;ǀĂůŽƌ͗�ϰ͕Ϭ�ƉŽŶƚŽƐͿ
*R1520149*
10
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RASCUNHO
1
2
ϯ
4
5
6
7
ϴ
9
10
11
12
ϭϯ
14
15
*R15201410*
11
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QUESTÃO DISCURSIVA 4
�ŵ�ĚĞƚĞƌŵŝŶĂĚĂ�ƌŽĚŽǀŝĂ͕�Ă�ƉĞƐĂŐĞŵ�ŽďƌŝŐĂƚſƌŝĂ�ĚĞ�ĐĂŵŝŶŚƁĞƐ�Ġ�ƌĞĂůŝnjĂĚĂ�ƉŽƌ�ďĂůĂŶĕĂƐ�ĂƵƚŽŵĂƟnjĂĚĂƐ͘��ůĠŵ�
ĚĂ�ƉůĂƚĂĨŽƌŵĂ�Ğ�ĚŽ�ŝŶĚŝĐĂĚŽƌ�ĐŽŵŽ�ŝƚĞŶƐ�ďĄƐŝĐŽƐ�ĚĂ�ďĂůĂŶĕĂ�ƌŽĚŽǀŝĄƌŝĂ͕�Ž�ƐŝƐƚĞŵĂ�ĚĞ�ƉĞƐĂŐĞŵ�Ġ�ĐŽŶƐƟƚƵşĚŽ�
ƉŽƌ�ĚŝǀĞƌƐŽƐ�ĐŽŵƉŽŶĞŶƚĞƐ͕�ĐŽŶĨŽƌŵĞ�ŝůƵƐƚƌĂĚŽ�ŶĂ�ĮŐƵƌĂ�ĂďĂŝdžŽ͘
�ĂůĂŶĕĂ�ƉĂƌĂ�ƉĞƐĂŐĞŵ�ĚŽ�ĐĂŵŝŶŚĆŽ͘
�ŝƐƉŽŶşǀĞů�Ğŵ͗�фŚƩƉ͗ͬͬďĂůĂŶĐĂƐĂĐŽƌĞƐ͘ĐŽŵ͘ďƌх͘��ĐĞƐƐŽ�Ğŵ͗�Ϯϵ�ũƵů͘ϮϬϭϰ�;ĂĚĂƉƚĂĚŽͿ͘
EŽ�ŵŽŵĞŶƚŽ�ĚĂ�ƉĞƐĂŐĞŵ͕�Ž�ĐĂŵŝŶŚĆŽ�ĚĞƐůŽĐĂͲƐĞ�ƉŽƌ�ƵŵĂ�ƉĞƋƵĞŶĂ� ŝŶĐůŝŶĂĕĆŽ�Ğ�ĂĐŽŵŽĚĂͲƐĞ�ƉĂƌĂ�ƋƵĞ�Ă�
ŵĞĚŝĕĆŽ�ƐĞũĂ�ƌĞĂůŝnjĂĚĂ�Ğ�ƌĞŐŝƐƚƌĂĚĂ͘��ƐƐŝŵ͕�ĚŽ�ƐŽůŽ�ĂƚĠ�Ă�ĂĐŽŵŽĚĂĕĆŽ�ĚŽ�ĐĂŵŝŶŚĆŽ͕�Ž�ƐŝŶĂů�ĂƉůŝĐĂĚŽ�ă�ďĂůĂŶĕĂ�
ƉŽĚĞ�ƐĞƌ�ĂƉƌŽdžŝŵĂĚŽ�ƉŽƌ�Ƶŵ�ĚĞŐƌĂƵ�ƵŶŝƚĄƌŝŽ͘
^ƵƉŽŶŚĂ�ƋƵĞ�Ž�ĐĂŵŝŶŚĆŽ�ĚĞ�ƵŵĂ�ĞŵƉƌĞƐĂ�ĚĞ�ƚƌĂŶƐƉŽƌƚĞ�ĚĞ�ĐĂƌŐĂƐ�ƚĞŶŚĂ�ƉĂƐƐĂĚŽ�ƉŽƌ�ĚƵĂƐ�ďĂůĂŶĕĂƐ�Ğŵ�ƵŵĂ�
ƌŽĚŽǀŝĂ�ĐŽŵ�ƉĞƐĂŐĞŵ�ĂƵƚŽŵĂƟnjĂĚĂ͘�K�ŐĞƌĞŶƚĞ�ĚĂ�ĞŵƉƌĞƐĂ��ĐŽŶƐƚĂƚŽƵ�ƋƵĞ�Ž�ĐĂŵŝŶŚĆŽ�ŚĂǀŝĂ�ƐŝĚŽ�ŵƵůƚĂĚŽ�
ŶĂ�ƐĞŐƵŶĚĂ�ďĂůĂŶĕĂ͕�ĂƉſƐ� ƚĞƌ�ƐŝĚŽ� ůŝďĞƌĂĚŽ�ƉĞůĂ�ƉƌŝŵĞŝƌĂ͘�WĂƌĂ� ƌĞĐŽƌƌĞƌ�ĚĂ�ŵƵůƚĂ͕� ƐŽůŝĐŝƚŽƵͲƐĞ�ƉĂƌĞĐĞƌ�ĚĞ�
Ƶŵ�ƉĞƌŝƚŽ�ĐŽŵ�ƌĞůĂĕĆŽ�ĂŽ�ƐŝƐƚĞŵĂ�ĚĞ�ĐŽŶƚƌŽůĞ�ĚĞ�ƉĞƐĂŐĞŵ�ĚĂƐ�ďĂůĂŶĕĂƐ͘�WĂƌĂ�ĂŶĄůŝƐĞ�Ğ�ĞŵŝƐƐĆŽ�ĚŽ�ůĂƵĚŽ͕�Ž�
ƉĞƌŝƚŽ�ƌĞĐĞďĞƵ�ĚŽ�ĨĂďƌŝĐĂŶƚĞ�ĚĂ�ďĂůĂŶĕĂ�Ă�ƐƵĂ�ĨƵŶĕĆŽ�ĚĞ�ƚƌĂŶƐĨĞƌġŶĐŝĂ͕�ƌĞƉƌĞƐĞŶƚĂĚĂ�ƉŽƌ͗
indicaobalanca(s)
=
16
pesocaminhao(s) s2 + 4s + 16
^ƵƉŽŶŚĂ͕�ĂŝŶĚĂ͕�ƋƵĞ�Ă�ĞŵƉƌĞƐĂ�ƌĞƐƉŽŶƐĄǀĞů�ƉĞůĂ�ŵĂŶƵƚĞŶĕĆŽ�ĚŽ�ƐŝƐƚĞŵĂ�ĚĞ�ĂƋƵŝƐŝĕĆŽ�ĚĞ�ĚĂĚŽƐ�ŝŶĨŽƌŵŽƵ�ĂŽ�
ƉĞƌŝƚŽ�ƋƵĞ͕�ŶĂ�ƉƌŝŵĞŝƌĂ�ďĂůĂŶĕĂ͕�Ž�ƉĞƐŽ�Ġ�ĂĚƋƵŝƌŝĚŽ�ϯ�Ɛ�ĂƉſƐ�Ă�ĞŶƚƌĂĚĂ�ĚŽ�ĐĂŵŝŶŚĆŽ�Ğ͕�ŶĂ�ƐĞŐƵŶĚĂ�ďĂůĂŶĕĂ͕�
ϭ͕Ϯ�Ɛ�ĂƉſƐ�Ă�ĞŶƚƌĂĚĂ�ĚŽ�ǀĞşĐƵůŽ͘��ŽŶƐŝĚĞƌĞ�ƋƵĞ͕�ŶŽ�ƉĞƌĐƵƌƐŽ�ĞŶƚƌĞ�ĂƐ�ďĂůĂŶĕĂƐ͕�ŶĆŽ�ŚŽƵǀĞ�ǀĂƌŝĂĕĆŽ�ĚĞ�ĐĂƌŐĂ�ŶŽ�ĐĂŵŝŶŚĆŽ͕�ƋƵĞ�ĂƐ�ĚŝĨĞƌĞŶĕĂƐ�ĐĂƵƐĂĚĂƐ�ƉĞůŽ�ĐŽŶƐƵŵŽ�ĚĞ�ĐŽŵďƵƐơǀĞů� ƐĆŽ�ĚĞƐƉƌĞnjşǀĞŝƐ�Ğ�ƋƵĞ�Ž�ƉĞƐŽ�Ġ�
ĮdžĂĚŽ�ĂƉſƐ�Ă�ĂĐŽŵŽĚĂĕĆŽ�ĚŽ�ƐŝƐƚĞŵĂ͘�
*R15201411*
12
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ĂͿ� �ĞŵŽŶƐƚƌĞ�Ă�ƉĂƌƟƌ�ĚĞ�ƋƵĂů�ŝŶƐƚĂŶƚĞ�ĚĞ�ƚĞŵƉŽ�ƐĞ�ŐĂƌĂŶƚĞ�ƋƵĞ�Ă�ŵĞĚŝĚĂ�ĚĂƐ�ďĂůĂŶĕĂƐ�ĞƐƚĂƌĄ�ĂĚĞƋƵĂĚĂ͘�
;ǀĂůŽƌ͗�ϲ͕Ϭ�ƉŽŶƚŽƐͿ
ďͿ� EĂ�ƋƵĂůŝĚĂĚĞ�ĚĞ�ƉĞƌŝƚŽ�ĐŽŶƚƌĂƚĂĚŽ͕�ĂƉƌĞƐĞŶƚĞ�ƐĞƵ�ƉĂƌĞĐĞƌ�ƉĂƌĂ�Ž�ĐĂƐŽ͕�ũƵƐƟĮĐĂŶĚŽͲŽ�ĐŽŵ�ďĂƐĞ�Ğŵ�ĚĂĚŽƐ�
ƚĠĐŶŝĐŽƐ͘�;ǀĂůŽƌ͗�ϰ͕Ϭ�ƉŽŶƚŽƐͿ
�ŽŶƐŝĚĞƌĞ�ĂƐ�ƐĞŐƵŝŶƚĞƐ�ŝŶĨŽƌŵĂĕƁĞƐ�ĐŽŵƉůĞŵĞŶƚĂƌĞƐ͗
&ƵŶĕĆŽ�ĚĞ�ƚƌĂŶƐĨĞƌġŶĐŝĂ�ŶŽƌŵĂůŝnjĂĚĂ�ĚĞ�Ƶŵ�ƐŝƐƚĞŵĂ�ĚĞ�Ϯǐ�ŽƌĚĞŵ͗
G(s) =
wn
2
s2 + 2] wns + wn
2
^ŽďƌĞƐƐŝŶĂů�ŵĄdžŝŵŽ͗ DƉс�
e
−ζπ√
1−ζ2
dĞŵƉŽ�ĚĞ�ƉŝĐŽ͗ ƚƉ�с� π
wn
√
1− ζ2
dĞŵƉŽ�ĚĞ�ĂĐŽŵŽĚĂĕĆŽ͗ ƚƐ�с�
4
]wn
RASCUNHO
1
2
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4
5
6
7
ϴ
9
10
11
12
ϭϯ
14
15
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QUESTÃO DISCURSIVA 5
�ŽŶƐŝĚĞƌĞ�ƋƵĞ�Ğŵ�ƵŵĂ�ĐĠůƵůĂ�ĚĞ�ƉƌŽĚƵĕĆŽ�ĚĞ�ĚĞƚĞƌŵŝŶĂĚĂ�ĨĄďƌŝĐĂ�ŽƉĞƌĂͲƐĞ�ƚŽĚŽƐ�ŽƐ�ĚŝĂƐ�Ğŵ�ϯ�ƚƵƌŶŽƐ�
;ϰ�ĨƵŶĐŝŽŶĄƌŝŽƐ͕�Ƶŵ�ƉŽƌ�ƚƵƌŶŽ�Ğ�Ƶŵ�ƉĂƌĂ�ƌĞǀĞƐĂŵĞŶƚŽͿ�ƉĂƌĂ�ĞdžĞĐƵƚĂƌ�ŽƐ�ƉůĂŶŽƐ�ĚĞ�ƉƌŽĚƵĕĆŽ�ĚĞ�ƵŵĂ�ĨĂŵşůŝĂ�ĚĞ�
ƉĞĕĂƐ͘�K�ƉƌŽƉƌŝĞƚĄƌŝŽ�ĚĂ�ĨĄďƌŝĐĂ͕�ƋƵĞ�ƉŽƐƐƵŝ�ĐŽŶŚĞĐŝŵĞŶƚŽ�ŶĂ�ĄƌĞĂ�ĚĞ�ĂƵƚŽŵĂĕĆŽ͕�ĞƐƚĄ�ĂǀĂůŝĂŶĚŽ�Ă�ŚŝƉſƚĞƐĞ�
ĚĞ�ƐƵďƐƟƚƵŝƌ�ŽƐ�ĨƵŶĐŝŽŶĄƌŝŽƐ�ĚĂ�ĐĠůƵůĂ�ĚĞ�ƉƌŽĚƵĕĆŽ�ƉŽƌ�Ƶŵ�ƌŽďƀ�ŵĂŶŝƉƵůĂĚŽƌ͘ ���ŝŶƐƚĂůĂĕĆŽ�Ġ�ĐŽŵƉŽƐƚĂ�ƉŽƌ�
Ƶŵ�ĐĞŶƚƌŽ�ĚĞ�ƵƐŝŶĂŐĞŵ��E��Ğ�ƉŽƌ�Ƶŵ�ƐŝƐƚĞŵĂ�ĚĞ�ǀŝƐĆŽ͕�ƐĞŶĚŽ�ϭϲϬ�Đŵ�Ă�ĚŝƐƚąŶĐŝĂ�ĞŶƚƌĞ�ŽƐ�ƌĞƐƉĞĐƟǀŽƐ�ƉŽŶƚŽƐ�
ĚĞ�ŵĂŶŝƉƵůĂĕĆŽ͘�K�ƉĞƐŽ�ĚĂƐ�ƉĞĕĂƐ�ƉƌŽĚƵnjŝĚĂƐ�ǀĂƌŝĂ�ĚĞ�Ϯ�ŬŐĨ�Ă�ϱ�ŬŐĨ�Ğ�ŽƉƚŽƵͲƐĞ�ƉĞůĂ�ƵƟůŝnjĂĕĆŽ�ĚĞ�Ƶŵ�ďƌĂĕŽ�
ƌŽďſƟĐŽ�ĞƋƵŝƉĂĚŽ�ĐŽŵ�ƵŵĂ�ŐĂƌƌĂ�ƉŶĞƵŵĄƟĐĂ�ĚĞ�ϭ͕ϱ�ŬŐĨ͘
K�ƋƵĂĚƌŽ�Ă�ƐĞŐƵŝƌ�ĂƉƌĞƐĞŶƚĂ�ĂƐ�ƉƌŝŶĐŝƉĂŝƐ�ĐĂƌĂĐƚĞƌşƐƟĐĂƐ�ĚĞ�ŵŽĚĞůŽƐ�ƌŽďſƟĐŽƐ�ĚŝƐƉŽŶşǀĞŝƐ�ŶŽ�ŵĞƌĐĂĚŽ͘
Robô �ĂƉĂĐŝĚĂĚĞ�ĚĞ��ĂƌŐĂ�;ŬŐĨͿ Alcance (m) Eixos Custo (R$)
DŽĚĞůŽ�� 6 Ϭ͕ϳϬϬ 6 ϲϳ�ϬϬϬ͕ϬϬ
DŽĚĞůŽ�� 6 ϭ͕ϲϯϮ 6 ϳϱ�ϬϬϬ͕�ϬϬ
DŽĚĞůŽ�� 7 Ϭ͕ϵϭϭ 6 ϴϳ�ϬϬϬ͕�ϬϬ
DŽĚĞůŽ�� 7 ϭ͕ϲϯϮ 6 ϭϬϰ�ϬϬϬ͕�ϬϬ
DŽĚĞůŽ�� 10 ϭ͕ϰϱϬ 5 ϭϮϰ�ϬϬϬ͕�ϬϬ
�ŵ�ƌĞůĂĕĆŽ�ĂŽ�ĐĂƐŽ�ĂƉƌĞƐĞŶƚĂĚŽ͕�ĨĂĕĂ�Ž�ƋƵĞ�ƐĞ�ƉĞĚĞ�ŶŽƐ�ŝƚĞŶƐ�Ă�ƐĞŐƵŝƌ͘
ĂͿ� /ŶĚŝƋƵĞ�Ž�ŵŽĚĞůŽ�ŵĂŝƐ�ĞĐŽŶƀŵŝĐŽ�ƋƵĞ�ƐĞũĂ�ĂĚĞƋƵĂĚŽ�ƉĂƌĂ�ƌĞĂůŝnjĂƌ�Ž�ƚƌĂŶƐƉŽƌƚĞ�ĚĞ�ƉĞĕĂƐ�ĞŶƚƌĞ�ŽƐ�ĚŽŝƐ�
ĞƋƵŝƉĂŵĞŶƚŽƐ͕�ĐŽŶƐŝĚĞƌĂŶĚŽ�ŽƐ�ĚĂĚŽƐ�ĚŽ�ƋƵĂĚƌŽ�Ğ�Ž�ƉŽƐŝĐŝŽŶĂŵĞŶƚŽ�ĐĞŶƚƌĂů�ĚŽ�ƌŽďƀ�Ğŵ�ƌĞůĂĕĆŽ�ĂŽƐ�
ĞƋƵŝƉĂŵĞŶƚŽƐ�Ğ�ũƵƐƟĮƋƵĞ�ƐƵĂ�ĞƐĐŽůŚĂ͘�;ǀĂůŽƌ͗�ϯ͕Ϭ�ƉŽŶƚŽƐͿ
ďͿ� �ŝƚĞ� ĚƵĂƐ� ǀĂŶƚĂŐĞŶƐ� Ğ� ĚƵĂƐ� ĚĞƐǀĂŶƚĂŐĞŶƐ� ƌĞůĂĐŝŽŶĂĚĂƐ� ă� ƐƵďƐƟƚƵŝĕĆŽ� ĚŽ� ƐĞƌ� ŚƵŵĂŶŽ� ƉŽƌ� ƌŽďƀƐ� Ğŵ�
ƐŝƐƚĞŵĂƐ�ĚĞ�ƉƌŽĚƵĕĆŽ͘�;ǀĂůŽƌ͗�ϯ͕Ϭ�ƉŽŶƚŽƐͿ͘
ĐͿ� �ĞƚĞƌŵŝŶĞ�Ž�ƚĞŵƉŽ�ŶĞĐĞƐƐĄƌŝŽ�ƉĂƌĂ�Ă�ƌĞĐƵƉĞƌĂĕĆŽ�ĚŽ�ŝŶǀĞƐƟŵĞŶƚŽ�ŝŶŝĐŝĂů͕�ƐĞ�Ă�ƚĂdžĂ�ŵşŶŝŵĂ�ĚĞ�ĂƚƌĂƟǀŝĚĂĚĞ�
ĨŽƌ�ŝŐƵĂů�Ă�njĞƌŽ͘��ŽŶƐŝĚĞƌĞ�ƋƵĞ�Ă�ƐŽůƵĕĆŽ�ƌŽďſƟĐĂ�ƚĞŶŚĂ�Ƶŵ�ĐƵƐƚŽ�ƚŽƚĂů�ĚĞ�ZΨ�ϯϬϬ�ŵŝů�;ŝŶĐůƵŝŶĚŽ�Ă�ĂƋƵŝƐŝĕĆŽ�
ĚŽ�ŵĂŶŝƉƵůĂĚŽƌ� Ğ� ĂƐ� ĚĞƐƉĞƐĂƐ�ĚĞ� ŝŶƐƚĂůĂĕĆŽͿ͕� ƋƵĞ�Ž� ĐƵƐƚŽ�ĚĞ�ŽƉĞƌĂĕĆŽ�Ğ�ŵĂŶƵƚĞŶĕĆŽ� ƐĞũĂ�ĚĞ�ZΨ�ϰϬ�
ŵŝůͬĂŶŽ�Ğ�ƋƵĞ�Ă�ƉƌŽĚƵĕĆŽ�ĂŶƵĂů�ƐĞũĂ�ĚĞ�ZΨ�ϭϬϬ�ŵŝů͘��ŵ�ĐŽŶƚƌĂƉĂƌƟĚĂ͕�Ž�ĐƵƐƚŽ�ĚĞ�ĐĂĚĂ�ĨƵŶĐŝŽŶĄƌŝŽ� ũĄ�
ĐĂƉĂĐŝƚĂĚŽ�Ġ�ĚĞ�ZΨ�ϭϱ�ŵŝůͬĂŶŽ�Ğ�ƐƵĂ�ƉƌŽĚƵĕĆŽ�ĂŶƵĂů�Ġ�ĚĞ�ZΨ�ϴϬ�ŵŝů͘�;ǀĂůŽƌ͗�ϰ͕Ϭ�ƉŽŶƚŽƐͿ
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14
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RASCUNHO
1
2
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4
5
6
7
ϴ
9
10
11
12
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15
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QUESTÃO 09
^ƵƉŽŶŚĂ�ƋƵĞ�Ă�ĚŝƐƚąŶĐŝĂ�ƉĞƌĐŽƌƌŝĚĂ�ƉŽƌ�Ƶŵ�ĐŝĐůŝƐƚĂ�
ƋƵĞ� ƉĞĚĂůĂ� ƌĞŐƵůĂƌŵĞŶƚĞ� ƉŽĚĞ� ƐĞƌ� ŝŶĨĞƌŝĚĂ� ƉĞůĂ�
ǀĂƌŝĄǀĞů�ĂůĞĂƚſƌŝĂ�x͕�ĐŽŵ�ĚĞŶƐŝĚĂĚĞ�ĚĞ�ƉƌŽďĂďŝůŝĚĂĚĞ�
ŶŽƌŵĂů͕
f(x;μ, σ2) =
1√
2πσ2
e−
(x−μ)2
2σ2
ĐŽŵ� μ = 25km e σ2 = 25km2 ͘� �� ĚƵƌĂĕĆŽ�ŵĠĚŝĂ� ĚŽ�
ƐĞƵ�ƚƌĞŝŶŽ�Ġ�ĚĞ�ϭŚϭϱŵŝŶ͘
�Žŵ�ďĂƐĞ�ŶĞƐƐĞƐ�ĚĂĚŽƐ͕�ĂǀĂůŝĞ�ĂƐ�ĂĮƌŵĂĕƁĞƐ�ĂďĂŝdžŽ͘
/͘� �� ǀĞůŽĐŝĚĂĚĞ� ŵĠĚŝĂ� ĚĞ� ĐĂĚĂ� ƚƌĞŝŶŽ� Ġ� ĚĞ�
Ϯϭ͕ϳ�ŬŵͬŚ͘
//͘� ��ĚŝƐƚąŶĐŝĂ�ŵĠĚŝĂ�ƉĞƌĐŽƌƌŝĚĂ�Ğŵ�ĐĂĚĂ�ƚƌĞŝŶŽ�
Ġ�ĚĞ�Ϯϱ�Ŭŵ͘
///͘� ��ĄƌĞĂ�ŵĠĚŝĂ�ƉĞƌĐŽƌƌŝĚĂ�Ğŵ�ĐĂĚĂ�ƚƌĞŝŶŽ�Ġ�ĚĞ�
Ϯϱ�Ŭŵ2.
