Question

A wind turbine has 12,000 kg blades that are 40 m long. the blades spin at 23 rpm . you may want to review (pages 164 - 169) . part a 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 find the inward force necessary for the blade's centripetal acceleration, we calculated the centripetal acceleration and then used it along with the blade's mass to calculate the centripetal force.

Step-by-step explanation:

To calculate the centripetal force necessary to provide each blade's centripetal acceleration, we need to first convert the angular velocity from revolutions per minute (rpm) to radians per second. Angular velocity (ω) in radians per second is given by ω = 2π * (revolutions per second). Since 23 rpm is approximately 2.42 rad/s, the centripetal acceleration (ac) can be calculated using the formula ac = ω2 * r, where r is the radius. Since the blade length is 40 m, the radius (half of the blade length) will be 20 m.

The centripetal acceleration is therefore (2.42 rad/s)2 * 20m = 116.64 m/s2. So, the centripetal force (Fc) can be calculated using the formula Fc = m * ac, where m is the mass of the blade. For a 12,000 kg blade, the centripetal force is 12,000 kg * 116.64 m/s2 = 1,399,680 N.