# College Physics

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In Chapter 3 we learned that the force of air drag on an object moving rapidly through the air is proportional to v2, where v is the speed of the ball relative to the air. The same relation applies to the force of the wind on the blades of a wind turbine (Figure 9.4), where v is the speed of the wind. The angular velocity of the turbine is also proportional to the wind speed.

(a) Show that the mechanical power exerted by the wind on a turbine varies as Pvá and find the value of á .

P is proportional to V to the power of alpha". In otherwords P~V^a, which means that P = K * V^a, where K is some number that we don't know, but it does not depend on velocity.

(b) At some promising sites for wind energy, the wind speed averages about 51 mph. If a wind turbine at this site produces 9 MW with a wind speed of 51 mph, what power would it produce when the wind speed is 49 mph? Your answer should show why it is important to place wind turbines at places where the wind speed is largest.