/s͘ � ��ĚŝƐƚąŶĐŝĂ�ƉĞƌĐŽƌƌŝĚĂ�ĚĞ�ĐĂĚĂ�ƚƌĞŝŶŽ͕�Ğŵ�Ƶŵ�
ĚĞƐǀŝŽͲƉĂĚƌĆŽ͕�ĞƐƚĄ�ĞŶƚƌĞ�ϮϬ�Ŭŵ�Ğ�ϯϬ�Ŭŵ͘
V. �� ǀĞůŽĐŝĚĂĚĞ�ŵĠĚŝĂ� ĚĞ� ĐĂĚĂ� ƚƌĞŝŶŽ͕� Ğŵ� Ƶŵ�
ĚĞƐǀŝŽͲƉĂĚƌĆŽ͕�ĞƐƚĄ�ĞŶƚƌĞ�ϭϲ�ŬŵͬŚ�Ğ�Ϯϰ�ŬŵͬŚ͘
��ĐŽƌƌĞƚŽ�ĂƉĞŶĂƐ�Ž�ƋƵĞ�ƐĞ�ĂĮƌŵĂ�Ğŵ
A /͘
B /�Ğ�/s͘
C //�Ğ�///͘
D ///�Ğ�s͘
E //͕�/s�Ğ�s͘
ÁREA LIVRE
QUESTÃO 10
�ĞŶŽŵŝŶĂŵͲƐĞ�ĐĂƌŐĂƐ�ŽƐ�ĞůĞŵĞŶƚŽƐ�ĚĞ�Ƶŵ�ĐŝƌĐƵŝƚŽ�
ĞůĠƚƌŝĐŽ� ƋƵĞ� ƐĞ� ŽƉƁĞŵ� ă� ƉĂƐƐĂŐĞŵ� ĚĞ� ĐŽƌƌĞŶƚĞ�
ĞůĠƚƌŝĐĂ͘��ƐƐĞŶĐŝĂůŵĞŶƚĞ͕�ĚŝƐƟŶŐƵĞŵͲƐĞ�ƚƌġƐ�ƟƉŽƐ�ĚĞ�
ĐĂƌŐĂƐ͗� ƌĞƐŝƐƟǀĂƐ͕� ĐĂƉĂĐŝƟǀĂƐ� Ğ� ŝŶĚƵƟǀĂƐ͘� �Ɛ� ĐĂƌŐĂƐ�
ƌĞƐŝƐƟǀĂƐ�ĚŝƐƐŝƉĂŵ�ĞŶĞƌŐŝĂ͕�ĞŶƋƵĂŶƚŽ�ĂƐ�ƉƵƌĂŵĞŶƚĞ�
ĐĂƉĂĐŝƟǀĂƐ�ŽƵ�ƉƵƌĂŵĞŶƚĞ�ŝŶĚƵƟǀĂƐ�ƐĆŽ�ĐŽŶƐŝĚĞƌĂĚĂƐ�
ĂƌŵĂnjĞŶĂĚŽƌĂƐ�ĚĞ�ĞŶĞƌŐŝĂ͘
+
�
L2
L1
L3
1F
12 V
1H
^e�Ž�ĐŝƌĐƵŝƚŽ�ŵŽƐƚƌĂĚŽ�ĂĐŝŵĂ�Ġ�ĂůŝŵĞŶƚĂĚŽ�ƉŽƌ�ƵŵĂ�
ĨŽŶƚĞ�ĚĞ�ƚĞŶƐĆŽ�ĐŽŶơŶƵĂ�ĚĞ�ϭϮ�s�Ğ�ĂƐ�ůąŵƉĂĚĂƐ�ƐĆŽ�
ĚĞ�ϭϮ�sͬϲ�t͕�ŽďƐĞƌǀĂͲƐĞ�ƋƵĞ͕�Ğŵ�ƌĞŐŝŵĞ�ƉĞƌŵĂŶĞŶƚĞ͕
A ĂƐ� ƚƌġƐ� ůąŵƉĂĚĂƐ͕� >ϭ͕� >Ϯ�Ğ�>ϯ͕�ĮĐĂƌĆŽ�ĂƉĂŐĂĚĂƐ͕�
ƉŽŝƐ� ůąŵƉĂĚĂƐ� ŝŶĐĂŶĚĞƐĐĞŶƚĞƐ� Ɛſ� ŽƉĞƌĂŵ� ĐŽŵ�
ĐŽƌƌĞŶƚĞ�ĂůƚĞƌŶĂĚĂ͘
B ƐŽŵĞŶƚĞ�>Ϯ�Ğ�>ϯ�ĮĐĂƌĆŽ�ĂĐĞƐĂƐ͕�ƉŽŝƐ�Ă�ĐŽƌƌĞŶƚĞ�
ƋƵĞ�ƉĂƐƐĂ�Ğŵ�>Ϯ�Ġ�Ă�ƐŽŵĂ�ĚĂƐ�ĐŽƌƌĞŶƚĞƐ�Ğŵ�>ϯ�Ğ�
ŶŽ�ŝŶĚƵƚŽƌ͘
C ĂƐ�ƚƌġƐ�ůąŵƉĂĚĂƐ͕�>ϭ͕�>Ϯ�Ğ�>ϯ͕�ĮĐĂƌĆŽ�ĂĐĞƐĂƐ͕�ƉŽŝƐ�
ĞƐƚĆŽ�ůŝŐĂĚĂƐ�ă�ĨŽŶƚĞ�ĚĞ�ĂůŝŵĞŶƚĂĕĆŽ͘
D ƐŽŵĞŶƚĞ�>Ϯ�ĮĐĂƌĄ�ĂĐĞƐĂ͕�ƉŽŝƐ�ĞƐƚĄ�Ğŵ�ƐĠƌŝĞ�ĐŽŵ�Ă�
ĨŽŶƚĞ�ĚĞ�ĂůŝŵĞŶƚĂĕĆŽ͘
E ƐŽŵĞŶƚĞ�>ϭ�ĮĐĂƌĄ�ĂĐĞƐĂ͕�ƉŽŝƐ�ĞƐƚĄ�Ğŵ�ƐĠƌŝĞ�ĐŽŵ�Ž�
ĐĂƉĂĐŝƚŽƌ͘
ÁREA LIVRE
*R15201415*
16
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QUESTÃO 11 
����K�;�ĞŵĂŶĚĂ��ŝŽƋƵşŵŝĐĂ�ĚĞ�KdžŝŐġŶŝŽͿ�ĚĞ�ƵŵĂ�ĂŵŽƐƚƌĂ�ĚĞ�ĄŐƵĂ�Ġ�Ă�ƋƵĂŶƟ�ĚĂĚĞ�ĚĞ�ŽdžŝŐġŶŝŽ�ŶĞĐĞƐƐĄƌŝĂ�
ƉĂƌĂ�ŽdžŝĚĂƌ�Ă�ŵĂƚĠƌŝĂ�ŽƌŐąŶŝĐĂ�ƉŽƌ�ĚĞĐŽŵƉŽƐŝĕĆŽ�ĂĞƌſďŝĂ͘�YƵĂŶĚŽ�Ă�ĂŵŽƐƚƌĂ�Ġ�ŐƵĂƌĚĂĚĂ�ƉŽƌ�ϱ�ĚŝĂƐ�Ğŵ�ƵŵĂ�
ƚĞŵƉĞƌĂƚƵƌĂ�ĚĞ�ŝŶĐƵďĂĕĆŽ�ĚĞ�ϮϬΣ�͕�ĞůĂ�Ġ�ƌĞĨĞƌŝĚĂ�ĐŽŵŽ���Kϱ͕ϮϬ͕�ƋƵĞ�Ġ�ŶŽƌŵĂůŵĞŶƚĞ�ƵƟ�ůŝnjĂĚĂ�ĐŽŵŽ�Ƶŵ�ĚŽƐ�
ƉĂƌąŵĞƚƌŽƐ�ƉĂƌĂ�ǀĞƌŝĮ�ĐĂĕĆŽ�ĚĂ�ƋƵĂůŝĚĂĚĞ�ĚĂ�ĄŐƵĂ͘
K�ƐĞŐƵŝŶƚĞ�ƋƵĂĚƌŽ�ĐůĂƐƐŝĮ�ĐĂ�Ƶŵ�ĐƵƌƐŽ�Ě Ą͛ŐƵĂ�Ğŵ�ĨƵŶĕĆŽ�ĚĂ�ƐƵĂ���Kϱ͕ϮϬ
�ůĂƐƐŝĮ�ĐĂĕĆŽ DBO5,20 (mg/L)
DƵŝƚŽ�ůŝŵƉŽ �ƚĠ�ϭ
>ŝŵƉŽ DĂŝŽƌ�ƋƵĞ�ϭ�ĂƚĠ�Ϯ
ZĂnjŽĄǀĞů DĂŝŽƌ�ƋƵĞ�Ϯ�ĂƚĠ�ϰ
ZƵŝŵ DĂŝŽƌ�ƋƵĞ�ϰ�ĂƚĠ�ϲ
WĠƐƐŝŵŽ DĂŝŽƌ�ƋƵĞ�ϲ
��ŝŵĂŐĞŵ�ĂďĂŝdžŽ�ŵŽƐƚƌĂ�Ƶŵ�ƚƌĞĐŚŽ�ĚĞ�Ƶŵ�ƌŝŽ�ĐŽŵ�ϱ�ƐĞĕƁĞƐ�;y͕�z͕ �͕�t�Ğ�dͿ͕�Ğŵ�ƋƵĞ�ƐĆŽ�ĐŽůĞƚĂĚĂƐ�ĂŵŽƐƚƌĂƐ�
ĚĞ�ĄŐƵĂ�ƉĂƌĂ�Ă�ĚĞƚĞƌŵŝŶĂĕĆŽ�ĚĞ���Kϱ͕ϮϬ�Ğŵ�ůĂďŽƌĂƚſƌŝŽ͘
Ponto de
lançamento de
esgoto
Ponto de
lançamento de
esgoto
Ponto de
lançamento de
esgoto
X Y Z W T
Imagem sem escala
Q
K�ƋƵĂĚƌŽ�ĂďĂŝdžŽ�ĂƉƌĞƐĞŶƚĂ�ŽƐ�ƌĞƐƵůƚĂĚŽƐ͕�Ğŵ�ĚŝĨĞƌĞŶƚĞƐ�ƵŶŝĚĂĚĞƐ͕�ĚĂƐ�ĂŵŽƐƚƌĂƐ�ĐŽůŚŝĚĂƐ͘
Seção DBO5,20
X Ϭ͕ϰ�Őͬŵϯ
Y ϯ�ϴϱϬ�ŵŐͬŵϯ
Z Ϯ�ϱϬϬ�ŵŐͬŵϯ
W ϯ�ϬϬϬ�ŵŐͬŵϯ
T Ϭ͕Ϭϭ�ŬŐͬŵϯ
�ŽŶƐŝĚĞƌĂŶĚŽ�ƋƵĞ�ƉŽĚĞ�ŽĐŽƌƌĞƌ�ĂƵƚŽĚĞƉƵƌĂĕĆŽ�ŶŽ�ƌŝŽ͕�Ğŵ�ƋƵĂů�ƐĞĕĆŽ�ĚĞůĞ�Ă�ĄŐƵĂ�ŶĆŽ�ƉŽĚĞ�ƐĞƌ�ĐůĂƐƐŝĮ�ĐĂĚĂ͕�
ŶŽ�ŵşŶŝŵŽ͕�ĐŽŵŽ�͞ƌĂnjŽĄǀĞů͍͟
A y͘
B z͘
C ͘
D t͘
E d͘
*R15201416*
17
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 12 
hŵ�ĂŵďŝĞŶƚĞ�ƚĞƌŵŝĐĂŵĞŶƚĞ�ĐŽŶĨŽƌƚĄǀĞů�Ġ�ƵŵĂ�ĚĂƐ�
ĐŽŶĚŝĕƁĞƐ�ƋƵĞ�ĚĞǀĞŵ�ƐĞƌ�ĐŽŶƐŝĚĞƌĂĚĂƐ�Ğŵ�ƉƌŽũĞƚŽƐ�
ĚĞ�ĞĚŝĮ�ĐĂĕƁĞƐ͘���Į�ŵ�ĚĞ�ƉƌŽũĞƚĂƌ�Ƶŵ�ĂŵďŝĞŶƚĞ�ŝŶƚĞƌŶŽ�
ĐŽŵ� ƚĞŵƉĞƌĂƚƵƌĂ� ĚĞ� ϮϬΣ�� ƉĂƌĂ� ƵŵĂ� ƚĞŵƉĞƌĂƚƵƌĂ�
ĞdžƚĞƌŶĂ�ŵĠĚŝĂ�ĚĞ�ϯϱΣ�͕�Ƶŵ�ĞŶŐĞŶŚĞŝƌŽ�ĐŽŶƐŝĚĞƌŽƵ͕�
ŶŽ�ĚŝŵĞŶƐŝŽŶĂŵĞŶƚŽ͕�Ƶŵ�Ň�ƵdžŽ�ĚĞ�ĐĂůŽƌ�ĂƚƌĂǀĠƐ�ĚĞ�
ƵŵĂ�ƉĂƌĞĚĞ�ĞdžƚĞƌŶĂ�ĚĞ�ϭϬϱ�tͬŵϸ͕�ĐŽŶĨŽƌŵĞ�ŝůƵƐƚƌĂ�
Ă�Į�ŐƵƌĂ�ĂďĂŝdžŽ͘
Tint = 20°C
20 cm
Text = 35°C
105 W/m2
��ƚĂďĞůĂ�Ă�ƐĞŐƵŝƌ�ĂƉƌĞƐĞŶƚĂ�ŽƐ�ǀĂůŽƌĞƐ�ĚĂ�ĐŽŶĚƵƟ�ǀŝĚĂĚĞ�
ƚĠƌŵŝĐĂ�ƉĂƌĂ�ĂůŐƵŶƐ�ŵĂƚĞƌŝĂŝƐ�ĚĞ�ĐŽŶƐƚƌƵĕĆŽ͘
Material
�ŽŶĚƵƟ�ǀŝĚĂĚĞ�
térmica
O (W.m�1.K�1)
�ŽŶĐƌĞƚŽ ϭ͕ϰϬ
WĞĚƌĂ�ŶĂƚƵƌĂů ϭ͕ϬϬ
WůĂĐĂ�ĚĞ�ĂŐůŽŵĞƌĂĚŽ�ĚĞ�Į�ďƌĂƐ�ĚĞ�ŵĂĚĞŝƌĂ Ϭ͕ϮϬ
WůĂĐĂ�ĚĞ�ŵĂĚĞŝƌĂ�ƉƌĞŶƐĂĚĂ Ϭ͕ϭϬ
WůĂĐĂ�ĐŽŵ�ĞƐƉƵŵĂ�ƌşŐŝĚĂ�ĚĞ�ƉŽůŝƵƌĞƚĂŶŽ Ϭ͕Ϭϯ
�^^K�/���K��Z�^/>�/Z�����EKZD�^�d��E/��^͘�E�Z�ϭϱϮϮϬͲϭ͗�
�ĞƐĞŵƉĞŶŚŽ�ƚĠƌŵŝĐŽ�ĚĞ�ĞĚŝĨŝĐĂĕƁĞƐ�Ͳ�WĂƌƚĞ�ϭ͗��ĞĨŝŶŝĕƁĞƐ͕�
ƐşŵďŽůŽƐ�Ğ�ƵŶŝĚĂĚĞƐ͘�ZŝŽ�ĚĞ�:ĂŶĞŝƌŽ͕�ϮϬϬϱ͕�Ɖ͘�ϴ�;ĂĚĂƉƚĂĚŽͿ͘
��Į�ŵ�ĚĞ� ƐĞ�ŽďƚĞƌ� Ă� ƚĞŵƉĞƌĂƚƵƌĂ� ŝŶƚĞƌŶĂ�ĚĞƐĞũĂĚĂ͕�
ƋƵĂů� ĚĞǀĞ� ƐĞƌ� Ž� ŵĂƚĞƌŝĂů� ƐĞůĞĐŝŽŶĂĚŽ͕� ĞŶƚƌĞ� ŽƐ�
ĂƉƌĞƐĞŶƚĂĚŽƐ�ŶĂ�ƚĂďĞůĂ�ĂĐŝŵĂ͕�ƉĂƌĂ�ĐŽŵƉŽƐŝĕĆŽ�ĚĂ�
ƉĂƌĞĚĞ�ĞdžƚĞƌŶĂ͍
A �ŽŶĐƌĞƚŽ͘
B WĞĚƌĂ�ŶĂƚƵƌĂů͘
C WůĂĐĂ�ĚĞ�ŵĂĚĞŝƌĂ�ƉƌĞŶƐĂĚĂ͘
D WůĂĐĂ�ĐŽŵ�ĞƐƉƵŵĂ�ƌşŐŝĚĂ�ĚĞ�ƉŽůŝƵƌĞƚĂŶŽ͘
E WůĂĐĂ�ĚĞ�ĂŐůŽŵĞƌĂĚŽ�ĚĞ�Į�ďƌĂƐ�ĚĞ�ŵĂĚĞŝƌĂ͘
QUESTÃO 13 
�ŶŐĞŶŚĞŝƌŽƐ�ĚĞ�ƵŵĂ�ĞŵƉƌĞƐĂ�ŚŽůĂŶĚĞƐĂ�ĞŶĐŽŶƚƌĂƌĂŵ�
ƵŵĂ�ŵĂŶĞŝƌĂ�ĚĞ�ĨĂnjĞƌ�ĐŽŵ�ƋƵĞ�ŽƐ�ĞůĞǀĂĚŽƌĞƐ�ƚĞƌƌĞƐƚƌĞƐ�
ƐƵďĂŵ� ĂƚĠ� Ž� ƚŽƉŽ� ĚĞ� ĞĚŝİ�ĐŝŽƐ� ĐŽŵ� ϭ� ϬϬϬ�ŵĞƚƌŽƐ� ĚĞ�
ĂůƚƵƌĂ͕�ƉŽŝƐ�ŽƐ�ĐĂďŽƐ�ĚĞ�ĂĕŽ�ƵƐĂĚŽƐ�ŶŽƐ�ĞůĞǀĂĚŽƌĞƐ�ĂƚƵĂŝƐ�Ɛſ�ĐŽŶƐĞŐƵĞŵ�ĂůĕĄͲůŽƐ�Ă�ĂůƚƵƌĂƐ�ĚĞ͕�ĂƉƌŽdžŝŵĂĚĂŵĞŶƚĞ͕�
ϱϬϬ� ŵĞƚƌŽƐ͘� /ƐƐŽ� ƐĞƌĄ� ƉŽƐƐşǀĞů� ĐŽŵ� Ă� ĐƌŝĂĕĆŽ� ĚĞ� Ƶŵ�
ŶŽǀŽ�ĐĂďŽ�ƐƵƉĞƌůĞǀĞ�Ğ�ƐƵƉĞƌĨŽƌƚĞ͕�ŽƵ�ƐĞũĂ͕�ƵŵĂ�ĞƐƉĠĐŝĞ�
ĚĞ�ĐŝŶƚĂ͕�ƚĞĐŝĚĂ�ĐŽŵ�Į�ďƌĂƐ�ĚĞ�ĐĂƌďŽŶŽ͘��ŵ�ǀĞnj�ĚŽƐ�Į�ŽƐ�
ĚĞ�ĂĕŽ�ĞŶƚƌĞůĂĕĂĚŽƐ�ƵƐĂĚŽƐ�ŶŽƐ�ĐĂďŽƐ�ĚĞ�ĂĕŽ�ĐŽŵƵŶƐ͕�
Ă�ĐŝŶƚĂ�Ġ�ĨŽƌŵĂĚĂ�ƉŽƌ�ƋƵĂƚƌŽ�Į�ƚĂƐ�ĚĞ�Į�ďƌĂ�ĚĞ�ĐĂƌďŽŶŽ�
ƐĞůĂĚĂƐ�Ğŵ�ƉůĄƐƟ�ĐŽ�ƚƌĂŶƐƉĂƌĞŶƚĞ͘�K�ƉůĄƐƟ�ĐŽ�Ġ�ŶĞĐĞƐƐĄƌŝŽ�
ƉĂƌĂ�ƉƌŽƚĞŐĞƌ�ĚŽ�ĂƚƌŝƚŽ�ĂƐ�Į�ďƌĂƐ�ĚĞ�ĐĂƌďŽŶŽ�Ğ�ĂƵŵĞŶƚĂƌ�
Ă�ǀŝĚĂ�ƷƟ�ů�ĚŽ�ĐŽŶũƵŶƚŽ͘��ĂĚĂ�Į�ƚĂ�ƚĞŵ�ϰ�ĐĞŶơ�ŵĞƚƌŽƐ�ĚĞ�
ůĂƌŐƵƌĂ�ƉŽƌ�ϰ�ŵŝůşŵĞƚƌŽƐ�ĚĞ�ĞƐƉĞƐƐƵƌĂ͘��ůĂƐ�ƐĆŽ�ƉĂƌĞĐŝĚĂƐ�
ĐŽŵ� ƵŵĂ� ƌĠŐƵĂ� ĞƐĐŽůĂƌ� Ň�ĞdžşǀĞů͘� �ƐƐĞ� ŶŽǀŽ� ŵĂƚĞƌŝĂů�
ƐƵƉĞƌĂ�ůŝŐĞŝƌĂŵĞŶƚĞ�Ă�ƌĞƐŝƐƚġŶĐŝĂ�ă�ƚĞŶƐĆŽ�ĚŽ�ĂĕŽ͕�ŵĂƐ�
ƉĞƐĂ�ƐĞƚĞ�ǀĞnjĞƐ�ŵĞŶŽƐ�ƋƵĞ�Ž�ĂƚƵĂůŵĞŶƚĞ�ƵƐĂĚŽ͘��ƐƐŝŵ͕�
Ă� ĨŽƌĕĂ� ŐĂƐƚĂ� ƉĂƌĂ� ƐƵƐƚĞŶƚĂƌ� Ž� ƉĞƐŽ� ĚŽ� ƉƌſƉƌŝŽ� ĐĂďŽ�
ƉĂƐƐĂ�Ă�ƐĞƌ�ĂƉůŝĐĂĚĂ�ƉĂƌĂ�ƐƵƐƚĞŶƚĂƌ�ĂƉĞŶĂƐ�Ž�ĞůĞǀĂĚŽƌ͕ �Ğ�
Ž�ĐŽŶƐƵŵŽ�ĚĞ�ĞŶĞƌŐŝĂ�ĚŽƐ�ĞůĞǀĂĚŽƌĞƐ�ƚĂŵďĠŵ�Ġ�ĐĞƌĐĂ�
ĚĞ�ϭϱй�ŵĞŶŽƌ�ĚŽ�ƋƵĞ�ŽƐ�ĂŶƚĞƌŝŽƌĞƐ͘
��ŝƐƉŽŶşǀĞů�Ğŵ͗�фŚƩ�Ɖ͗ͬͬǁǁǁ͘ŝŶŽǀĂĐĂŽƚĞĐŶŽůŽŐŝĐĂ͘ĐŽŵ͘ďƌх͘�
�ĐĞƐƐŽ�Ğŵ͗�Ϯϳ�ũƵů͘�ϮϬϭϰ�;ĂĚĂƉƚĂĚŽͿ͘
dĞŶĚŽ� Ğŵ� ǀŝƐƚĂ� Ă� ƐŝƚƵĂĕĆŽ� ĚĞƐĐƌŝƚĂ͕� ĂǀĂůŝĞ� ĂƐ�
ĂĮ�ƌŵĂĕƁĞƐ�Ă�ƐĞŐƵŝƌ͘
/͘� K� ĐĂďŽ�ĚĞ�Į�ďƌĂ�ĚĞ� ĐĂƌďŽŶŽ� ƐƵƉŽƌƚĂ�ĞůĞǀĂĚĂƐ�
ĐĂƌŐĂƐ�ĚĞǀŝĚŽ�ă�ƐƵĂ�ĞůĞǀĂĚĂ�ƌĞƐŝƐƚġŶĐŝĂ�ă�ƚƌĂĕĆŽ͘
//͘� �� Į�ďƌĂ� ĚĞ� ĐĂƌďŽŶŽ� ƚŽƌŶĂ� Ž� ĐĂďŽ� ďĞŵ�ŵĂŝƐ�
Ň�ĞdžşǀĞů͕�Ž�ƋƵĞ͕�ĂůŝĂĚŽ�Ă�ƐƵĂ�ƌĞƐŝƐƚġŶĐŝĂ�ă�ƚƌĂĕĆŽ͕�
ƉƌŽƉŽƌĐŝŽŶĂ� Ă� ĞƐƐĞ� ŵĂƚĞƌŝĂů� ƵŵĂ� ǀĂŶƚĂŐĞŵ�
Ğŵ�ƌĞůĂĕĆŽ�ĂŽƐ�ĐĂďŽƐ�ĚĞ�ĂĕŽ�ĐŽŶǀĞŶĐŝŽŶĂŝƐ͘
///͘� �� ƌĞůĂĕĆŽ� ƌĞƐŝƐƚġŶĐŝĂͬƉĞƐŽ�ĚŽ� ĐĂďŽ�ĚĞ�Į�ďƌĂ�ĚĞ�
ĐĂƌďŽŶŽ�ĂƐƐĞŐƵƌĂ�ǀĂŶƚĂŐĞŵ�ĚĞƐƐĞ�ŵĂƚĞƌŝĂů�Ğŵ�
ƌĞůĂĕĆŽ�ĂŽƐ�ĐĂďŽƐ�ĚĞ�ĂĕŽ �͕ƉŽŝƐ�Ă�ĞĐŽŶŽŵŝĂ�ĚŽ�ƉĞƐŽ�
ƉƌſƉƌŝŽ�ĚŽ�ĐĂďŽ�ƉŽĚĞ�ƐĞƌ�ƵƐĂĚĂ�ƉĂƌĂ�ƐƵƐƚĞŶƚĂƌ�Ž�
