Work Power and Energy 5 Question 7
9. 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 electrical energy. For wind speed $v$, the electrical power output will be proportional to
$(2000,2 M)$
(a) $v$
(b) $v^{2}$
(c) $v^{3}$
(d) $v^{4}$
Show Answer
Answer:
Correct Answer: 9. (c)
Solution:
- Power $=\mathbf{F} \cdot \mathbf{v}=F v$
$$ F=v \frac{d m}{d t}=v \frac{d(\rho \times \text { volume })}{d t} $$
$$ =\rho v \quad \frac{d(\text { volume })}{d t}=\rho v(A v)=\rho A v^{2} $$
$\therefore \quad$ Power, $P=\rho A v^{3} \quad$ or $\quad P \propto v^{3}$
