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" bydesigning 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. The wind speed correlates very well with the tangential speed of the cups because they are very light and rotate with almost no friction. This company wants to simply place a coil (solenoid) at the center ofthe 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 asshown. 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 in the bulbs is at least 10.5 W. The bulbs only have a resistance of 10 ?, but since the coil is providing for the voltage to light the bulb, the resistance of the coil must also be taken into account. 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 8.0 cm. You are allowed to use copper wire to make the coil, and you can use any size (diameter) wire you'd like. Just keep in mind that the size of the wire will affect the resistance...Also, assume you can wrap up to 10 layers of wire to make the solenoid. 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, is it possible to achieve the necessary induced voltage to light up the bulb while also managing the size restrictions of the device? Assume that "dangerous" wind speeds are 85 mph and the company wants for the bulbs to light up at this speed threshold. To receive full credit you MUST show all your work and give very detailed explanations for your reasoning.
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?