ĞůĞǀĂĚŽƌ�Ğ�ƌĞĚƵnjŝƌ�Ž�ĐŽŶƐƵŵŽ�ĚĞ�ĞŶĞƌŐŝĂ͘
/s͘ � �ƉĞƐĂƌ� ĚĂ� ƌĞƐŝƐƚġŶĐŝĂ� ă� ƚĞŶƐĆŽ� ƐĞƌ� ĂƉĞŶĂƐ�
ůŝŐĞŝƌĂŵĞŶƚĞ� ŵĂŝŽƌ� ŶŽ� ĐĂďŽ� ĚĞ� Į�ďƌĂ� ĚĞ�
ĐĂƌďŽŶŽ͕�Ă�ǀĂŶƚĂŐĞŵ�ƉƌŝŶĐŝƉĂů�ĚĞ�ƐĞƵ�ƵƐŽ�Ġ�Ă�
ĂůƚĂ�ƌĞůĂĕĆŽ�ƌĞƐŝƐƚġŶĐŝĂͬƉĞƐŽ͘
��ĐŽƌƌĞƚŽ�ĂƉĞŶĂƐ�Ž�ƋƵĞ�ƐĞ�ĂĮ�ƌŵĂ�Ğŵ
A /͘
B //͘
C /�Ğ�///͘
D //�Ğ�/s͘
E ///�Ğ�/s͘
*R15201417*
ϭϴ
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 14
K�ƚƌĂŶƐƉŽƌƚĞ�ĚĞ�Ƶŵ�ŇƵŝĚŽ�ĞŶƚƌĞ�ĚŽŝƐ�ƉŽŶƚŽƐ�ŶŽ�ŝŶƚĞƌŝŽƌ�
ĚĞ�Ƶŵ�ƚƵďŽ�ŽĐŽƌƌĞ�ƐŝŵƵůƚĂŶĞĂŵĞŶƚĞ͕�ĐŽŵ�ƉĞƌĚĂ�ĚĞ�
ĞŶĞƌŐŝĂ͕�ĚĞǀŝĚŽ�ĂŽ�ĂƚƌŝƚŽ�ĚŽ�ŇƵŝĚŽ�ĐŽŵ�Ă�ƉĂƌĞĚĞ�Ğ�ĂŽ�
ĞƐĐŽĂŵĞŶƚŽ�ƚƵƌďƵůĞŶƚŽ͘�WŽƌƚĂŶƚŽ͕�ƋƵĂŶƚŽ�ŵĂŝŽƌ�ĨŽƌ�
Ă�ƌƵŐŽƐŝĚĂĚĞ�ĚĂ�ƉĂƌĞĚĞ�ĚĂ�ƚƵďƵůĂĕĆŽ�ŽƵ�ŵĂŝƐ�ǀŝƐĐŽƐŽ�
ĨŽƌ�Ž�ŇƵŝĚŽ͕�ŵĂŝŽƌ�ƐĞƌĄ�Ă�ƉĞƌĚĂ�ĚĞ�ĞŶĞƌŐŝĂ͘���ĨŽƌŵĂ�
ĚĞ�ĚĞƚĞƌŵŝŶĂĕĆŽ�ĚŽ�ĨĂƚŽƌ�ĚĞ�ĂƚƌŝƚŽ�ĨŽŝ�ĞƐƚĂďĞůĞĐŝĚĂ�
Ğŵ�ϭϵϯϵ͕�ƉŽƌ�ŝŶƚĞƌŵĠĚŝŽ�ĚĂ�ĞƋƵĂĕĆŽ�ĚĞ��ŽůĞďƌŽŽŬͲ
tŚŝƚĞ͕�ĂƉƌĞƐĞŶƚĂĚĂ�Ă�ƐĞŐƵŝƌ͘
1√
f
= −2 log10
(
k
3, 7D
+
2, 51
Re
√
f
)
Ğŵ�ƋƵĞ
f���Ġ�Ž�ĨĂƚŽƌ�ĚĞ�ĂƚƌŝƚŽ�ĚĞ��ĂƌĐLJͲtĞŝƐďĂĐŚ�;ĂĚŝŵĞŶƐŝŽŶĂůͿ͖
k�Ġ�Ă�ƌƵŐŽƐŝĚĂĚĞ�ĞƋƵŝǀĂůĞŶƚĞ�ĚĂ�ƉĂƌĞĚĞ�ĚŽ�ƚƵďŽ�;ŵͿ͖
D Ġ�Ž�ĚŝąŵĞƚƌŽ�ŝŶƚĞƌŶŽ�ĚŽ�ƚƵďŽ�;ŵͿ͖
Re�Ġ�Ž�ŶƷŵĞƌŽ�ĚĞ�ZĞLJŶŽůĚƐ�;ĂĚŝŵĞŶƐŝŽŶĂůͿ͘
�� ƌĞƐŽůƵĕĆŽ� ĚĞƐƐĂ� ĞƋƵĂĕĆŽ� ƌĞƋƵĞƌ� Ƶŵ� ƉƌŽĐĞƐƐŽ�
ŝƚĞƌĂƟǀŽ͕�ƉŽŝƐ�Ă�ĨƵŶĕĆŽ�Ġ�ŝŵƉůşĐŝƚĂ�Ğŵ�ƌĞůĂĕĆŽ�ĂŽ�ĨĂƚŽƌ�
ĚĞ�ĂƚƌŝƚŽ�;ƉƌĞƐĞŶƚĞ�ŶŽƐ�ĚŽŝƐ�ŵĞŵďƌŽƐ�ĚĂ�ĞƋƵĂĕĆŽͿ͘�
�ŵ�ϭϵϯϵ͕�Ă�ƌĞƐŽůƵĕĆŽ�ĚĞ�ĞƋƵĂĕƁĞƐ�ƉŽƌ�ƉƌŽĐĞĚŝŵĞŶƚŽƐ�
ŝƚĞƌĂƟǀŽƐ� ĚĞŵĂŶĚĂǀĂ� ĞdžĐĞƐƐŽ� ĚĞ� ƚĞŵƉŽ͕� ŵĂƐ͕�
ĐŽŵ� Ž� ĚĞƐĞŶǀŽůǀŝŵĞŶƚŽ� ĚŽƐ� ĐŽŶŚĞĐŝŵĞŶƚŽƐ� ĚĞ�
ĐŽŵƉƵƚĂĕĆŽ͕�ĞƐƐĞ�ƉƌŽďůĞŵĂ�ĨŽŝ�ƐŽůƵĐŝŽŶĂĚŽ͘
�Ɛ�ĞƚĂƉĂƐ�ĚĞ�Ƶŵ�ĂůŐŽƌŝƚŵŽ�ƋƵĞ�ƐŽůƵĐŝŽŶĂ�Ă�ĞƋƵĂĕĆŽ͕�
ƐĞŵ�ŽƌĚĞŶĂĕĆŽ� ůſŐŝĐĂ͕� ĂƐƐŝŵ� ĐŽŵŽ� ƐĞƵ�ŇƵdžŽŐƌĂŵĂ�
ƐĆŽ�ĂƉƌĞƐĞŶƚĂĚŽƐ�Ă�ƐĞŐƵŝƌ͘ �
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tŚŝƚĞ
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:Ϳ�sŝƐƵĂůŝnjĂĕĆŽ�ĚŽ�ƌĞƐƵůƚĂĚŽ
1
2
3
4
5
6
7
8
9
10
�Žŵ� ďĂƐĞ� ŶĞƐƐĂƐ� ŝŶĨŽƌŵĂĕƁĞƐ͕� ǀĞƌŝĮĐĂͲƐĞ� ƋƵĞ� Ă�
ƐŽůƵĕĆŽ�ĚĂ�ĞƋƵĂĕĆŽ�Ġ�ŽďƟĚĂ�ƉĞůĂ�ƐĞŐƵŝŶƚĞ�ĂƐƐŽĐŝĂĕĆŽ�
ĚĂƐ�ĞƚĂƉĂƐ�ĚŽ�ĂůŐŽƌŝƚŵŽ�ĐŽŵ�Ž�ŇƵdžŽŐƌĂŵĂ
A
1 2 ϯ 4 5 6 7 ϴ 9 10
� � , ' � � � : / F
B
1 2 ϯ 4 5 6 7 ϴ 9 10
� , � ' � � � : F /
C
1 2 ϯ 4 5 6 7 ϴ 9 10
� ' � , � � : � / F
D
1 2 ϯ 4 5 6 7 ϴ 9 10
� � � , ' � : � F /
E
1 2 ϯ 4 5 6 7 ϴ 9 10
� � ' , � � � : / F
*R15201418*
19
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 15
KďƐĞƌǀĞ� Ž� ƉƌŽŐƌĂŵĂ� ĐůĂƐƐŝĮĐĂĚŽƌ� ;͞ƐŽƌƚ͟Ϳ͕� Ğŵ�
ƉƐĞƵĚŽĐſĚŝŐŽ͕�ĂƉƌĞƐĞŶƚĂĚŽ�ĂďĂŝdžŽ͘
�ƐƐĞ�ƉƌŽŐƌĂŵĂ�ĐůĂƐƐŝĮĐĂ͕�Ğŵ�ŽƌĚĞŵ
A ĚĞĐƌĞƐĐĞŶƚĞ͕�ŶŽƚĂƐ�ĚĞ�ĂůƵŶŽƐ�Ğ�ŶŽŵĞƐ�ĚĞ�ĂůƵŶŽƐ�
ĚĞ�ŵĞƐŵĂ�ŶŽƚĂ͘
B ĂůĨĂďĠƟĐĂ�ĐƌĞƐĐĞŶƚĞ͕�ŶŽŵĞƐ�Ğ�ŶŽƚĂƐ�ĚĞ�ĂůƵŶŽƐ�ĚĞ�
ŵĞƐŵŽ�ŶŽŵĞ͘
C ĚĞĐƌĞƐĐĞŶƚĞ͕�ŶŽƚĂƐ�ĚĞ�ĂůƵŶŽƐ͘
D ĂůĨĂďĠƟĐĂ�ĐƌĞƐĐĞŶƚĞ͕�ŶŽŵĞƐ�ĚĞ�ĂůƵŶŽƐ͘
E ĐƌĞƐĐĞŶƚĞ͕�ŶŽƚĂƐ�ĚĞ�ĂůƵŶŽƐ͘
ÁREA LIVRE
QUESTÃO 16
hŵĂ� ŝŶĚƷƐƚƌŝĂ� ĚĞ� ďůŽĐŽƐ� ĐĞƌąŵŝĐŽƐ� ƉƌĞƚĞŶĚĞ�
ƵƟůŝnjĂƌ�ƋƵĞŝŵĂ�ĚĞ�ďŝŽŵĂƐƐĂ� ƌĞƐƵůƚĂŶƚĞ�ĚĞ� ƌĞƐşĚƵŽƐ�
ĚĞ� ŵĂĚĞŝƌĂ͕� ƉĂƌĂ� ŐĞƌĂƌ� ĞŶĞƌŐŝĂ� ƚĠƌŵŝĐĂ� ƉĂƌĂ� ƐĞƵƐ�
ĨŽƌŶŽƐ͕� ƋƵĞ͕� ĂƚƵĂůŵĞŶƚĞ͕� ƵƟůŝnjĂŵ� ŐĄƐ� ŶĂƚƵƌĂů͘� dĂů�
ŝŶŝĐŝĂƟǀĂ�ƉŽĚĞƌĄ�ƌĞĚƵnjŝƌ�Ž�ĐŽŶƐƵŵŽ�ĚĞ�ĐŽŵďƵƐơǀĞů͕�
ƉŽƌĠŵ�ƐĞƌĄ�ŶĞĐĞƐƐĄƌŝŽ�Ƶŵ�ŝŶǀĞƐƟŵĞŶƚŽ�ŶŽ�ǀĂůŽƌ�ĚĞ�
ϮϬй�ĚŽ�ĐŽŶƐƵŵŽͬĂŶŽ�ĂƚƵĂů�ĚĞ�ĐŽŵďƵƐơǀĞů͕�ǀŝƐĂŶĚŽ�
ă� ĂĚĂƉƚĂĕĆŽ� ĚŽƐ� ĨŽƌŶŽƐ͘� �ůĠŵ� ĚŝƐƐŽ͕� Ž� ƚƌĂŶƐƉŽƌƚĞ�
ĂŶƵĂů�ĚŽƐ�ƌĞƐşĚƵŽƐ�ĚĂ�ĨŽŶƚĞ�ŐĞƌĂĚŽƌĂ�ĂƚĠ�Ă�ŝŶĚƷƐƚƌŝĂ�
ŝƌĄ�ĐƵƐƚĂƌ�ϱй�ĚŽ�ĐŽŶƐƵŵŽͬĂŶŽ�ĂƚƵĂů�ĚĞ�ĐŽŵďƵƐơǀĞů͘�
�ƐƟŵĂͲƐĞ� ƋƵĞ� ĞƐƐĂ� ĂůƚĞƌĂĕĆŽ� ƉƌŽŵŽǀĂ� ƵŵĂ�
ĞĐŽŶŽŵŝĂ͕� ŶŽ� ĐŽŶƐƵŵŽͬĂŶŽ� ĂƚƵĂů� ĚĞ� ĐŽŵďƵƐơǀĞů͕�
ĚĞ�ϭϬй�ĂŽ�ĂŶŽ͘
��ƉĂƌƟƌ�ĚĂ�ƐŝƚƵĂĕĆŽ�ĚĞƐĐƌŝƚĂ͕�ĂǀĂůŝĞ�ĂƐ�ĂĮƌŵĂĕƁĞƐ�Ă�
ƐĞŐƵŝƌ͘
/͘� ��ƉĂƌƟƌ�ĚŽ�ƋƵŝŶƚŽ�ĂŶŽ͕�Ă�ŝŶĚƷƐƚƌŝĂ�ĐŽŵĞĕĂƌŝĂ�
Ă�ƚĞƌ�ďĞŶĞİĐŝŽƐ�ĞĐŽŶƀŵŝĐŽƐ͘
//͘� EĂ� ƉƌŽƉŽƐƚĂ� ĂƉƌĞƐĞŶƚĂĚĂ͕� Ă� ŝŶĚƷƐƚƌŝĂ�
ƐƵďƐƟƚƵŝƌŝĂ�Ž�ĐŽŵďƵƐơǀĞů�ĂƚƵĂů�ƉŽƌ�ƵŵĂ�ĨŽŶƚĞ�
ĚĞ�ĞŶĞƌŐŝĂ�ĐŽŵ�ŵĞŶŽƌ�ƉƌŽĚƵĕĆŽ�Ğ�ĞŵŝƐƐĆŽ�ĚĞ�
ƉĂƌơĐƵůĂƐ�ĚĞǀŝĚŽ�ĂŽ�ƉƌŽĐĞƐƐŽ�ĚĞ�ĐŽŵďƵƐƚĆŽ�
;ƉĂƌƟĐƵůĂĚŽƐͿ͘
///͘� EĂ� ƉƌŽƉŽƐƚĂ� ĂƉƌĞƐĞŶƚĂĚĂ͕� Ă� ŝŶĚƷƐƚƌŝĂ�
ƐƵďƐƟƚƵŝƌŝĂ�Ž�ĐŽŵďƵƐơǀĞů�ĂƚƵĂů�ƉŽƌ�ƵŵĂ�ĨŽŶƚĞ�
ƌĞŶŽǀĄǀĞů�ĚĞ�ĞŶĞƌŐŝĂ͘
/s͘ � K�ǀĂůŽƌ�ĚŽ�ŝŶǀĞƐƟŵĞŶƚŽ�ƐƵƉĞƌĂ�ŽƐ�ďĞŶĞİĐŝŽƐ�
ƉƌŽŵŽǀŝĚŽƐ�ĐŽŵ�Ă�ĞĐŽŶŽŵŝĂ�ĚĞ�ĐŽŵďƵƐơǀĞů�
ĚƵƌĂŶƚĞ�ŽƐ�ϱ�ƉƌŝŵĞŝƌŽƐ�ĂŶŽƐ͘
��ĐŽƌƌĞƚŽ�ĂƉĞŶĂƐ�Ž�ƋƵĞ�ƐĞ�ĂĮƌŵĂ�Ğŵ
A //͘
B /s͘
C /�Ğ�//͘
D /�Ğ�///͘
E ///�Ğ�/s͘
ÁREA LIVRE
*R15201419*
20
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 17
�džŝƐƚĞŵ�ĐŽŶƚƌŽǀĠƌƐŝĂƐ�ĂĐĞƌĐĂ�ĚĂ�ŵĂŐŶŝƚƵĚĞ�ĚŽƐ�ĨĂƚŽƌĞƐ�ƋƵĞ�ŝŶŇƵĞŶĐŝĂŵ�Ž�ǀŽƚŽ�ĚŽ�ĞůĞŝƚŽƌ͘ ��ŵďŽƌĂ͕�ĂƚƵĂůŵĞŶƚĞ͕�
ĂƐ�ƉĞƐƋƵŝƐĂƐ�ĞůĞŝƚŽƌĂŝƐ�ƉŽƐƐĂŵ�ƐĞƌ�ĚŝǀƵůŐĂĚĂƐ�ƉƌſdžŝŵŽ�ĂŽ�ĚŝĂ�ĚĂ�ĞůĞŝĕĆŽ͕�ĚƵƌĂŶƚĞ�ŵƵŝƚŽ�ƚĞŵƉŽ�ĞƐƐĂ�ĚŝǀƵůŐĂĕĆŽ�
ŶĆŽ�ĞƌĂ�ƉĞƌŵŝƟĚĂ�ƐŽď�Ă�ĂůĞŐĂĕĆŽ�ĚĞ�ƋƵĞ�ĂƐ�ŵĞƐŵĂƐ�ŝŶŇƵĞŶĐŝĂǀĂŵ�Ă�ĚĞĐŝƐĆŽ�ĚĞ�Ƶŵ�ƟƉŽ�ƉĂƌƟĐƵůĂƌ�ĚĞ�ĞůĞŝƚŽƌ͕ �
Ž�ƋƵĂů�ĚĞƐĞũĂǀĂ�͞ǀŽƚĂƌ�ŶŽ�ĐĂŶĚŝĚĂƚŽ�ŐĂŶŚĂĚŽƌ͟�Ğ�ƚĞŶĚŝĂ�Ă�ǀŽƚĂƌ�ŶŽƐ�ĐĂŶĚŝĚĂƚŽƐ�ĐƵũĂ�ƐƵƉŽƐƚĂ�ƉƌŽďĂďŝůŝĚĂĚĞ�
ĚĞ�ǀŝƚſƌŝĂ�Ġ�ŵĂŝŽƌ͕ �ŝŶĚĞƉĞŶĚĞŶƚĞŵĞŶƚĞ�ĚŽ�ĐŽŶƚĞƷĚŽ�ĚĂ�ƉƌŽƉŽƐƚĂ�ƉŽůşƟĐĂ�ĂƉƌĞƐĞŶƚĂĚĂ͘
0
5
15
25
35
45
55
60
P
or
ce
nt
ag
em
 d
e 
Vo
to
s
Candidato
A
Candidato
B
Gráfico I
40
45
50
55
60
P
or
ce
nt
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 d
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Vo
to
s
Candidato
A
Candidato
B
Gráfico II
�ŽŶƐŝĚĞƌĂŶĚŽ�ƋƵĞ�Ž��ĂŶĚŝĚĂƚŽ���ĞƐƚĞũĂ�ŝŶƚĞƌĞƐƐĂĚŽ�ŶŽ�ǀŽƚŽ�ĚŽ�ƟƉŽ�ĚĞ�ĞůĞŝƚŽƌ�ŵĞŶĐŝŽŶĂĚŽ�ŶŽ�ƚĞdžƚŽ�Ğ�ĞƐƚĞũĂ�
ĞdžĂŵŝŶĂŶĚŽ�ŽƐ�ĚŽŝƐ�ŐƌĄĮĐŽƐ�ĂĐŝŵĂ�ƉĂƌĂ�ĂƉƌĞƐĞŶƚĂƌ͕ �Ğŵ�ƐĞƵ�ŵĂƚĞƌŝĂů�ĚĞ�ƉƌŽƉĂŐĂŶĚĂ͕�ŽƐ�ƌĞƐƵůƚĂĚŽƐ�ĚĞ�ƵŵĂ�
ƉĞƐƋƵŝƐĂ�ĞůĞŝƚŽƌĂů͕�ĂǀĂůŝĞ�ĂƐ�ĂĮƌŵĂĕƁĞƐ�ƋƵĞ�ƐĞ�ƐĞŐƵĞŵ͘
/͘� KƐ�ĚŽŝƐ�ŐƌĄĮĐŽƐ�ĂƉƌĞƐĞŶƚĂŵ�ƌĞƐƵůƚĂĚŽƐ�ĚŝĨĞƌĞŶƚĞƐ͘
//͘� �ŵ�ƌĞůĂĕĆŽ�ĂŽƐ�ŽďũĞƟǀŽƐ�ĚŽ��ĂŶĚŝĚĂƚŽ��͕�Ž�ŐƌĄĮĐŽ�/�Ġ�ŵĂŝƐ�ĂĚĞƋƵĂĚŽ�ƋƵĞ�Ž�//͘
///͘� ��ĚĞĐŝƐĆŽ�Ă�ƐĞƌ�ƚŽŵĂĚĂ�ĂƉƌĞƐĞŶƚĂ�ŝŵƉůŝĐĂĕƁĞƐ�ĚĞ�ŶĂƚƵƌĞnjĂ�ĠƟĐĂ͕�ĂůĠŵ�ĚĂƐ�ĚĞ�ŶĂƚƵƌĞnjĂ�ƚĠĐŶŝĐĂ͘
��ĐŽƌƌĞƚŽ�Ž�ƋƵĞ�ƐĞ�ĂĮƌŵĂ�Ğŵ
A /͕�ĂƉĞŶĂƐ͘
B ///͕�ĂƉĞŶĂƐ͘
C /�Ğ�//͕�ĂƉĞŶĂƐ͘
D //�Ğ�///͕�ĂƉĞŶĂƐ͘
E /͕�//�Ğ�///͘
*R15201420*
21
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 18
EŽ��ƌĂƐŝů͕�Ġ�ĐŽŵĞƌĐŝĂůŝnjĂĚĂ�ƵŵĂ�ĐĂĚĞŝƌĂ�ĚĞ�ƌŽĚĂƐ�ĚĞ�ĂůƵŵşŶŝŽ�ĐŽŵ�ƉĞƐŽ�ĂƉƌŽdžŝŵĂĚŽ�ĚĞ�ϭϮ�ŬŐ͕�ƋƵĞ�ƌĞƉƌĞƐĞŶƚĂ�
ĐĞƌĐĂ� ĚĂ�ŵĞƚĂĚĞ�ĚŽ� ƉĞƐŽ� ĚĞ� Ƶŵ�ŵŽĚĞůŽ� ĐŽŶǀĞŶĐŝŽŶĂů͘� �ŽŶƐƚƌƵşĚĂ� Ğŵ�ĞƐƚƌƵƚƵƌĂ� ƚƵďƵůĂƌ� ĚĞ� ƵŵĂ� ůŝŐĂ� ĚĞ�
ĂůƵŵşŶŝŽ�ĂĞƌŽŶĄƵƟĐŽ͕�ĞƐƐĂ�ĐĂĚĞŝƌĂ�ĚĞ�ƌŽĚĂƐ�ƉŽƐƐƵŝ�ĂůƚĂ�ƌĞƐŝƐƚġŶĐŝĂ�ŵĞĐąŶŝĐĂ͕�ĂůĠŵ�ĚĞ�ƚĞƌ�ĐƵƐƚŽ�ƌĞĚƵnjŝĚŽ.
