First slide

Power

Question

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

Moderate

A

v
B

v²
C

v³
D

v⁴

Solution

The force F exerted by the wind on the blades of the generator is given by
$F = {ρAv}^{2} where, ρ = density of air A = area of cross-section of blade V = velocity of wind ∴ Power output, P = \int Fdv = \int {ρAv}^{2} dv = {ρAv}^{3} / 3 ρ \propto v^{3}$

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