A generator is mounted on a bicycle wheelto power a small headlight. A small whe

Question

A generator is mounted on a bicycle wheelto power a small headlight. A small wheel on the shaft of the generator is pressed against the bike tire and turns the armature of the generator 30 times for each revolutions of the tire. The armature of the generator has 60 turns of wire, each with an area of 3 x 10-3 m2, and rotates in a magnetic field of 0.10 Tesla.

Our goal in this problem is to determine how fast we must pedal the bike in order to produce a

maximum emf, Emax, of 6.0 Volts to run the headlight.

(a) The relation Emax = NAB provides the key equation for the solution to this problem. Determine how fast, , the armature must rotate at in order to produce this peak emf of 6.0 V. Express your answer in units of rad/s and also rev/s.

(b) Using the fact that the bicycle wheel turns the generator armature 30 times for each revolution of the bicycle tire, determine how fast the bicycle wheel must rotate at for this to occur

(c) Assuming that the tire has a radius of 0.33 m, determine the linear speed v that the bicycle must travel at in order to turn the tire this fast. Is this a realistic speed for the bicycle to travel at ? Convert your speed to units of mph to find out.

Explanation / Answer

peak emf given by E = BAN
= E/BAN
= 6.0V/(0.1T)3E-3 m²)(60) = 333.3 rad/s

Cycle wheel rotates at 333.3/30 = 11.12 rad/s

v=r .. v = 0.3 m x 12.82 rad/s .. .. = 3.846 m/s

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