�ŝƐƉŽŶşǀĞů�Ğŵ͗фŚƩƉ͗ͬͬǁǁǁ͘ŚŽƐƉŝƚĂůĂƌ͘ĐŽŵх͘��ĐĞƐƐŽ�Ğŵ͗�Ϯϲ�ũƵů͘�ϮϬϭϰ�;ĂĚĂƉƚĂĚŽͿ͘
K�ĂůƵŵşŶŝŽ�ĂĞƌŽŶĄƵƟĐŽ�ƉŽƐƐƵŝ�ƵŵĂ�ĐŽŵďŝŶĂĕĆŽ�ƷŶŝĐĂ�ĚĞ�ƉƌŽƉƌŝĞĚĂĚĞƐ�ƋƵĞ�Ž�ƚŽƌŶĂ�Ƶŵ�ŵĂƚĞƌŝĂů�ĚĞ�ĐŽŶƐƚƌƵĕĆŽ�
ǀĞƌƐĄƟů͕�ĂůƚĂŵĞŶƚĞ�ƵƟůŝnjĄǀĞů�Ğ�ĂƚƌĂƟǀŽ͘��ƐƐĂƐ�ĐĂƌĂĐƚĞƌşƐƟĐĂƐ�ƐĆŽ�ĚĞǀŝĚĂƐ�Ă�ƋƵĂŝƐ�ƉƌŽƉƌŝĞĚĂĚĞƐ͍
A �ůƚĂ�ƌĞƐŝƐƚġŶĐŝĂ�ŵĞĐąŶŝĐĂ�Ğ�ďĂŝdžĂ�ĚĞŶƐŝĚĂĚĞ͘
B �ĂŝdžĂ�ƉůĂƐƟĐŝĚĂĚĞ�Ğ�ĂůƚŽ�ƉŽŶƚŽ�ĚĞ�ĨƵƐĆŽ͘C �ůƚĂ�ĚƵƌĞnjĂ�Ă�ƋƵĞŶƚĞ�Ğ�ďĂŝdžĂ�ĚƵƟůŝĚĂĚĞ͘
D �ĂŝdžĂ�ƉůĂƐƟĐŝĚĂĚĞ�Ğ�ĂůƚĂ�ƐŽůĚĂďŝůŝĚĂĚĞ͘
E �ůƚĂ�ĚƵƌĞnjĂ�Ğ�ĂůƚĂ�ĚĞŶƐŝĚĂĚĞ.
ÁREA LIVRE
*R15201421*
22
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 19
hŵ� ĚĞƚĞĐƚŽƌ� ĚĞ� ĨƵŵĂĕĂ� Ġ� ƵŵĂ� ĐąŵĂƌĂ� ĨŽƌŵĂĚĂ� ƉŽƌ� ĚŽŝƐ� ĐŽŵƉĂƌƟŵĞŶƚŽƐ� ŶŽƐ� ƋƵĂŝƐ� ƐĆŽ� ŝŶƐĞƌŝĚĂƐ� ĚƵĂƐ�
ĐĠůƵůĂƐ�ĨŽƚŽĐŽŶĚƵƚŽƌĂƐ͕�ƋƵĞ�ƐĆŽ�ĞůĞŵĞŶƚŽƐ�ĐƵũĂ�ƌĞƐŝƐƚġŶĐŝĂ�ǀĂƌŝĂ�ĐŽŵ�Ă�ůƵŵŝŶŽƐŝĚĂĚĞ͕�Ğ�ƵŵĂ�ĨŽŶƚĞ�ĚĞ�ůƵnj͕�
ĐŽŶĨŽƌŵĞ� ŝůƵƐƚƌĂ�Ă�ĮŐƵƌĂ� /͘��ŵ�ĐŽŶĚŝĕƁĞƐ�ŶŽƌŵĂŝƐ͕�ŽƐ�ƌĂŝŽƐ�ĚĞ� ůƵnj�ƉƌŽǀĞŶŝĞŶƚĞƐ�ĚĂ�ĨŽŶƚĞ�ĂƟŶŐĞŵ�ĂƐ�ĚƵĂƐ�
ĐĠůƵůĂƐ�ŝŐƵĂůŵĞŶƚĞ͘�EĂ�ŽĐŽƌƌġŶĐŝĂ�ĚĞ�Ƶŵ�ŝŶĐġŶĚŝŽ͕�ĂƉĞŶĂƐ�Ă�ĐąŵĂƌĂ�ŝŶĨĞƌŝŽƌ�ƐĞƌĄ�ƉƌĞĞŶĐŚŝĚĂ�ƉĞůĂ�ĨƵŵĂĕĂ�Ğ͕�
ĂƐƐŝŵ͕�Ă��ůƵŵŝŶŽƐŝĚĂĚĞ�ŶĂ�ĐĠůƵůĂ�ƐĞƌĄ�ĂůƚĞƌĂĚĂ͕�ĐĂƵƐĂŶĚŽ�ŵƵĚĂŶĕĂ�ŶĂ�ƐƵĂ�ƌĞƐŝƐƚġŶĐŝĂ͘
Barreira Opaca
Refletor
Células
Fotocondutivas
Célula de
Referência
Detector
de Fumaça
Refletor
Lâmpada
Plástico
Transparente
Sala Passagem da
Fumaça
&ŝŐƵƌĂ�/�Ͳ��ƐƋƵĞŵĄƟĐŽ�ĚŽ�ĚĞƚĞĐƚŽƌ�ĚĞ�ĨƵŵĂĕĂ
�Kz>�^d��͕�Z͘�>͘�Introdução à Análise de Circuitos͕�ϭϬ�ĞĚ͘�WĞĂƌƐŽŶ�WƌĞŶƟĐĞ�,Ăůů͕�ϮϬϬϰ͘
K�ĐŝƌĐƵŝƚŽ�ĚŽ�ĚĞƚĞĐƚŽƌ�ĚĞ�ĨƵŵĂĕĂ�Ġ�ŵŽƐƚƌĂĚŽ�ŶĂ�ĨŝŐƵƌĂ�//͕�ŶŽ�ƋƵĂů�ĞdžŝƐƚĞ�ƵŵĂ�ƉŽŶƚĞ�ĚĞ�tŚĞĂƚƐƚŽŶĞ͘�
�ŵ�ĐŽŶĚŝĕƁĞƐ�ŶŽƌŵĂŝƐ͕�ĂƐ�ƌĞƐŝƐƚġŶĐŝĂƐ�ĚĂƐ�ĚƵĂƐ�ĐĠůƵůĂƐ�ƐĆŽ�ŝŐƵĂŝƐ�Ğ�Ž�ĐŝƌĐƵŝƚŽ�ĞƐƚĄ�ĞƋƵŝůŝďƌĂĚŽ͕�ĚĞ�ŵŽĚŽ�ƋƵĞ�
Ă�ƚĞŶƐĆŽ�sĂď�Ġ�ŶƵůĂ͘�EĂ�ƉƌĞƐĞŶĕĂ�ĚĞ�ĨƵŵĂĕĂ͕�ĂƐ�ƌĞƐŝƐƚġŶĐŝĂƐ�ĚĂƐ�ĐĠůƵůĂƐ�ĨŽƚŽĐŽŶĚƵƟǀĂƐ�ƚŽƌŶĂŵͲƐĞ�ĚŝĨĞƌĞŶƚĞƐ�
Ğ͕�ĂƐƐŝŵ͕�ƐƵƌŐĞ�ƵŵĂ�ĚŝĨĞƌĞŶĕĂ�ĚĞ�ƉŽƚĞŶĐŝĂů�ĞŶƚƌĞ�ŽƐ�ƉŽŶƚŽƐ�Ă�Ğ�ď͘�^Ğ�ĞƐƐĂ�ƚĞŶƐĆŽ�ĨŽƌ�ŵĂŝŽƌ�ƋƵĞ�Ƶŵ�ǀĂůŽƌ�ƉƌĠͲ
ĞƐƚĂďĞůĞĐŝĚŽ͕�Ƶŵ�ƌĞůĠ�ƐĞƌĄ�ĂĐŝŽŶĂĚŽ͕�Ž�ƋƵĞ�ƉŽƌ�ƐƵĂ�ǀĞnj͕�ĚŝƐƉĂƌĂƌĄ�Ƶŵ�ĂůĂƌŵĞ͘����������
*R15201422*
Ϯϯ
�E'�E,�Z/������KEdZK>�����hdKD���K
R1 R2
10k:
R3
10k:
8V
+
+
R4
20k:
b a
+
�
N/F
Para o
AlarmeRelé
N/A
Referência
Detector
de Fumaça
Lâmpada
Fonte CC
12V
-
-
-Vab
&ŝŐƵƌĂ�//�Ͳ��ŝƌĐƵŝƚŽ�ĚŽ�ĚĞƚĞĐƚŽƌ�ĚĞ�ĨƵŵĂĕĂ
�Kz>�^d��͕�Z͘�>͘�Introdução à Análise de Circuitos͕�ϭϬ�ĞĚ͘�WĞĂƌƐŽŶ�WƌĞŶƟĐĞ�,Ăůů͕�ϮϬϬϰ�;ĂĚĂƉƚĂĚŽͿ͘
�ŽŶƐŝĚĞƌĂŶĚŽ�Ž�ĐŝƌĐƵŝƚŽ�Ğ�ŽƐ�ĚĂĚŽƐ�ĚĂ�ĮŐƵƌĂ�//͕�Ğŵ�ƋƵĞ�ǀĂůŽƌ�ĚĞǀĞƌĄ�ƐĞƌ�ĂũƵƐƚĂĚĂ�Ă�ƌĞƐŝƐƚġŶĐŝĂ�ǀĂƌŝĄǀĞů�Zϭ�ƉĂƌĂ�
ƋƵĞ͕�Ğŵ�ĐŽŶĚŝĕƁĞƐ�ŶŽƌŵĂŝƐ͕�Ă�ƚĞŶƐĆŽ�sĂď�ƐĞũĂ�ŶƵůĂ͍
A 5kΩ.
B 10kΩ.
C 12kΩ.
D 15kΩ.
E 20kΩ.
ÁREA LIVRE
*R15201423*
24
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 20
�ŽŶƐŝĚĞƌĞ�Ž�ƐŝƐƚĞŵĂ�ĚĞ�ĐŽŶƚƌŽůĞ�ĚĞ�Ƶŵ�ƉƌŽĐĞƐƐŽ�ŝŶĚƵƐƚƌŝĂů�ĚĞƐĐƌŝƚŽ�ƉĞůŽ�ĚŝĂŐƌĂŵĂ�ĚĞ�ďůŽĐŽƐ�ĂƉƌĞƐĞŶƚĂĚŽ�ŶĂ�
ĮŐƵƌĂ�ĂďĂŝdžŽ͗
X(s) + E(s)
1
H1(s)
H2(s)
H3(s) G(s)
U(s)
P(s)
Y(s)++
+
+
+
+
+
R(s)
EŽ�ĚŝĂŐƌĂŵĂ, X(s), Y(s), E(s), U(s), P(s) e R(s)�ƌĞƉƌĞƐĞŶƚĂŵ͕�ƌĞƐƉĞĐƟǀĂŵĞŶƚĞ͕�ŽƐ�ƐŝŶĂŝƐ�ĚĞ�ƌĞĨĞƌġŶĐŝĂ͕�ƐĂşĚĂ͕�
ĞƌƌŽ͕�ĂĕĆŽ�ĚĞ�ĐŽŶƚƌŽůĞ͕�ƉĞƌƚƵƌďĂĕĆŽ�ŶĂ�ĞŶƚƌĂĚĂ�ĚĂ�ƉůĂŶƚĂ�Ğ�ƌƵşĚŽ�ĚĞ�ŵĞĚŝĕĆŽ͘�G(s)�Ġ�Ă�ĨƵŶĕĆŽ�ĚĞ�ƚƌĂŶƐĨĞƌġŶĐŝĂ�
ĚĂ�ƉůĂŶƚĂ�Ă�ƐĞƌ�ĐŽŶƚƌŽůĂĚĂ͘�KƐ�ĚĞŵĂŝƐ�ďůŽĐŽƐ�ĐŽŶƐƟƚƵĞŵ�Ž�ĐŽŶƚƌŽůĂĚŽƌ͕ �ƋƵĞ�Ġ�ĚĞƐĐƌŝƚŽ�ƉĞůĂƐ�ƐĞŐƵŝŶƚĞƐ�ĨƵŶĕƁĞƐ�
ĚĞ�ƚƌĂŶƐĨĞƌġŶĐŝĂ͗
1. H1 (s) =
1
τ1s
2. H2 (s) =
τ2s
1 + ατ2s
3. H3 (s) = K
Ğŵ�ƋƵĞτ1 , τ2 ͕�α e K ƐĆŽ�ĂƐ�ĐŽŶƐƚĂŶƚĞƐ�ŶĆŽ�ŶƵůĂƐ�ƐŝŶƚŽŶŝnjĂĚĂƐ�ƉĞůŽ�ƉƌŽũĞƟƐƚĂ�ĚŽ�ƐŝƐƚĞŵĂ�ĚĞ�ĐŽŶƚƌŽůĞ͘
�ŽŶƐŝĚĞƌĞ�ƋƵĞ͕�ŶŽƐ�ƚĞƐƚĞƐ͕�ĚƵƌĂŶƚĞ�Ž�ĐŽŵŝƐƐŝŽŶĂŵĞŶƚŽ�ĚŽ�ƐŝƐƚĞŵĂ͕�ǀĞƌŝĮĐŽƵͲƐĞ�ƋƵĞ�Ă�ĂƉůŝĐĂĕĆŽ�ĚĞ�Ƶŵ�ƐŝŶĂů�
ĚĞ�ƌĞĨĞƌġŶĐŝĂ�x(t)�ĚŽ�ƟƉŽ�ĚĞŐƌĂƵ�ƌĞƐƵůƚĂ�Ğŵ�ƵŵĂ�ĂĕĆŽ�ĚĞ�ĐŽŶƚƌŽůĞ�u(t)�ĐŽŵ�Ƶŵ�ĞůĞǀĂĚŽ�ƉƵůƐŽ�ŝŵĞĚŝĂƚĂŵĞŶƚĞ�
ĂƉſƐ�Ă�ĂƉůŝĐĂĕĆŽ�ĚŽ�ĚĞŐƌĂƵ͘��ƐƐĞ�ƉƵůƐŽ�Ġ�ŝŶĂĚĞƋƵĂĚŽ�ƉĂƌĂ�Ž�ƉƌŽĐĞƐƐŽ͕�ƉŽŝƐ�ĐĂƵƐĂ�ĨĂĚŝŐĂ�ƉƌĞĐŽĐĞ�ĚŽ�ĂƚƵĂĚŽƌ͘ �
WĂƌĂ�ĐŽŶƚŽƌŶĂƌ�ĞƐƐĞ�ƉƌŽďůĞŵĂ͕�Ġ�ŶĞĐĞƐƐĄƌŝŽ
A ĂůƚĞƌĂƌ�Ă�ĞƐƚƌƵƚƵƌĂ�ĚŽ�ĐŽŶƚƌŽůĂĚŽƌ͕ �ĨĂnjĞŶĚŽ�ĐŽŵ�ƋƵĞ�Ă�ĂĕĆŽ�ƉƌŽƉŽƌĐŝŽŶĂů�ĂƚƵĞ�ƐŽŵĞŶƚĞ�ƐŽďƌĞ�Ž�ƉĞƌĐƵƌƐŽ�
ĚĞ�ƌĞƚƌŽĂĕĆŽ͘
B ĂůƚĞƌĂƌ�Ă�ĞƐƚƌƵƚƵƌĂ�ĚŽ�ĐŽŶƚƌŽůĂĚŽƌ͕ �ĨĂnjĞŶĚŽ�ĐŽŵ�ƋƵĞ�Ă�ĂĕĆŽ�ĚĞƌŝǀĂƟǀĂ�ĂƚƵĞ�ƐŽŵĞŶƚĞ�ƐŽďƌĞ�Ž�ƉĞƌĐƵƌƐŽ�
ĚĞ�ƌĞƚƌŽĂĕĆŽ͘
C ŝŶƐĞƌŝƌ�Ƶŵ�ĮůƚƌŽ�ƉĂƌĂ�ĂƚĞŶƵĂƌ�Ž�ĞĨĞŝƚŽ�ĚĂ�ƉĞƌƚƵƌďĂĕĆŽ͕�ĂƉſƐ�Ă�ĂůƚĞƌĂĕĆŽ�ĂďƌƵƉƚĂ�ĚŽ�ǀĂůŽƌ�ĚĞ�ƌĞĨĞƌġŶĐŝĂ͘
D ŝŶƐĞƌŝƌ�Ƶŵ�ĮůƚƌŽ�ƉĂƌĂ�ĂƚĞŶƵĂƌ�Ž�ĞĨĞŝƚŽ�ĚŽ�ƌƵşĚŽ͕�ĂƉſƐ�Ă�ĂůƚĞƌĂĕĆŽ�ĂďƌƵƉƚĂ�ĚŽ�ǀĂůŽƌ�ĚĞ�ƌĞĨĞƌġŶĐŝĂ͘
E ĂůƚĞƌĂƌ�Ă�ĞƐƚƌƵƚƵƌĂ�ĚŽ�ĐŽŶƚƌŽůĂĚŽƌ�ĂƚƵĂů�ƉĂƌĂ�Ƶŵ�W/��ƚƌĂĚŝĐŝŽŶĂů͘
*R15201424*
25
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 21
^ĞŶƐŽƌĞƐ� ƵůƚƌĂƐƐƀŶŝĐŽƐ� ƐĆŽ� ƵƐĂĚŽƐ� ŶĂ� ŵĞĚŝĕĆŽ� ĚĞ�
ŐƌĂŶĚĞnjĂƐ� ĐŽŵŽ� ĚŝƐƚąŶĐŝĂ� Ğ� ŶşǀĞů͘� �ůŐƵŶƐ� ĚĞƐƐĞƐ�
ƐĞŶƐŽƌĞƐ�ĞŵŝƚĞŵ�Ƶŵ�ƐŝŶĂů�ŶĂ�ĨƌĞƋƵġŶĐŝĂ�ĚĞ�ϰϬ�Ŭ,nj�
ƋƵĞ͕�ĂŽ�ĂƟŶŐŝƌ�Ƶŵ�ŽďũĞƚŽ͕�ƌĞƚŽƌŶĂ�Ğ͕�ƋƵĂŶĚŽ�ĐĂƉƚĂĚŽ͕�
ƉĞƌŵŝƚĞ�ĐĂůĐƵůĂƌ�Ă�ĚŝƐƚąŶĐŝĂ�ĚŽ�ŽďũĞƚŽ�ĂŽ�ƐĞŶƐŽƌ͘
EĞƐƐĞ�ĐŽŶƚĞdžƚŽ͕�ĂǀĂůŝĞ�ĂƐ�ĂĮƌŵĂĕƁĞƐ�Ă�ƐĞŐƵŝƌ͘
/͘� K� ĐĄůĐƵůŽ� ĚĂ� ĚŝƐƚąŶĐŝĂ� ƉŽĚĞ� ƐĞƌ� ŽďƟĚŽ�
ƵƐĂŶĚŽͲƐĞ�ĞƋƵĂĕƁĞƐ�ĚĂ�ŵĞĐąŶŝĐĂ�ĐůĄƐƐŝĐĂ͘
//͘� WĂƌĂ� ĞǀŝƚĂƌ� ƵŵĂ� ŝŶƚĞƌĨĞƌġŶĐŝĂ� ĞŶƚƌĞ� Ž� ƐŝŶĂů�
ĞŶǀŝĂĚŽ�Ğ�ƐŝŶĂŝƐ�ĞƐƉƷƌŝŽƐ�ĂĚǀŝŶĚŽƐ�ĚĞ�ĨŽŶƚĞƐ�
ĞůĞƚƌŽŵĂŐŶĠƟĐĂƐ͕�ĚĞǀĞͲƐĞ�ƵƐĂƌ�Ƶŵ�ĮůƚƌŽ͘
///͘� EŽ�ĐĂƐŽ�ĞƐƉĞĐşĮĐŽ�ĚĞ�Ƶŵ�ƐĞŶƐŽƌ�ƵůƚƌĂƐƐƀŶŝĐŽ͕�
Ž�ĐĄůĐƵůŽ�ĚĂ�ĚŝƐƚąŶĐŝĂ�ďĂƐĞŝĂͲƐĞ�ŶĂ�ǀĂƌŝĂĕĆŽ�ĚĂ�
ǀĞůŽĐŝĚĂĚĞ�Ğ͕�ĚĞƐƐĂ�ĨŽƌŵĂ͕�ŶŽ�ĞĨĞŝƚŽ�doppler.
