Electrical power produced by a wind turbine. The force of the wind on the blades of a wind turbine (Fig. 9.4A) is proportional to v², where v is the speed of the wind (Chapter 3). 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 P ? v^? and find the value of ?.?

(b) At some promising sites for wind energy, the wind speed averages about 20 mi/h (about 9 m/s). If a wind turbine at this site produces 1.0 MW with a wind speed of 20 mi/h, what power would it produce when the wind speed is 25 mi/h? Your answer should show why it is important to place wind turbines at places where the wind speed is fastest.

Figure 9.4A

?