Sapling Learning macmillan learning Anemometers (pictured) are used to measure w

Question

Sapling Learning macmillan learning Anemometers (pictured) are used to measure wind speeds. Wind striking the cups causes the assembly to rotate; a gauge measures the frequency of this rotation and translates the data into wind speed. The length of each arm, as measured from cup to cup, is 43.5 cm. The friction in the bearings is negligible, so the tangential speed of the cups matches the wind speed fairly closely bulb Your company makes anemometers and plans to install light bulbs orn them for high wind warnings.The idea is to attach a coil of wire of radius 13.2 cm to one of the arms and use the EMF induced by the magnetic field of the Earth to light the bulb. The bulbs possess 234 of internal resistance but need 12.5 W of rms power dissipation to be visible at night. (The resistance of the wire is negligible.) coil Although company management wants this new feature, you have doubts about its practicality. Assuming the magnetic field of the Earth is _ 0.500 gauss and is oriented roughly horizontal with the Earth, and that B 91.5 mph is considered the threshold of dangerous wind speed, calculate the number of turns in the coil wire needed to light the bulb. Dy wind Number 161641 turns

Explanation / Answer

Rms Induced emf

Erms=sqrt[PR] =sqrt[12.5*234] =54.08 Volts

Maximum induced emf

Emax=sqrt(2)*54.08=76.485 Volts

angular speed

W=V/r =(91.5*0.44704)/(0.435/2)=188.065 rad/s

Since Induced emf is

Emax=NBAW

76.485 =N*(0.5*10-4)*(pi*0.1322)*188.065

N=148594 turns

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