/s͘ � WĂƌĂ�ƵŵĂ�ůĞŝƚƵƌĂ�ĂĚĞƋƵĂĚĂ�ĚŽ�ƐŝŶĂů�ĚĞƐƐĞ�ƐĞŶƐŽƌ�
Ğŵ�Ƶŵ�ƐŝƐƚĞŵĂ�ĚĞ�ĂƋƵŝƐŝĕĆŽ�ĚĞ�ĚĂĚŽƐ͕�ĚĞǀĞͲƐĞ�
ƵƟůŝnjĂƌ�ƵŵĂ�ƚĂdžĂ�ĚĞ�ĂŵŽƐƚƌĂŐĞŵ�ĚĞ�ŶŽ�ŵşŶŝŵŽ�
ϴϬ�Ŭ,nj�ĚĞ�ĨŽƌŵĂ�Ă�ĞǀŝƚĂƌ�Ž�ĞĨĞŝƚŽ�aliasing.
��ĐŽƌƌĞƚŽ�ĂƉĞŶĂƐ�Ž�ƋƵĞ�ƐĞ�ĂĮƌŵĂ�Ğŵ
A /�Ğ�/s͘
B //�Ğ�///͘
C ///�Ğ�/s͘
D /͕�//�Ğ�///͘
E /͕�//�Ğ�/s͘
ÁREA LIVRE
QUESTÃO 22
hŵ�ĞŶŐĞŶŚĞŝƌŽ͕�ƉƌĞŽĐƵƉĂĚŽ�ĐŽŵ�Ž�ƵƐŽ�ƌĂĐŝŽŶĂů�ĚĞ�
ĞŶĞƌŐŝĂ͕� ĚĞƐĞŶǀŽůǀĞƵ�ƉĂƌĂ� Ă� ƐĂůĂ� ĚĞ� ƐƵĂ� ƌĞƐŝĚġŶĐŝĂ�
Ƶŵ� ƐŝƐƚĞŵĂ� ŵŝĐƌŽĐŽŶƚƌŽůĂĚŽ� ƉĂƌĂ� ĂũƵƐƚĞ� ŐƌĂĚĂƟǀŽ�
ĚĂ� ŝůƵŵŝŶĂĕĆŽ� ƉŽƌ� ŵĞŝŽ� ĚŽ� ĂĐŝŽŶĂŵĞŶƚŽ� ĚĞ� ƐĞƚĞ�
ĚŝĨĞƌĞŶƚĞƐ�ĐŝƌĐƵŝƚŽƐ�ĚĞ� ŝůƵŵŝŶĂĕĆŽ�Ğ�ĚĂ�ĂďĞƌƚƵƌĂ�ŽƵ�
ĨĞĐŚĂŵĞŶƚŽ�ĚĞ�ũĂŶĞůĂƐ͘�K�ƐŝƐƚĞŵĂ�ĐŽŶƚĞŵƉůĂ͗
1. ƐĞŶƐŽƌĞƐ� ĂŶĂůſŐŝĐŽƐ� ĚĞ� ůƵŵŝŶŽƐŝĚĂĚĞ� ŝŶƚĞƌŶĂ� Ğ�
ĞdžƚĞƌŶĂ�ĐŽŵ�ǀĂƌŝĂĕĆŽ�ůŝŶĞĂƌ�ŶŽŵŝŶĂů�ĚŽ�ƐŝŶĂů�ĚĞ�
Ϭ�Ă�ϱ�s͖
2. ƐĞŶƐŽƌ�ĚŝŐŝƚĂů�ĚĞ�ĐŚƵǀĂ͕�ĐŽŵ�ŶşǀĞů�ĂůƚŽ�ƋƵĂŶĚŽ�
ĞƐƚĄ�ĐŚŽǀĞŶĚŽ͘�K� ƚƌĂƚĂŵĞŶƚŽ�ĚĞƐƚĞ�ƐŝŶĂů�ĚĞǀĞ�
ƚĞƌ� ƉƌŝŽƌŝĚĂĚĞ� ƐŽďƌĞ� ƋƵĂůƋƵĞƌ� ŽƵƚƌĂ� ĂƟǀŝĚĂĚĞ�
ĚŽ�ƉƌŽŐƌĂŵĂ͖
ϯ͘� ƐŝƐƚĞŵĂ�ĚĞ�ĐŽŵĂŶĚŽ�ƉĂƌĂ�ĂďĞƌƚƵƌĂ�Ğ�ĨĞĐŚĂŵĞŶƚŽ�
ĚĂ�ũĂŶĞůĂ͕�ƌĞĂůŝnjĂĚŽ�ĐŽŵ�Ƶŵ�ŵŽƚŽƌ����ĚĞ�ϲ�s�ĐŽŵ�
ĐŽŶƐƵŵŽ�ĚĞ�ϯϬ�t͕�ĂĐŝŽŶĂĚŽ�ƉŽƌ�Ƶŵ�ƐŝŶĂů�WtD�
ĐŽŵ� ĨƌĞƋƵġŶĐŝĂ� ĚĞ� ĐŚĂǀĞĂŵĞŶƚŽ� ĚĞ� ϭ� Ŭ,nj� Ğ�
ƌĞƐŽůƵĕĆŽ�ĚĞ�ϭй�ŶĂ�ǀĂƌŝĂĕĆŽ�ĚĂ�ůĂƌŐƵƌĂ�ĚŽƐ�ƉƵůƐŽƐ͖
4. ĐŽŵĂŶĚŽ� ĚŝŐŝƚĂů� ĚĞ� ĐĂĚĂ� Ƶŵ� ĚŽƐ� ĐŝƌĐƵŝƚŽƐ�
ĚĞ� ŝůƵŵŝŶĂĕĆŽ͕� ƉŽƐƐŝďŝůŝƚĂŶĚŽ� ĂũƵƐƚĞ� ƚŽƚĂů� ĚĂ�
ŝůƵŵŝŶĂĕĆŽ�ĂƌƟĮĐŝĂů� ĚŽ�ĂŵďŝĞŶƚĞ�Ğŵ�ĚŝĨĞƌĞŶƚĞƐ�
ŶşǀĞŝƐ͘
WĂƌĂ� ƐĞůĞĕĆŽ� Ğ� ƉƌŽŐƌĂŵĂĕĆŽ� ĚŽ� ŵŝĐƌŽĐŽŶƚƌŽůĂĚŽƌ͕ �
ĂǀĂůŝĞ�ĂĮƌŵĂĕƁĞƐ�Ă�ƐĞŐƵŝƌ͘
/͘� K�ŵŝĐƌŽĐŽŶƚƌŽůĂĚŽƌ�ĚĞǀĞ�ƉŽƐƐƵŝƌ�ŶŽ�ŵşŶŝŵŽ�
ƵŵĂ� ĞŶƚƌĂĚĂ� ĐŽŵ� ĨƵŶĕĆŽ� ĚĞ� ŝŶƚĞƌƌƵƉĕĆŽ�
ĞdžƚĞƌŶĂ͘
//͘� hŵ� ĐŝƌĐƵŝƚŽ� ĞdžƚĞƌŶŽ� ĂŽ� ŵŝĐƌŽĐŽŶƚƌŽůĂĚŽƌ�
ĚĞǀĞ�ƐĞƌ�ƵƟůŝnjĂĚŽ�ƉĂƌĂ�ĂĐŝŽŶĂƌ�Ž�ŵŽƚŽƌ͘
///͘� K� ƐĞŶƐŽƌ� ĚĞ� ůƵnj� ƵƟůŝnjĂĚŽ� ƉŽƐƐƵŝ� ǀĂƌŝĂĕĆŽ�
ŶŽŵŝŶĂů�ĚĞ�Ϭ�Ă�ϱ�s͕�ƉŽƌĠŵ͕�ŶĂ�ƐƵĂ�ĐĂůŝďƌĂĕĆŽ�
ŶŽ�ĂŵďŝĞŶƚĞ�ƌĞĂů͕�ƐƵƉŽŶŚĂ�ƋƵĞ�Ž�ĞŶŐĞŶŚĞŝƌŽ�
ŽďƐĞƌǀŽƵ� ƋƵĞ� Ă� ǀĂƌŝĂĕĆŽ� ůŝŵŝƚĂͲƐĞ� Ă� ǀĂůŽƌĞƐ�
ĞŶƚƌĞ� Ϯ� s� Ğ� ϯ� s͘ � EĞƐƐĞ� ĐĂƐŽ͕� ƉĂƌĂ� ƌĞĂůŝnjĂƌ� Ă�
ĂƋƵŝƐŝĕĆŽ�ĚĞƐƚĂ�ŝŶĨŽƌŵĂĕĆŽ�ĐŽŵ�ϭϬ�ŶşǀĞŝƐ�ĚĞ�
ƐĞŶƐŝďŝůŝĚĂĚĞ͕� Ġ� ŶĞĐĞƐƐĄƌŝŽ� ƋƵĞ� Ž� ĐŽŶǀĞƌƐŽƌ�
�ͬ��ƚĞŶŚĂ�ƌĞƐŽůƵĕĆŽ�ŵşŶŝŵĂ�ĚĞ�ϭϬ�ďŝƚƐ͘
��ĐŽƌƌĞƚŽ�Ž�ƋƵĞ�ƐĞ�ĂĮƌŵĂ�Ğŵ
A /͕�ĂƉĞŶĂƐ͘
B ///͕�ĂƉĞŶĂƐ͘
C /�Ğ�//͕�ĂƉĞŶĂƐ͘
D //�Ğ�///͕�ĂƉĞŶĂƐ͘
E /͕�//�Ğ�///͘
*R15201425*
26
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 23
EĂ�ŵŽĚĞůĂŐĞŵ�Ƶŵ�ƐŝƐƚĞŵĂ�ůŝŶĞĂƌ�ŝŶǀĂƌŝĂŶƚĞ�ŶŽ�ƚĞŵƉŽ�ĞƐƚĄǀĞů͕�ĨŽŝ�ůĞǀĂŶƚĂĚĂ�Ă�ƐƵĂ�ƌĞƐƉŽƐƚĂ�Ğŵ�ĨƌĞƋƵġŶĐŝĂ͕�
ŽďƚĞŶĚŽͲƐĞ�ŽƐ�ƐĞŐƵŝŶƚĞƐ�ĚŝĂŐƌĂŵĂƐ�ĚĞ��ŽĚĞ͗
Diagrama de Bode
�20
�30
�40
�50
�60
�70
�80
M
ód
ul
o 
(d
B
)
0
�45
�90
Fa
se
 (d
eg
)
10�3 10�2 10�1 10� 101 102 103 104
Frequência (rad/s)
��ĨƵŶĕĆŽ�ĚĞ�ƚƌĂŶƐĨĞƌġŶĐŝĂ�ƋƵĞ�ŵĞůŚŽƌ�ƌĞƉƌĞƐĞŶƚĂ�Ž�ƐŝƐƚĞŵĂ�Ġ
A G(s) =
s− 0, 1
(s + 10)(s + 100)
B G(s) =
s− 1
(s + 0, 1)(s + 100)
C G(s) =
s + 0, 1
(s + 10)(s + 100)
D G(s) =
s + 1
(s− 0, 1)(s + 100)
E G(s) =
s + 1
(s + 0, 1)(s + 100)
*R15201426*
27
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 24
�Ɛ�ƌĞĚĞƐ�ĚĞ�ĐŽŵƵŶŝĐĂĕĆŽ�ƐĆŽ�ĞƐƐĞŶĐŝĂŝƐ�ƉĂƌĂ�Ž�ƉƌŽĐĞƐƐŽ�ĚĞ�ĂƵƚŽŵĂĕĆŽ� ŝŶĚƵƐƚƌŝĂů͘��džŝƐƚĞŵ�ĚŝǀĞƌƐŽƐ�ƟƉŽƐ�ĚĞ�
ƌĞĚĞ͕�ĂƐ�ƋƵĂŝƐ�ƐĞ�ĚŝĨĞƌĞŶĐŝĂŵ�Ğŵ�ĂůŐƵŶƐ�ĂƐƉĞĐƚŽƐ͕�ĐŽŵŽ�ƚŽƉŽůŽŐŝĂ�ĚĞ�ĐŽŶĞdžĆŽ͕�ƟƉŽƐ�ĚĞ�ĚŝƐƉŽƐŝƟǀŽƐ�ĂŽƐ�ƋƵĂŝƐ�ƐĞ�
ĐŽŶĞĐƚĂŵ�Ğ�ǀĞůŽĐŝĚĂĚĞ�ĚĞ�ƚƌĂŶƐŵŝƐƐĆŽ͕�ĞŶƚƌĞ�ŽƵƚƌŽƐ͘�^ĆŽ�ĞdžĞŵƉůŽƐ�ĚĞ�ƌĞĚĞƐ�ŝŶĚƵƐƚƌŝĂŝƐ͗��^/͕�,�Zd͕ ��ĞǀŝĐĞEĞƚ͕�
WƌŽĮďƵƐ͕��ƚŚĞƌŶĞƚ͘�EĆŽ�ĞdžŝƐƚĞ�ƵŵĂ�ƌĞĚĞ�ĐĞƌƚĂ�ŽƵ�ĞƌƌĂĚĂ͕�ŵĂƐ͕�Ɛŝŵ͕�ƵŵĂ�ƌĞĚĞ�ŵĂŝƐ�ĂƉƌŽƉƌŝĂĚĂ�ƉĂƌĂ�ĚĞƚĞƌŵŝŶĂĚĂ�ĂƉůŝĐĂĕĆŽ͘��Ğ�ĂĐŽƌĚŽ�ĐŽŵ�Ž�ƟƉŽ�ĚĞ�ĚŝƐƉŽƐŝƟǀŽ�ƋƵĞ�ĂƐ� ƌĞĚĞƐ�ĐŽŶĞĐƚĂŵ͕�ĞůĂƐ�ƐĆŽ�ĐůĂƐƐŝĮĐĂĚĂƐ�Ğŵ�Sensorbus͕�
DeviceBus͕�FieldBus e Databus͘���ĮŐƵƌĂ�ĂďĂŝdžŽ�ĂƉƌĞƐĞŶƚĂ�Ƶŵ�ĞƐƋƵĞŵĂ�ĚĂ�ĨĂŝdžĂ�ĚĞ�ĂƉůŝĐĂĕĆŽ�ĚĂƐ�ƌĞĚĞƐ͘
Ethernet
Fieldbus
DeviceBus
Controle de
Processo
Controle
Lógico
Dispositivos Simples
Bit
Dispositivos Complexos
BlocoByte
Tipo de Mensagem
Tipos de dispositivos
Sensorbus
�ŵ�ƌĞůĂĕĆŽ�ă�ĐůĂƐƐŝĮĐĂĕĆŽ�ĚĂƐ�ƌĞĚĞƐ�ĚĞ�ĐŽŵƵŶŝĐĂĕĆŽ�ƉĂƌĂ�ĂƵƚŽŵĂĕĆŽ͕�ĂǀĂůŝĞ�ĂĮƌŵĂĕƁĞƐ�Ă�ƐĞŐƵŝƌ͘
/͘� �Ɛ� ƌĞĚĞƐ� Sensorbus� ƐĆŽ� ĚĞ� ďĂŝdžŽ� ĐƵƐƚŽ͕� ƵƟůŝnjĂĚĂƐ� ƉĂƌĂ� Ă� ĐŽŵƵŶŝĐĂĕĆŽ� ĚĞ� ƐĞŶƐŽƌĞƐ� Ğ� ĂƚƵĂĚŽƌĞƐ�
ĚŝƐĐƌĞƚŽƐ͕�ĐŽŶƚĞŵƉůĂŶĚŽ�ĚŝƐƚąŶĐŝĂƐ�ƉĞƋƵĞŶĂƐ͘
//͘� �Ɛ�ƌĞĚĞƐ�Devicebus�ĐŽŶĞĐƚĂŵ�ĚŝƐƉŽƐŝƟǀŽƐ�ĐŽŵŽ��>WƐ͕�ĐŽŶƚƌŽůĂĚŽƌĞƐ͕�ƐŝƐƚĞŵĂƐ�ĚĞ�ŵĞĚŝĕĆŽ�ŝŶƚĞůŝŐĞŶƚĞƐ͕�
drivers�Ğ�ŽƵƚƌŽƐ�ĚŝƐƉŽƐŝƟǀŽƐ�ƋƵĞ�ƐĞ�ĐŽŵƵŶŝĐĂŵ�ƉŽƌ�ĚĂĚŽƐ�Ğŵ�ĨŽƌŵĂƚŽ�ĚĞ�bytes.
