Problem 9.26: Dental hygiene. Electric toothbrushes can be effective in removing

Question

Problem 9.26: Dental hygiene. Electric toothbrushes can be effective in removing dental plaque. One model consists of a head 1.1 cm in diameter. In one cycle the brush head rotates forward 70.0 and then back. The brush head completes 7300 cycles per minute. The rim of the head contains a thin row of bristles. (See (Figure 1) .) Part A What is the average angular speed in each direction of the rotating head? Express your answer in radians per second to three significant figures. rad/s SubmitMy AnswersGive Up Part B What is the average linear speed in each direction of the bristles against the teeth? Express your answer in meters per second to two significant figures. m/s SubmitMy AnswersGive Up Part C Using your own observations, what is the approximate speed of the bristles against your teeth when you brush by hand with an ordinary toothbrush? Assume r=0.55cm for the toothbrush. (Estimate that the toothbrush turns back and forth through 45 five times per second) Express your answer in centimeters per second to two significant figures. cm/s

Explanation / Answer

360 degree = 2pi rad in one back and forth cycle the head terns through 70 degree = 1.22173 rad

1 minute = 60 s,the head turns through 7300 x 1.22173 = 8.9186 x 10^3 rad

w = theta / t = (8.9186 x 10^3) / 60 = 148.64 rad/sec

b)

v = rw = (0.55 cm) x 148.64 = 81.75 cm/s = 0.8175 m/s

c)

w = theta / t = [5*90*2pi rad / 360)] / 1 sec = 7.9 rad /sec

v = 0.55 x 7.9 = 4 cm/sec = 0.04 m/s

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