Question

A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$Force=m\frac{dv}{dt}+v\frac{dm}{dt}$
Since velocity of wind is constant, we are only concerned with the $v\frac{dm}{dt}$ term.
$Force=v\frac{d}{dt}(V\times \rho )$
Where V is the concerned volume and $\rho$ is the density.
$Force=v\rho \frac{d}{dt}[A\times l]$
$=v\rho A\frac{dl}{dt}=\rho A{v}^2$

$Power=F\times v=\rho A{v}^2\times v=\rho A{v}^3\therefore P\propto v^3$