Question

The blades on modern wind turbines are typically 20 to 40 meters in length. Two different turbines have their blades attached with one end at the center of rotation. Consider two points, each at the outer end of a blade on each of the turbines: one with a blade length of 23.6 m, and the other with a blade length of 37.2 m. Each blade is rotating with a constant angular speed of 3.93 rad/s, and the rotation is considered for 11.2 s. (a) What is the speed of each point in meters per second? V23.6 = 1 m/s 137.2 m/s (b) What is the angular distance traveled by each point? A023.6 = rad A037.2 = rad (c) What is the translational distance traveled by each point? $23.6 - $37.2 - (d) What is the magnitude of the centripetal acceleration that would be experienced by an object located at each point? 2c, 23.6 = m/s2 ac, 37.2 m/s2

Answer 1

Hi,

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PART (a):

Given that:

Distance/radius from center of rotation to the point, for blade 1,

r1 = 23.6 m

Distance/radius from center of rotation to the point, for blade 2,

r2 = 37.2 m

Angular speed,

w=3.93 rad) s

Therefore, Linear speed is given by:

V23.6 = 11.w= 23.6 m x 3.93 rad/s

:: V23.6 = 92.748 m/s

V37.2 = r2.w = 37.2 m x 3.93 rad/s

:: V37.2 = 146.196 m/s

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PART (b):

Given that, Time taken is 11.2 s

A623.6 =w.t = 3.93 rad/s x 11.2 s

:. 423,6 = 44.016 rad

A437.2 =w.t = 3.93 rad/s x 11.2 s

:. A0372 = 44.016 rad

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PART (c):

Translational distances covered is given by:

S23.6 = 71.4823.6 = 44.016 x 23.6 m

:: $23,6 = 1038.7776 m

S37.2 = r2.46372 = 44.016 x 37.2 m

:. 37.2 = 1637.3952 m

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PART (c):

Centripetal acceleration is given by:

(V23.6) (123,6 = (92.748 m/s) 23.6 m

1.0 23.6 = 364.49964 m/s2

037.2 =- (V37.2)?_(146.196 m/s)? 37.2 m

.. a 23.6 = 574.55028 m/s2

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