Modern wind turbines are larger than they appear, and despite their apparently l

Question

Modern wind turbines are larger than they appear, and despite their apparently lazy motion, the speed of the blades tips can be quite high-many times higher than the wind speed. A turbine has blades 54 m long that spin at 14 rpm .

Part A

At the tip of a blade, what is the speed?

Express your answer to two significant figures and include the appropriate units.

Part B

At the tip of a blade, what is the centripetal acceleration?

Express your answer to two significant figures and include the appropriate units.

Problem 13 Modern wind turbines are larger than they appear, and despite their apparently lazy motion, the speed of the blades tips can be quite high-many times higher than the wind speed. A turbine has blades 54 m long that spin at 14 rpm (Figure 1) You may want to review (D pages 161-163) Figure 1 of 1 Part A At the tip of a blade, what is the speed? Express your answer to two significant figures and include the appropriate units. Value Units Submit My Answers Give U Part B At the tip of a blade, what is the centripetal acceleration? Express your answer to two significant figures and include the appropriate units. ar Value Units Submit My Answers Give Up Provide Feedback Continue

Explanation / Answer

First turn the rpm to radians per second.

1 rev = 2 pi() radians

1 minute = 60 s

so

14 turns per minute = 14 * 2pi() radians per minute-> 14 * 2pi() / 60 radians per second.

Now

v = wr = 14 * 2 * pi() / 60 * 54 = 79.16 m/s

a = w^2 r
= ( 14 * 2 * pi() / 60 ) ^ 2 * 54 =116.06 m/s^2

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