///͘� �Ɛ�ƌĞĚĞƐ�Fieldbus�ĐŽŶĞĐƚĂŵ�ĚŝƐƉŽƐŝƟǀŽƐ�ŵŝĐƌŽƉƌŽĐĞƐƐĂĚŽƐ�Ğ�ƉŽĚĞŵ�ƚƌĂŶƐŵŝƟƌ�ǀĄƌŝŽƐ�ƟƉŽƐ�ĚĞ�ĚĂĚŽƐ͗�
ĚŝƐĐƌĞƚŽƐ͕�ĂŶĂůſŐŝĐŽƐ͕�ƉĂƌąŵĞƚƌŽƐ͕�ƉƌŽŐƌĂŵĂƐ�Ğ�ŝŶĨŽƌŵĂĕƁĞƐ�ĚĞ�ƵƐƵĄƌŝŽƐ͘
/s͘ � �Ɛ�ƌĞĚĞƐ�Fieldbus ƐĆŽ�ŵĂŝƐ�ĂƉƌŽƉƌŝĂĚĂƐ�ƉĂƌĂ�ĂƉůŝĐĂĕƁĞƐ�ĚĞ�ĐŽŶƚƌŽůĞ�ĚĞ�ƉƌŽĐĞƐƐŽƐ�ĚŝƐƚƌŝďƵşĚŽƐ�ƉŽƌƋƵĞ�
ƉŽƐƐƵĞŵ�ĂůƚĂ�ƚĂdžĂ�ĚĞ�ƚƌĂŶƐŵŝƐƐĆŽ�ĚĞ�ĚĂĚŽƐ͘
��ĐŽƌƌĞƚŽ�ĂƉĞŶĂƐ�Ž�ƋƵĞ�ƐĞ�ĂĮƌŵĂ�Ğŵ
A //͘
B /�Ğ�/s͘
C /͕�//�Ğ�///͘
D /͕�///�Ğ�/s͘
E //͕�///�Ğ�/s͘
*R15201427*
Ϯϴ
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 25
�� ĮŐƵƌĂ� ĂďĂŝdžŽ� ƌĞƉƌĞƐĞŶƚĂ� Ƶŵ� ƐĞŶƐŽƌ� ĚĞ� ǀĂnjĆŽ�
ĚĞ� ǀſƌƟĐĞ� ǀŽůƵŵĠƚƌŝĐŽ� ;ĐŽŵƉŽƐƚŽ� ƉŽƌ� ƚƌĂŶƐĚƵƚŽƌ�
Ğ� ƚƌĂŶƐŵŝƐƐŽƌͿ� ŝŶƐƚĂůĂĚŽ� Ğŵ� ƵŵĂ� ƚƵďƵůĂĕĆŽ� ƉĂƌĂ�
ŵĞĚŝĕĆŽ� ĚĞ� ǀĂnjĆŽ� ĚĞ� ĄŐƵĂ� ƋƵĞ� ĂďĂƐƚĞĐĞ� ƵŵĂ�
ĐĂůĚĞŝƌĂ͕�ŶĂ�ƋƵĂů�Ġ�ĂƌďŝƚƌĂĚŽ�Ƶŵ�ƐĞŶƟĚŽ�ĚĞ�ŇƵdžŽ͘�
�ƐƐĞ� ƐĞŶƐŽƌ� ƉŽĚĞ� ƐĞƌ� ĂĚƋƵŝƌŝĚŽ� ŶĂ� ĐŽŶĮŐƵƌĂĕĆŽ�
ϰͲϮϬ�ŵ�ͬϬͲϮϬ�ŵϯͬŚ�ŽƵ�ϬͲϭϬ�sͬϬͲϮϬ�ŵϯͬŚ͘
Sensor
Fluxo
Tubulação
�KEd��,͘��ŽŶƚĞĐŚ�^ĠƌŝĞƐ�DϮϮ�Ğ�DϮϯ�ŵĞĚŝĚŽƌĞƐ�ĚĞ�ǀĂnjĆŽ�ĚĞ�ǀſƌƟĐĞ�
ǀŽůƵŵĠƚƌŝĐŽ�WƌŽͲsΡ͗�ŵŽĚĞůŽ�DϮϮͲs�Ğ�ŵŽĚĞůŽ�DϮϯͲs͘ �Ξ�ϭϵϵϳ͘�
�ŝƐƉŽŶşǀĞů�Ğŵ͗�фŚƩƉ͗ͬͬǁǁǁ͘ĐŽŶƚĞĐŚŝŶĚ͘ĐŽŵ͘ďƌх͘�
�ĐĞƐƐŽ�Ğŵ͗�Ϯϴ�ũƵů͘�ϮϬϭϰ͘
EĞƐƐĞ�ĐŽŶƚĞdžƚŽ͕�ĂǀĂůŝĞ�ĂƐ�ĂĮƌŵĂĕƁĞƐ�Ă�ƐĞŐƵŝƌ͘
/͘� �Ɛ�ĚƵĂƐ�ĐŽŶĮŐƵƌĂĕƁĞƐ�ĂƉƌĞƐĞŶƚĂŵ�Ž�ŵĞƐŵŽ�
ĂůĐĂŶĐĞ�;spanͿ͘
//͘� �Ɛ�ĚƵĂƐ�ĐŽŶĮŐƵƌĂĕƁĞƐ�ĂƉƌĞƐĞŶƚĂŵ�Ă�ŵĞƐŵĂ�
ĨĂŝdžĂ�ĚĞ�ŵĞĚŝĚĂ�;rangeͿ͘
///͘� �� ŵĞĚŝĕĆŽ� ĚĞ� ǀĂnjĆŽ� ĚĞ� ĄŐƵĂ� ŝŶĚĞƉĞŶĚĞ�
ĚŽ� ƐĞŶƟĚŽ� ĚĞ� ƉĂƐƐĂŐĞŵ� ĚĞ� ŇƵdžŽ� ĚĞ� ĄŐƵĂ�
ĂƌďŝƚƌĂĚŽ�ŶŽ�ƐĞŶƐŽƌ͘
/s͘ � K�ƐĞŶƐŽƌ�ĐŽŵ�ĐŽŶĮŐƵƌĂĕĆŽ�ϬͲϭϬ�sͬϬͲϮϬ�ŵϯͬŚ�
ĨŽƌŶĞĐĞ� ŵĞŶŽƌ� ĐŽŶĮĂďŝůŝĚĂĚĞ� ƋƵĞ� Ž� ƐĞŶƐŽƌ�
ĐŽŵ�ĐŽŶĮŐƵƌĂĕĆŽ�ϰͲϮϬ�ŵ�ͬϬͲϮϬ�ŵϯͬŚ͘
V. ��ĐŽŶĮŐƵƌĂĕĆŽ�ϬͲϭϬ�sͬϬͲϮϬ�ŵϯͬŚ�ƚĞŵ�ŵĞůŚŽƌ�
ŝŵƵŶŝĚĂĚĞ�Ă�ƌƵşĚŽ͕�ĞŶƋƵĂŶƚŽ�Ă�ĐŽŶĮŐƵƌĂĕĆŽ�
ϰͲϮϬ�ŵ�ͬϬͲϮϬ�ŵϯͬŚ�Ġ�ŵĞůŚŽƌ�ƉĂƌĂ�ĂƉůŝĐĂĕƁĞƐ�
Ğŵ�ƉĞƋƵĞŶĂƐ�ĚŝƐƚąŶĐŝĂƐ͘
��ĐŽƌƌĞƚŽ�ĂƉĞŶĂƐ�Ž�ƋƵĞ�ƐĞ�ĂĮƌŵĂ�Ğŵ
A /�Ğ�s͘
B /͕�//�Ğ�/s͘
C /͕�///�Ğ�/s͘
D //͕�///�Ğ�s͘
E //͕�///͕�/s�Ğ�s͘
QUESTÃO 26
KƐ� ƐŝƐƚĞŵĂƐ� ŝŶƚĞŐƌĂĚŽƐ� ĚĞ� ŵĂŶƵĨĂƚƵƌĂ� ;^/DͿ�
ĂƉƌĞƐĞŶƚĂŵ�ƵŵĂ�ĂďŽƌĚĂŐĞŵ�ĞƐƚƌĂƚĠŐŝĐĂ�ĞŵďĂƐĂĚĂ�
Ğŵ� ƚĞĐŶŽůŽŐŝĂ͕� ƋƵĞ� ƌĞƐƉŽŶĚĞŵ� ĂŽƐ� ĚĞƐĂĮŽƐ�
ĐŽŵƉĞƟƟǀŽƐ� ĚĞ� ĨĂďƌŝĐĂĕĆŽ͘� hŵĂ� ĨŽƌŵĂ� ĚĞ�
ĐĂƌĂĐƚĞƌŝnjĂƌ� ĞƐƐĞƐ� ƐŝƐƚĞŵĂƐ� Ġ� Ă� ƉĂƌƟƌ� ĚĂ�ŵĂƚƌŝnj� ĚĞ�
ǀĂƌŝĞĚĂĚĞ� ;ĚĞ� ƉĂƌƚĞƐͬƉĞĕĂƐ� ĚŝĨĞƌĞŶƚĞƐͿ� Ğ� ǀŽůƵŵĞ�
;ĚĂ� ƋƵĂŶƟĚĂĚĞ� ĚĞ� ƉĂƌƚĞƐͬƉĞĕĂƐ� ƉƌŽĚƵnjŝĚĂƐͿ� ĚĂ�
ŵĂŶƵĨĂƚƵƌĂ͕�ĐŽŶĨŽƌŵĞ�ŝůƵƐƚƌĂ�Ă�ĮŐƵƌĂ�ĂďĂŝdžŽ͘
C1 C2 C3
B1 B2 B3
A1 A2 A3
va
rie
da
de
volume
�ŽŶƐŝĚĞƌĂŶĚŽ� Ă� ŵĂƚƌŝnj� ĚĞ� ǀĂƌŝĞĚĂĚĞ� dž� ǀŽůƵŵĞ�
ƌĞƉƌĞƐĞŶƚĂĚĂ�ŶĂ�ĮŐƵƌĂ͕�ĂǀĂůŝĞ�ĂƐ�ĂĮƌŵĂĕƁĞƐ�Ă�ƐĞŐƵŝƌ͘
/͘� ^ŝƐƚĞŵĂƐ� ƚŽƚĂůŵĞŶƚĞ� ĚĞĚŝĐĂĚŽƐ� ƐĆŽ�
ĂĚĞƋƵĂĚŽƐ� ƉĂƌĂ� ƉƌŽĚƵnjŝƌ� ƵŵĂ� ǀĂƌŝĞĚĂĚĞ�
ůŝŵŝƚĂĚĂ� ĚĞ� ĐŽŶĮŐƵƌĂĕƁĞƐ� ĚĞ� ƉĂƌƚĞƐͬƉĞĕĂƐ͕�
ŶŽ� ĞŶƚĂŶƚŽ͕� ƉŽĚĞŵ� ƚƌĂďĂůŚĂƌ� ĐŽŵ� ǀŽůƵŵĞƐ�
ŵƵŝƚŽ�ĂůƚŽƐ�ĚĞ�ƉƌŽĚƵĕĆŽ͕�ŽĐƵƉĂŶĚŽ�Ă�ĨĂŝdžĂ��ϯ�
ĚĂ�ŵĂƚƌŝnj͘
//͘� ^ŝƐƚĞŵĂƐ� ŇĞdžşǀĞŝƐ� ĚĞ� ŵĂŶƵĨĂƚƵƌĂ� ;&D^Ϳ�
ƉŽĚĞŵ� ŽĐƵƉĂƌ� Ž� ŶşǀĞů� ŵĂŝƐ� ĂůƚŽ� ĚĂ� ŵĂƚƌŝnj�
ĚĞ� ǀŽůƵŵĞ� Ğ� ǀĂƌŝĞĚĂĚĞ͕� ŽĐƵƉĂŶĚŽ� Ă� ĨĂŝdžĂ�
�ϯ͕�ŽƵ�ƐĞũĂ͕�ƐĆŽ�ĐĂƉĂnjĞƐ�ĚĞ�ƐĞ�ĂĚĞƋƵĂƌ�Ă�ĂůƚĂ�
ǀĂƌŝĞĚĂĚĞ�ĚĞ�ƉĂƌƚĞƐͬƉĞĕĂƐ�Ğ�ĂůƚŽ�ǀŽůƵŵĞ�ĚĞ�
ƉƌŽĚƵĕĆŽ�ĚĞ�ƉĂƌƚĞƐͬƉĞĕĂƐ͘
///͘� ^ŝƐƚĞŵĂƐ� ƋƵĞ� ƵƟůŝnjĂŵ� ŵĄƋƵŝŶĂƐ� ďĂƐĞĂĚĂƐ�
Ğŵ� �E�� ;ĐŽŵƉƵƚĂĚŽƌ� ŶƵŵĞƌŝĐĂŵĞŶƚĞ�
ĐŽŶƚƌŽůĂĚŽͿ� ƉŽĚĞŵ� ƚƌĂďĂůŚĂƌ� ĐŽŵ� ĂůƚĂ�
ǀĂƌŝĞĚĂĚĞ� ĚĞ� ƉƌŽŐƌĂŵĂĕĆŽ� ĚĞ� ƉĂƌƚĞƐͬƉĞĕĂƐ͕�
ŽĐƵƉĂŶĚŽ� Ă� ĨĂŝdžĂ� �ϭ� ĚĂ�ŵĂƚƌŝnj͕�ŵĂƐ� ƉŽĚĞŵ�
ƐĞƌ�ŝŶǀŝĄǀĞŝƐ�ĞĐŽŶŽŵŝĐĂŵĞŶƚĞ�ƐĞ�ŽƐ�ǀŽůƵŵĞƐ�
ŶĆŽ�ĨŽƌĞŵ�ďĂŝdžŽƐ͘
��ĐŽƌƌĞƚŽ�Ž�ƋƵĞ�ƐĞ�ĂĮƌŵĂ�Ğŵ
A /͕�ĂƉĞŶĂƐ͘
B //͕�ĂƉĞŶĂƐ͘
C /�Ğ�///͕�ĂƉĞŶĂƐ͘
D //�Ğ�///͕�ĂƉĞŶĂƐ͘
E /͕�//�Ğ�///͘
*R15201428*
29
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 27
hŵ�ƉƌŽĐĞƐƐŽ�ƋƵĞ�ĞŶǀŽůǀĞ�ƵŵĂ�ĂŶƚĞŶĂ�ƉŽĚĞ�ƐĞƌ�ƌĞƉƌĞƐĞŶƚĂĚŽ�ƉĞůŽ�ƐŝƐƚĞŵĂ�ĚĞ�ϯǐ͘�ŽƌĚĞŵ�ĂƉƌĞƐĞŶƚĂĚŽ�ŶĂ�ĮŐƵƌĂ�/͘
K G(s) = 
s(s+1)(s+5)
1
H(s) = 1
Elemento de Medida
R(s)
Controlador Planta
C(s)+
�
&ŝŐƵƌĂ�/
��ĮŐƵƌĂ�//�ĂƉƌĞƐĞŶƚĂ�Ž�ůƵŐĂƌ�ĚĂƐ�ƌĂşnjĞƐ�ĚĞƐƐĞ�ƐŝƐƚĞŵĂ͕�Ğŵ�ŵĂůŚĂ�ĂďĞƌƚĂ͕�ƋƵĂŶĚŽ�ƐĞ�ǀĂƌŝĂ�Ž�ŐĂŶŚŽ�<͘��
eixo real
ei
xo
 im
ag
in
ár
io
 (i
w
)
10
5
�5
�10
�10 �8 �6 �4 �2 2 4 6 8 100
&ŝŐƵƌĂ�//
�ŽŶƐŝĚĞƌĂŶĚŽ�ƋƵĞ�Ž�ŐĂŶŚŽ�<�Ġ�ƉŽƐŝƟǀŽ�Ğ�ƉŽĚĞ�ǀĂƌŝĂƌ�ĚĞ�Ϭ�Ă�ŝŶĮŶŝƚŽ͕�ĂǀĂůŝĞ�ĂƐ�ĂĮƌŵĂĕƁĞƐ�Ă�ƐĞŐƵŝƌ͘
/͘� hŵ�ƐŝƐƚĞŵĂ�ĐŽŵ�ϭϬ�ф�<�ф�ϮϬ�Ġ�ĞƐƚĄǀĞů͘
//͘� WĂƌĂ�<�с�ϲϬ͕�Ž�ƐŝƐƚĞŵĂ�Ġ�ĐƌŝƟĐĂŵĞŶƚĞ�ĂŵŽƌƚĞĐŝĚŽ͘
///͘� �džŝƐƚĞ�Ƶŵ�ǀĂůŽƌ�ĚĞ�<�ƋƵĞ�ƚŽƌŶĂ�Ž�ƐŝƐƚĞŵĂ�ŵĂƌŐŝŶĂůŵĞŶƚĞ�ĞƐƚĄǀĞů͘
/s͘ � K� ƐŝƐƚĞŵĂ� ĐŽŵ� <� с� ϯϬ� ĂƉƌĞƐĞŶƚĂ� ƌĞƐƉŽƐƚĂ� ƚĞŵƉŽƌĂů͕� ƉĂƌĂ� ƵŵĂ� ĞŶƚƌĂĚĂ� Ğŵ� ĚĞŐƌĂƵ� ƵŶŝƚĄƌŝŽ͕� ĐŽŵ�
ŽƐĐŝůĂĕƁĞƐ�ĐŽŶƐƚĂŶƚĞƐ�Ğ�ĚĞ�ŵĞƐŵĂ�ĂŵƉůŝƚƵĚĞ͘
��ĐŽƌƌĞƚŽ�ĂƉĞŶĂƐ�Ž�ƋƵĞ�ƐĞ�ĂĮƌŵĂ�Ğŵ
A /�Ğ�//͘
B /�Ğ�///͘
C //�Ğ�/s͘
D /͕�///�Ğ�/s͘
E //͕�///�Ğ�/s͘
*R15201429*
ϯϬ
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 28
��ĮŐƵƌĂ�ĂďĂŝdžŽ�ĐŽŶƚĠŵ�Ă�ƌĞƉƌĞƐĞŶƚĂĕĆŽ�ĞƐƋƵĞŵĄƟĐĂ�ĚĞ�ƵŵĂ�ĂƉůŝĐĂĕĆŽ�ƉĂƌĂ�Ž�ĐŽŶƚƌŽůĞ�ĚĞ�ƚĞŵƉĞƌĂƚƵƌĂ�ĚĞ�
Ƶŵ�ĨŽƌŶŽ�ƵƟůŝnjĂŶĚŽ�Ƶŵ�ĐŽŶƚƌŽůĂĚŽƌ�ůſŐŝĐŽ�ƉƌŽŐƌĂŵĄǀĞů�;�>WͿ͘�K�ƐĞŶƐŽƌ�ĚĞ�ƚĞŵƉĞƌĂƚƵƌĂ�Ğŵ�ĐŽŶũƵŶƚŽ�ĐŽŵ�Ž�
ƚƌĂŶƐĚƵƚŽƌ�ĨŽƌŶĞĐĞ�Ƶŵ�ƐŝŶĂů�ĂŶĂůſŐŝĐŽ�ϬͲϭϬ�s�ͬ�ϮϬͲϭϱϬΣ��ĞŶǀŝĂĚŽ�ĂŽ��>W͕ �Ž�ƋƵĂů�ƉŽƌ�ƐƵĂ�ǀĞnj͕�ĞŶǀŝĂ�Ƶŵ�ƐŝŶĂů�
ĚĞ�ϬͲϮϬ�ŵ��ƉĂƌĂ�Ă�ǀĄůǀƵůĂ͕�ƉĞƌŵŝƟŶĚŽ�Ă�ǀĂƌŝĂĕĆŽ�ĚĞ�ƐƵĂ�ĂďĞƌƚƵƌĂ�Ğ�Ă�ĚŽƐĂŐĞŵ�ŐƌĂĚĂƟǀĂ�ĚĂ�ƋƵĂŶƟĚĂĚĞ�ĚĞ�
ĐŽŵďƵƐơǀĞů�ĞŶǀŝĂĚŽ�ĂŽ�ĨŽƌŶŽ͘��ƐƐŝŵ͕�ƉŽĚĞͲƐĞ�ŵŽĚŝĮĐĂƌ�Ă�ƚĞŵƉĞƌĂƚƵƌĂ�ĚŽ�ĨŽƌŶŽ�ĐŽŶĨŽƌŵĞ�Ă�ŶĞĐĞƐƐŝĚĂĚĞ͘
Sinal de comando de
abertura da válvula
Sensor de temperatura
0-10 V/ 20-150 °C
Combustível
Válvula proporcional
Sinal de controle da temperatura
Forno
Chama Transdutor
0-20 mA
Unidade
A/D CLP
Unidade
D/A
&ŝŐƵƌĂ�ϭ
WZh��Ed�͘�Automação industrial͗�W>�͕�ƚĞŽƌŝĂ�Ğ�ĂƉůŝĐĂĕƁĞƐ�;ĐƵƌƐŽ�ďĄƐŝĐŽͿ͘�ZŝŽ�ĚĞ�:ĂŶĞŝƌŽ͗�>d�͕�ϮϬϭϬ�;ĂĚĂƉƚĂĚŽͿ͘
�ŵ�ƌĞůĂĕĆŽ�ĂŽ�ƐŝƐƚĞŵĂ�ĚĞ�ĂƵƚŽŵĂĕĆŽ�ĂƉƌĞƐĞŶƚĂĚŽ͕�ĂǀĂůŝĞ�ĂƐ�ĂĮƌŵĂĕƁĞƐ�Ă�ƐĞŐƵŝƌ͘
/͘� K�ƵƐŽ�ĚĂ�ƵŶŝĚĂĚĞ��ͬ��ĚĞ�ϴ�ďŝƚƐ�ŶŽ��>W�ƉĞƌŵŝƚĞ�ĂƋƵŝƐŝĕĆŽ�ĚĞ�ƚĞŵƉĞƌĂƚƵƌĂ�ĐŽŵ�ƵŵĂ�ƌĞƐŽůƵĕĆŽ�ĚĞ͕�
ĂƉƌŽdžŝŵĂĚĂŵĞŶƚĞ͕�Ϭ͕ϱϬϴ�Σ�͘
//͘� ��ƵŶŝĚĂĚĞ��ͬ��ŶŽ��>W�ƉŽĚĞ�ƐĞƌ�ƐƵďƐƟƚƵşĚĂ�ƉŽƌ�Ƶŵ�ŵſĚƵůŽ�ĚĞ�ƐĂşĚĂ�ĚŝŐŝƚĂů�Ă�ƌĞůĠ�ĞƐƉĞĐŝĮĐĂĚŽ�ƉĂƌĂ��Ƶŵ�
ǀĂůŽƌ�ĚĞ�ƐĂşĚĂ�ĚĞ�ĐŽƌƌĞŶƚĞ�ĚĞ�ĂƚĠ�ϭϬ��͕�ǀĂůŽƌ�ŵĂŝŽƌ�ƋƵĞ�Ž�ƐŝŶĂů�ĚĞ�ƐĂşĚĂ�ĞŶǀŝĂĚŽ�ƉĂƌĂ�Ă�ǀĄůǀƵůĂ͘
///͘� WĂƌĂ�ĐŽŵƵŶŝĐĂĕĆŽ�ĞŶƚƌĞ�Ž��>W�Ğ�Ƶŵ�ƐŝƐƚĞŵĂ�^�����;ƐƵƉĞƌǀŝƐŽƌLJ�ĐŽŶƚƌŽů�ĂŶĚ�ĚĂƚĂ�ĂĐƋƵŝƐŝƟŽŶͿ͕��ƉŽĚĞŵ�
