Question

A wind turbine has 12,000 kg blades that are 40 m long. The blades spin at 22 rpm.

If we model a blade as a point mass at the midpoint of the blade, what is the inward force necessary to provide each blade's centripetal acceleration?

Answer 1

To calculate the centripetal force on a wind turbine blade, one must convert the rotational speed to radians per second, calculate the centripetal acceleration, and then use the mass of the blade to find the force. The required centripetal force for a blade mass of 12,000 kg and a rotation rate of 22 rpm is 12,676,320 N.

Step-by-step explanation:

Calculating the Centripetal Force on a Wind Turbine Blade

The question requires computing the centripetal force needed for a wind turbine blade to maintain its circular path. To find this force, we use the formula F = m × a, where m is the mass and a is the centripetal acceleration. The centripetal acceleration (a) is calculated using the formula a = r × ω², where r is the radius of the circular path (half the blade length) and ω is the angular velocity in radians per second.

First, we need to convert the rotation speed from rpm to radians per second:

• 22 rpm × (2π radians/1 rev) × (1 min/60 s) = 2.309 radians/s

Then, we calculate the centripetal acceleration:

• a = (20 m) × (2.309 radians/s)² = 1056.36 m/s²

Finally, we compute the

centripetal force

:

• F = 12,000 kg × 1056.36 m/s² = 12,676,320 N