Final answer:
With a tip speed ratio of 10 and a wind speed of 11 m/s, the tip of the blades on a wind turbine with a 100 m rotor diameter is moving at 110 m/s. The time it takes for one full rotation is approximately 2.856 seconds.
Step-by-step explanation:
To calculate how long it takes for the rotor to make one rotation, we need to find the rotational speed of the wind turbine's blades. With a tip speed ratio of 10, the tip of the blades is moving 10 times the speed of the wind. The wind speed is given as 11 m/s, so the tip of the blades is moving at 110 m/s.
The circumference of the rotor (considering it to be a circle) can be calculated using the formula for the circumference of a circle, which is C = πd, where d is the diameter. With a rotor diameter of 100 m, the circumference is C = π * 100 m, which is approximately 314.16 m.
To find the time for one complete rotation, we divide the circumference by the tip speed: Time = Circumference / Tip Speed. Therefore, Time = 314.16 m / 110 m/s, which equals approximately 2.856 seconds for one full rotation.