ƐĞƌ�ƵƐĂĚĂƐ͕�ĞŶƚƌĞ�ŽƵƚƌĂƐ͕�ƌĞĚĞ�ŝŶĚƵƐƚƌŝĂů�WZK&/�h^�ŽƵ�ĐŽŵƵŶŝĐĂĕĆŽ�ƐĞƌŝĂů�ĐŽŵ�ƉƌŽƚŽĐŽůŽ�DK��h^͕�
ƐĞŶĚŽ�Ă�ƉƌŝŵĞŝƌĂ�ŵĂŝƐ�ŽŶĞƌŽƐĂ�ƋƵĞ�Ă�ƐĞŐƵŶĚĂ͘
/s͘ � K�ƐŝƐƚĞŵĂ�ƐƵƉĞƌǀŝƐſƌŝŽ�ƉŽĚĞ�ƐĞƌ�ƉƌŽŐƌĂŵĂĚŽ�ĚŝƌĞƚĂŵĞŶƚĞ�ŶŽ��>W͕ �ƐĞŵ�Ă�ŶĞĐĞƐƐŝĚĂĚĞ�ĚĞ�ĚŝƐƉŽƐŝƟǀŽƐ�
ĂĚŝĐŝŽŶĂŝƐ͕�ƌĞĚƵnjŝŶĚŽ�Ž�ĐƵƐƚŽ�ĚĞ�ŝŵƉůĞŵĞŶƚĂĕĆŽ�ĚŽ�ƐŝƐƚĞŵĂ�ĐŽŵŽ�Ƶŵ�ƚŽĚŽ͘
V. ��ƌĞĂůŝnjĂĕĆŽ�ĚĞƐƐĂ�ĂƵƚŽŵĂĕĆŽ�ƌĞƋƵĞƌ�Ƶŵ��>W�ĚĞ�ŐƌĂŶĚĞ�ƉŽƌƚĞ͕�ĚĞǀŝĚŽ�ĂŽ�ƐŝƐƚĞŵĂ�ŽƉĞƌĂƌ�Ğŵ�ŵĂůŚĂ�
ĨĞĐŚĂĚĂ͕�Ž�ƋƵĞ�ŝŵƉůŝĐĂ�Ž�ƵƐŽ�ĚĞ�ďůŽĐŽƐ�ĞƐƉĞĐşĮĐŽƐ�ĚĞ�ƉƌŽŐƌĂŵĂĕĆŽ͘
��ĐŽƌƌĞƚŽ�ĂƉĞŶĂƐ�Ž�ƋƵĞ�ƐĞ�ĂĮƌŵĂ�Ğŵ
A /�Ğ�//͘
B /�Ğ�///͘
C //�Ğ�/s͘
D ///�Ğ�s͘
E /s�Ğ�s͘
*R15201430*
ϯϭ
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 29
K�ĞƐƚƵĚŽ�ĚĂ� ĐŝŶĞŵĄƟĐĂ�ĚŝƌĞƚĂ� ĚĞ�Ƶŵ�ŵĂŶŝƉƵůĂĚŽƌ�
ƌŽďſƟĐŽ� ƚĞŵ� ĐŽŵŽ� ŽďũĞƟǀŽ� ŽďƚĞƌ� ĞƋƵĂĕƁĞƐ� ƉĂƌĂ�
Ž� ĐĄůĐƵůŽ� ĚĂ� ƉŽƐŝĕĆŽ� Ğ� ĚĂ� ŽƌŝĞŶƚĂĕĆŽ� ĚŽ� ĞĨĞƚƵĂĚŽƌ�
ĚŽ� ƌŽďƀ� Ğŵ� ƌĞůĂĕĆŽ� ă� ƐƵĂ� ďĂƐĞ� ĐŽŵŽ� ĨƵŶĕĆŽ� ĚĂƐ�
ǀĂƌŝĄǀĞŝƐ� ĚĂƐ� ũƵŶƚĂƐ͘� WĂƌĂ� ĚĞƚĞƌŵŝŶĂƌ� ĂƐ� ĞƋƵĂĕƁĞƐ�
ĚĂ� ĐŝŶĞŵĄƟĐĂ� ĚŝƌĞƚĂ� ĚĞ� ŵĂŶŝƉƵůĂĚŽƌĞƐ� ƌŽďſƟĐŽƐ�
ĚĞ� ĐĂĚĞŝĂ� ĂďĞƌƚĂ͕� ƵƐƵĂůŵĞŶƚĞ� ƐĆŽ� ƵƟůŝnjĂĚŽƐ� ŽƐ�
ƉĂƌąŵĞƚƌŽƐ�ĚĞ��ĞŶĂǀŝƚͲ,ĂƌƚĞŶďĞƌŐ͘�K�ƋƵĂĚƌŽ�ĂďĂŝdžŽ�
ƚƌĂnj� ĞƐƐĞƐ� ƉĂƌąŵĞƚƌŽƐ� ƉĂƌĂ� Ƶŵ� ƌŽďƀ� ĐŽŵĞƌĐŝĂů�
ĞƐƉĞĐşĮĐŽ͘
WĂƌąŵĞƚƌŽƐ�ĚĞ��ĞŶĂǀŝƚͲ,ĂƌƚĞŶďĞƌŐ
:ƵŶƚĂ�i ai ;ŐƌĂƵƐͿ ai ;ĐŵͿ di θi ;ŐƌĂƵƐͿ
1 0 0 50 θ1
2 90 0 d2 90
�ϯ0 0 d3 0
4 0 0 150 θ4
5 0 0 10 θ5
�Žŵ�ďĂƐĞ�ŶĂ�ƐŝƚƵĂĕĆŽ�ĚĞƐĐƌŝƚĂ͕�ĂǀĂůŝĞ�ĂƐ�ĂƐƐĞƌĕƁĞƐ�Ă�
ƐĞŐƵŝƌ�Ğ�Ă�ƌĞůĂĕĆŽ�ƉƌŽƉŽƐƚĂ�ĞŶƚƌĞ�ĞůĂƐ͘
/͘� K� ƌŽďƀ� ĐŽŵĞƌĐŝĂů� ĂƉƌĞƐĞŶƚĂĚŽ� ƉŽƐƐƵŝ� ĐŝŶĐŽ�
ŐƌĂƵƐ�ĚĞ� ůŝďĞƌĚĂĚĞ͕� ƐĞŶĚŽ� ĐůĂƐƐŝĮĐĂĚŽ� ĐŽŵŽ�
ƌŽďƀ�ĚŽ�ƟƉŽ�ƉŽůĂƌ͘
PORQUE
//͘� �ĂƐ� ĐŝŶĐŽ� ǀĂƌŝĄǀĞŝƐ� ĚŽ� ƌŽďƀ͕� ĂƐ� ƋƵĞ�
ĐŽƌƌĞƐƉŽŶĚĞŵ� ăƐ� ƚƌġƐ� ƉƌŝŵĞŝƌĂƐ� ũƵŶƚĂƐ�
ƐĆŽ͗� ƵŵĂ� ĚĞ� ƌŽƚĂĕĆŽ� Ğ� ĚƵĂƐ� ĚĞ� ƚƌĂŶƐůĂĕĆŽ͕�
ƌĞƐƉĞĐƟǀĂŵĞŶƚĞ͘
��ƌĞƐƉĞŝƚŽ�ĚĞƐƐĂƐ�ĂƐƐĞƌĕƁĞƐ͕�ĂƐƐŝŶĂůĞ�Ă�ŽƉĕĆŽ�ĐŽƌƌĞƚĂ͘
A �Ɛ�ĂƐƐĞƌĕƁĞƐ�/�Ğ�//�ƐĆŽ�ƉƌŽƉŽƐŝĕƁĞƐ�ǀĞƌĚĂĚĞŝƌĂƐ͕�Ğ�
Ă�//�Ġ�ƵŵĂ�ũƵƐƟĮĐĂƟǀĂ�ĐŽƌƌĞƚĂ�ĚĂ�/͘
B �Ɛ�ĂƐƐĞƌĕƁĞƐ� /� Ğ� //� ƐĆŽ�ƉƌŽƉŽƐŝĕƁĞƐ� ǀĞƌĚĂĚĞŝƌĂƐ͕�
ŵĂƐ�Ă�//�ŶĆŽ�Ġ�ƵŵĂ�ũƵƐƟĮĐĂƟǀĂ�ĐŽƌƌĞƚĂ�ĚĂ�/͘
C ��ĂƐƐĞƌĕĆŽ�/�Ġ�ƵŵĂ�ƉƌŽƉŽƐŝĕĆŽ�ǀĞƌĚĂĚĞŝƌĂ͕�Ğ�Ă�//�Ġ�
ƵŵĂ�ƉƌŽƉŽƐŝĕĆŽ�ĨĂůƐĂ͘
D ��ĂƐƐĞƌĕĆŽ�/�Ġ�ƵŵĂ�ƉƌŽƉŽƐŝĕĆŽ�ĨĂůƐĂ͕�Ğ�Ă�//�Ġ�ƵŵĂ�
ƉƌŽƉŽƐŝĕĆŽ�ǀĞƌĚĂĚĞŝƌĂ͘
E �Ɛ�ĂƐƐĞƌĕƁĞƐ�/�Ğ�//�ƐĆŽ�ƉƌŽƉŽƐŝĕƁĞƐ�ĨĂůƐĂƐ͘
QUESTÃO 30
hŵ�ĞŶŐĞŶŚĞŝƌŽ�ĚĞ�ĐŽŶƚƌŽůĞ�Ğ�ĂƵƚŽŵĂĕĆŽ�ŶĞĐĞƐƐŝƚĂ�
ĞƐƉĞĐŝĮĐĂƌ� Ƶŵ� ƚƌĂŶƐĚƵƚŽƌ� ĚĞ� ƚĞŵƉĞƌĂƚƵƌĂ� ƉĂƌĂ�
Ƶŵ� ƉƌŽũĞƚŽ� ĚĞ� ĐŽŶƚƌŽůĞ� ĂƵƚŽŵĄƟĐŽ� ĚĞ� Ƶŵ� ĨŽƌŶŽ͘�
�� ƌĞƋƵŝƐŝƚŽ� ĚĞ� ƉƌŽũĞƚŽ� ƋƵĞ� Ž� ĐŽŶƚƌŽůĂĚŽƌ� ůſŐŝĐŽ�
ƉƌŽŐƌĂŵĄǀĞů� ;�>WͿ� ĞƐƚĞũĂ� ůŽĐĂůŝnjĂĚŽ� ŶĂ� ƐĂůĂ� ĚĞ�
ĐŽŵĂŶĚŽ͕�Ă�ƋƵĂů�ĞƐƚĄ�Ă�ƵŵĂ�ĚŝƐƚąŶĐŝĂ�ĚĞ�ϯϬϬ�ŵĞƚƌŽƐ�
ĚŽ�ĨŽƌŶŽ͘
EĞƐƐĞ�ĐŽŶƚĞdžƚŽ͕� ĐŽŶƐŝĚĞƌĂŶĚŽͲƐĞ�ƋƵĞ�Ž�ĞŶŐĞŶŚĞŝƌŽ�
ĞƐĐŽůŚĞƵ�Ƶŵ�ƚƌĂŶƐĚƵƚŽƌ�ĐŽŵ�ƚƌĂŶƐŵŝƐƐĆŽ�ŶŽ�ƉĂĚƌĆŽ�
ϰ� ŵ�� Ă� ϮϬ� ŵ�͕� ĂǀĂůŝĞ� ĂƐ� ƐĞŐƵŝŶƚĞƐ� ĂƐƐĞƌĕƁĞƐ� Ğ� Ă�
ƌĞůĂĕĆŽ�ƉƌŽƉŽƐƚĂ�ĞŶƚƌĞ�ĞůĂƐ͘
/͘� �� ƚƌĂŶƐŵŝƐƐĆŽ� ĚĞ� ƐŝŶĂů� ĚĞ� ƚƌĂŶƐĚƵƚŽƌĞƐ�
ĚŝƐƚĂŶƚĞƐ�ĚŽ��>W�Ġ�ŵĂŝƐ�ƐĞŐƵƌĂ�ŶŽ�ƉĂĚƌĆŽ�
ϰ�ŵ��Ă�ϮϬ�ŵ�͕�ƋƵĞ�ŶŽƐ�ƉĂĚƌƁĞƐ�Ϭ�s�Ă�ϱ�s�
ŽƵ�Ϭ�ŵ��Ă�ϮϬ�ŵ�͘
PORQUE
//͘� EŽ�ƉĂĚƌĆŽ�ϰ�ŵ��Ă�ϮϬ�ŵ��Ġ�ƉŽƐƐşǀĞů�ŝĚĞŶƟĮĐĂƌ�
ƉĞƌĚĂ�ĚĞ�ƐŝŶĂů�ŶŽƐ�ĐĂďŽƐ�ĚĞ�ƚƌĂŶƐŵŝƐƐĆŽ͕�ĐŽŵŽ͕�
ƉŽƌ�ĞdžĞŵƉůŽ͕�Ğŵ�ƉƌŽďůĞŵĂƐ�ĚĞ�ƌŽŵƉŝŵĞŶƚŽ�
ĚĞ�ĐĂďŽ�ŽƵ�ĚĞƐĐŽŶĞdžĆŽ�ĐŽŵ�Ž��>W͘ ��
��ƌĞƐƉĞŝƚŽ�ĚĞƐƐĂƐ�ĂƐƐĞƌĕƁĞƐ͕�ĂƐƐŝŶĂůĞ�Ă�ŽƉĕĆŽ�ĐŽƌƌĞƚĂ͘
A �Ɛ�ĂƐƐĞƌĕƁĞƐ�/�Ğ�//�ƐĆŽ�ƉƌŽƉŽƐŝĕƁĞƐ�ǀĞƌĚĂĚĞŝƌĂƐ͕�Ğ�
Ă�//�Ġ�ƵŵĂ�ũƵƐƟĮĐĂƟǀĂ�ĐŽƌƌĞƚĂ�ĚĂ�/͘
B �Ɛ�ĂƐƐĞƌĕƁĞƐ� /� Ğ� //� ƐĆŽ�ƉƌŽƉŽƐŝĕƁĞƐ� ǀĞƌĚĂĚĞŝƌĂƐ͕�
ŵĂƐ�Ă�//�ŶĆŽ�Ġ�ƵŵĂ�ũƵƐƟĮĐĂƟǀĂ�ĐŽƌƌĞƚĂ�ĚĂ�/͘
C ��ĂƐƐĞƌĕĆŽ�/�Ġ�ƵŵĂ�ƉƌŽƉŽƐŝĕĆŽ�ǀĞƌĚĂĚĞŝƌĂ͕�Ğ�Ă�//�Ġ�
ƵŵĂ�ƉƌŽƉŽƐŝĕĆŽ�ĨĂůƐĂ͘
D ��ĂƐƐĞƌĕĆŽ�/�Ġ�ƵŵĂ�ƉƌŽƉŽƐŝĕĆŽ�ĨĂůƐĂ͕�Ğ�Ă�//�Ġ�ƵŵĂ�
ƉƌŽƉŽƐŝĕĆŽ�ǀĞƌĚĂĚĞŝƌĂ͘
E �Ɛ�ĂƐƐĞƌĕƁĞƐ�/�Ğ�//�ƐĆŽ�ƉƌŽƉŽƐŝĕƁĞƐ�ĨĂůƐĂƐ͘
ÁREA LIVRE
*R15201431*
ϯϮ
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 31
K�ƐŽŌͲƐƚĂƌƚĞƌ�Ġ�Ƶŵ�ĚŝƐƉŽƐŝƟǀŽ�ĞůĞƚƌƀŶŝĐŽ�ĨŽƌŵĂĚŽ�ƉŽƌ�ƐĞŝƐ�ƟƌŝƐƚŽƌĞƐ͕�ƐĞŶĚŽ�ƵƟůŝnjĂĚŽ�ƉĂƌĂ�Ă�ƉĂƌƟĚĂ�ĚĞ�ŵŽƚŽƌĞƐ�
ĚĞ�ŝŶĚƵĕĆŽ�Ğŵ�ŐĂŝŽůĂ͘�K�ĚŝĂŐƌĂŵĂ�Ă�ƐĞŐƵŝƌ�ŝůƵƐƚƌĂ�ƵŵĂ�ĂƉůŝĐĂĕĆŽ�ĚĞƐƐĞ�ĚŝƐƉŽƐŝƟǀŽ͘
Rede
Elétrica
Trifásica
Tiristores
Motor de Indução
Circuito de Controle
e Disparo
Bobinas
do motor
�ŽŶƐŝĚĞƌĂŶĚŽ�Ž�ĚŝĂŐƌĂŵĂ�ĂĐŝŵĂ�Ğ�ŽƐ�ƉƌŝŶĐşƉŝŽƐ�ĚĞ�ĨƵŶĐŝŽŶĂŵĞŶƚŽ�ĚĞ�ƵŵĂ�ŵĄƋƵŝŶĂ�ĚĞ�ŝŶĚƵĕĆŽ͕�ĂǀĂůŝĞ�ĂƐ�
ĂĮƌŵĂĕƁĞƐ�Ă�ƐĞŐƵŝƌ͘
/͘� ��ĮŶĂůŝĚĂĚĞ�ƉƌŝŶĐŝƉĂů�ĚŽ�ƐŽŌͲƐƚĂƌƚĞƌ�Ġ�ƌĞĚƵnjŝƌ�Ă�ĐŽƌƌĞŶƚĞ�ĚĞ�ƉĂƌƟĚĂ�Ğŵ�ŵŽƚŽƌĞƐ�ĚĞ�ŝŶĚƵĕĆŽ�Ğŵ�ŐĂŝŽůĂ͘
//͘� ��ĐŽŶĮŐƵƌĂĕĆŽ�ĚŽ�ĚŝĂŐƌĂŵĂ�ƉĞƌŵŝƚĞ�ƵƟůŝnjĂƌ�Ž�ƐŽŌͲƐƚĂƌƚĞƌ�ƉĂƌĂ�ƌĞĂůŝnjĂƌ�Ă�ĨƌĞŶĂŐĞŵ�ĚŽ�ŵŽƚŽƌ�ĚĞ�ŝŶĚƵĕĆŽ͘�
///͘� K�ƐŽŌͲƐƚĂƌƚĞƌ�ƚĂŵďĠŵ�ƉŽĚĞ�ƐĞƌ�ƵƟůŝnjĂĚŽ�ƉĂƌĂ�ĐŽŶƚƌŽůĂƌ�Ă�ǀĞůŽĐŝĚĂĚĞ�ĚŽ�ŵŽƚŽƌ�ĚĞ�ŝŶĚƵĕĆŽ�Ğŵ�ŐĂŝŽůĂ�
ƉĂƌĂ�ĂƉůŝĐĂĕƁĞƐ�Ğŵ�ƐĞƌǀŽŵĞĐĂŶŝƐŵŽƐ͘
/s͘ � WĂƌĂ�ƌĞĂůŝnjĂƌ�Ă�ƉĂƌƟĚĂ�ƐƵĂǀĞ�ĚŽ�ŵŽƚŽƌ͕ �Ž�ƐŽŌͲƐƚĂƌƚĞƌ�ǀĂƌŝĂ�Ă�ĨƌĞƋƵġŶĐŝĂ�ĚĂ�ƚĞŶƐĆŽ�ĂƉůŝĐĂĚĂ�ĂŽ�ŵŽƚŽƌ͕ �
ŝŶŝĐŝĂŶĚŽ�Ğŵ�Ϭ�,nj�;ŵĄƋƵŝŶĂ�ƉĂƌĂĚĂͿ�Ğ�ĂƵŵĞŶƚĂŶĚŽ�ŐƌĂĚĂƟǀĂŵĞŶƚĞ�ĂƚĠ�ĂƟŶŐŝƌ�Ă�ĨƌĞƋƵġŶĐŝĂ�ŶŽŵŝŶĂů͘
��ĐŽƌƌĞƚŽ�ĂƉĞŶĂƐ�Ž�ƋƵĞ�ƐĞ�ĂĮƌŵĂ�Ğŵ
A /�Ğ�//͘
B /�Ğ�///͘
C ///�Ğ�/s͘
D /͕�//�Ğ�/s͘
E //͕�///�Ğ�/s͘ �
ÁREA LIVRE
*R15201432*
ϯϯ
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 32
K�ƐŝƐƚĞŵĂ�ĚĞ�ĚŝƐƚƌŝďƵŝĕĆŽ�ĚĞ�ƉĞĕĂƐ�ŵŽƐƚƌĂĚŽ�ŶĂ�ĮŐƵƌĂ�/�Ġ�ĐŽŵƉŽƐƚŽ�ƉŽƌ�ƵŵĂ�ĞƐƚĞŝƌĂ�ĚĞ�ĞŶƚƌĂĚĂ�ĚĞ�ƉĞĕĂƐ�;�ϭͿ͕�
ƵŵĂ�ĞƐƚĞŝƌĂ�ĚĞ�ĚŝƐƚƌŝďƵŝĕĆŽ�ĚĞ�ƉĞĕĂƐ�;�ϮͿ͕�ĚƵĂƐ�ĞƐƚĞŝƌĂƐ�ĚĞ�ƐĂşĚĂ�;�ϯ�Ğ��ϰͿ͕�Ğ�ĚŽŝƐ�ĐŝůŝŶĚƌŽƐ�ƉŶĞƵŵĄƟĐŽƐ�ĚĞ�
ĂĕĆŽ�ƐŝŵƉůĞƐ�ĐŽŵ�ƉŽƐŝĕĆŽ�ĚĞ�ƌĞƉŽƵƐŽ�ƌĞĐƵĂĚŽ�;�ϭ�Ğ��ϮͿ͘��Ɛ�ĞƐƚĞŝƌĂƐ�ĚĞ�ƐĂşĚĂ��ϯ�Ğ��ϰ�ĞƐƚĆŽ�ƐĞŵƉƌĞ�ůŝŐĂĚĂƐ͘
b
a
c
e
dE2
C1 C2
E1 E3 E4
g
&ŝŐƵƌĂ�/
K�ƐŝƐƚĞŵĂ�ĚĞǀĞ�ĨƵŶĐŝŽŶĂƌ�ĚĞ�ĨŽƌŵĂ�ƋƵĞ�ĂƐ�ƉĞĕĂƐ�ĚĞǀĞŵ�ƐĞƌ�ĚŝƐƚƌŝďƵşĚĂƐ�ƉĂƌĂ�ĂƐ�ĞƐƚĞŝƌĂƐ�ĚĞ�ƐĂşĚĂ��ϯ�Ğ��ϰ͕�
ĂůƚĞƌŶĂĚĂŵĞŶƚĞ͕�ŝƐƚŽ�Ġ͕�ƋƵĂŶĚŽ�ƵŵĂ�ƉĞĕĂ�Ġ�ĞŵƉƵƌƌĂĚĂ�ƉĞůŽ�ĐŝůŝŶĚƌŽ��ϭ͕�Ă�ƉƌſdžŝŵĂ�ĚĞǀĞ�ƐĞƌ�ĞŵƉƵƌƌĂĚĂ�ƉĞůŽ�
ĐŝůŝŶĚƌŽ��Ϯ͕�Ğ�ǀŝĐĞͲǀĞƌƐĂ͘���ƉƌŝŵĞŝƌĂ�ƉĞĕĂ�ƋƵĞ�ĞŶƚƌĂ�ŶŽ�ƐŝƐƚĞŵĂ�ĚĞǀĞ�ƐĞƌ�ĚŝƐƚƌŝďƵşĚĂ�ƉĂƌĂ�Ă�ĞƐƚĞŝƌĂ��ϯ͘�KƐ�ƐŝŶĂŝƐ�
ďŝŶĄƌŝŽƐ�ĚŽ�ƐŝƐƚĞŵĂ�ƐĆŽ�ĂƉƌĞƐĞŶƚĂĚŽƐ�ŶŽ�ƋƵĂĚƌŽ�ϭ�Ğ�Ă�ĮŐƵƌĂ�//�ĂƉƌĞƐĞŶƚĂ�Ž�ĚŝĂŐƌĂŵĂ�>ĂĚĚĞƌ�ƋƵĞ�ĐŽŶƚƌŽůĂ�Ž�
ƐŝƐƚĞŵĂ͕�Ğŵ�ƋƵĞ�Ă�ůŝŶŚĂ�ϯ�ĞƐƚĄ�ŽŵŝƟĚĂ͘
a �^ĞŶƐŽƌ�ĚĞ�ƉƌĞƐĞŶĕĂ�ŶĂ�ĞŶƚƌĂĚĂ�ĚĂ�ĞƐƚĞŝƌĂ��ϭ�
b �^ĞŶƐŽƌ�ĚĞ�ƉƌĞƐĞŶĕĂ�ŶĂ�ĞŶƚƌĂĚĂ�ĚĂ�ĞƐƚĞŝƌĂ��Ϯ
c �^ĞŶƐŽƌ�ĚĞ�ƉƌĞƐĞŶĕĂ�Ğŵ�ĨƌĞŶƚĞ�ĂŽ�ĐŝůŝŶĚƌŽ��ϭ
d �^ĞŶƐŽƌ�ĚĞ�ƉƌĞƐĞŶĕĂ�Ğŵ�ĨƌĞŶƚĞ�ĂŽ�ĐŝůŝŶĚƌŽ��Ϯ
e �^ĞŶƐŽƌ�ĚĞ�ƉƌĞƐĞŶĕĂ�ŶĂ�ĞŶƚƌĂĚĂ�ĚĂ�ĞƐƚĞŝƌĂ��ϯ
