Each blade on a wind turbine is engineered to produce an effective force through its center of mass that is perpendicular to its long axis. (Figure 1) The magnitude of the force produced by each blade in a wind of speed v is F=(40.0 kg/s)v. If the center of mass of each blade is r_1 = 13.8 mm , what is U_1, the total work done by the wind turbine's blades, in a wind of speed v_1 = 8.80 m/s after 10 revolutions?

Respuesta :

The total work done by the wind turbine's blades after 10 revolutions in a wind of speed v_1 = 8.80 m/s is U_1 = 5.344e4 J.

What is turbine's?

A turbine is a rotary engine that converts the energy of a moving fluid (such as water or steam) into mechanical energy. A turbine is made up of a rotor, or a series of blades, and a stator, or a stationary part. The fluid enters the rotor, which is set in motion by its pressure and kinetic energy, and is directed towards the stator. The stator is designed to capture the energy from the fluid and convert it into mechanical energy, which can then be used to drive a generator, a compressor, or other machinery. Turbines are widely used in industry for power generation and for other applications such as water pumps.

U_1 = F * r_1 * 10 revolutions
U_1 = (40.0 kg/s)v_1 * 13.8 mm * 10 revolutions
U_1 = 5.344e4 J

The total work done by the wind turbine's blades after 10 revolutions in a wind of speed v_1 = 8.80 m/s is U_1 = 5.344e4 J. This calculation is based on the magnitude of the force produced by each blade (F=(40.0 kg/s)v) and the center of mass of each blade (r_1 = 13.8 mm). The force F is multiplied by the distance r_1 and then multiplied by the number of revolutions (10) to calculate the total work done by the blades.

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