A wind-powered generator converts wind energy into electrical energy. Assume that the generator conv

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\

Professor PC Thomas Classes · Answer

(c) : Force $=v 	imes \frac{d m}{d t}$\ $=v 	imes \frac{d}{d t}($ volume $	imes$ density $)=v \frac{d}{d t}(A x 	imes ho)$\ $=v 	imes A ho \frac{d x}{d t}=A ho v^{2}$\ $	herefore \quad$ Power $=$ Force $	imes$ velocity $=\left(A ho v^{2}ight)$\ $(v)=A ho v^{3}$\ $	herefore \quad$ Power $\propto v^{3}$.\