(a) Use dimensional analysis to show that the electric power output of a wind turbine is proportional to the cube of the wind speed. The relevant quantities on which the power can depend are the length L of the rotor blades, the density p of air (SI units kg/m3), and the wind speed v. 

(b) One day, the wind blows at a steady 8.0 m/s for 2.0 h, then at 6.0 m/s for 4.0 h. During which time interval is the energy output of the turbine larger? By what factor is it larger?