Question
Answers must be very legible and concise
Yet another company (you sure are popular!) is interested in hiring you to build something for their use. They want to make a wind speed measuring device called an anemometer. Typically anemometers require their own internal power source and a small generator in order to deduce information about wind speeds by measuring an induced EMF or current. This company believes they can revolutionize the "industry" by designing an anemometer that can utilize the Earth's magnetic field only, and therefore will not require a secondary generator setup. A basic diagram of their design is shown below. The four cups "pick up" the wind and as a result turn the entire structure so that it rotates with some angular frequency (omega , angular velocity). The wind speed correlates very well with the tangential speed of the cups because they rotate with almost no friction. This company wants to simply place a coil (solenoid) at the center of the rotating structure so that it too will rotate due to the wind blowing. This rotation combined with the Earth's magnetic field will induce a voltage/current in the coil which can be connected to a light bulb on top as shown. The company really just wants this device to be able to serve as a warning for dangerous wind speeds. Therefore they have provided light bulbs that will light up sufficiently to be seen at night if a peak power dissipation in the bulbs is at least 10.5 W. The bulbs have a total resistance of 235 omega. The structure is made such that the length of each arm from cup to cup is 43 cm and the radius of the coil is 13 cm. The Earth's magnetic field is 0.50 Gauss and can be assumed to be in the direction shown in the figure above. While the company's idea is interesting, they need an expert like you to determine if it is feasible. Based on the dimensions and parameters given, how many turns must the coil have so that dangerous wind speeds of 85 mph will lead to enough power to light up the bulb sufficiently? Is this a realistic design? Does it seem possible that the number of turns required will be able to "fit" on the coil and in turn on the anemometer arms? Explain why you think this design will work, or if you think it needs improvement, what could possibly be changed in order to make it more realistic?
Explanation / Answer
V = W N A B sin(W t) ====> W= angular velocity velocity = 85 mph = 38 mps ====>V= 0.5 X N X 3.141 X 0.13 X 0.13 X [ 38 / 0.215 ] ====> now , v= rW W= v/r now , power = V^2 /R = 10.5 ====> V= sqrt( 10.5 X 235) = 49.67 N= 10.58 == 11 turns ====> No this is not a realistic design, the earths magnetic field is very feeble , and it cannot be used to generate voltage ====> the changes that can be made are : the coil must be perpendicular to the erths magnetic fileld . a coil with much less resistance must be used , so that too much heat wont be dissipated in the circuit
