A wind turbine converts some of the kinetic energy of the wind into electric energy. Suppose that the blades of a small wind turbine have length L = 4.0 m.
(a) When a 10 m/s (22 mi/h) wind blows head-on, what volume of air (in m3) passes through the circular area swept out by the blades in 1.0 s?
(b) What is the mass of this much air? Each cubic meter of air has a mass of 1.2 kg.
(c) What is the translational kinetic energy of this mass of air?
(d) If the turbine can convert 40% of this kinetic energy into electric energy, what is its electric power output?
(e) What happens to the power output if the wind speed decreases to 1/2 of its initial value? What can you conclude about electric power production by wind turbines?