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) $v^{4}$

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Answer:

Correct Answer: 9. (c)

Solution:

  1. 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 $\quad P \propto v^{3}$



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