Question

Realizando análise dimensional em situações hipotéticas que envolvem as

representações a, b, c, d e e, escrevas as unidades de a, b, c, d e e.

Y = m*s; z = kg * m ; w = kg /m2 ; k = s-1

a) a = y*z*k - Feita

b) b = z * w /k - Feita

c) Y = z * k* c

d) w = d * y * x/z

e) k = y/e * z * w​

Answer 1

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⠀⠀☞ As dimensões das unidades são a = [kg * m⁻²]; b = [kg² * s * m⁻¹]; c = [s² * kg⁻¹]; d = [kg² * m⁻²]; e = [m² * s² * kg⁻²] . ✅

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⠀⠀ Através da análise dimensional podemos compreender o fenômeno que está sendo abordado e conferir se as operações que realizamos resulta de fato no fenômeno que desejamos. Seja portanto:

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$\blue{\Large\sf~~\begin{cases}\sf~y = [m \cdot s];\\\\ \sf~z = [kg \cdot m];\\\\\sf~w = [kg \cdot m^{-2}];\\\\\sf~k = [s^{-1}].\end{cases}}$

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a) a = y * z * k

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$\blue{\Large\sf~a~\begin{cases}\sf~ = [m \cdot s] \cdot [kg \cdot m] \cdot [s^{-1}]\\\\ \sf~ = \boxed{\sf [kg \cdot m^2]} \end{cases}}$ ✅

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b) b = z * w /k

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$\blue{\Large\sf~b~\begin{cases}\sf~ = [kg \cdot m] \cdot [kg \cdot m^{-2}] \div [s^{-1}]\\\\ \sf~ = [kg^2 \cdot m^{-1}] \cdot [s] \\\\\text{ \sf~ = \boxed{\sf [kg^2 \cdot s \cdot m^{-1}]} }\end{cases}}$ ✅

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c) y = z * k* c

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$\blue{\Large\sf~c~\begin{cases}\sf~ = [m \cdot s] \div [kg \cdot m] \div [s^{-1}]\\\\ \sf~ = [m \cdot s] \cdot [kg^{-1} \cdot m^{-1}] \cdot [s]\\\\\text{ \sf~ = \boxed{\sf [s^2 \cdot kg^{-1}]} }\end{cases}}$ ✅

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d) w = d * y * k/z

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$\blue{\large\sf~d~\begin{cases}\sf~ = [kg \cdot m] \cdot  [kg \cdot m^{-2}] \div [m \cdot s] \div [s^{-1}]\\\\ \sf~ = [kg^2 \cdot m^{-1}] \cdot [m^{-1} \cdot s^{-1}] \cdot [s]\\\\\text{ \sf~ = \boxed{\sf [kg^2  \cdot m^{-2}]} }\end{cases}}$ ✅

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e) k = y/e * z * w

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$\blue{\large\sf~e~\begin{cases}\sf~ = [m \cdot s] \div [s^{-1}] \div [kg \cdot m] \div [kg \cdot m^{-2}]\\\\\sf~ = [m \cdot s] \cdot [s] \cdot [kg^{-1} \cdot m^{-1}] \cdot [kg^{-1} \cdot m^2]\\\\ \text{ \sf~ = \boxed{\sf [m^2 \cdot s^2 \cdot kg^{-2}]} } }\end{cases}}$ ✅

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