(ITA 2017) - QUESTÃO

Considere um corpo esférico de raio r totalmente envolvido por um fluido de viscosidade 𝛈 com velocidade média v. De acordo com a lei de Stokes, para baixas velocidades, esse corpo sofrerá a ação de uma força de arrasto viscoso dada por F = - 6𝚷r𝛈v. A dimensão de 𝛈 é dada por
a) m.s-1
b) m.s-2
c) kg.m.s-2
d) kg.m.s-3
e) kg.m-1.s-1


------------------------------------------------------------------------------------------------ RESPOSTA: E

  • Resposta Comentada:
  • «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»F«/mi»«/mfenced»«mo»=«/mo»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»M«/mi»«/mfenced»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»L«/mi»«/mfenced»«msup»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»T«/mi»«/mfenced»«mrow»«mo»-«/mo»«mn»2«/mn»«/mrow»«/msup»«mspace linebreak=¨newline¨/»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»v«/mi»«/mfenced»«mo»=«/mo»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»L«/mi»«/mfenced»«mo».«/mo»«msup»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»T«/mi»«/mfenced»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mspace linebreak=¨newline¨/»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»r«/mi»«/mfenced»«mo»=«/mo»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»L«/mi»«/mfenced»«/math»
    Como a força de arrasto viscoso é dada por«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#x000A0;«/mo»«mi mathvariant=¨normal¨»F«/mi»«mo»=«/mo»«mo»-«/mo»«mn»6«/mn»«mi»§#x003C0;r§#x003B7;v«/mi»«/math», temos:
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»F«/mi»«/mfenced»«mo»=«/mo»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»r«/mi»«/mfenced»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»§#x003B7;«/mi»«/mfenced»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»v«/mi»«/mfenced»«mo»§#x021D2;«/mo»«mspace linebreak=¨newline¨/»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»M«/mi»«/mfenced»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»L«/mi»«/mfenced»«msup»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»T«/mi»«/mfenced»«mrow»«mo»-«/mo»«mn»2«/mn»«/mrow»«/msup»«mo»=«/mo»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»L«/mi»«/mfenced»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»§#x003B7;«/mi»«/mfenced»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»L«/mi»«/mfenced»«msup»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»T«/mi»«/mfenced»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»§#x021D2;«/mo»«mspace linebreak=¨newline¨/»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»§#x003B7;«/mi»«/mfenced»«mo»=«/mo»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»M«/mi»«/mfenced»«msup»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»L«/mi»«/mfenced»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«msup»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»T«/mi»«/mfenced»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/math»
    Em unidades do S.I.:
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«mi mathvariant=¨normal¨»§#x003B7;«/mi»«/mfenced»«mo»=«/mo»«mi»kg«/mi»«mo».«/mo»«msup»«mi mathvariant=¨normal¨»m«/mi»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo».«/mo»«msup»«mi mathvariant=¨normal¨»s«/mi»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/math»

Nenhum comentário:

Postar um comentário