g �^ĞŶƐŽƌ�ĚĞ�ƉƌĞƐĞŶĕĂ�ŶĂ�ĞŶƚƌĂĚĂ�ĚĂ�ĞƐƚĞŝƌĂ��ϰ
E1 ��ĐŝŽŶĂ�Ă�ĞƐƚĞŝƌĂ��ϭ
E2 ��ĐŝŽŶĂ�Ă�ĞƐƚĞŝƌĂ��Ϯ
C1 ��ĐŝŽŶĂ�Ž�ĐŝůŝŶĚƌŽ��ϭ
C2 ��ĐŝŽŶĂ�Ž�ĐŝůŝŶĚƌŽ��Ϯ
R
a E2 C1 C2 E1
E1 b E2
E1
R
C1 C1
C2
E2
h
C2C2 g
e
d hE2
S
b
S
R
R
R
1
2
3
4
5
6
S
YƵĂĚƌŽ�ϭ
&ŝŐƵƌĂ�//
*R15201433*
ϯϰ
�E'�E,�Z/������KEdZK>�����hdKD���K
�Žŵ�ďĂƐĞ�ŶĂƐ�ŝŶĨŽƌŵĂĕƁĞƐ�ĂƉƌĞƐĞŶƚĂĚĂƐ �͕ĐŽŶĐůƵŝͲƐĞ�ƋƵĞ�Ă�
ůŝŶŚĂ�ϯ�ƋƵĞ�ĐŽŵƉůĞƚĂ�Ž�ĐſĚŝŐŽ�ĐŽƌƌĞƚĂŵĞŶƚĞ�ŶŽ�ĚŝĂŐƌĂŵĂ�Ġ
A
S
R
S
C1c hE1
h
E2
B
S
R
S
C1h cE2
E2
h
C
S
R
S
C1h cE1
E2
h
D
S
R
S
C1c hE2
E2
h
E
S
R
S
C1c hE2
E2
h
QUESTÃO 33
hŵ� ǀĞşĐƵůŽ� ĂĠƌĞŽ� ŶĆŽ� ƚƌŝƉƵůĂĚŽ� ;s�EdͿ͕� ƚĂŵďĠŵ�
ĐŚĂŵĂĚŽ�h�s� ;ĚŽ� ŝŶŐůġƐ�Unmaned Aerial VehicleͿ͕� Ġ�
ƚŽĚŽ�Ğ�ƋƵĂůƋƵĞƌ�ƟƉŽ�ĚĞ�ĂĞƌŽŶĂǀĞ�ƋƵĞ�ŶĆŽ�ŶĞĐĞƐƐŝƚĂ�ĚĞ�
ƉŝůŽƚŽƐ�ĞŵďĂƌĐĂĚŽƐ�ƉĂƌĂ�ƐĞƌ�ŐƵŝĂĚĂ͘��ƐƐĞƐ�ǀĞşĐƵůŽƐ�ƐĆŽ�
ĐŽŶƚƌŽůĂĚŽƐ�ƉŽƌ�ŵĞŝŽƐ�ĞůĞƚƌƀŶŝĐŽƐ�Ğ�ĐŽŵƉƵƚĂĐŝŽŶĂŝƐ͕�
ƐŽď� Ă� ƐƵƉĞƌǀŝƐĆŽ� ŚƵŵĂŶĂ� ƌĞŵŽƚĂ� ŽƵ� ƐĞŵ� Ă� ƐƵĂ�
ŝŶƚĞƌǀĞŶĕĆŽ͘
�ŝƐƉŽŶşǀĞů�Ğŵ͗�фŚƩƉ͗ͬͬƉƚ͘ǁŝŬŝƉĞĚŝĂ͘ŽƌŐͬх͘��ĐĞƐƐŽ�Ğŵ͗�ϭϯ�ĂŐŽ͘�ϮϬϭϰ�
;ĂĚĂƉƚĂĚŽͿ͘
��ƌĞƐƉĞŝƚŽ�ĚĂ�ŶĂǀĞŐĂĕĆŽ�ĂƵƚƀŶŽŵĂ�ĚŽƐ�s�EdƐ͕�ĂǀĂůŝĞ�
ĂƐ�ĂĮƌŵĂĕƁĞƐ�Ă�ƐĞŐƵŝƌ͘
/͘� K� 'W^� ƚĞŵ� ĐŽŵŽ� ĨƵŶĐŝŽŶĂůŝĚĂĚĞ� ďĄƐŝĐĂ�
ĚĞƚĞƌŵŝŶĂƌ�ĐŽŽƌĚĞŶĂĚĂƐ�ŐĞŽŐƌĄĮĐĂƐ͘
//͘� K� ĂĐĞůĞƌƀŵĞƚƌŽ� ƚĞŵ� ĐŽŵŽ� ĨƵŶĐŝŽŶĂůŝĚĂĚĞ�
ďĄƐŝĐĂ�ĚĞƚĞƌŵŝŶĂƌ�ǀĂƌŝĂĕĆŽ�ŶĂ�ŽƌŝĞŶƚĂĕĆŽ͘
///͘� K�ŐŝƌŽƐĐſƉŝŽ�ƚĞŵ�ĐŽŵŽ�ĨƵŶĐŝŽŶĂůŝĚĂĚĞ�ďĄƐŝĐĂ�
ĚĞƚĞƌŵŝŶĂƌ�ǀĂƌŝĂĕĆŽ�ŶŽ�ƉŽƐŝĐŝŽŶĂŵĞŶƚŽ�͘
��ĐŽƌƌĞƚŽ�Ž�ƋƵĞ�ƐĞ�ĂĮƌŵĂ�Ğŵ
A /͕�ĂƉĞŶĂƐ͘
B ///͕�ĂƉĞŶĂƐ͘
C /�Ğ�//͕�ĂƉĞŶĂƐ͘
D //�Ğ�///͕�ĂƉĞŶĂƐ͘
E /͕�//͕�///͘
ÁREA LIVRE
*R15201434*
ϯϱ
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 34
hŵ�ƉƌŽũĞƚŽ�ĚĞ�ĂƵƚŽŵĂĕĆŽ�ĚĞ�Ƶŵ�ƐŝƐƚĞŵĂ�ĐŽŶƐŝƐƚĞ�Ğŵ�ďŽƚŽĞŝƌĂƐ�ĚĞ� ůŝŐĂ�Ğ�ĚĞƐůŝŐĂ� ůŽĐĂŝƐ�ĐŽŵ�ƌĞƋƵŝƐŝƚŽ�ĚĞ�
ĚĞƐůŝŐĂŵĞŶƚŽ�ƐĞŐƵƌŽ͕�ĚĞ�ŵŽĚŽ�ƋƵĞ͕�Ğŵ�ĐĂƐŽ�ĚĞ�ĚĞƐĐŽŶĞdžĆŽ�ĚĂ�ďŽƚŽĞŝƌĂ�ĚĞ�ĚĞƐůŝŐĂ�ĚŽ��>W͕ �Ž�ƐŝƐƚĞŵĂ�ĚĞǀĞƌĄ�
ĚĞƐůŝŐĂƌ�ĂƵƚŽŵĂƟĐĂŵĞŶƚĞ�Ğ�ŶĆŽ�ƉĞƌŵŝƟƌ�ŶŽǀŽ�ůŝŐĂŵĞŶƚŽ�ůŽĐĂů�ĂƚĠ�ƋƵĞ�Ă�ďŽƚŽĞŝƌĂ�ĚĞ�ĚĞƐůŝŐĂ�ƐĞũĂ�ĚĞƐƚƌĂǀĂĚĂ͘�
�ŽŶƐŝĚĞƌĂŶĚŽ�ƋƵĞ��>�Ġ�Ă�ďŽƚŽĞŝƌĂ�ĚĞ�ůŝŐĂ͕����Ġ�Ă�ďŽƚŽĞŝƌĂ�ĚĞ�ĚĞƐůŝŐĂ�Ğ�<ϭ�Ġ�Ă�ĐĂƌŐĂ�Ă�ƐĞƌ�ĂĐŝŽŶĂĚĂ͕�Ž�ĐŝƌĐƵŝƚŽ�
ƋƵĞ�ŝŵƉůĞŵĞŶƚĂ�Ă�ůſŐŝĐĂ�ĚĞ�ůŝŐĂͬĚĞƐůŝŐĂ�ĐŽŵ�ƐĞůŽ�Ğ�ĐŽŵ�Ž�ĚĞƐůŝŐĂŵĞŶƚŽ�ƐĞŐƵƌŽ�ƌĞƋƵŝƐŝƚĂĚŽ�Ġ
A
l4 Q1
Q1
l124V l1 l2 l3 l4 l5 l6 l7 l8
0V Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8
+24V
BL BD
K1
0V
D
l4 Q1
Q1
l124V l1 l2 l3 l4 l5 l6 l7 l8
0V Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8
+24V
BL BD
K1
0V
B
l4 Q1
Q1
l124V l1 l2 l3 l4 l5 l6 l7 l8
0V Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8
+24V
BL BD
K1
0V
E
l4 Q1
Q1
l124V l1 l2 l3 l4 l5 l6 l7 l8
0V Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8
+24V
BL BD
K1
0V
C
l4 Q1
Q1
l124V l1 l2 l3 l4 l5 l6 l7 l8
0V Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8
+24V
BL BD
K1
0V
*R15201435*
ϯϲ
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 35
hŵ�ĞŶŐĞŶŚĞŝƌŽ�ĚĞ�ĐŽŶƚƌŽůĞ�Ğ�ĂƵƚŽŵĂĕĆŽ͕�ƌĞƐƉŽŶƐĄǀĞů�ƉŽƌ�ŐĞƌĞŶĐŝĂƌ�Ă�ŝŶƐƚĂůĂĕĆŽ�ĚĞ�Ƶŵ�ƐŝƐƚĞŵĂ�ĚĞ�ĐŽŶƚƌŽůĞ�
ĚĞ�Ƶŵ�ƌĞƐĞƌǀĂƚſƌŝŽ�ĚĞ�ĄŐƵĂ�ƋƵĞŶƚĞ�ĚĞ�Ƶŵ�ŚŽƐƉŝƚĂů͕�ĚĞǀĞ�ĂƐƐĞƐƐŽƌĂƌ�Ă�ĞƋƵŝƉĞ�ĞŶĐĂƌƌĞŐĂĚĂ�ĚĞ�ƐƵĂ�ŵŽŶƚĂŐĞŵ͘�
��ŵĂůŚĂ�ĚĞ�ĐŽŶƚƌŽůĞ�ĚŽ�ƚĂŶƋƵĞ�ĚĞ�ĂƋƵĞĐŝŵĞŶƚŽ�ĞƐƚĄ�ƌĞƉƌĞƐĞŶƚĂĚĂ�ŶĂ�ĮŐƵƌĂ�ĂďĂŝdžŽ͘
R
L
U
Ts
PV
SP LIC
1
MV
LT
1
TY
1A
TE
1
TY
1B
TIC
1
CARGA
Qe Te
Qs
�ŝƐƉŽŶşǀĞů�Ğŵ͗�фŚƩƉ͗ͬͬǁǁǁ͘ĚĞƋƵŝ͘ĞĞů͘ƵƐƉ͘ďƌͬх͘��ĐĞƐƐŽ�Ğŵ͗�ϭϲ�ũƵů͘�ϮϬϭϰ͘
�Žŵ� ďĂƐĞ�ŶĂ� ĂŶĄůŝƐĞ� ĚŽ� ĚŝĂŐƌĂŵĂ� ĚĞ� ŝŶƐƚƌƵŵĞŶƚĂĕĆŽ� Ğ� ĐŽŶƚƌŽůĞ͕� ĞƐĐŽůŚĂ� Ă� ŽƉĕĆŽ� Ğŵ� ƋƵĞ� ĂƐ� ǀĂƌŝĄǀĞŝƐ�
ŵĂŶŝƉƵůĂĚĂƐ�;DsͿ�Ğ�ĂƐ�ǀĂƌŝĄǀĞŝƐ�ĚĞ�ƉƌŽĐĞƐƐŽ�;WsͿ�ĞƐƚĆŽ�ĐŽƌƌĞƚĂŵĞŶƚĞ�ƌĞůĂĐŝŽŶĂĚĂƐ�ŶĂ�ĨŽƌŵĂ�Ds�ͬ�Ws�ƉĂƌĂ�
ƵŵĂ�ŵĞƐŵĂ�ŵĂůŚĂ�ĚĞ�ĐŽŶƚƌŽůĞ͘
A EşǀĞů�ĚĂ�ĄŐƵĂ�ͬ�sĂnjĆŽ�ĚĞ�ĞŶƚƌĂĚĂ͖�dĞŵƉĞƌĂƚƵƌĂ�ĚĂ�ĄŐƵĂ�ͬ�dĞŶƐĆŽ�ŶĂ�ƌĞƐŝƐƚġŶĐŝĂ͘
B EşǀĞů�ĚĂ�ĄŐƵĂ�ͬ�sĂnjĆŽ�ĚĞ�ĞŶƚƌĂĚĂ͖�dĞŶƐĆŽ�ŶĂ�ƌĞƐŝƐƚġŶĐŝĂ�ͬdĞŵƉĞƌĂƚƵƌĂ�ĚĂ�ĄŐƵĂ͘
C dĞŵƉĞƌĂƚƵƌĂ�ĚĂ�ĄŐƵĂ�ͬ�sĂnjĆŽ�ĚĞ�ĞŶƚƌĂĚĂ͖�EşǀĞů�ĚĂ�ĄŐƵĂ�ͬ�dĞŶƐĆŽ�ŶĂ�ƌĞƐŝƐƚġŶĐŝĂ͘
D sĂnjĆŽ�ĚĞ�ĞŶƚƌĂĚĂ�ͬ�dĞŵƉĞƌĂƚƵƌĂ�ĚĂ�ĄŐƵĂ͖�dĞŶƐĆŽ�ŶĂ�ƌĞƐŝƐƚġŶĐŝĂ�ͬ�EşǀĞů�ĚĂ�ĄŐƵĂ͘
E sĂnjĆŽ�ĚĞ�ĞŶƚƌĂĚĂ�ͬ�EşǀĞů�ĚĂ�ĄŐƵĂ͖�dĞŶƐĆŽ�ŶĂ�ƌĞƐŝƐƚġŶĐŝĂ�ͬ�dĞŵƉĞƌĂƚƵƌĂ�ĚĂ�ĄŐƵĂ͘
ÁREA LIVRE
*R15201436*
ϯϳ
�E'�E,�Z/������KEdZK>�����hdKD���K
QUESTÃO 1
YƵĂů� Ž� ŐƌĂƵ� ĚĞ� ĚŝĮĐƵůĚĂĚĞ� ĚĞƐƚĂ� ƉƌŽǀĂ� ŶĂ� ƉĂƌƚĞ� ĚĞ�
&ŽƌŵĂĕĆŽ�'ĞƌĂů͍
A�DƵŝƚŽ�ĨĄĐŝů͘
B�&ĄĐŝů͘
C�DĠĚŝŽ͘
D��ŝİĐŝů͘
E�DƵŝƚŽ�ĚŝİĐŝů͘
QUESTÃO 2 
YƵĂů� Ž� ŐƌĂƵ� ĚĞ� ĚŝĮĐƵůĚĂĚĞ� ĚĞƐƚĂ� ƉƌŽǀĂ� ŶĂ� ƉĂƌƚĞ� ĚĞ�
�ŽŵƉŽŶĞŶƚĞ��ƐƉĞĐşĮĐŽ͍
A�DƵŝƚŽ�ĨĄĐŝů͘
B�&ĄĐŝů͘
C�DĠĚŝŽ͘
D��ŝİĐŝů͘
E�DƵŝƚŽ�ĚŝİĐŝů͘
QUESTÃO 3 
�ŽŶƐŝĚĞƌĂŶĚŽ�Ă�ĞdžƚĞŶƐĆŽ�ĚĂ�ƉƌŽǀĂ͕�Ğŵ�ƌĞůĂĕĆŽ�ĂŽ�ƚĞŵƉŽ�
ƚŽƚĂů͕�ǀŽĐġ�ĐŽŶƐŝĚĞƌĂ�ƋƵĞ�Ă�ƉƌŽǀĂ�ĨŽŝ
A�ŵƵŝƚŽ�ůŽŶŐĂ͘
B�ůŽŶŐĂ͘
C�ĂĚĞƋƵĂĚĂ͘
D�ĐƵƌƚĂ͘
E�ŵƵŝƚŽ�ĐƵƌƚĂ͘
QUESTÃO 4 
KƐ� ĞŶƵŶĐŝĂĚŽƐ� ĚĂƐ� ƋƵĞƐƚƁĞƐ� ĚĂ� ƉƌŽǀĂ� ŶĂ� ƉĂƌƚĞ� ĚĞ�
&ŽƌŵĂĕĆŽ�'ĞƌĂů�ĞƐƚĂǀĂŵ�ĐůĂƌŽƐ�Ğ�ŽďũĞƟǀŽƐ͍
A�^ŝŵ͕�ƚŽĚŽƐ͘
B�^ŝŵ͕�Ă�ŵĂŝŽƌŝĂ͘
C��ƉĞŶĂƐ�ĐĞƌĐĂ�ĚĂ�ŵĞƚĂĚĞ͘
D�WŽƵĐŽƐ͘
E�EĆŽ͕�ŶĞŶŚƵŵ͘
QUESTÃO 5 
KƐ� ĞŶƵŶĐŝĂĚŽƐ� ĚĂƐ� ƋƵĞƐƚƁĞƐ� ĚĂ� ƉƌŽǀĂ� ŶĂ� ƉĂƌƚĞ� ĚĞ�
�ŽŵƉŽŶĞŶƚĞ��ƐƉĞĐşĮĐŽ�ĞƐƚĂǀĂŵ�ĐůĂƌŽƐ�Ğ�ŽďũĞƟǀŽƐ͍
A�^ŝŵ͕�ƚŽĚŽƐ͘
B�^ŝŵ͕�Ă�ŵĂŝŽƌŝĂ͘
C��ƉĞŶĂƐ�ĐĞƌĐĂ�ĚĂ�ŵĞƚĂĚĞ͘
D�WŽƵĐŽƐ͘
E�EĆŽ͕�ŶĞŶŚƵŵ͘
QUESTÃO 6
�Ɛ� ŝŶĨŽƌŵĂĕƁĞƐͬŝŶƐƚƌƵĕƁĞƐ� ĨŽƌŶĞĐŝĚĂƐ� ƉĂƌĂ� Ă� ƌĞƐŽůƵĕĆŽ�
ĚĂƐ�ƋƵĞƐƚƁĞƐ�ĨŽƌĂŵ�ƐƵĮĐŝĞŶƚĞƐ�ƉĂƌĂ�ƌĞƐŽůǀġͲůĂƐ͍
A�^ŝŵ͕�ĂƚĠ�ĞdžĐĞƐƐŝǀĂƐ͘
B�^ŝŵ͕�Ğŵ�ƚŽĚĂƐ�ĞůĂƐ͘
C�^ŝŵ͕�ŶĂ�ŵĂŝŽƌŝĂ�ĚĞůĂƐ͘
D�^ŝŵ͕�ƐŽŵĞŶƚĞ�Ğŵ�ĂůŐƵŵĂƐ͘
E�EĆŽ͕�Ğŵ�ŶĞŶŚƵŵĂ�ĚĞůĂƐ͘
QUESTÃO 7 
sŽĐġ�ƐĞ�ĚĞƉĂƌŽƵ�ĐŽŵ�ĂůŐƵŵĂ�ĚŝĮĐƵůĚĂĚĞ�ĂŽ�ƌĞƐƉŽŶĚĞƌ�
ă�ƉƌŽǀĂ͘�YƵĂů͍
A��ĞƐĐŽŶŚĞĐŝŵĞŶƚŽ�ĚŽ�ĐŽŶƚĞƷĚŽ͘
B�&ŽƌŵĂ�ĚŝĨĞƌĞŶƚĞ�ĚĞ�ĂďŽƌĚĂŐĞŵ�ĚŽ�ĐŽŶƚĞƷĚŽ͘
C��ƐƉĂĕŽ�ŝŶƐƵĮĐŝĞŶƚĞ�ƉĂƌĂ�ƌĞƐƉŽŶĚĞƌ�ăƐ�ƋƵĞƐƚƁĞƐ͘
D�&ĂůƚĂ�ĚĞ�ŵŽƟǀĂĕĆŽ�ƉĂƌĂ�ĨĂnjĞƌ�Ă�ƉƌŽǀĂ͘
E�EĆŽ�ƟǀĞ�ƋƵĂůƋƵĞƌ�ƟƉŽ�ĚĞ�ĚŝĮĐƵůĚĂĚĞ�ƉĂƌĂ�ƌĞƐƉŽŶĚĞƌ�
ă�ƉƌŽǀĂ͘
QUESTÃO 8 
�ŽŶƐŝĚĞƌĂŶĚŽ� ĂƉĞŶĂƐ� ĂƐ� ƋƵĞƐƚƁĞƐ� ŽďũĞƟǀĂƐ� ĚĂ� ƉƌŽǀĂ͕�
ǀŽĐġ�ƉĞƌĐĞďĞƵ�ƋƵĞ
A�ŶĆŽ�ĞƐƚƵĚŽƵ�ĂŝŶĚĂ�Ă�ŵĂŝŽƌŝĂ�ĚĞƐƐĞƐ�ĐŽŶƚĞƷĚŽƐ͘
B�ĞƐƚƵĚŽƵ�ĂůŐƵŶƐ�ĚĞƐƐĞƐ�ĐŽŶƚĞƷĚŽƐ͕�ŵĂƐ�ŶĆŽ�ŽƐ�ĂƉƌĞŶĚĞƵ͘
C�ĞƐƚƵĚŽƵ�Ă�ŵĂŝŽƌŝĂ�ĚĞƐƐĞƐ�ĐŽŶƚĞƷĚŽƐ �͕ŵĂƐ�ŶĆŽ�ŽƐ�ĂƉƌĞŶĚĞƵ͘
D�ĞƐƚƵĚŽƵ�Ğ�ĂƉƌĞŶĚĞƵ�ŵƵŝƚŽƐ�ĚĞƐƐĞƐ�ĐŽŶƚĞƷĚŽƐ͘
E�ĞƐƚƵĚŽƵ�Ğ�ĂƉƌĞŶĚĞƵ�ƚŽĚŽƐ�ĞƐƐĞƐ�ĐŽŶƚĞƷĚŽƐ͘
QUESTÃO 9 
YƵĂů�ĨŽŝ�Ž�ƚĞŵƉŽ�ŐĂƐƚŽ�ƉŽƌ�ǀŽĐġ�ƉĂƌĂ�ĐŽŶĐůƵŝƌ�Ă�ƉƌŽǀĂ͍
A�DĞŶŽƐ�ĚĞ�ƵŵĂ�ŚŽƌĂ͘
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