A bicyclist is traveling at night, and a generator mounted on the bike powers a

Question

A bicyclist is traveling at night, and a generator mounted on the bike powers a headlight. A small rubber wheel on the shaft of the generator presses against the bike tire and turns the coil at an angular speed that is 44 times as great as the angular speed of the tire itself. The tire has a radius of .33m. The coil consist of 75 turns, has an area of 2.6*10^-3m^2, and rotates in a 0.10 Tesla magnetic field. When the peak emf being generated is 6.0V, what is the linear speed of the bike?
Please show all work, step by step, Thankyou.

Explanation / Answer

radius of the tire r = 0.33 m number turns of the coil N = 75 area of the coil A = 2.6*10-3 m2 emf of the generator 0 = 6 V magnetic field B = 0.1 T .................................................................. emf of the generator 0 = 6 V magnetic field B = 0.1 T .................................................................. according to given problem ,    coil = 44 tire    tire = (1/44) tire    tire = (1/44) tire the relation between linear velocity and angular speed is                   v = rtire                          v = r [(1/44) coil]   ........... (1) A generator produces an emf when a coil of wire rotates in a magnetic field is              0 = NABcoil          coil = 0/ NAB   ............. (2) substitute the equation (2) in equation (1) , we get                v = (r) [( 1/44)(0/ NAB)]   ............. (3) substitute the given data in eq (3) , we get             velocity v = 2.3 m/s substitute the equation (2) in equation (1) , we get                v = (r) [( 1/44)(0/ NAB)]   ............. (3) substitute the given data in eq (3) , we get             velocity v = 2.3 m/s

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