1 A formula for calculating the lift force acting on the wings of an aircraft moving through the air is of the form $$F = k v ^ { \alpha } A ^ { \beta } \rho ^ { \gamma }$$ where \(F\) is the lift force in newtons, \(k\) is a dimensionless constant, \(v\) is the air velocity in \(\mathrm { m } \mathrm { s } ^ { - 1 }\), \(A\) is the surface area of the aircraft's wings in \(\mathrm { m } ^ { 2 }\), and \(\rho\) is the density of the air in \(\mathrm { kg } \mathrm { m } ^ { - 3 }\).
By using dimensional analysis, find the values of the constants \(\alpha , \beta\) and \(\gamma\).
[0pt] [6 marks]

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1 A formula for calculating the lift force acting on the wings of an aircraft moving through the air is of the form

$$F = k v ^ { \alpha } A ^ { \beta } \rho ^ { \gamma }$$

where $F$ is the lift force in newtons,\\
$k$ is a dimensionless constant,\\
$v$ is the air velocity in $\mathrm { m } \mathrm { s } ^ { - 1 }$,\\
$A$ is the surface area of the aircraft's wings in $\mathrm { m } ^ { 2 }$, and\\
$\rho$ is the density of the air in $\mathrm { kg } \mathrm { m } ^ { - 3 }$.\\
By using dimensional analysis, find the values of the constants $\alpha , \beta$ and $\gamma$.\\[0pt]
[6 marks]

\hfill \mbox{\textit{AQA M3 2015 Q1 [6]}}